@STRING{colt93 = "Proceedings of the Sixth Annual ACM Conference on
Computational Learning Theory" }
@STRING{jacm = "Journal of the Association for Computing Machinery" }
@STRING{jma = "Journal of Multivariate Analysis" }
@STRING{lncs = "Lecture Notes of Computer Science, Springer" }
@STRING{lncs = "Lecture Notes in Computer Science" }
@STRING{nips = "Advances in Neural Information Processing Systems" }
@STRING{pecs = "Colloquia Mathematica Societatis Janos Bolai, 57.\ Limit
Theorem in Probability and Statistics, Pecs (Hungary)" }
@STRING{spl = "Statistics \& Probability Letters" }
@Article{HauserETAL:12,
author = {H. Hauser and A. J. Ijspeert and R. M. Füchslin and R.
Pfeifer and W. Maass},
title = {Towards a Theoretical Foundation for Morphological
Computation with Compliant Bodies},
journal = {Biological Cybernetics},
year = {2012},
pages = {},
volume = {},
number = {},
abstract = {The control of compliant robots is, due to their often
nonlinear and complex dynamics, inherently difficult. The
vision of morphological computation proposes to view these
aspects not only as problems, but rather as parts of the
solution. Non-rigid body parts are not seen anymore as
imperfect realizations of rigid body parts, but rather as
potential computational resources. The applicability of
this vision has already been demonstrated for a variety of
complex robot control problems. Nevertheless, a theoretical
basis for understanding the capabilities and limitations of
morphological computation has been missing so far.We
present a model for morphological computation with
compliant bodies, where a precise mathematical
characterization of the potential computational
contribution of a complex physical body is feasible. The
theory suggests that complexity and nonlinearity, typically
unwanted properties of robots, are desired features in
order to provide computational power. We demonstrate that
simple generic models of physical bodies, based on
mass-spring systems, can be used to implement complex
nonlinear operators. By adding a simple readout (which is
static and linear) to the morphology, such devices are able
to emulate complex mappings of input to output streams in
continuous time. Hence, by outsourcing parts of the
computation to the physical body, the difficult problem of
learning to control a complex body, could be reduced to a
simple and perspicuous learning task, which can not get
stuck in local minima of an error function.},
note = {in press}
}
@Article{A:Circle-Homogen,
author = {P. Auer},
title = {The circle homogeneously covered by random walk on
{Z}$^2$},
journal = spl,
year = 1990,
pages = {403--407},
volume = 9
}
@InProceedings{A:CombinationTheories,
author = {P. Auer},
booktitle = {Word Equations and Related Topics},
pages = {177--186},
publisher = {Lecture Notes of Computer Science 677, Springer},
title = {Unification in the Combination of Disjoint Theories},
year = {1991}
}
@InProceedings{A:Hitting-Prob,
author = {P. Auer},
booktitle = pecs,
pages = {9--25},
title = {Some Hitting Probabilities of Random Walks on {Z}$^2$},
year = 1989
}
@InProceedings{A:Relative-Frequ,
author = {P. Auer and P. R\'{e}v\'{e}sz},
booktitle = pecs,
pages = {27--33},
title = {On the Relative Frequency of Points Visited by random Walk
on {Z}$^2$},
year = 1989
}
@InProceedings{A:WordEquations,
author = {P. Auer},
booktitle = {Word Equations and Related Topics},
key = {A:WordEquations},
pages = {103--132},
publisher = {Lecture Notes of Computer Science 677, Springer},
title = {Solving String Equations with Constant Restrictions},
year = {1991}
}
@InProceedings{AC94,
author = {P. Auer and N. C{esa-Bianchi}},
booktitle = {Algorithmic Learning Theory, AII'94, ALT'94},
editor = {Setsuo Arikawa and Klaus P. Jantke},
pages = {229--247},
publisher = {Lecture Notes in Artificial Intelligence 872, Springer},
title = {On-line Learning with Malicious Noise and the Closure
Algorithm},
year = {1994}
}
@Article{AC94j,
author = {P. Auer and N. C{esa-Bianchi}},
journal = {Annals of Mathematics and Artificial Intelligence},
title = {On-line Learning with Malicious Noise and the Closure
Algorithm},
year = {1998},
volume = {23},
pages = {83--99},
note = {A preliminary version has appeared in {\em Lecture Notes
in Artificial Intelligence} 872, Springer}
}
@InProceedings{AC96,
author = {P. Auer and P. Caianiello and N. Cesa-Bianchi},
booktitle = {Proceedings of the 15th Annual ACM Symposium on Principles
of Distributed Computing},
note = {Abstract},
pages = {312},
title = {Tight Bounds on the Cumulative Profit of Distributed
Voters},
year = {1996}
}
@InProceedings{ACFS95,
author = {P. Auer and N. Cesa-Bianchi and Y. Freund and R. E.
Schapire},
booktitle = {Proceedings of the 36th Annual Symposium on Foundations of
Computer Science},
pages = {322--331},
publisher = {IEEE Computer Society Press, Los Alamitos, CA},
title = {Gambling in a Rigged Casino: The Adversarial Multi-Armed
Bandit Problem},
year = {1995}
}
@Article{AH94gL,
author = {P. Auer and K. Hornik},
journal = {Journal of Multivariate Analysis},
pages = {37--51},
title = {The Number of Points of an Empirical or {Poisson} Process
Covered by Unions of Sets},
volume = {57},
year = {1996}
}
@Article{AH94jma,
author = {P. Auer and K. Hornik},
journal = jma,
number = {1},
pages = {115--156},
title = {On the Number of Points of a Homogeneous {P}oisson
Process},
volume = {48},
year = {1994}
}
@Article{AH96,
author = {P. Auer and K. Hornik},
journal = {Studia Scientiarum Mathematicarum Hungarica},
pages = {1--13},
title = {Limit Laws for the Maximal and Minimal Increments of the
{P}oisson Process},
volume = {31},
year = {1996}
}
@Article{AHR91,
author = {P. Auer and K. Hornik and P. R\'{e}v\'{e}sz},
journal = spl,
pages = {91--96},
title = {Some Limit Theorems for the Homogeneous {P}oisson
Process},
volume = 12,
year = 1991
}
@InCollection{AHW95,
author = {P. Auer and M. Herbster and M. K. Warmuth},
booktitle = {Advances in Neural Information Processing Systems 8},
editor = {D. S. Touretzky and M. C. Mozer and M. E. Hasselmo},
pages = {316--322},
publisher = {MIT Press},
title = {Exponentially Many Local Minima for Single Neurons},
year = {1996}
}
@Article{AL93,
author = {P. Auer and P. M. Long},
title = {Structural Results About On-line Learning Models With and
Without Queries},
journal = {Machine Learning},
year = {1999},
volume = {36},
pages = {147--181},
note = {A preliminary version has appeared in {\em Proceedings of
the 26th ACM Symposium on the Theory of Computing}}
}
@InProceedings{AL94,
author = {P. Auer and P. M. Long},
booktitle = {Proceedings of the 26th Annual ACM Symposium on the Theory
of Computing},
pages = {263--272},
publisher = {ACM Press},
title = {Simulating access to hidden information while learning},
year = {1994}
}
@InProceedings{ALS97,
author = {P. Auer and P. M. Long and A. Srinivasan},
booktitle = {Proc.\ 29th Ann.\ Symp.\ Theory of Computing},
month = {May},
pages = {314--323},
publisher = {ACM},
title = {Approximating Hyper-Rectangles: Learning and Pseudo-random
Sets},
year = {1997}
}
@Article{ALS97j,
author = {P. Auer and P. M. Long and A. Srinivasan},
title = {Approximating Hyper-Rectangles: Learning and Pseudorandom
Sets},
journal = {Journal of Computer and System Sciences},
year = {1998},
volume = {57},
number = {3},
pages = {376--388},
note = {A preliminary version has appeared in {\em Proc.\ 29th
Ann.\ Symp.\ Theory of Computing}}
}
@InProceedings{AW95,
author = {P. Auer and M. K. Warmuth},
booktitle = {Proceedings of the 36th Annual Symposium on Foundations of
Computer Science},
pages = {312--321},
publisher = {IEEE Computer Society Press},
title = {Tracking the Best Disjunction},
year = {1995}
}
@Article{AW95j,
author = {P. Auer and M. K. Warmuth},
title = {Tracking the Best Disjunction},
journal = {Machine Learning},
year = {1998},
volume = {32},
pages = {127--150},
note = {A preliminary version has appeared in {\em Proceedings of
the 36th Annual Symposium on Foundations of Computer
Science}}
}
@Article{AlonMaass:86,
author = {N. Alon and W. Maass},
journal = {Proceedings of the 27th Annual IEEE Symposium on
Foundations of Computer Science},
pages = {410--417},
title = {Meanders, Ramsey's theorem and lower bounds for branching
programs},
year = {1986}
}
@Article{AlonMaass:88,
author = {N. Alon and W. Maass},
journal = {J. Comput. System Sci.},
note = {Invited paper for a special issue of J. Comput. System
Sci.},
pages = {118--129},
title = {Meanders and their applications in lower bound arguments},
volume = {37},
year = {1988}
}
@InProceedings{Aue93,
author = {P. Auer},
booktitle = {Proceedings of the Sixth Annual ACM Conference on
Computational Learning Theory},
pages = {253--261},
publisher = {ACM Press, New York, NY},
title = {On-line Learning of Rectangles in Noisy Environments},
year = {1993}
}
@InProceedings{Aue95,
author = {P. Auer},
booktitle = {6th International Workshop, ALT`95, Proceedings},
editor = {Klaus P. Jantke and Takeshi Shinohara and Thomas
Zeugmann},
note = {LNAI 997},
pages = {123--137},
publisher = {Springer},
title = {Learning Nested Differences in the Presence of Malicious
Noise},
year = {1995}
}
@Article{Aue95j,
author = {P. Auer},
title = {Learning Nested Differences in the Presence of Malicious
Noise},
journal = {Theoretical Computer Science},
year = {1997},
volume = {185},
pages = {159--175},
note = {A preliminary version has appeared in {\em Proceedings of
the 6th International Workshop on Algorithmic Learning
Theory, ALT`95.}}
}
@InProceedings{Aue96,
author = {P. Auer},
booktitle = {Proc.\ 14th Int.\ Conf.\ Machine Learning},
editor = {D. H. Fisher},
pages = {21--29},
publisher = {Morgan Kaufmann},
title = {On Learning from Multi-Instance Examples: Empirical
Evaluation of a Theoretical Approach},
year = {1997}
}
@InProceedings{AuerETAL:01,
author = {P. Auer and H. Burgsteiner and W. Maass},
title = {Reducing Communication for Distributed Learning in Neural
Networks},
booktitle = {Proc. of
the International Conference on Artificial Neural Networks
-- ICANN 2002},
series = {Lecture Notes in Computer Science},
editor = {Jos\'{e} R. Dorronsoro},
pages = {123--128},
volume = {2415},
year = {2002},
publisher = {Springer},
keywords = {learning algorithm, perceptrons, parallel, aVLSI },
abstract = {A learning algorithm is presented for circuits consisting
of a single layer of perceptrons. We refer to such circuits
as parallel perceptrons. In spite of their simplicity,
these circuits are universal approximators for arbitrary
boolean and continuous functions. In contrast to backprop
for multi-layer perceptrons, our new learning algorithm -
the parallel delta rule (p-delta rule) - only has to tune a
single layer of weights, and it does not require the
computation and communication of analog values with high
precision. This distinguishes our new learning rule also
from other learning rules for such circuits such as
MADALINE with far higher communication. Our algorithm also
provides an interesting new hypothesis for the organization
of learning in biological neural systems. A theoretical
analysis shows that the p-delta rule does in fact implement
gradient descent - with regard to a suitable error measure
- although it does not require to compute derivatives.
Furthermore it is shown through experiments on common
real-world benchmark datasets that its performance is
competitive with that of other learning approaches from
neural networks and machine learning.}
}
@Article{AuerETAL:01a,
author = {P. Auer and H. Burgsteiner and W. Maass},
title = {A learning rule for very simple universal approximators
consisting of a single layer of perceptrons},
journal = {Neural Networks},
year = {2008},
volume = {21},
number = {5},
pages = {786--795},
abstract = {A learning algorithm is presented for circuits consisting
of a single layer of perceptrons (= threshold gates, or
equivalently gates with a Heaviside activation function).
We refer to such circuits as parallel perceptrons. In spite
of their simplicity, these circuits can compute any boolean
function if one views the majority of the binary perceptron
outputs as the binary outputs of the parallel perceptron,
and they are universal approximators for arbitrary
continuous functions with values in [0,1] if one views the
fraction of perceptrons that output 1 as the analog output
of the parallel perceptron. For a long time one has thought
that there exists no competitive learning algorithms for
these extremely simple circuits consisting of gates with
binary outputs, which also became known as committee
machines. It is commonly believed that one has to replace
the hard threshold gates by sigmoidal gates and that one
has to tune the weights on at least two successive layers
in order to get satisfactory learning results. We show that
this is not true by exhibiting a simple learning algorithm
for parallel perceptrons - the parallel delta rule (p-delta
rule), whose performance is comparable to that of backprop
for multilayer networks consisting of sigmoidal gates. In
contrast to backprop, the p-delta rule does not require the
computation and communication of analog values with high
precision, although it does in fact implement gradient
descent - with regard to a suitable error measure.
Therefore it provides an interesting new hypothesis for the
organization of learning in biological neural systems.}
}
@InProceedings{AuerETAL:93,
author = {P. Auer and P. M. Long and W. Maass and G. J. Woeginger},
booktitle = {Proceedings of the 5th Annual ACM Conference on
Computational Learning Theory},
pages = {392--401},
title = {On the complexity of function learning},
year = {1993}
}
@Article{AuerETAL:93j,
author = {P. Auer and P. M. Long and W. Maass and G. J. Woeginger},
title = {On the complexity of function learning},
journal = {Machine Learning},
note = {Invited paper in a special issue of Machine Learning},
year = {1995},
volume = {18},
pages = {187--230}
}
@InProceedings{AuerETAL:95,
author = {P. Auer and R. C. Holte and W. Maass},
booktitle = {Proc. of the 12th International Machine Learning
Conference, Tahoe City (USA)},
publisher = {Morgan Kaufmann (San Francisco)},
pages = {21--29},
title = {Theory and applications of agnostic {PAC}-learning with
small decision trees},
year = {1995}
}
@InProceedings{AuerETAL:96,
author = {P. Auer and S. Kwek and W. Maass and M. K. Warmuth},
booktitle = {Proc. of the 9th Conference on Computational Learning
Theory 1996},
pages = {333--343},
publisher = {ACM-Press (New York)},
title = {Learning of depth two neural nets with constant fan-in at
the hidden nodes},
year = {1996}
}
@Article{AuerMaass:98,
author = {P. Auer and W. Maass},
title = {Introduction to the Special Issue on Computational
Learning Theory},
journal = {Algorithmica},
year = {1998},
volume = {22},
number = {1/2},
pages = {1--2}
}
@MastersThesis{Bachler:05,
author = {M. Bachler},
title = {Task dependent feature optimization in machine learning},
school = {Technische Universitaet Graz},
year = 2005
}
@TechReport{Bachler:06,
author = {M. Bachler},
title = {Bayesian and information theoretic methods for the
selection and creation of high-level features applied to
real-world object classification tasks},
institution = {Technische Universitaet Graz},
year = {2006}
}
@Unpublished{BachlerMaass:06,
author = {M. Bachler and W. Maass},
title = {A {B}ayesian {H}ebb Rule for Incremental Learning of
Optimal Inference in {B}ayesian Networks},
note = {submitted for publication},
year = {2006}
}
@InCollection{BartlettMaass:03,
author = {Peter L. Bartlett and W. Maass},
title = {Vapnik-{C}hervonenkis Dimension of Neural Nets},
booktitle = {The Handbook of Brain Theory and Neural Networks},
publisher = {MIT Press (Cambridge)},
year = {2003},
editor = {M. A. Arbib},
edition = {2nd},
pages = {1188--1192}
}
@Article{BertschingerNatschlaeger:03,
author = {N. Bertschinger and T. Natschlaeger},
title = {Real-Time Computation at the Edge of Chaos in Recurrent
Neural Networks},
journal = {Neural Computation},
year = 2004,
volume = 16,
number = 7,
pages = {1413--1436},
urlwillbe = {psfiles/eoc-v11pl1.ps},
abstract = {Depending on the connectivity recurrent networks of simple
computational units can show very different types of
dynamics ranging from totally ordered to chaotic. We
analyze how the type of dynamics (ordered or chaotic)
exhibited by randomly connected networks of threshold gates
driven by a time varying input signal depends on the
parameters describing the distribution of the connectivity
matrix. In particular we calculate the critical boundary in
parameter space where the transition from ordered to
chaotic dynamics takes places. Employing a recently
developed framework for analyzing real-time computations we
show that only near the critical boundary such networks can
perform complex computations on time series. Hence, this
result strongly supports conjectures that dynamical systems
which are capable of doing complex computational tasks
should operate near the edge of chaos, i.e. the transition
from ordered to chaotic dynamics.}
}
@MastersThesis{Bill:08,
author = {J. Bill},
title = {Self-Stabilizing Network Architectures on a Neuromorphic
Hardware System},
school = {Universitaet Heidelberg},
year = {2008}
}
@Article{BillETAL:10,
author = {J. Bill and K. Schuch and D. Br\"uderle and J. Schemmel
and W. Maass and K. Meier},
title = {Compensating inhomogeneities of neuromorphic {VLSI}
devices via short-term synaptic plasticity},
journal = {Frontiers in Computational Neuroscience},
year = {2010},
volume = {4},
number = {},
pages = {1--14},
abstract = {Recent developments in neuromorphic hardware engineering
make mixed-signal VLSI neural network models promising
candidates for neuroscientific research tools and massively
parallel computing devices, especially for tasks which
exhaust the computing power of software simulations. Still,
like all analog hardware systems, neuromorphic models
suffer from a constricted configurability and
production-related fluctuations of device characteristics.
Since also future systems, involving ever-smaller
structures, will inevitably exhibit such inhomogeneities on
the unit level, self-regulation properties become a crucial
requirement for their successful operation. By applying a
cortically inspired self-adjusting network architecture, we
show that the activity of generic spiking neural networks
emulated on a neuromorphic hardware system can be kept
within a biologically realistic firing regime and gain a
remarkable robustness against transistorlevel variations.
As a first approach of this kind in engineering practice,
the short-term synaptic depression and facilitation
mechanisms implemented within an analog VLSI model of I\&F
neurons are functionally utilized for the purpose of
network level stabilization. We present experimental data
acquired both from the hardware model and from comparative
software simulations which prove the applicability of the
employed paradigm to neuromorphic VLSI devices.},
note = {article 129}
}
@Article{BorgwardtETAL:06,
author = {K. M. Borgwardt and A. Gretton and M. J. Rasch and H.-P.
Kriegel and B. Schoelkopf and A. J. Smola},
journal = {Bioinformatics},
title = {Integrating structured biological data by kernel {M}aximum
{M}ean {D}iscrepancy},
year = {2006},
volume = {22},
number = {14},
pages = {349--e57}
}
@Article{BretteETAL:07,
author = {R. Brette and M. Rudolph and T. Carnevale and M. Hines and
D. Beeman and J. M. Bower and M. Diesmann and A. Morrison
and P. H. Goodman and F. C. Harris and M. Zirpe and T.
Natschlaeger and D. Pecevski and B. Ermentrout and M.
Djurfeldt and A. Lansner and O. Rochel and T. Vieville and
E. Muller and A. P. Davison and S. ElBoustani and A.
Destexhe},
title = {Simulation of networks of spiking neurons: A review of
tools and strategies},
journal = {J. of Computational Neuroscience},
year = {2007},
volume = {23},
number = {3},
pages = {349--398},
note = {},
abstract = {We review different aspects of the simulation of spiking
neural networks. We start by reviewing the different types
of simulation strategies and algorithms that are currently
implemented. We next review the precision of those
simulation strategies, in particular in cases where
plasticity depends on the exact timing of the spikes. We
overview different simulators and simulation environments
presently available (restricted to those freely available,
open source and documented). For each simulation tool, its
advantages and pitfalls are reviewed, with an aim to allow
the reader to identify which simulator is appropriate for a
given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking
neurons, including Hodgkin-Huxley type, integrate-and-fire
models, interacting with current-based or conductance-based
synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the
different simulators, and the codes are made available. The
ultimate goal of this review is to provide a resource to
facilitate identifying the appropriate integration strategy
and simulation tool to use for a given modeling problem
related to spiking neural networks.}
}
@Article{BuesingETAL:09,
author = {L. Buesing and B. Schrauwen and R. Legenstein},
title = {Connectivity, Dynamics, and Memory in Reservoir Computing
with Binary and Analog Neurons},
journal = {Neural Computation},
year = {2010},
volume = {22},
number = {5},
pages = {1272-1311},
abstract = {Reservoir Computing (RC) systems are powerful models for
online computations on input sequences. They consist of a
memoryless readout neuron which is trained on top of a
randomly connected recurrent neural network. RC systems are
commonly used in two flavors: with analog or binary
(spiking) neurons in the recurrent circuits. Previous work
indicated a fundamental difference in the behavior of these
two implementations of the RC idea. The performance of a RC
system built from binary neurons seems to depend strongly
on the network connectivity structure. In networks of
analog neurons such clear dependency has not been observed.
In this article we address this apparent dichotomy by
investigating the influence of the network connectivity
(parametrized by the neuron in-degree) on a family of
network models that interpolates between analog and binary
networks. Our analyses are based on a novel estimation of
the Lyapunov exponent of the network dynamics with the help
of branching process theory, rank measures which estimate
the kernel-quality and generalization capabilities of
recurrent networks, and a novel mean-field predictor for
computational performance. These analyses reveal that the
phase transition between ordered and chaotic network
behavior of binary circuits qualitatively differs from the
one in analog circuits, leading to differences in the
integration of information over short and long time scales.
This explains the decreased computational performance
observed in binary circuits that are densely connected. The
mean-field predictor is also used to bound the memory
function of recurrent circuits of binary neurons.}
}
@Article{BuesingETAL:11,
author = {L. B\"using and J. Bill and B. Nessler and W. Maass},
title = {Neural Dynamics as Sampling: A Model for Stochastic
Computation in Recurrent Networks of Spiking Neurons},
journal = {PLoS Computational Biology},
year = {published 03 Nov 2011},
pages = {},
volume = {},
abstract = {The organization of computations in networks of spiking
neurons in the brain is still largely unknown, in
particular in view of the inherently stochastic features of
their firing activity and the experimentally observed
trial-to-trial variability of neural systems in the brain.
In principle there exists a powerful computational
framework for stochastic computations, probabilistic
inference by sampling, which can explain a large number of
macroscopic experimental data in neuroscience and cognitive
science. But it has turned out to be surprisingly difficult
to create a link between these abstract models for
stochastic computations and more detailed models of the
dynamics of networks of spiking neurons. Here we create
such a link, and show that under some conditions the
stochastic firing activity of networks of spiking neurons
can be interpreted as probabilistic inference via Markov
chain Monte Carlo (MCMC) sampling. Since common methods for
MCMC sampling in distributed systems, such as Gibbs
sampling, are inconsistent with the dynamics of spiking
neurons, we introduce a different approach based on
non-reversible Markov chains, that is able to reflect
inherent temporal processes of spiking neuronal activity
through a suitable choice of random variables. We propose a
neural network model and show by a rigorous theoretical
analysis that its neural activity implements MCMC sampling
of a given distribution, both for the case of discrete and
continuous time. This provides a step towards closing the
gap between abstract functional models of cortical
computations and more detailed models of networks of
spiking neurons.},
note = {doi:10.1371/journal.pcbi.1002211}
}
@InProceedings{BuesingMaass:07,
author = {L. Buesing and W. Maass},
title = {Simplified Rules and Theoretical Analysis for Information
Bottleneck Optimization and {PCA} with Spiking Neurons},
booktitle = {Proc. of NIPS 2007, Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2008},
volume = {20},
pages = {},
abstract = {We show that under suitable assumptions (primarily
linearization) a simple and perspicuous online learning
rule for Information Bottleneck optimization with spiking
neurons can be derived. This rule performs on common
benchmark tasks as well as a rather complex rule that has
previously been proposed [2]. Furthermore, the transparency
of this new learning rule makes a theoretical analysis of
its convergence properties feasible. If this learning rule
is applied to an assemble of neurons, it provides a
theoretically founded method for performing principal
component analysis ({PCA}) with spiking neurons. In
addition it makes it possible to preferentially extract
those principal components from incoming signals X that are
related to some additional target signal $Y_T$ . This
target signal $Y_T$ (also called relevance variable) could
represent in a biological interpretation proprioception
feedback, input from other sensory modalities, or top-down
signals.}
}
@Article{BuesingMaass:09,
author = {Buesing, L. and Maass, W.},
title = {A Spiking Neuron as Information Bottleneck},
journal = {submitted for publication},
year = {2009}
}
@Article{BuesingMaass:10,
author = {L. Buesing and W. Maass},
title = {A Spiking Neuron as Information Bottleneck},
journal = {Neural Computation},
year = {2010},
volume = {22},
number = {},
pages = {1961--1992},
abstract = {Neurons receive thousands of presynaptic input spike
trains while emitting a single output spike train. This
drastic dimensionality reduction suggests to consider a
neuron as a bottleneck for information transmission.
Extending recent results, we propose a simple learning rule
for the weights of spiking neurons derived from the
Information Bottleneck (IB) framework that minimizes the
loss of relevant information transmitted in the output
spike train. In the IB framework relevance of information
is defined with respect to contextual information, the
latter entering the proposed learning rule as a "third"
factor besides pre- and postsynaptic activities. This
renders the theoretically motivated learning rule a
plausible model for experimentally observed synaptic
plasticity phenomena involving three factors. Furthermore,
we show that the proposed IB learning rule allows spiking
neurons to learn a "predictive code",i.e. to extract those
parts of their input that are predictive for future
input.}
}
@InProceedings{BultmanMaass:91,
author = {W. J. Bultman and W. Maass},
booktitle = {Proceedings of the 4th Annual ACM Workshop on
Computational Learning Theory,},
pages = {337--353},
title = {Fast identification of geometric objects with membership
queries},
year = {1991}
}
@Article{BultmanMaass:91j,
author = {W. J. Bultman and W. Maass},
title = {Fast identification of geometric objects with membership
queries},
journal = {Information and Computation},
year = 1995,
volume = 118,
pages = {48--64}
}
@Article{BuonomanoMaass:08,
author = {D. Buonomano and W. Maass},
title = {State-dependent Computations: Spatiotemporal Processing in
Cortical Networks.},
journal = {Nature Reviews in Neuroscience},
year = {2009},
volume = {10},
number = {2},
pages = {113--125},
note = {},
abstract = {A conspicuous ability of the brain is to seamlessly
assimilate and process spatial and temporal features of
sensory stimuli. This ability is indispensable for the
recognition of natural stimuli. Yet, a general
computational framework for processing spatiotemporal
stimuli remains elusive. Recent theoretical and
experimental work suggests that spatiotemporal processing
emerges from the interaction between incoming stimuli and
the internal dynamic state of neural networks which
includes not only ongoing spiking activity, but also
'hidden' neuronal states such as short-term synaptic
plasticity.}
}
@MastersThesis{Burgsteiner:98,
author = {H. Burgsteiner},
title = {{N}eural {N}etworks with {S}piking {N}eurons},
school = {Graz University of Technology},
year = 1998,
month = {November},
keywords = {spiking neurons, dynamic synapses, pools of dynamic
synapses, aVLSI, hardware model, simulations},
abstract = {In this diploma thesis I investigate new models of
synapses called Dynamic Synapses (DS) and a possible
implementation in analog electronics which could be
realized in an analog very large scale integrated silicon
chip (aVLSI). These mathematical models of DS were first
introduced by Wolfgang Maass and Anthony Zador in 1998,
after recent results in neurobiology suggested that
synapses -- in their computational meanings -- could be
more than just static ``weights''. It soon became obvious
that this model exhibits a behavior very close to their
biological counterparts. For a better understanding of the
later presented material a few essential models of neurons
and also the typical use of synapses are discussed in the
beginning. The pages following after the introduction are
dedicated to the original model of the DS. Then a newer and
slightly different model of a dynamic synapse is introduced
which is easier to implement in aVLSI. I present results of
simulations that reveal the computational power in
comparison to the original model. At the end a possible
implementation in analog electronics and results of
simulations of such implementations are shown. In future
work a small neural network with these types of synapses
could be realized in aVLSI and applied in real world
studies.}
}
@TechReport{Burgsteiner:99,
author = {H. Burgsteiner},
title = {Integration of XVision and Khepera},
institution = {Institute for Theoretical Computer Science, Graz
University of Technology},
year = 1999,
abstract = {This paper was written as a part of a documentation for a
project at our institute, combining machine learning and
machine vision. I present an approach of integrating the
mobile robot platform Khepera with the machine vision
package XVision. Both products are introduced in brief. The
neccessary modifications and extensions to a typical
XVision source file are described for use under the free
operating system Linux. As an example, a simple tracker
based on XVision and the Khepera equipped with a camera is
presented. It uses blob detection and basic Khepera control
functions. Khepera tracks a ball and is able to rotate
around its z-axis to keep the ball centered in its view.},
keywords = {xvision, khepera, programming, robotic, vision}
}
@Article{BurgsteinerETAL:07,
author = {H. Burgsteiner and M. Kr\"{o}ll and A. Leopold and G.
Steinbauer},
title = {Movement Prediction from real-world Images using a Liquid
State Machine},
journal = {Applied Intelligence},
volume = {26},
number = {2},
pages = {99--109},
year = {2007}
}
@InProceedings{ChenMaass:92,
author = {Z. Chen and W. Maass},
booktitle = {Proceedings of the 5th Annual ACM Workshop on
Computational Learning Theory},
pages = {16--28},
title = {On-line learning of rectangles},
year = {1992}
}
@InProceedings{ChenMaass:92a,
author = {Z. Chen and W. Maass},
booktitle = {Proceedings of the 3rd Int. Workshop on Analogical and
Inductive Inference},
pages = {26--34},
publisher = {Springer},
series = {Lecture Notes in Artificial Intelligence},
title = {A solution of the credit assignment problem in the case of
learning rectangles},
volume = {642},
year = {1992}
}
@Article{ChenMaass:94,
author = {Z. Chen and W. Maass},
journal = {Machine Learning},
note = {Invited paper for a special issue of Machine Learning},
pages = {201--223},
title = {On-line learning of rectangles and unions of rectangles},
volume = {17},
year = {1994}
}
@Article{ClopathETAL:08,
author = {C. Clopath and L. Ziegler and E. Vasilaki and L. Buesing
and W. Gerstner},
title = {Tag-Trigger-Consolidation: A Model of Early and Late
Long-Term-Potentiation and Depression},
journal = {PLOS Computational Biology},
year = {2008},
volume = {4},
number = {12},
pages = {e1000248},
note = {},
abstract = {Changes in synaptic efficacies need to be long-lasting in
order to serve as a substrate for memory.
Experimentally,synaptic plasticity exhibits phases covering
the induction of long-term potentiation and depression
(LTP/LTD) during the early phase of synaptic plasticity,
the setting of synaptic tags, a trigger process for protein
synthesis, and a slow transition leading to synaptic
consolidation during the late phase of synaptic plasticity.
We present a mathematical model that describes these
different phases of synaptic plasticity. The model explains
a large body of experimental data on synaptic tagging and
capture, cross-tagging, and the late phases of LTP and LTD.
Moreover, the model accounts for the dependence of LTP and
LTD induction on voltage and presynaptic stimulation
frequency. The stabilization of potentiated synapses during
the transition from early to late LTP occurs by protein
synthesis dynamics that are shared by groups of synapses.
The functional consequence of this shared process is that
previously stabilized patterns of strong or weak synapses
onto the same postsynaptic neuron are well protected
against later changes induced by LTP/LTD protocols at
individual synapses. }
}
@Article{DietzfelbingerETAL:91a,
author = {M. Dietzfelbinger and W. Maass and G. Schnitger},
journal = {Theoretical Computer Science},
pages = {113--129},
title = {The complexity of matrix transposition on one-tape
off-line {T}uring machines},
volume = {82},
year = {1991}
}
@InProceedings{DietzfelbingerMaass:85,
author = {M. Dietzfelbinger and W. Maass},
booktitle = {Proceedings of the 1984 Recursion Theory Week Oberwolfach,
Germany},
pages = {89--120},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Mathematics},
title = {Strong reducibilities in alpha- and beta-recursion
theory},
volume = {1141},
year = {1985}
}
@InProceedings{DietzfelbingerMaass:86,
author = {M. Dietzfelbinger and W. Maass},
booktitle = {Proceedings of the Structure in Complexity Theory
Conference, Berkeley 1986},
pages = {163--183},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
title = {Two lower bound arguments with ``inaccessible'' numbers},
volume = {223},
year = {1986}
}
@Article{DietzfelbingerMaass:88,
author = {M. Dietzfelbinger and W. Maass},
journal = {J. Comput. System Sci.},
note = {Invited paper for a special issue of J. Comput. System
Sci.},
pages = {313--335},
title = {Lower bound arguments with ``inaccesible'' numbers},
volume = {36},
year = {1988}
}
@InProceedings{DietzfelbingerMaass:88a,
author = {M. Dietzfelbinger and W. Maass},
booktitle = {Proceedings of the 15th International Colloquium on
Automata, Languages and Programming},
pages = {188--200},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
title = {The complexity of matrix transposition on one-tape
off-line {T}uring machines with output tape},
volume = {317},
year = {1988}
}
@Article{DietzfelbingerMaass:93,
author = {M. Dietzfelbinger and W. Maass},
journal = {Theoretical Computer Science},
pages = {271--290},
title = {The complexity of matrix transposition on one-tape
off-line {T}uring machines with output tape},
volume = {108},
year = {1993}
}
@Article{DobkinETAL:96,
author = {D. P. Dobkin and D. Gunopulos and W. Maass},
journal = {Journal of Computer and System Sciences},
month = {June},
number = {3},
pages = {453--470},
title = {Computing the maximum bichromatic discrepancy, with
applications to computer graphics and machine learning},
volume = {52},
year = {1996}
}
@InProceedings{FregnacETAL:05,
author = {Y. Fregnac and M. Blatow and J.-P. Changeux and J. de
Felipe and A. Lansner and W. Maass and D. A. McCormick and
C. M. Michel and H. Monyer and E. Szathmary and R. Yuste},
title = {U{P}s and {DOWN}s in Cortical Computation},
booktitle = {The Interface between Neurons and Global Brain Function},
editor = {S. Grillner and A. M. Graybiel},
year = {2006},
pages = {393--433},
chapter = {19},
publisher = {MIT Press},
series = {Dahlem Workshop Report 93}
}
@Article{GrettonETAL:05,
author = {A. Gretton and R. Herbrich and A. Smola and O. Bousquet
and B. Sch\"olkopf},
title = {Kernel Methods for Measuring Independence},
journal = {Journal of Machine Learning Research},
year = {2005},
pages = {2075--2129},
volume = {6}
}
@Article{GrettonETAL:06,
author = {A. Gretton and K. M. Borgwardt and M. J. Rasch and A. J.
Smola},
title = {Data-content based schema matching via {M}aximum {M}ean
{D}iscrepancy},
journal = {submitted for publication},
year = {2006}
}
@InProceedings{GrettonETAL:06b,
author = {A. Gretton and K. M. Borgwardt and M. J. Rasch and B.
Sch\"olkopf and A. J. Smola},
title = {A Kernel Method for the Two-Sample-Problem},
booktitle = {Proceedings of the 2006 Conference Advances in Neural
Information Processing Systems 19},
editor = {},
publisher = {MIT Press},
year = {2006},
volume = {20},
pages = {513--520}
}
@InProceedings{GrettonETAL:06c,
author = {A. Gretton and K. M. Borgwardt and M. J. Rasch and B.
Sch\"olkopf and A. J. Smola},
title = {A Kernel Method to Comparing Distributions},
booktitle = {Proceedings of the Twenty-Second AAAI Conference on
Artificial Intelligence (AAAI-07)},
editor = {},
publisher = {AAAI Press, Menlo Park, CA, USA},
year = {2007},
volume = {22},
pages = {1637--1641}
}
@Article{HSWA,
author = {K. Hornik and M. Stinchcombe and H. White and P. Auer},
journal = {Neural Computation},
pages = {1262--1275},
title = {Degree of approximation results for feedforward networks
approximating unknown mappings and their derivatives},
volume = {6},
year = {1994}
}
@Article{HabenschussETAL:11,
author = {S. Habenschuss and H. Purr and W. Maass},
title = {Emergence of optimal decoding of population codes through
{STDP}},
journal = {in preparation},
year = {2011},
pages = {},
volume = {}
}
@Article{HaeuslerETAL:03,
author = {S. Haeusler and H. Markram and W. Maass},
title = {Perspectives of the High Dimensional Dynamics of Neural
Microcircuits from the Point of View of Low-Dimensional
Readouts},
journal = {Complexity (Special Issue on Complex Adaptive Systems)},
year = {2003},
volume = {8},
number = {4},
pages = {39--50}
}
@Article{HaeuslerETAL:07,
author = {S. Haeusler and W. Singer and W. Maass and D. Nikolic},
title = {Superposition of information in large ensembles of neurons
in primary visual cortex},
journal = {37th Annual Conference of the Society for Neuroscience,
Program 176.2, Poster II23},
year = {2007},
volume = {},
number = {},
pages = {},
abstract = {We applied methods from machine learning in order to
analyze the temporal evolution of stimulus-related
information in the spiking activity of large ensembles of
around 100 neurons in primary visual cortex of anesthetized
cats. We present ed sequences of up to 3 different visual
stimuli (letters) that lasted 100 ms and followed at
intervals of 100 ms. We f ound that most of the information
about visual stimuli extractable by advanced methods from
machine learning (e.g., Sup port Vector Machines) could
also be extracted by simple linear classifiers
(perceptrons). Hence, in principle this info rmation can be
extracted by a biological neuron. A surprising result was
that new stimuli did not erase information abo ut previous
stimuli. In fact, information about the nature of the
preceding stimulus remained as high as the informatio n
about the current stimulus. Separately trained linear
readouts could retrieve information about both the current
and the preceding stimulus from responses to the current
stimulus. This information was encoded both in the
discharge rates (response amplitudes) of the ensemble of
neurons and in the precise timing of individual spikes, and
persisted for seve ral 100 ms beyond the offset of stimuli.
This superposition of information about sequentially
presented stimuli constrains computational models for
visual proce ssing. It poses a conundrum for models that
assume separate classification processes for each frame of
visual input and supports models for cortical computation
([Buonomano, Merzenich, 1995], [Maass, Natschlaeger,
Markram, 2002]) which arg ue that a frame-by frame
processing is neither feasible within highly recurrent
networks nor useful for classifying and predicting rapidly
changing stimulus sequences. Specific predictions of these
alternative computational models are tha i) information
from different frames of visual input is superimposed in
recurrent circuits and ii) nonlinear combinations of
different information components are immediately provided
in the spike output. Our results indicate that the network
from which we recorded provided nonlinear combinations of
information from sequen tial frames. Such nonlinear
preprocessing increases the discrimination capability of
any linear readout neurons receivi ng distributed input
from the kind of cells we recorded from. These readout
neurons could be implemented within V1 and/ or at
subsequent processing levels.}
}
@Article{HaeuslerETAL:08,
author = {S. Haeusler and K. Schuch and W. Maass},
title = {Motif distribution, dynamical properties, and
computational performance of two data-based cortical
microcircuit templates},
journal = {J. of Physiology (Paris)},
year = {2009},
volume = {103},
number = {1-2},
pages = {73--87},
abstract = {The neocortex is a continuous sheet composed of rather
stereotypical local microcircuits that consist of neurons
on several laminae with characteristic synaptic
connectivity patterns. An understanding of the structure
and computational function of these cortical microcircuits
may hold the key for understanding the enormous
computational power of the neocortex. Two templates for the
structure of laminar cortical microcircuits have recently
been published by Thomson et al. and Binzegger et al., both
resulting from long-lasting experimental studies (but based
on different methods). We analyze and compare in this
article the structure of these two microcircuit templates.
In particular, we examine the distribution of network
motifs, i.e. of subcircuits consisting of a small number of
neurons. The distribution of these building blocks has
recently emerged as a method for characterizing
similarities and differences among complex networks. We
show that the two microcircuit templates have quite
different distributions of network motifs, although they
both have a characteristic small-world property. In order
to understand the dynamical and computational properties of
these two microcircuit templates, we have generated
computer models of them, consisting of Hodgkin-Huxley point
neurons with conductance based synapses that have a
biologically realistic short-term plasticity. The
performance of these two cortical microcircuit models was
studied for seven generic computational tasks that require
accumulation and merging of information contained in two
afferent spike inputs. Although the two models exhibit a
different performance for some of these tasks, their
average computational performance is very similar. When we
changed the connectivity structure of these two
microcircuit models in order to see which aspects of it are
essential for computational performance, we found that the
distribution of degrees of nodes is a common key factor for
their computational performance. We also show that their
computational performance is correlated with specific
statistical properties of the circuit dynamics that is
induced by a particular distribution of degrees of nodes.}
}
@Article{HaeuslerETAL:08a,
author = {S. Haeusler and K. Schuch and W. Maass},
title = {Motif distribution and computational performance of two
data-based cortical microcircuit templates},
journal = {38th Annual Conference of the Society for Neuroscience,
Program 220.9},
year = {2008},
volume = {},
number = {},
pages = {},
abstract = {The neocortex is a continuous sheet composed of rather
stereotypical local microcircuits that consist of neurons
on several laminae with characteristic synaptic
connectivity patterns. An understanding of the structure
and computational function of these cortical microcircuits
may hold the key for understanding the enormous
computational power of the neocortex. Two templates for the
structure of laminar cortical microcircuits have recently
been published by Thomson et al. (2002) and Binzegger et
al. (2004), both resulting from long-lasting experimental
studies (but based on different methods). We analyze and
compare in this study the structure and computational
properties of these two microcircuit templates. In
particular, we examine the distribution of network motifs,
i.e. of sub-circuits consisting of a small number of
neurons. The distribution of these building blocks of
complex networks has recently emerged as a method for
characterizing similarities and differences among complex
networks. We show that the two microcircuit templates have
quite different distributions of network motifs, although
they both share characteristic global structural
properties, like degree distributions (distribution of the
number of synapses per neuron) and small-world properties.
In order to understand the computational properties of the
two microcircuit templates, we have generated computer
models of them, consisting of Hodgkin-Huxley point neurons
with conductance based synapses that have a biologically
realistic short-term plasticity. The information processing
capabilities of the two cortical microcircuit models were
studied for 7 generic computational tasks that require
accumulation and merging of information contained in two
afferent spike inputs. Although the two models exhibit a
different performance for some of these tasks, their
average computational performance is very similar. When we
changed the connectivity structure of these two
microcircuit models in order to see which aspects of it are
essential for computational performance, we found that the
distribution of degrees of nodes is a key factor for their
computational performance. References Thomson et al.
(2002), Cerebral Cortex, 12(9):936 Binzegger et al. (2004),
J. Neurosci., 24(39):8441}
}
@Article{HaeuslerMaass:04,
author = {S. Haeusler and W. Maass},
title = {A statistical analysis of information processing
properties of lamina-specific cortical microcircuit
models},
journal = {Cerebral Cortex},
year = 2007,
volume = {17},
number = {1},
pages = {149-162}
}
@Article{HaeuslerMaass:06,
author = {S. Haeusler and W. Maass},
title = {Computational impact of laminar structure and small world
properties of cortical microcircuit models},
journal = {submitted for publication},
year = 2006
}
@InProceedings{HajnalETAL:87a,
author = {A. Hajnal and W. Maass and P. Pudlak and M. Szegedy and G.
Turan},
booktitle = {Proceedings of the 28th Annual IEEE Symposium on
Foundations of Computer Science},
pages = {99--110},
title = {Threshold circuits of bounded depth},
year = {1987}
}
@InProceedings{HajnalETAL:88,
author = {A. Hajnal and W. Maass and G. Turan},
booktitle = {Proceedings of the 20th Annual ACM Symposium on Theory of
Computing},
pages = {186--191},
title = {On the communication complexity of graph properties},
year = {1988}
}
@Article{HajnalETAL:93,
author = {A. Hajnal and W. Maass and P. Pudlak and M. Szegedy and G.
Turan},
journal = {J. Comput. System Sci.},
pages = {129--154},
title = {Threshold circuits of bounded depth},
abstract = {We examine a powerful model of parallel computation:
polynomial size threshold circuits of bounded depth (the
gates compute threshold functions with polynomial weights).
Lower bounds are given to separate polynomial size
threshold circuits of depth 2 from polynomial size
threshold circuits of depth 3 and from probabilistic
polynomial size circuits of depth 2. With regard to the
unreliability of bounded depth circuits, it is shown that
the class of functions computed reliably with bounded depth
circuits of unreliable A, v , 1 gates is narrow. On the
other hand, functions computable by bounded depth,
polynomial-size threshold circuits can also be computed by
such circuits of unreliable threshold gates. Furthermore we
examine to what extent imprecise threshold gates (which
behave unpredictably near the threshold value) can compute
nontrivial functions in bounded depth and a bound is given
for the permissible amount of imprecision. We also discuss
threshold quantifiers and prove an undefinability result
for graph connectivity.},
volume = {46},
year = {1993}
}
@InProceedings{HauserETAL:07,
author = {H. Hauser and G. Neumann and A. J. Ijspeert and W. Maass},
booktitle = {Proceedings of the {IEEE}-{RAS} 7th {I}nternational
{C}onference on {H}umanoid {R}obots ({H}umanoids 2007)},
title = {Biologically Inspired Kinematic Synergies Provide a New
Paradigm for Balance Control of Humanoid Robots},
publisher = {},
year = {2007},
pages = {},
abstract = {Nature has developed methods for controlling the movements
of organisms with many degrees of freedom which differ
strongly from existing approaches for balance control in
humanoid robots: Biological organisms employ kinematic
synergies that simultaneously engage many joints, and which
are apparently designed in such a way that their
superposition is approximately linear. We show in this
article that this control strategy can in principle also be
applied to balance control of humanoid robots. In contrast
to existing approaches, this control strategy reduces the
need to carry out complex computations in real time
(replacing the iterated solution of quadratic optimization
problems by a simple linear controller), and it does not
require knowledge of a dynamic model of the robot.
Therefore it can handle unforeseen changes in the dynamics
of the robot that may for example arise from wind or other
external forces. We demonstrate the feasibility of this
novel approach to humanoid balance control through
simulations of the humanoid robot HOAP-2 for tasks that
require balance control on a randomly moving surfboard.},
note = {Best {P}aper {A}ward.
http://planning.cs.cmu.edu/humanoids07/p/37.pdf}
}
@Article{HauserETAL:11,
author = {H. Hauser and G. Neumann and A. J. Ijspeert and W. Maass},
title = {Biologically Inspired Kinematic Synergies Enable Linear
Balance Control of a Humanoid Robot},
journal = {Biological Cybernetics},
year = {2011},
pages = {235--249},
volume = {104},
note = {},
abstract = {Despite many efforts, balance control of humanoid robots
in the presence of unforeseen external or internal forces
has remained an unsolved problem. The difficulty of this
problem is a consequence of the high dimensionality of the
action space of a humanoid robot, due to its large number
of degrees of freedom (joints), and of nonlinearities in
its kinematic chains. Biped biological organisms face
similar difficulties, but have nevertheless solved this
problem. Experimental data reveal that many biological
organisms reduce the high dimensionality of their action
space by generating movements through linear superposition
of a rather small number of stereotypical combinations of
simultaneous movements of many joints, to which we refer as
kinematic synergies in this paper. We show that by
constructing two suitable nonlinear kinematic synergies for
the lower part of the body of a humanoid robot, balance
control can in fact be reduced to a linear control problem,
at least in the case of relatively slow movements. We
demonstrate for a variety of tasks that the humanoid robot
HOAP-2 acquires through this approach the capability to
balance dynamically against unforeseen disturbances that
may arise from external forces or from manipulating unknown
loads.}
}
@InProceedings{HochbaumMaass:84,
author = {D. Hochbaum and W. Maass},
booktitle = {Proceedings of Symp. on Theoretical Aspects of Computer
Science (Paris 1984)},
pages = {55--62},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
title = {Approximation schemes for covering and packing problems in
robotics and {VLSI} (extended abstract)},
volume = {166},
year = {1984}
}
@Article{HochbaumMaass:85,
author = {D. Hochbaum and W. Maass},
journal = {J. Assoc. Comp. Mach.},
pages = {130--136},
title = {Approximation algorithms for covering and packing problems
in image processing and {VLSI}},
volume = {32},
year = {1985}
}
@Article{HochbaumMaass:87,
author = {D. Hochbaum and W. Maass},
journal = {J. Algorithms},
pages = {305--323},
title = {Fast approximation algorithms for a nonconvex problem},
volume = {8},
year = {1987}
}
@TechReport{HoeflerBachler:06,
author = {M. Hoefler and M. Bachler},
title = {A software framework for adaptive biologically inspired
image classification},
institution = {Technische Universitaet Graz},
year = {2006}
}
@MastersThesis{Hoerzer:08,
author = {G. Hoerzer},
title = {Extraction of information about the behavioral state of
monkeys from neuronal recordings with methods from machine
learning},
school = {Graz University of Technology, Institute for Theoretical
Computer Sciences},
year = {2008}
}
@TechReport{Hoerzer:09,
author = {G. Hoerzer},
title = {Methods for the Analysis of Uni-, Bi- and Multivariate
Data},
institution = {University of Technology, Institute for Theoretical
Computer Sciences},
year = {2009}
}
@Article{HomerMaass:83,
author = {S. Homer and W. Maass},
journal = {Theoretical Computer Science},
pages = {279--289},
title = {Oracle dependent properties of the lattice of {NP}-sets},
volume = {24},
year = {1983}
}
@InProceedings{JahrerETAL:10,
author = {M. Jahrer and A. T\"oscher and R. Legenstein},
title = {Combining Predictions for Accurate Recommender Systems},
booktitle = {KDD '10: Proceedings of the 16th ACM SIGKDD international
conference on Knowledge discovery and data mining},
year = {2010},
isbn = {978-1-4503-0055-1},
pages = {693--702},
location = {Washington, DC, USA},
doi = {http://doi.acm.org/10.1145/1835804.1835893},
publisher = {ACM},
address = {New York, NY, USA},
abstract = {We analyze the application of ensemble learning to
recommender systems on the Netflix Prize dataset. For our
analysis we use a set of diverse state-of-the-art
collaborative filtering (CF) algorithms, which include:
SVD, Neighborhood Based Approaches, Restricted Boltzmann
Machine, Asymmetric Factor Model and Global Effects. We
show that linearly combining (blending) a set of CF
algorithms increases the accuracy and outperforms any
single CF algorithm. Furthermore, we show how to use
ensemble methods for blending predictors in order to
outperform a single blending algorithm. The dataset and the
source code for the ensemble blending are available
online.}
}
@MastersThesis{Joshi:02,
author = {P. Joshi},
title = {Synthesis of a Liquid State Machine with Hopfield/Brody
Transient Synchrony},
school = {Center for Advanced Computer Studies, University of
Louisiana, Lafayette, USA},
year = 2002,
month = {November},
abstract = {Understanding the mechanism of spatiotemporal integration
used by our brain to perform recognition of complex
temporal sequences is a challenge for current researchers
in neuroscience. Recent research has proposed transient
synchrony as a plausible mechanism for spatiotemporal
integration. This thesis studies a biologically plausible
network architecture made of simulated minicolumns that
performs a temporal integration task, specifically
spoken-word recognition. The network's ability to recognize
a spoken word and its natural variants is independent of
variations across speakers, simple masking noises and
variations in system parameters. The network demonstrates
inter columnar and intra columnar synchrony, which in turn
leads to word recognition. The intra columnar synchrony of
minicolumns acts as an event detection mechanism for events
in a particular frequency band. The inter columnar
transient synchrony enables the network to recognize words.
Each of the minicolumns exhibit a very unique temporal
signature when presented with a temporal input. These
signatures looked nearly the same for similar inputs (e.g.,
the same word spoken by different speakers etc.) and were
strikingly different for different temporal inputs (e.g.,
different words).}
}
@InProceedings{Joshi:06,
author = {P. Joshi},
title = {Modeling working memory and decision making using generic
neural microcircuits},
editor = {Stefanos Kollias and Andreas Stafylopatis and
W{\l}odzis{\l}aw Duch and Erkki Oja},
booktitle = {Artificial Neural Networks -- ICANN 2006},
pages = {515--524},
year = {2006},
volume = {4131},
series = {Lecture Notes in Computer Science},
publisher = {Springer},
isbn = {3-540-38625-4},
abstract = {Classical behavioral experiments to study working memory
typically involve three phases. First the subject receives
a stimulus, then holds it in the working memory, and
finally makes a decision by comparing it with another
stimulus. A neurocomputational model using generic neural
microcircuits with feedback is presented here that
integrates the three computational stages into a single
unified framework. The architecture is tested using the
two-interval discrimination and delayed-match-to-sample
experimental paradigms as benchmarks.}
}
@Article{Joshi:06b,
author = {P. Joshi},
title = {From memory based decisions to decision based movements: A
model of interval discrimination followed by action
selection},
journal = {Neural Networks},
volume = {20},
year = {2007},
publisher = {},
pages = {298--311},
abstract = {The interval discrimination task is a classical
experimental paradigm that is employed to study working
memory and decision making and typically involves four
phases. First, the subject receives a stimulus, then holds
it in the working memory, then makes a decision by
comparing it with another stimulus and finally acts on this
decision, usually by pressing one of the two buttons
corresponding to the binary decision. This article
demonstrates that simple linear readouts from generic
neural microcircuits that send feedback of their activity
to the circuit, can be trained using identical learning
mechanisms to perform quite separate tasks of decision
making and generation of subsequent motor commands. In this
sense, the neurocomputational algorithm presented here is
able to integrate the four computational stages into a
single unified framework. The algorithm is tested using
two-interval discrimination and delayed-match-to-sample
experimental paradigms as benchmarks.}
}
@PhDThesis{Joshi:07,
author = {P. Joshi},
title = {On the role of feedback in enhancing the computational
power of generic neural microcircuits},
school = {Graz University of Technology},
year = 2007,
abstract = {Circuits of neurons in the brain perform diverse cortical
computations in parallel, endowing the organism with
diverse cortical modalities, e.g. motor control, vision,
and audition; and higher order cognitive processes, e.g.
planning, and decision making. It is believed that these
computations are carried out by network of neurons in
cortical microcircuits, where each microcircuit is composed
of rather stereotypical circuit of neurons within a
cortical column. A characteristic property of these
cortical circuits is the presence of abundant feedback
connections, be it on the level of recurrent axon
collaterals projecting back onto the same neuron, or on the
network level between different cortical areas. This thesis
explores the functional role of neural feedback in
enhancing the computational power of generic neural
microcircuits. It is shown that feedback endows standard
models for neural circuits with the capability to emulate
arbitrary Turing machines. In fact, with a suitable
feedback such circuits can simulate any dynamical system,
in particular any conceivable analog computer. Under
realistic noise conditions the computational power of these
circuits is obviously reduced. However it is demonstrated
through computer simulations that feedback also provides a
significant gain in computational power for quite detailed
models of cortical microcircuits with in-vivo-like high
levels of noise. Furthermore neurocomputational models
using generic neural microcircuits with feedback are
explored in the context of motor control, decision making,
and ``action selection in presence of decisions''.}
}
@InProceedings{Joshi:08a,
author = {P. Joshi and J. Triesch},
title = {A Globally Asymptotically Stable Plasticity Rule for
Firing Rate Homeostasis},
editor = {},
booktitle = {Artificial Neural Networks -- ICANN 2008},
pages = {},
year = {2008},
volume = {},
series = {},
publisher = {},
isbn = {},
abstract = {How can neural circuits maintain stable activity states
when they are constantly being modified by Hebbian
processes that are notori- ous for being unstable? A new
synaptic plasticity mechanism is presented here that
enables a neuron to obtain homeostasis of its firing rate
over longer timescales while leaving the neuron free to
exhibit fluctuating dynamics in response to external
inputs. Mathematical results demon- strate that this rule
is globally asymptotically stable. Performance of the rule
is benchmarked through simulations from single neuron to
network level, using sigmoidal neurons as well as spiking
neurons with dynamic synapses. }
}
@InProceedings{Joshi:08b,
author = {C. Savin and P. Joshi and J. Triesch},
title = {ICA with spiking neurons},
booktitle = {Submitted for publication},
abstract = {We propose a biologically plausible mechanism for
performing ICA with spiking neurons. We show that a
stochastically spiking neuron is able to learn one inde-
pendent component in the input, by combining spike-timing
dependent plasticity (STDP) with an intrinsic plasticity
rule, which regulates the neuron response prop- erties to
maximize information transmission, under the constraint of
a fixed mean firing rate. A population of such neurons is
shown to perform ICA when their activities are decorrelated
by adaptive lateral inhibition. },
year = {2008},
volume = {},
pages = {},
publisher = {},
editor = {}
}
@InProceedings{Joshi:08c,
author = {P. Joshi and J. Triesch},
title = {Rules for information-maximization in spiking neurons
using intrinsic plasticity},
booktitle = {Submitted for publication},
abstract = {Information theory predicts the need for information
maximization as sensory in- formation must be compressed
into a limited range of responses that spiking neu- rons
can generate. We propose computational theory and learning
rules based on information theory that lead to information
maximization using intrinsic plasticity in a stochastically
spiking neuron model. Computer simulations are used to
verify the theoretical results. Further experiments show
that the intrinsic plasticity rules described in this
article lead to a desired exponential output distribution,
firing- rate homeostasis, and adaptation to sensory
deprivation in our model as observed in cortical neurons.
},
year = {2008},
volume = {},
pages = {},
publisher = {},
editor = {}
}
@Article{JoshiETAL:09,
author = {P. Joshi and G. Rainer and W. Maass},
title = {Computational role of theta oscillations in
delayed-decision tasks},
journal = {in preparation},
year = {2009},
pages = {},
volume = {}
}
@InProceedings{JoshiMaass:03,
author = {P. Joshi and W. Maass},
title = {Movement Generation and Control with Generic Neural
Microcircuits},
booktitle = {Biologically Inspired Approaches to Advanced Information
Technology. First International Workshop, Bio{ADIT} 2004,
Lausanne, Switzerland, January 2004, Revised Selected
Papers},
pages = {258--273},
year = {2004},
editor = {A. J. Ijspeert and M. Murata and N. Wakamiya},
volume = {3141},
series = {Lecture Notes in Computer Science},
publisher = {Springer Verlag},
abstract = {Simple linear readouts from generic neural microcircuit
models consisting of spiking neurons and dynamic synapses
can be trained to generate and control basic movements, for
example, reaching with an arm to various target points.
After suitable training of these readouts on a small number
of target points; reaching movements to other target points
can also be generated. Sensory or proprioceptive feedback
turns out to be essential for such movement control, even
if it is noisy and substantially delayed. Such feedback
turns out to optimally improve the performance of the
neural microcircuit model if it arrives with a biologically
realistic delay of 100 to 200 ms. Furthermore, additional
feedbacks of ``prediction of sensory variables'' are shown
to improve the performance significantly. The proposed
model also provides a new approach for movement control in
robotics. Existing control methods in robotics that take
the particular dynamics of the sensors and actuators into
account (``embodiment of robot control'') are taken one
step further by this approach, which provides methods for
also using the ``embodiment of computation'', i.e. the
inherent dynamics and spatial structure of neural circuits,
for the design of robot movement controllers.}
}
@Article{JoshiMaass:04,
author = {P. Joshi and W. Maass},
journal = {Neural Computation},
title = {Movement Generation with Circuits of Spiking Neurons},
year = {2005},
volume = 17,
number = 8,
pages = {1715--1738},
abstract = {How can complex movements that take hundreds of
milliseconds be generated by stereotypical neural
microcircuits consisting of spiking neurons with a much
faster dynamics? We show that linear readouts from generic
neural microcircuit models can be trained to generate basic
arm movements. Such movement generation is independent of
the arm-model used and the type of feedbacks that the
circuit receives. We demonstrate this by considering two
different models of a two-jointed arm, a standard model
from robotics and a standard model from biology, that each
generate different kinds of feedback. Feedbacks that arrive
with biologically realistic delays of 50--280 ms turn out
to give rise to the best performance. If a feedback with
such desirable delay is not available, the neural
microcircuit model also achieves good performance if it
uses internally generated estimates of such feedback.
Existing methods for movement generation in robotics that
take the particular dynamics of sensors and actuators into
account (``embodiment of motor systems'') are taken one
step further with this approach, which provides methods for
also using the ``embodiment of motion generation
circuitry'', i.e., the inherent dynamics and spatial
structure of neural circuits, for the generation of
movements.}
}
@Article{KWA97,
author = {J. Kivinen and M. K. Warmuth and P. Auer},
title = {The Perceptron algorithm vs. {Winnow}: linear vs.
logarithmic mistake bounds when few input variables are
relevant},
journal = {Artificial Intelligence},
year = {1997},
pages = {325--343}
}
@Article{KaskeBertschinger:05,
author = {A. Kaske and N. Bertschinger},
title = {Travelling wave patterns in a model of the spinal pattern
generator using spiking neurons},
journal = {Biol. Cybern.},
year = 2005,
volume = 92,
number = 3,
pages = {206--218}
}
@Article{KaskeMaass:04,
author = {A. Kaske and W. Maass},
title = {A model for the interaction of oscillations and pattern
generation with real-time computing in generic neural
microcircuit models},
journal = {Neural Networks},
year = {2006},
volume = {19},
number = {5},
pages = {600--609},
abstract = {It is shown that real-time computations on spike patterns
and temporal integration of information in neural
microcircuit models are compatible with potentially
descruptive additional inputs such as oscillations. A minor
change in the connection statistics of such circuits
(making synaptic connections to more distal target neurons
more likely for excitatory than for inhibitory neurons)
endows such generic neural microcircuit model with the
ability to generate periodic patterns autonomously. We show
that such pattern generation can also be multiplexed with
pattern classification and temporal integration of
information in the same neural circuit. These results can
be interpreted as showing that periodic activity provides a
second channel for communication in neural systems which
can be used to synchronize or coordinate spatially
separated processes, without encumbering local real-time
computations on spike trains in diverse neural circuits.}
}
@MastersThesis{Klampfl:06,
author = {S. Klampfl},
title = {Extracting Statistically Independent Components with a
Generalized {BCM} Rule for Spiking Neurons},
school = {Graz University of Technology},
year = {2006}
}
@Article{KlampflETAL:07,
author = {S. Klampfl and R. Legenstein and W. Maass},
title = {Spiking neurons can learn to solve information bottleneck
problems and extract independent components},
journal = {Neural Computation},
year = {2009},
volume = {21},
number = {4},
pages = {911--959},
abstract = {Independent Component Analysis (or blind source
separation) is assumed to be an essential component of
sensory processing in the brain and could provide a less
redundant representation about the external world. Another
powerful processing strategy is the optimization of
internal representations according to the information
bottleneck method. This method would allow to extract
preferentially those components from high-dimensional
sensory input streams that are related to other information
sources, such as internal predictions or proprioceptive
feedback. However there exists a lack of models that could
explain how spiking neurons could learn to execute either
of these two processing strategies. We show in this article
how stochastically spiking neurons with refractoriness
could in principle learn in an unsupervised manner to carry
out both information bottleneck optimization and the
extraction of independent components. We derive suitable
learning rules, which extend the well known BCM-rule, from
abstract information optimization principles. These rules
will simultaneously keep the firing rate of the neuron
within a biologically realistic range.}
}
@InProceedings{KlampflETAL:07b,
author = {S. Klampfl and R. Legenstein and W. Maass},
title = {Information Bottleneck Optimization and Independent
Component Extraction with Spiking Neurons},
booktitle = {Proc. of NIPS 2006, Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2007},
volume = {19},
pages = {713--720},
abstract = {The extraction of statistically independent components
from high-dimensional multi-sensory input streams is
assumed to b e an essential component of sensory processing
in the brain. Such independent component analysis (or blind
source separat ion) could provide a less redundant
representation of inform ation about the external world.
Another powerful processing strategy is to extract
preferentially those components from high-dimensional input
streams that are related to other inf ormation sources,
such as internal predictions or propriocep tive feedback.
This strategy allows the optimization of inte rnal
representation according to the information bottleneck
method. However, concrete learning rules that implement
thes e general unsupervised learning principles for spiking
neuro ns are still missing. We show how both information
bottlenec k optimization and the extraction of independent
components can in principle be implemented with
stochastically spiking neurons with refractoriness. The new
learning rule that achi eves this is derived from abstract
information optimization principles.}
}
@Article{KlampflETAL:09,
author = {S. Klampfl and S.V. David and P. Yin and S.A. Shamma and
W. Maass},
title = {Integration of stimulus history in information conveyed by
neurons in primary auditory cortex in response to tone
sequences},
journal = {39th Annual Conference of the Society for Neuroscience,
Program 163.8, Poster T6 },
year = {2009},
volume = {},
number = {},
pages = {},
abstract = {A critical component of auditory processing is integrating
information about sound features that change over time.
Previous studies have shown that the context of a sound --
the immediate history of auditory stimulation -- can have a
substantial effect on responses of auditory neurons to a
current sound. In order to characterize these effects, we
measured the information contained in the neural activity
in primary auditory cortex (A1) about both current and
preceding sounds. Neural recordings were made from single
A1 neurons (n=122) isolated from 23 multi-channel
recordings in 4 passively listening ferrets. The stimulus
was a sequence of tones (150 ms duration). The frequency
step between two consecutive tones was always half an
octave up or down. For each neuron, we measured at
particular points in time the mutual information (MI)
between its response during a sliding window (20ms) and the
identity of the current and preceding tone. Since direct
estimates of MI from spike trains typically suffer from a
systematic error (bias) due to the limited number of
available response trials for a given stimulus, we used a
recently proposed shuffling-based estimator with additional
quadratic extrapolation bias correction (Panzeri et al.,
2007). This method produces reliable information estimates
for this particular setup. We found that most responses
(102 out of 122 neurons) contained significant information
about the stimulus throughout the duration of the tone. Of
this information, on average, 60\% was about the current
tone, while 40\% was about the previous tone. We also
trained linear classifiers (Support Vector Machines with
linear kernel) on the low-pass filtered response spike
trains of multiple simultaneously recorded neurons (4-10)
to discriminate between the two possible predecessors for a
given tone. The performance the linear classifier can be
viewed as a lower bound on the information contained in the
responses about the previous tone. Performance of up to
80\% was achieved. These results quantify the amount of
information contained in the responses of A1 neurons about
both currently and previously played tones and demonstrate
that neurons in A1 integrate information about previous
input into their current responses. References: Panzeri et
al. (2007), J Neurophysiol, 98(3):1064}
}
@Article{KlampflMaass:09,
author = {S. Klampfl and W. Maass},
title = {A neuron can learn anytime classification of trajectories
of network states without supervision},
journal = {submitted for publication},
year = {Feb. 2009},
volume = {},
number = {},
pages = {},
note = {}
}
@Article{KlampflMaass:09a,
author = {S. Klampfl and W. Maass},
title = {A theoretical basis for emergent pattern discrimination in
neural systems through slow feature extraction},
journal = {submitted},
year = {2009},
pages = {},
volume = {}
}
@InProceedings{KlampflMaass:09b,
author = {S. Klampfl and W. Maass},
title = {Replacing supervised classification learning by {S}low
{F}eature {A}nalysis in spiking neural networks},
booktitle = {Proc. of NIPS 2009: Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2010},
volume = {22},
pages = {988--996},
abstract = {Many models for computations in recurrent networks of
neurons assume that the network state moves from some
initial state to some fixed point attractor or limit cycle
that represents the output of the computation. However
experimental data show that in response to a sensory
stimulus the network state moves from its initial state
through a trajectory of network states and eventually
returns to the initial state, without reaching an attractor
or limit cycle in between. This type of network response,
where salient information about external stimuli is encoded
in characteristic trajectories of continuously varying
network states, raises the question how a neural system
could compute with such code, and arrive for example at a
temporally stable classification of the external stimulus.
We show that a known unsupervised learning algorithm, Slow
Feature Analysis (SFA), could be an important ingredient
for extracting stable information from these network
trajectories. In fact, if sensory stimuli are more often
followed by another stimulus from the same class than by a
stimulus from another class, SFA approaches the
classification capability of Fisher’s Linear Discriminant
(FLD), a powerful algorithm for supervised learning. We
apply this principle to simulated cortical microcircuits,
and show that it enables readout neurons to learn
discrimination of spoken digits and detection of repeating
firing patterns within a stream of spike trains with the
same firing statistics, without requiring any supervision
for learning.}
}
@Article{KlampflMaass:10,
author = {S. Klampfl and W. Maass},
title = {A theoretical basis for emergent pattern discrimination in
neural systems through slow feature extraction},
journal = {Neural Computation},
year = {2010},
volume = {22},
number = {12},
pages = {2979--3035},
abstract = {Neurons in the brain are able to detect and discriminate
salient spatio-temporal patterns in the firing activity of
presynaptic neurons. It is open how they can learn to
achieve this, especially without the help of a supervisor.
We show that a well-known unsupervised learning algorithm
for linear neurons, Slow Feature Analysis (SFA), is able to
acquire the discrimination capability of one of the best
algorithms for supervised linear discrimination learning,
the Fisher Linear Discriminant (FLD), given suitable input
statistics. We demonstrate the power of this principle by
showing that it enables readout neurons from simulated
cortical microcircuits to learn without any supervision to
discriminate between spoken digits, and to detect repeated
firing patterns that are embedded into a stream of noise
spike trains with the same firing statistics. Both these
computer simulations and our theoretical analysis show that
slow feature extraction enables neurons to extract and
collect information that is spread out over a trajectory of
firing states that lasts several hundred ms. In addition,
it enables neurons to learn without supervision to keep
track of time (relative to a stimulus onset, or the
initiation of a motor response). Hence these results
elucidate how the brain could compute with trajectories of
firing states, rather than only with fixed point
attractors. It also provides a theoretical basis for
understanding recent experimental results on the emergence
of view- and position-invariant classification of visual
objects in inferior temporal cortex.},
note = {Epub 2010 Sep 21}
}
@InProceedings{KranakisETAL:95,
author = {E. Kranakis and D. Krizanc and B. Ruf and J. Urrutia and
G. Woeginger},
booktitle = {Graph-theoretic concepts in computer science},
editor = {M. Nagl},
pages = {1--13},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
title = {{VC}-dimensions for graphs},
volume = {1017},
year = {1995},
keywords = {VC-Dimensions, graphs}
}
@Article{KranakisETAL:97,
author = {E. Kranakis and D. Krizanc and B. Ruf and J. Urrutia and
G. Woeginger},
journal = {Journal of Discrete Applied Mathematics},
pages = {237--257},
title = {The {VC}-dimension of set-systems defined by graphs},
volume = {77},
year = {1997},
keywords = {VC-dimensions, graph}
}
@PhDThesis{Legenstein:02a,
author = {R. A. Legenstein},
title = {The Wire-Length Complexity of Neural Networks},
school = {Graz University of Technology},
year = 2002,
abstract = {The ability of our nervous system to rapidly process and
react on the huge amount of sensory input data is grounded
on its massively parallel architecture. Arguably, physical
cost for communication, that is to say the space needed for
wires, is the most severe bottleneck in biological as well
as in artificial architectures of this type. In this thesis
the complexity of wiring in biological and artificial
neural networks, the implications of wiring constraints to
models for brain circuits, and the implementation of
wire-efficient circuit designs in hardware are studied. We
present a simple mathematical framework that allows us to
study the wiring complexity of neural circuits in a formal
and general manner. In this model, the complexity of a
circuit is measured by the total length of wires needed to
implement the circuit, a complexity measure that is one of
the most salient ones if real-world constraints of
implementations in hardware or ``wetware'' are
considered.Furthermore, we study the layout of general
computational structures like tree computations. We give
tight upper and lower bounds on the wire length of
constrained tree layouts and show efficient layout
strategies for prefix computations.}
}
@Article{Legenstein:02b,
author = {R. A. Legenstein},
title = {On the Complexity of Knock-Knee Channel Routing with
3-Terminal Nets},
journal = {Technical Report},
year = {2002},
abstract = {In this article we consider a basic problem in the layout
of VLSI-circuits, the channel-routing problem in the
knock-knee mode. We show that knock-knee channel routing
with 3-terminal nets is NP-complete and thereby settling a
problem that was open for more than a decade. In 1987,
Sarrafzadeh showed that knock-knee channel routing with
5-terminal nets is NP-complete. Furthermore, it is known
that this problem is solvable in polynomial time if only
2-terminal nets are involved (This problem was addressed
for example by Frank in 1982 and by Formann, D. Wagner, and
F. Wagner in 1993).}
}
@MastersThesis{Legenstein:99,
author = {R. A. Legenstein},
title = {Effizientes {L}ayout von {N}euronalen {N}etzen},
school = {Technische Universitaet Graz},
year = 1999,
month = {September}
}
@Article{LegensteinETAL:03,
author = {R. Legenstein and H. Markram and W. Maass},
title = {Input Prediction and Autonomous Movement Analysis in
Recurrent Circuits of Spiking Neurons},
year = {2003},
journal = {Reviews in the Neurosciences (Special Issue on
Neuroinformatics of Neural and Artificial Computation)},
volume = {14},
number = {1--2},
pages = {5--19},
abstract = {Temporal integration of information and prediction of
future sensory inputs are assumed to be important
computational tasks of generic cortical microcircuits.
However it has remained open how cortical microcircuits
could possibly achieve this, especially since they consist
in contrast to most neural network models of neurons and
synapses with heterogeneous dynamic responses. However it
turns out that the diversity of computational units
increases the capability of microcircuit models for
temporal integration. Furthermore the prediction of future
input may be rather easy for such circuits since it
suffices to train the readouts from such microcircuits. In
this article we show that very simple readouts from a
generic recurrently connected circuit of integrate-and-fire
neurons with diverse dynamic synapses can be trained in an
unsupervised manner to predict movements of different
objects, that move within an unlimited number of
combinations of speed, angle, and offset over a simulated
sensor field. The autonomously trained microcircuit model
is also able to compute the direction of motion, which is a
computationally difficult problem ("aperture problem")
since it requires disambiguation of local sensor readings
through the context of other sensor readings at the current
and preceding moments. Furthermore the same circuit can be
trained simultaneously in a supervised manner to also
report the shape and velocity of the moving object. Finally
it is shown that the trained neural circuit supports
novelty detection and the generation of "imagined
movements". Altogether the results of this article suggest
that it is not necessary to construct specific and
biologically unrealistic neural circuit models for specific
sensory processing tasks, since "found" generic cortical
microcircuit models in combination with very simple
perceptron-like readouts can easily be trained to solve
such computational tasks.}
}
@Article{LegensteinETAL:04,
author = {R. Legenstein and C. Naeger and W. Maass},
title = {What can a Neuron Learn with Spike-Timing-Dependent
Plasticity?},
journal = {Neural Computation},
year = {2005},
volume = {17},
number = {11},
pages = {2337--2382},
abstract = {Spiking neurons are very flexible computational modules,
which can implement with different values of their
adjustable synaptic parameters an enormous variety of
different transformations F from input spike trains to
output spike trains. We examine in this letter the question
to what extent a spiking neuron with biologically realistic
models for dynamic synapses can be taught via
spike-timing-dependent plasticity (STDP) to implement a
given transformation F. We consider a supervised learning
paradigm where during training, the output of the neuron is
clamped to the target signal (teacher forcing). The
well-known perceptron convergence theorem asserts the
convergence of a simple supervised learning algorithm for
drastically simplified neuron models (McCulloch-Pitts
neurons). We show that in contrast to the perceptron
convergence theorem, no theoretical guarantee can be given
for the convergence of STDP with teacher forcing that holds
for arbitrary input spike patterns. On the other hand, we
prove that average case versions of the perceptron
convergence theorem hold for STDP in the case of
uncorrelated and correlated Poisson input spike trains and
simple models for spiking neurons. For a wide class of
cross-correlation functions of the input spike trains, the
resulting necessary and sufficient condition can be
formulated in terms of linear separability, analogously as
the well-known condition of learnability by perceptrons.
However, the linear separability criterion has to be
applied here to the columns of the correlation matrix of
the Poisson input. We demonstrate through extensive
computer simulations that the theoretically predicted
convergence of STDP with teacher forcing also holds for
more realistic models for neurons, dynamic synapses, and
more general input distributions. In addition, we show
through computer simulations that these positive learning
results hold not only for the common interpretation of
STDP, where STDP changes the weights of synapses, but also
for a more realistic interpretation suggested by
experimental data where STDP modulates the initial release
probability of dynamic synapses.}
}
@InProceedings{LegensteinETAL:04a,
author = {R. Legenstein and W. Maass},
title = {A criterion for the convergence of learning with spike
timing dependent plasticity},
booktitle = {Advances in Neural Information Processing Systems},
editor = {Y. Weiss and B. Schoelkopf and J. Platt},
volume = {18},
pages = {763--770},
year = 2006,
publisher = {MIT Press},
abstract = {We investigate under what conditions a neuron can learn by
experimentally supported rules for spike timing dependent
plasticity (STDP) to predict the arrival times of strong
``teacher inputs'' to the same neuron. It turns out that in
contrast to the famous Perceptron Convergence Theorem,
which predicts convergence of the perceptron learning rule
for a strongly simplified neuron model whenever a stable
solution exists, no equally strong convergence guarantee
can be given for spiking neurons with STDP. But we derive a
criterion on the statistical dependency structure of input
spike trains which characterizes exactly when learning with
STDP will converge on average for a simple model of a
spiking neuron. This criterion is reminiscent of the linear
separability criterion of the Perceptron Convergence
Theorem, but it applies here to the rows of a correlation
matrix related to the spike inputs. In addition we show
through computer simulations for more realistic neuron
models that the resulting analytically predicted positive
learning results not only hold for the common
interpretation of STDP where STDP changes the weights of
synapses, but also for a more realistic interpretation
suggested by experimental data where STDP modulates the
initial release probability of dynamic synapses.}
}
@InProceedings{LegensteinETAL:08,
author = {R. Legenstein and D. Pecevski and W. Maass},
title = {Theoretical Analysis of Learning with Reward-Modulated
Spike-Timing-Dependent Plasticity},
booktitle = {Proc. of NIPS 2007, Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2008},
volume = {20},
pages = {881--888},
abstract = {Reward-modulated spike-timing-dependent plasticity
({STDP}) has recently emerged as a candidate for a learning
rule that could explain how local learning rules at single
synapses support behaviorally relevant adaptive changes in
complex networks of spiking neurons. However the potential
and limitations of this learning rule could so far only be
tested through computer simulations. This article provides
tools for an analytic treatment of reward-modulated {STDP},
which allow us to predict under which conditions
reward-modulated {STDP} will be able to achieve a desired
learning effect. In particular, we can produce in this way
a theoretical explanation and a computer model for a
fundamental experimental finding on biofeedback in monkeys
(reported in [1])}
}
@Article{LegensteinETAL:08a,
author = {R. Legenstein and D. Pecevski and W. Maass},
title = {A Learning Theory for Reward-Modulated
Spike-Timing-Dependent Plasticity with Application to
Biofeedback},
journal = {PLoS Computational Biology},
year = {2008},
volume = {4},
number = {10},
pages = {1--27},
abstract = {Reward-modulated spike-timing-dependent plasticity
({STDP}) has recently emerged as a candidate for a learning
rule that could explain how behaviorally relevant adaptive
changes in complex networks of spiking neurons could be
achieved in a self-organizing manner through local synaptic
plasticity. However the capabilities and limitations of
this learning rule could so far only be tested through
computer simulations. This article provides tools for an
analytic treatment of reward-modulated {STDP}, which allows
us to predict under which conditions reward-modulated
{STDP} will achieve a desired learning effect. These
analytical results imply that neurons can learn through
reward-modulated {STDP} to classify not only spatial, but
also temporal firing patterns of presynaptic neurons. They
also can learn to respond to specific presynaptic firing
patterns with particular spike patterns. Finally, the
resulting learning theory predicts that even difficult
credit-assignment problems, where it is very hard to tell
which synaptic weights should be modified in order to
increase the global reward for the system, can be solved in
a self-organizing manner through reward-modulated {STDP}.
This yields an explanation for a fundamental experimental
result on biofeedback in monkeys by Fetz and Baker. In this
experiment monkeys were rewarded for increasing the firing
rate of a particular neuron in the cortex, and were able to
solve this extremely difficult credit assignment problem.
Our model for this experiment relies on a combination of
reward-modulated {STDP} with variable spontaneous firing
activity. Hence it also provides a possible functional
explanation for trial-to-trial variability, which is
characteristic for cortical networks of neurons, but has no
analogue in currently existing artificial computing
systems. In addition our model demonstrates that
reward-modulated {STDP} can be applied to all synapses in a
large recurrent neural network without endangering the
stability of the network dynamics.}
}
@Article{LegensteinETAL:08b,
author = {R. Legenstein and D. Pecevski and W. Maass},
title = {Supplementary Information to: "{A} Learning Theory for
Reward-Modulated Spike-Timing-Dependent Plasticity with
Application to Biofeedback"},
journal = {PLoS Computational Biology},
year = {2008},
volume = {4},
number = {10},
pages = {}
}
@Article{LegensteinETAL:08c,
author = {R. Legenstein and S. A. Chase and A. B. Schwartz and W.
Maass},
title = {A model for learning effects in motor cortex that may
facilitate the brain control of neuroprosthetic devices},
journal = {38th Annual Conference of the Society for Neuroscience,
Program 517.6},
year = {2008},
volume = {},
number = {},
pages = {},
abstract = {Recent experimental results have shown that the direction
preference of neurons in monkey motor cortex changes in
order to compensate for purposeful misreading of preferred
directions for brain control of a robot arm. We show that a
simple neural network model in combination with a new rule
for reward-modulated Hebbian plasticity can explain this
effect. This rule requires substantial trial-to-trial
variability of the neuronal output for exploration. In
contrast to previously proposed rules for reward-modulated
Hebbian plasticity, the new rule does not require that the
plasticity mechanism `knows' the noise explicitly. It is
able to optimize the performance of the model system within
biologically realistic periods of time and under high noise
levels. When the neuronal noise is fitted to experimental
data, the model produces learning effects similar to those
found in monkey experiments. We quantified these effects
and found a surprisingly good match to those observed in
experiments. This study shows that reward-modulated
learning can explain detailed experimental results about
neuronal tuning changes in a motor control task and
suggests that reward-modulated learning is an essential
plasticity mechanism in the cortex for the acquisition of
goal-directed behavior. Self-tuning effects of the type
considered in this model are obviously important for
successful use of neuroprosthetic devices.}
}
@InProceedings{LegensteinETAL:09,
author = {B. Schrauwen and L. Buesing and R. Legenstein},
title = {On Computational Power and the Order-Chaos Phase
Transition in Reservoir Computing},
booktitle = {Proc. of NIPS 2008, Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2009},
volume = {21},
pages = {1425--1432},
abstract = {Randomly connected recurrent neural circuits have proven
to be very powerful models for online computations when a
trained memoryless readout function is appended. Such {\em
Reservoir Computing (RC)} systems are commonly used in two
flavors: with analog or binary (spiking) neurons in the
recurrent circuits. Previous work showed a fundamental
difference between these two incarnations of the RC idea.
The performance of a RC system build from binary neurons
seems to depend strongly on the network connectivity
structure. In networks of analog neurons such dependency
has not been observed. In this article we investigate this
apparent dichotomy in terms of the in-degree of the circuit
nodes. Our analyses based amongst others on the Lyapunov
exponent reveal that the phase transition between ordered
and chaotic network behavior of binary circuits
qualitatively differs from the one in analog circuits. This
explains the observed decreased computational performance
of binary circuits of high node in-degree. Furthermore, a
novel mean-field predictor for computational performance is
introduced and shown to accurately predict the numerically
obtained results.}
}
@InProceedings{LegensteinETAL:09a,
author = {R. Legenstein and S. A. Chase and A. B. Schwartz and W.
Maass},
title = {Functional network reorganization in motor cortex can be
explained by reward-modulated {H}ebbian learning},
booktitle = {Proc. of NIPS 2009: Advances in Neural Information
Processing Systems},
editor = {D. Koller and D. Schuurmans and Y. Bengio and L. Bottou},
publisher = {MIT Press},
year = {2010},
volume = {22},
pages = {1105--1113},
abstract = {The control of neuroprosthetic devices from the activity
of motor cortex neurons benefits from learning effects
where the function of these neurons is adapted to the
control task. It was recently shown that tuning properties
of neurons in monkey motor cortex are adapted selectively
in order to compensate for an erroneous interpretation of
their activity. In particular, it was shown that the tuning
curves of those neurons whose preferred directions had been
misinterpreted changed more than those of other neurons. In
this article, we show that the experimentally observed
self-tuning properties of the system can be explained on
the basis of a simple learning rule. This learning rule
utilizes neuronal noise for exploration and performs
Hebbian weight updates that are modulated by a global
reward signal. In contrast to most previously proposed
reward-modulated Hebbian learning rules, this rule does not
require extraneous knowledge about what is noise and what
is signal. The learning rule is able to optimize the
performance of the model system within biologically
realistic periods of time and under high noise levels. When
the neuronal noise is fitted to experimental data, the
model produces learning effects similar to those found in
monkey experiments.}
}
@Article{LegensteinETAL:09b,
author = {R. Legenstein and S. M. Chase and A. B. Schwartz and W.
Maass},
title = {A reward-modulated {H}ebbian learning rule can explain
experimentally observed network reorganization in a brain
control task},
journal = {The Journal of Neuroscience},
year = {2010},
volume = {30},
number = {25},
pages = {8400--8410},
abstract = {It has recently been shown in a brain-computer interface
experiment that motor cortical neurons change their tuning
properties selectively to compensate for errors induced by
displaced decoding parameters. In particular, it was shown
that the three-dimensional tuning curves of neurons whose
decoding parameters were reassigned changed more than those
of neurons whose decoding parameters had not been
reassigned. In this article, we propose a simple learning
rule that can reproduce this effect. Our learning rule uses
Hebbian weight updates driven by a global reward signal and
neuronal noise. In contrast to most previously proposed
learning rules, this approach does not require extrinsic
information to separate noise from signal. The learning
rule is able to optimize the performance of a model system
within biologically realistic periods of time under high
noise levels. Furthermore, when the model parameters are
matched to data recorded during the brain-computer
interface learning experiments described above, the model
produces learning effects strikingly similar to those found
in the experiments.}
}
@InProceedings{LegensteinETAL:09sup,
author = {B. Schrauwen and L. Buesing and R. Legenstein},
title = {Supplementary Material to: On Computational Power and the
Order-Chaos Phase Transition in Reservoir Computing},
booktitle = {Proc. of NIPS 2008, Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2009},
volume = {21},
note = {in press},
pages = {}
}
@Article{LegensteinETAL:10,
author = {R. Legenstein and N. Wilbert and L. Wiskott},
title = {Reinforcement Learning on Slow Features of
High-Dimensional Input Streams},
journal = {PLoS Computational Biology},
year = {2010},
volume = {6},
number = {8},
pages = {e1000894},
abstract = {Humans and animals are able to learn complex behaviors
based on a massive stream of sensory information from
different modalities. Early animal studies have identified
learning mechanisms that are based on reward and punishment
such that animals tend to avoid actions that lead to
punishment whereas rewarded actions are reinforced.
However, most algorithms for reward-based learning are only
applicable if the dimensionality of the state-space is
sufficiently small or its structure is sufficiently simple.
Therefore, the question arises how the problem of learning
on high-dimensional data is solved in the brain. In this
article we propose a biologically plausible generic
two-stage learning system that can directly be applied to
raw high-dimensional input streams. The system is composed
of a hierarchical slow feature analysis (SFA) network for
preprocessing and a simple neural network on top that is
trained based on rewards. We demonstrate by computer
simulations that this generic architecture is able to learn
quite demanding reinforcement learning tasks on
high-dimensional visual input streams in a time that is
comparable to the time needed when an explicit highly
informative low-dimensional state-space representation is
given instead of the high-dimensional visual input. The
learning speed of the proposed architecture in a task
similar to the Morris water maze task is comparable to that
found in experimental studies with rats. This study thus
supports the hypothesis that slowness learning is one
important unsupervised learning principle utilized in the
brain to form efficient state representations for
behavioral learning. }
}
@TechReport{LegensteinMaass:04,
author = {R. Legenstein and W. Maass},
title = {Additional material to the paper: What can a Neuron Learn
with Spike-Timing-Dependent Plasticity?},
institution = {Institute for Theoretical Computer Science, Graz
University of Technology},
htmlnote = {(PDF)},
year = {2004}
}
@InCollection{LegensteinMaass:05,
author = {R. Legenstein and W. Maass},
title = {What makes a dynamical system computationally powerful?},
booktitle = {New Directions in Statistical Signal Processing: From
Systems to Brains},
publisher = {MIT Press},
editor = {S. Haykin and J. C. Principe and T.J. Sejnowski and J.G.
McWhirter},
pages = {127--154},
year = {2007},
abstract = {We review methods for estimating the computational
capability of a complex dynamical system. The main examples
that we discuss are models for cortical neural
microcircuits with varying degrees of biological accuracy,
in the context of online computations on complex input
streams. We address in particular the question to what
extent earlier results ab out the relationship between the
edge of chaos and the compu tational power of dynamical
systems in discrete time for off -line computing also apply
to this case.}
}
@Article{LegensteinMaass:05a,
author = {R. Legenstein and W. Maass},
title = {Edge of Chaos and Prediction of Computational Performance
for Neural Circuit Models},
journal = {Neural Networks},
year = {2007},
volume = {20},
number = {3},
pages = {323--334},
note = {},
abstract = {We analyze in this article the significance of the edge of
chaos for real-time computations in neural microcircuit
models consisting of spiking neurons and dynamic synapses.
We find that the edge of chaos predicts quite well those
values of circuit parameters that yield maximal
computational performance. But obviously it makes no
prediction of their computational performance for other
parameter values. Therefore, we propose a new method for
predicting the computational performance of neural
microcircuit models. The new measure estimates directly the
kernel property and the generalization capability of a
neural microcircuit.We validate the proposed measure by
comparing its prediction with direct evaluations of the
computational performance of various neural microcircuit
models. The proposed method also allows us to quantify
differences in the computational performance and
generalization capability of neural circuits in different
dynamic regimes (UP- and DOWN-states) that have been
demonstrated through intracellular recordings in vivo.}
}
@Article{LegensteinMaass:07,
author = {R. Legenstein and W. Maass},
title = {On the classification capability of sign-constrained
perceptrons},
journal = {Neural Computation},
volume = {20},
number = {1},
pages = {288--309},
year = {2008},
abstract = {The perceptron (also referred to as McCulloch-Pitts
neuron, or linear threshold gate) is commonly used as a
simplified model for the discrimination and learning
capability of a biological neuron. Criteria that tell us
when a perceptron can implement (or learn to implement) all
possible dichotomies over a given set of input patterns are
well-known, but only for the idealized case where one
assumes that the sign of a synaptic weight can be switched
during learning. We present in this article an analysis of
the classification capability of the biologically more
realistic model of a sign-constrained perceptron, where the
signs of synaptic weights remain fixed during learning
(which is the case for most types of biological synapses).
In particular, the VC-dimension of sign-constrained
perceptrons is determined, and a necessary and sufficient
criterion is provided that tells us when all $2^m$
dichotomies over a given set of m patterns can be learned
by sign-constrained perceptron. We also show that
uniformity of {L1} norms of input patterns is a sufficient
condition for full representation power in the case where
all weights are required to be nonnegative. Finally, we
also exhibit cases where the sign-constraint of a
perceptron drastically reduces its classification
capability. Our theoretical analysis is complemented by
computer simulations, which demonstrate in particular that
sparse input patterns improve the classification capability
of sign-constrained perceptrons.}
}
@Article{LegensteinMaass:09,
author = {R. Legenstein and W. Maass},
title = {An integrated learning rule for branch strength
potentiation and {STDP}},
journal = {39th Annual Conference of the Society for Neuroscience,
Program 895.20, Poster HH36},
year = {2009},
volume = {},
number = {},
pages = {},
abstract = {Recent experimental data (Losonczy, Makara, and Magee,
Nature 2008) show that not only the strength of synaptic
efficacy is plastic, but also the coupling between
dendritic branches and the soma (via dendritic spikes).
More precisely, the strength of this coupling can be
increased both through a coincidence of dendritic branch
activations with action potential generation, and through a
coincidence of branch activation with ACh. This effect has
been called Branch Strength Potentiation (BSP). We show
through theoretical analysis and computer simulations that
the learning capability of single neurons is substantially
increased if STDP is combined with BSP. More precisely, we
show that a simple learning rule, based on a
error-minimization principle, contains both BSP and STDP as
special cases. The learning rule includes a homeostatic
mechanism which acts locally at the site of the dendritic
branch. The depression that was observed for
post-before-pre pairings in standard STDP experiments is
also observed in simulations of this learning rule. It can
be explained by the combined effect of this local
homeostatic mechanism and the backpropagating action
potential. This powerful new learning rule endows single
neurons with learning capabilities which were previously
unattainable. For example, a single neuron acquires through
this new learning rule the capability to solve a "binding
problem". I.e., a single neuron can learn to respond to
fire upon activation of presynaptic pools A and B, and also
upon activation of presynaptic pools C and D, but NOT in
response to concurrent activation of presynaptic pools A
and C, or B and D. We also consider a variation of this
learning rule where changes at synapses and branches are
not only based on local activity, but also on a global
reward signal that is indicated to the neuron by the
concentration of a neuromodulatory signal such as ACh. We
show that this biologically plausible learning rule for
reward-based learning is much more efficient than
previously proposed rules based on simple neuron models
without nonlinear branches.}
}
@Article{LegensteinMaass:11,
author = {R. Legenstein and W. Maass},
title = {Branch-specific plasticity enables self-organization of
nonlinear computation in single neurons},
journal = {The Journal of Neuroscience},
year = {2011},
volume = {31},
number = {30},
pages = {10787--10802},
abstract = {It has been conjectured that nonlinear processing in
dendritic branches endows individual neurons with the
capability to perform complex computational operations that
are needed in order to solve for example the binding
problem. However, it is not clear how single neurons could
acquire such functionality in a self-organized manner,
since most theoretical studies of synaptic plasticity and
learning concentrate on neuron models without nonlinear
dendritic properties. In the meantime, a complex picture of
information processing with dendritic spikes and a variety
of plasticity mechanisms in single neurons has emerged from
experiments. In particular, new experimental data on
dendritic branch strength potentiation in rat hippocampus
have not yet been incorporated into such models. In this
article, we investigate how experimentally observed
plasticity mechanisms, such as depolarization-dependent
STDP and branch-strength potentiation could be integrated
to self-organize nonlinear neural computations with
dendritic spikes. We provide a mathematical proof that in a
simplified setup these plasticity mechanisms induce a
competition between dendritic branches, a novel concept in
the analysis of single neuron adaptivity. We show via
computer simulations that such dendritic competition
enables a single neuron to become member of several
neuronal ensembles, and to acquire nonlinear computational
capabilities, such as for example the capability to bind
multiple input features. Hence our results suggest that
nonlinear neural computation may self-organize in single
neurons through the interaction of local synaptic and
dendritic plasticity mechanisms.},
htmlnote = {(Commentary by R. P. Costa and P. J. Sj\"ostr\"om in
Frontiers in Synaptic Neuroscience PDF)}
}
@Article{LiebeETAL:09,
author = {S. Liebe and G. Hoerzer and N.K. Logothetis and W. Maass
and G. Rainer},
title = {Long range coupling between {V4} and {PF} in theta band
during visual short-term memory},
journal = {39th Annual Conference of the Society for Neuroscience,
Program 652.20, Poster Y31},
year = {2009},
volume = {},
number = {},
pages = {},
abstract = {Both extrastriate area V4 and the lateral prefrontal
cortex (PF) are thought to be part of a neural network
contributing to sensory and mnemonic processing of visual
information. However, it is not well understood how V4 and
PF might interact during visual memory. Here, we addressed
this question by recording Local Field Potentials (LFP)
simultaneously in both brain regions while two rhesus
monkeys performed a delayed matching-to sample task. In the
task, a sample stimulus (250ms) was presented followed by a
probe stimulus (600ms) after a delay period (1500ms). A
lever press was required if the sample stimulus matched the
probe. We assessed coupling between LFP sites within and
between the different brain regions by both measuring
pair-wise phase-synchrony (phase locking value, PLV) using
a wavelet based method and employing a coupling measure
that relies on the concept of Granger causality
(partial-directed coherence; PDC) using multivariate
autoregressive (MVAR) modeling. In both monkeys we
consistently found increases in theta-band phase synchrony
(3.5-7 Hz) between V4 and PF LFP site pairs during the
delay period of the task. Specifically, a significant
proportion of pairs (26.1\%, 62/231 for monkey 1 and 25\%,
40/160 for monkey 2, p<0.001) showed increased coherence
during the delay phase compared to the pre-stimulus
baseline period. In contrast, only a small proportion of
sites showed significant coupling in gamma (42-97 Hz,
5.9\%/13\% for monkeys 1/2, respectively) or beta (16-36Hz,
6.9\%/16\%) frequencies. In addition, we obtained
comparable results using PDC, which also assesses the
directionality of information flow between the brain areas.
Our preliminary results indicate that the interaction
between V4 and PF during short-term memory might be
primarily mediated through neuronal coherence in the theta
band. Furthermore, our analyses using MVAR modeling suggest
that this interaction can be characterized by a
bidirectional information flow between these areas. These
findings support the idea that long-range interactions play
an important role in short-term maintenance of short-term
memory.}
}
@InCollection{Maass:00,
author = {W. Maass},
title = {Spike trains -- Im {R}hythmus neuronaler {Z}ellen},
booktitle = {Katalog der steirischen Landesausstellung gr2000az},
pages = {36--42},
publisher = {Springer Verlag},
year = {2000},
editor = {H. Konrad, R. Kriesche}
}
@InCollection{Maass:00a,
author = {W. Maass},
title = {Lernende {M}aschinen},
booktitle = {Katalog der steirischen Landesausstellung gr2000az},
pages = {50--56},
publisher = {Springer Verlag},
year = 2000,
editor = {H. Konrad, R. Kriesche}
}
@InCollection{Maass:00b,
author = {W. Maass},
title = {Neural computation: a research topic for theoretical
computer science? {S}ome thoughts and pointers},
booktitle = {Current Trends in Theoretical Computer Science, Entering
the 21th Century},
publisher = {World Scientific Publishing},
year = {2001},
pages = {680--690},
editor = {Rozenberg G. and Salomaa A. and Paun G.}
}
@InProceedings{Maass:00c,
author = {W. Maass},
title = {Neural computation: a research topic for theoretical
computer science? {S}ome thoughts and pointers},
booktitle = {Bulletin of the European Association for Theoretical
Computer Science (EATCS)},
pages = {149--158},
year = {2000},
volume = {72}
}
@InProceedings{Maass:01a,
author = {W. Maass},
title = {wetware ({E}nglish version)},
booktitle = {{TAKEOVER}: {W}ho is {D}oing the {A}rt of {T}omorrow
({A}rs {E}lectronica 2001)},
pages = {148--152},
year = {2001},
publisher = {Springer}
}
@InProceedings{Maass:01b,
author = {W. Maass},
title = {wetware (deutsche {V}ersion)},
booktitle = {{TAKEOVER}: {W}ho is {D}oing the {A}rt of {T}omorrow
({A}rs {E}lectronica 2001)},
year = {2001},
pages = {153--157},
publisher = {Springer}
}
@Article{Maass:02,
author = {W. Maass},
title = {Computing with Spikes},
journal = {Special Issue on Foundations of Information Processing of
{TELEMATIK}},
year = {2002},
pages = {32--36},
volume = {8},
number = {1}
}
@InProceedings{Maass:02a,
author = {W. Maass},
title = {On the Computational Power of Neural Microcircuit Models:
Pointers to the Literature},
booktitle = {Proc. of
the International Conference on Artificial Neural Networks
-- ICANN 2002},
pages = {254--256},
year = {2002},
editor = {Jos\'{e} R. Dorronsoro},
volume = {2415},
series = {Lecture Notes in Computer Science},
publisher = {Springer}
}
@InCollection{Maass:03,
author = {W. Maass},
title = {Computation with Spiking Neurons},
booktitle = {The Handbook
of Brain Theory and Neural Networks},
edition = {2nd},
publisher = {MIT Press (Cambridge)},
editor = {M. A. Arbib},
year = {2003},
pages = {1080--1083}
}
@Article{Maass:06,
author = {W. Maass},
title = {Book Review of "{I}mitation of life: how biology is
inspiring computing" by {N}ancy {F}orbes},
journal = {Pattern Analysis and Applications},
year = {2006},
volume = {8},
number = {4},
pages = {390--391},
note = {Springer (London)}
}
@InProceedings{Maass:07,
author = {W. Maass},
booktitle = {Proceedings of the Conference CiE'07: {COMPUTABILITY IN
EUROPE} 2007, Siena (Italy)},
title = {Liquid Computing},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
volume = {},
year = {2007},
pages = {507--516},
abstract = {This review addresses structural differences between that
type of computation on which computability theory and
computational complexity theory have focused so far, and
those computations that are usually carried out in
biological organisms (either in the brain, or in the form
of gene regulation within a single cell). These differences
concern the role of time, the way in which the input is
presented, the way in which an algorithm is implemented,
and in the end also the definition of what a computation
is. This article describes liquid computing as a new
framework for analyzing those types of computations that
are usually carried out in biological organisms.}
}
@InCollection{Maass:09,
author = {W. Maass},
title = {Liquid State Machines: Motivation, Theory, and
Applications},
booktitle = {Computability in Context: Computation and Logic in the
Real World},
editor = {B. Cooper and A. Sorbi},
year = {2010},
publisher = {Imperial College Press},
pages = {275--296},
keywords = {},
note = {},
abstract = {The Liquid State Machine (LSM) has emerged as a
computational model that is more adequate than the Turing
machine for describing computations in biological networks
of neurons. Characteristic features of this new model are
(i) that it is a model for adaptive computational systems,
(ii) that it provides a method for employing randomly
connected circuits, or eve "found" physical objects for
meaningful computations, (iii) that it provides a
theoretical context where heterogeneous, rather than
stereotypical, local gates or processors increase the
computational power of a circuit, (iv) that it provides a
method for multiplexing different computations (on a common
input) within the same circuit. This chapter reviews the
motivation for this model, its theoretical background, and
current work on implementations of this model in innovative
artificial computing devices.}
}
@InProceedings{Maass:75,
author = {W. Maass},
booktitle = {Proof Theory Symposium Kiel 1974},
editor = {J. Diller and G. H. Mueller},
journal = {Lecture Notes in Mathematics, Springer (Berlin)},
pages = {257--263},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Mathematics},
title = {Church Rosser Theorem fuer Lambda-Kalkuele mit unendlich
langen Termen},
volume = {500},
year = {1975}
}
@Article{Maass:76,
author = {W. Maass},
journal = {Archive Math. Logik Grundlagen},
pages = {27--46},
title = {Eine {F}unktionalinterpretation der praedikativen
{A}nalysis},
volume = {18},
year = {1976}
}
@Article{Maass:77,
author = {W. Maass},
journal = {Archive Math. Logik Grundlagen},
pages = {169--186},
title = {On minimal pairs and minimal degrees in higher recursion
theory},
volume = {18},
year = {1977}
}
@Article{Maass:78,
author = {W. Maass},
journal = {Ann. of Math. Logic},
pages = {149--170},
title = {Inadmissibility, tame r.e. sets and the admissible
collapse},
volume = {13},
year = {1978}
}
@Article{Maass:78a,
author = {W. Maass},
journal = {J. Symbolic Logic},
pages = {270-279},
title = {The uniform regular set theorem in alpha-recursion
theory},
volume = {43},
year = {1978}
}
@InProceedings{Maass:78b,
author = {W. Maass},
booktitle = {Higher Set Theory},
editor = {G. H. Mueller and D. Scott},
pages = {339--359},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Mathematics},
title = {Fine structure theory of the constructible universe in
alpha- and beta-recursion theory},
volume = {669},
year = {1978}
}
@MastersThesis{Maass:78c,
author = {W. Maass},
note = {Minerva Publikation (Muenchen)},
school = {Ludwig-Maximilians-Universitaet Muenchen},
title = {Contributions to alpha- and beta-recursion theory},
type = {Habilitationsschrift},
year = {1978}
}
@InCollection{Maass:78d,
author = {W. Maass},
booktitle = {Generalized Recursion Theory II},
editor = {E. Fenstad and R. O. Gandy and G. E. Sacks},
pages = {239--269},
publisher = {North-Holland (Amsterdam)},
title = {High alpha-recursively enumerable degrees},
year = {1978}
}
@Conference{GuptaMaass:91,
author = {A. Gupta and W. Maass},
booktitle = {Advances in Neural Information Processing Systems},
editor = {R. P. Lippmann and J. E. Moody and D. S. Touretzky},
pages = {825--831},
publisher = {Morgan Kaufmann, (San Mateo)},
title = {A method for the efficient design of {B}oltzmann machines
for classification problems},
volume = {3},
year = {1991}
}
@Article{Maass:79,
author = {W. Maass},
journal = {Ann. of Math. Logic},
pages = {205--231},
title = {On alpha- and beta-recursively enumerable degrees},
volume = {16},
year = {1979}
}
@InProceedings{Maass:81,
author = {W. Maass},
booktitle = {Proceedings of the Conf. on Recursion Theory and
Computational Complexity},
editor = {G. Lolli},
pages = {229--236},
publisher = {Liguori editore (Napoli)},
title = {Recursively invariant beta-recursion theory -- a
preliminary survey},
year = {1981}
}
@Article{Maass:81a,
author = {W. Maass},
journal = {Proceedings Amer. Math. Soc.},
pages = {267--270},
title = {A countable basis for sigma-one-two sets and recursion
theory on aleph-one},
volume = {82},
year = {1981}
}
@Article{Maass:81b,
author = {W. Maass},
journal = {Ann. of Math. Logic},
pages = {27--73},
title = {Recursively invariant beta-recursion theory},
volume = {21},
year = {1981}
}
@Article{Maass:83,
author = {W. Maass},
journal = {J. Symbolic Logic},
pages = {809--823},
title = {Recursively enumerable generic sets},
volume = {47},
year = {1983}
}
@Article{Maass:83a,
author = {W. Maass},
journal = {Trans. Amer. Math. Soc.},
pages = {311--336},
title = {Characterization of recursively enumerable sets with
supersets effectively isomorphic to all recursively
enumerable sets},
volume = {279},
year = {1983}
}
@Article{Maass:84,
author = {W. Maass},
journal = {J. Symbolic Logic},
pages = {51--62},
title = {On the orbits of hyperhypersimple sets},
volume = {49},
year = {1984}
}
@InProceedings{Maass:84a,
author = {W. Maass},
booktitle = {Proceedings of 16th Annual ACM Symp. on Theory of
Computing},
pages = {401--408},
title = {Quadratic lower bounds for deterministic and
nondeterministic one-tape {T}uring machines},
abstract = {We introduce new techniques for proving quadratic lower
bounds for deterministic and nondeterministic i-tape Turing
machines (all considered Turing machines have an additional
oneway input tape). In particular we produce quadratic
lower bounds for the simulation of 2-tape TM's by l-tape
TM's and thus answer a rather old question (problem No.1
and No.7 in the l i s t of Duris, Galil, Paul, Reischuk
[3]). Further we demo6strate a substantial superiority of
nondeterminism over determinism and of co-nondeterminism
over nondeterminism for l-tape TM's.},
year = {1984}
}
@Article{Maass:85,
author = {W. Maass},
journal = {J. Symbolic Logic},
pages = {138--148},
title = {Variations on promptly simple sets},
volume = {50},
year = {1985}
}
@Article{Maass:85a,
author = {W. Maass},
journal = {Proceedings of Symposia in Pure Mathematics},
pages = {21--32},
title = {Major subsets and automorphisms of recursively enumerable
sets},
volume = {42},
year = {1985}
}
@Article{Maass:85b,
author = {W. Maass},
journal = {Transactions of the American Mathematical Society},
pages = {675--693},
title = {Combinatorial lower bound arguments for deterministic and
nondeterministic {T}uring machines},
abstract = {We introduce new techniques for proving quadratic lower
bounds for deterministic and nondeterminisitc 1-tape
{T}uring machines (all considered {T}uring machines have an
additional one-way input tape). In particular, we derive
for the simulation of 2-tape {T}uring machines by 1-tape
{T}uring machines an optimal quadratic lower bound in the
deterministic case and a nearly optimal lower bound in the
nonderterministic case. This answers the rather old
question whether the computing power of the considered
types of {T}uring machines is significantly increased when
more than one tape is used (problem Nos. 1 and 7 in the
list of {D}uris, {G}alil, {P}aul, {R}eischuk [3]). Further,
we demonstrate a substantial superiority of nonderterminism
over determinism and of co-nondeterminism over
nondeterminism for 1-tage {T}uring machines},
volume = {292},
number = {2},
year = {1985},
note = {hard copy}
}
@InProceedings{Maass:86,
author = {W. Maass},
booktitle = {Proceedings of the International Conference on Logic,
Methodology and Philosphy of Science, Salzburg 1983},
pages = {141--158},
publisher = {North-Holland (Amsterdam)},
title = {Are recursion theoretic arguments useful in complexity
theory},
year = {1986}
}
@Article{Maass:86a,
author = {W. Maass},
journal = {SIAM J. Computing},
pages = {453--467},
title = {On the complexity of nonconvex covering},
volume = {15},
year = {1986}
}
@Article{Maass:88,
author = {W. Maass},
journal = {J. Symbolic Logic},
pages = {1098--1109},
title = {On the use of inaccessible numbers and order
indiscernibles in lower bound arguments for random access
machines},
volume = {53},
year = {1988}
}
@InProceedings{Maass:91,
author = {W. Maass},
booktitle = {Proceedings of the 4th Annual ACM Workshop on
Computational Learning Theory},
pages = {167--175},
publisher = {Morgan Kaufmann (San Mateo)},
title = {On-line learning with an oblivious environment and the
power of randomization},
year = {1991}
}
@InProceedings{Maass:93,
author = {W. Maass},
booktitle = {Proceedings of the 25th Annual ACM Symposium on Theory
Computing},
pages = {335-344},
title = {Bounds for the computational power and learning complexity
of analog neural nets},
year = {1993}
}
@Article{Maass:93j,
author = {W. Maass},
title = {Bounds for the computational power and learning complexity
of analog neural nets},
journal = {SIAM J. on Computing},
year = 1997,
volume = 26,
number = 3,
pages = {708--732}
}
@InProceedings{Maass:94,
author = {W. Maass},
booktitle = {Advances in Neural Information Processing Systems},
pages = {311--318},
title = {Agnostic {PAC}-learning of functions on analog neural
nets},
editors = {G. Tesauro and D. S. Touretzky and T. K. Leen},
volume = {7},
year = {1995}
}
@InProceedings{Maass:94a,
author = {W. Maass},
booktitle = {Proceedings of the International Conference on Artificial
Neural Networks 1994 (ICANN'94)},
pages = {581--584},
publisher = {Springer (Berlin)},
title = {Neural nets with superlinear {VC}-dimension},
year = {1994}
}
@InCollection{Maass:94b,
author = {W. Maass},
booktitle = {Theoretical Advances in Neural Computation and Learning},
editor = {V. P. Roychowdhury and K. Y. Siu and A. Orlitsky},
pages = {295-336},
publisher = {Kluwer Academic Publishers (Boston)},
title = {Perspectives of current research about the complexity of
learning on neural nets},
year = {1994}
}
@InProceedings{Maass:94c,
author = {W. Maass},
booktitle = {Theoretical Andvances in Neural Computation and Learning},
editor = {V. P. Roychowdhury and K. Y. Siu and A. Orlitsky},
pages = {153--172},
publisher = {Kluwer Academics Publisher (Boston)},
title = {Computing on analog neural nets with arbitrary real
weights},
year = {1994}
}
@InProceedings{Maass:94d,
author = {W. Maass},
booktitle = {Proc. of the 7th Annual ACM Conference on Computational
Learning Theory},
pages = {67--75},
title = {Efficient agnostic {PAC}-learning with simple hypotheses},
year = {1994}
}
@InCollection{Maass:94e,
author = {W. Maass},
booktitle = {Computational Learning Theory: EuroColt'93},
editor = {J. Shawe-Taylor and M. Anthony},
pages = {1--17},
publisher = {Oxford University Press (Oxford)},
title = {On the complexity of learning on neural nets},
year = {1994}
}
@Article{Maass:94f,
author = {W. Maass},
title = {Agnostic {PAC}-learning of functions on analog neural
nets},
journal = {Neural Computation},
year = 1995,
volume = 7,
pages = {1054--1078}
}
@Article{Maass:94j,
author = {W. Maass},
title = {Neural nets with superlinear {VC}-dimension},
journal = {Neural Computation},
year = 1994,
volume = 6,
pages = {877--884}
}
@InProceedings{Maass:95,
author = {W. Maass},
booktitle = {Proc. of the 7th Italian Workshop on Neural Nets 1995},
pages = {99--104},
publisher = {World Scientific (Singapore)},
title = {Analog computations on networks of spiking neurons
(extended abstract)},
year = {1996}
}
@InCollection{Maass:95a,
author = {W. Maass},
booktitle = {The Handbook of Brain Theory and Neural Networks},
editor = {M.~A.~Arbib},
pages = {1000--1003},
publisher = {MIT Press (Cambridge)},
title = {Vapnik-{C}hervonenkis dimension of neural nets},
year = {1995}
}
@InProceedings{Maass:95b,
author = {W. Maass},
booktitle = {Advances in Neural Information Processing Systems},
editor = {G. Tesauro and D. S. Touretzky and T. K. Leen},
pages = {183--190},
publisher = {MIT Press (Cambridge)},
title = {On the computational complexity of networks of spiking
neurons},
volume = {7},
year = {1995}
}
@Article{Maass:95c,
author = {W. Maass},
journal = {Telematik},
pages = {53--60},
volume = {1},
title = {{N}euronale {N}etze und {M}aschinelles {L}ernen am
{I}nstitut fuer {G}rundlagen der {I}nformationsverarbeitung
an der {T}echnischen {U}niversitaet {G}raz},
year = {1995}
}
@Article{Maass:96,
author = {W. Maass},
journal = {Neural Computation},
pages = {1--40},
title = {Lower Bounds for the Computational Power of Networks of
Spiking Neurons},
volume = {8},
number = {1},
year = {1996}
}
@InProceedings{Maass:96a,
author = {W. Maass},
booktitle = {Advances in Neural Information Processing Systems},
editor = {D. Touretzky and M. C. Mozer and M. E. Hasselmo},
pages = {211--217},
publisher = {MIT Press (Cambridge)},
title = {On the computational power of noisy spiking neurons},
volume = {8},
year = {1996}
}
@InProceedings{Maass:96b,
author = {W. Maass},
title = {Networks of spiking neurons: the third generation of
neural network models},
booktitle = {Proc. of the 7th Australian Conference on Neural Networks
1996 in Canberra, Australia},
pages = {1-10},
year = {1996}
}
@Article{Maass:97a,
author = {W. Maass},
journal = {Neural Computation},
pages = {279--304},
title = {Fast sigmoidal networks via spiking neurons},
volume = {9},
year = {1997}
}
@Article{Maass:97b,
author = {W. Maass},
howpublished = {FTP-host: archive.cis.ohio-state.edu FTP-filename:
/pub/neuroprose/maass.third-generation.ps.Z},
journal = {Neural Networks},
pages = {1659--1671},
title = {Networks of spiking neurons: the third generation of
neural network models},
volume = {10},
year = {1997}
}
@InProceedings{Maass:97c,
author = {W. Maass},
booktitle = {Computational Neuroscience: Trends in research},
editor = {James Bower},
pages = {123--127},
title = {A model for fast analog computations with noisy spiking
neurons},
year = {1997}
}
@InCollection{Maass:97d,
author = {W. Maass},
booktitle = {Spatiotemporal Models in Biological and Artificial
Systems},
editor = {F. L. Silva},
pages = {97-104},
publisher = {IOS-Press},
title = {Analog computations with temporal coding in networks of
spiking neurons},
year = {1997}
}
@InProceedings{Maass:97e,
author = {W. Maass},
booktitle = {Advances in Neural Information Processing Systems},
editor = {M. Mozer and M. I. Jordan and T. Petsche},
pages = {211--217},
publisher = {MIT Press (Cambridge)},
title = {Noisy spiking neurons with temporal coding have more
computational power than sigmoidal neurons},
volume = {9},
year = {1997}
}
@InProceedings{Maass:97f,
author = {W. Maass},
booktitle = {Proc. of the 8th International Conference on Algorithmic
Learning Theory in Sendai (Japan)},
editor = {M. Li and A. Maruoka},
pages = {364--384},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
title = {On the relevance of time in neural computation and
learning},
volume = {1316},
year = {1997}
}
@Article{Maass:97g,
author = {W. Maass},
title = {On the relevance of time in neural computation and
learning},
journal = {Theoretical Computer Science},
year = 2001,
volume = {261},
pages = {157-178}
}
@InProceedings{Maass:98a,
author = {W. Maass},
booktitle = {Proc. of the Federated Conference of CLS'98 and MFCS'98,
Mathematical Foundations of Computer Science 1998},
title = {On the role of time and space in neural computation},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
volume = {1450},
year = {1998},
pages = {72-83},
note = {Invited talk}
}
@Article{Maass:98b,
author = {W. Maass},
journal = {Network: Computation in Neural Systems},
number = {3},
pages = {381-397},
title = {A simple model for neural computation with firing rates
and firing correlations},
volume = {9},
year = {1998}
}
@InProceedings{Maass:98d,
author = {W. Maass},
title = {Models for fast analog computation with spiking neurons},
booktitle = {Proc. of the International Conference on Neural
Information Processing 1998 (ICONIP'98) in Kytakyusyu,
Japan},
pages = {187--188},
year = 1998,
publisher = {IOS Press (Amsterdam)},
note = {Invited talk at the special session on ``Dynamic Brain''}
}
@InProceedings{Maass:98e,
author = {W. Maass},
title = {Spiking neurons},
booktitle = {Proceedings of the ICSC/IFAC Symposium on Neural
Computation 1998 (NC'98)},
pages = {16--20},
year = 1998,
publisher = {ICSC Academic Press (Alberta)},
note = {Invited talk}
}
@InCollection{Maass:98f,
author = {W. Maass},
title = {Computing with spiking neurons},
booktitle = {Pulsed Neural Networks},
pages = {55--85},
publisher = {MIT Press (Cambridge)},
year = {1999},
editor = {W. Maass and C.~M.~Bishop}
}
@InProceedings{Maass:99,
author = {W. Maass},
title = {Neural Computation with Winner-Take-All as the only
Nonlinear Operation},
booktitle = {Advances in Information Processing Systems},
editor = {Sara A. Solla and Todd K. Leen and Klaus-Robert Mueller},
volume = {12},
publisher = {MIT Press (Cambridge)},
year = {2000},
pages = {293--299}
}
@InCollection{Maass:99a,
author = {W. Maass},
title = {Das menschliche {G}ehirn -- nur ein {R}echner?},
booktitle = {Zur Kunst des Formalen Denkens},
publisher = {Passagen Verlag (Wien)},
year = 2000,
pages = {209-233},
editor = {R. E. Burkard and W. Maass and P. Weibel}
}
@InCollection{Maass:99c,
author = {W. Maass},
title = {Paradigms for computing with spiking neurons},
booktitle = {Models of Neural Networks. Early Vision and Attention},
publisher = {Springer (New York)},
year = {2002},
editor = {J. L. van Hemmen and J. D. Cowan and E. Domany},
volume = {4},
chapter = {9},
pages = {373--402}
}
@Article{Maass:99e,
author = {W. Maass},
title = {On the computational power of winner-take-all},
year = {2000},
journal = {Neural Computation},
volume = {12},
number = {11},
pages = {2519--2535}
}
@Article{MaassETAL:00,
author = {W. Maass and A. Pinz and R. Braunstingl and G. Wiesspeiner
and T. Natschlaeger and O. Friedl and H. Burgsteiner},
title = {Konstruktion von {L}ernfaehigen {R}obotern im
{S}tudentenwettbewerb ``{R}obotik 2000'' an der
{T}echnischen {U}niversitaet {G}raz},
journal = {in: Telematik},
year = {2000},
pages = {20--24}
}
@Article{MaassETAL:01a,
author = {W. Maass and T. Natschlaeger and H. Markram},
title = {Real-time Computing Without Stable States: A New Framework
for Neural Computation Based on Perturbations},
journal = {Neural Computation},
volume = 14,
number = 11,
pages = {2531-2560},
year = 2002,
abstract = {A key challenge for neural modeling is to explain how a
continuous stream of multi-modal input from a rapidly
changing environment can be processed by stereotypical
recurrent circuits of integrate-and-fire neurons in
real-time. We propose a new framework for neural
computation that provides an alternative to previous
approaches based on attractor neural networks. It is shown
that the inherent transient dynamics of the
high-dimensional dynamical system formed by a neural
circuit may serve as a universal source of information
about past stimuli, from which readout neurons can extract
particular aspects needed for diverse tasks in real-time.
Stable internal states are not required for giving a stable
output, since transient internal states can be transformed
by readout neurons into stable target outputs due to the
high dimensionality of the dynamical system. Our approach
is based on a rigorous computational model, the liquid
state machine, that unlike Turing machines, does not
require sequential transitions between discrete internal
states. Like the Turing machine paradigm it allows for
universal computational power under idealized conditions,
but for real-time processing of time-varying input. The
resulting new framework for neural computation has novel
implications for the interpretation of neural coding, for
the design of experiments and data-analysis in
neurophysiology, and for neuromorphic engineering.}
}
@InProceedings{MaassETAL:02,
author = {W. Maass and G. Steinbauer and R. Koholka},
title = {Autonomous fast learning in a mobile robot},
booktitle = {Sensor Based Intelligent Robots. International Workshop,
Dagstuhl Castle, Germany, October 15--25, 2000, Selected
Revised Papers },
pages = {345--356},
year = {2002},
editor = {G. D. Hager and H. I. Christensen and H. Bunke and R.
Klein},
volume = {2238},
series = lncs,
publisher = {Springer
(Berlin)}
}
@InProceedings{MaassETAL:02a,
author = {W. Maass and R. Legenstein and H. Markram},
title = {A New Approach towards Vision suggested by Biologically
Realistic Neural Microcircuit Models},
booktitle = {Biologically Motivated Computer Vision. Proc. of the
Second International Workshop, BMCV 2002, Tuebingen,
Germany, November 22--24, 2002},
editor = {H. H. Buelthoff and S. W. Lee and T. A. Poggio and C.
Wallraven},
series = {Lecture Notes in Computer Science},
volume = {2525},
pages = {282--293},
year = {2002},
publisher = {Springer (Berlin)},
abstract = {We propose an alternative paradigm for processing
time-varying visual inputs, in particular for tasks
involving temporal and spatial integration, which is
inspired by hypotheses about the computational role of
cortical microcircuits. Since detailed knowledge about the
precise structure of the microcircuit is not needed for
that, it can in principle also be implemented with
partially unknown or faulty analog hardware. In addition,
this approach supports parallel realtime processing of
time-varying visual inputs for diverse tasks, since
different readouts can be trained to extract concurrently
from the same microcircuit completely different information
components.}
}
@InProceedings{MaassETAL:02b,
author = {W. Maass and T. Natschlaeger and H. Markram},
title = {A Model for Real-Time Computation in Generic Neural
Microcircuits},
booktitle = {Proc. of NIPS 2002, Advances in Neural Information
Processing Systems},
editor = {S. Becker and S. Thrun and K. Obermayer},
publisher = {MIT Press},
year = {2003},
volume = {15},
pages = {229--236},
abstract = {A key challenge for neural modeling is to explain how a
continuous stream of multi-modal input from a rapidly
changing environment can be processed by stereotypical
recurrent circuits of integrate-and-fire neurons in
real-time. We propose a new computational model that does
not require a task-dependent construction of neural
circuits. Instead it is based on principles of high
dimensional dynamical systems in combination with
statistical learning theory, and can be implemented on
generic evolved or found recurrent circuitry.}
}
@Article{MaassETAL:02c,
author = {W. Maass and T. Natschlaeger and H. Markram},
title = {Fading Memory and Kernel Properties of Generic Cortical
Microcircuit Models},
journal = {Journal of Physiology -- Paris},
year = {2004},
pages = {315--330},
volume = {98},
number = {4--6},
abstract = {It is quite difficult to construct circuits of spiking
neurons that can carry out complex computational tasks. On
the other hand even randomly connected circuits of spiking
neurons can in principle be used for complex computational
tasks such as time-warp invariant speech recognition. This
is possible because such circuits have an inherent tendency
to integrate incoming information in such a way that simple
linear readouts can be trained to transform the current
circuit activity into the target output for a very large
number of computational tasks. Consequently we propose to
analyze circuits of spiking neurons in terms of their roles
as analog fading memory and nonlinear kernels, rather than
as implementations of specific computational operations and
algorithms. This article is a sequel to \cite{LSM}, and
contains new results about the performance of generic
neural microcircuit models for the recognition of speech
that is subject to linear and nonlinear time-warps, as well
as for computations on time-varying firing rates. These
computations rely, apart from general properties of generic
neural microcircuit models, just on capabilities of simple
linear readouts trained by linear regression. This article
also provides detailed data on the fading memory property
of generic neural microcircuit models, and a quick review
of other new results on the computational power of such
circuits of spiking neurons.}
}
@InCollection{MaassETAL:03,
author = {W. Maass and T. Natschlaeger and H. Markram},
title = {Computational Models for Generic Cortical Microcircuits},
booktitle = {Computational Neuroscience: A Comprehensive Approach},
publisher = {Chapman \& Hall/CRC},
year = {2004},
editor = {J. Feng},
chapter = {18},
pages = {575--605},
address = {Boca Raton},
abstract = {The human nervous system processes a continuous stream of
multi-modal input from a rapidly changing environment. A
key challenge for neural modeling is to explain how the
neural microcircuits (columns, minicolumns, etc.) in the
cerebral cortex whose anatomical and physiological
structure is quite similar in many brain areas and species
achieve this enormous computational task. We propose a
computational model that could explain the potentially
universal computational capabilities and does not require a
task-dependent construction of neural circuits. Instead it
is based on principles of high dimensional dynamical
systems in combination with statistical learning theory,
and can be implemented on generic evolved or found
recurrent circuitry. This new approach towards
understanding neural computation on the micro-level also
suggests new ways of modeling cognitive processing in
larger neural systems. In particular it questions
traditional ways of thinking about neural coding.}
}
@InProceedings{MaassETAL:04,
author = {W. Maass and R. Legenstein and N. Bertschinger},
booktitle = {Advances in Neural Information Processing Systems},
title = {Methods for Estimating the Computational Power and
Generalization Capability of Neural Microcircuits},
year = {2005},
volume = {17},
pages = {865--872},
editor = {L. K. Saul and Y. Weiss and L. Bottou},
publisher = {MIT Press},
abstract = {What makes a neural microcircuit computationally powerful?
Or more precisely, which measurable quantities could
explain why one microcircuit $C$ is better suited for a
particular family of computational tasks than another
microcircuit $C'$? We propose in this article quantitative
measures for evaluating the computational power and
generalization capability of a neural microcircuit, and
apply them to generic neural microcircuit models drawn from
different distributions. We validate the proposed measures
by comparing their prediction with direct evaluations of
the computational performance of these microcircuit models.
This procedure is applied first to microcircuit models that
differ with regard to the spatial range of synaptic
connections and with regard to the scale of synaptic
efficacies in the circuit, and then to microcircuit models
that differ with regard to the level of background input
currents and the level of noise on the membrane potential
of neurons. In this case the proposed method allows us to
quantify differences in the computational power and
generalization capability of circuits in different dynamic
regimes (UP- and DOWN-states) that have been demonstrated
through intracellular recordings in vivo.}
}
@InProceedings{MaassETAL:06,
author = {W. Maass and P. Joshi and E. D. Sontag},
title = {Principles of real-time computing with feedback applied to
cortical microcircuit models},
booktitle = {Advances in Neural Information Processing Systems},
abstract = {The network topology of neurons in the brain exhibits an
abundance of feedback connections, but the computational
function of these feedback connections is largely unknown.
We present a computational theory that characterizes the
gain in computational power achieved through feedback in
dynamical systems with fading memory. It implies that many
such systems acquire through feedback universal
computational capabilities for analog computing with a
non-fading memory. In particular, we show that feedback
enables such systems to process time-varying input streams
in diverse ways according to rules that are implemented
through internal states of the dynamical system. In
contrast to previous attractor-based computational models
for neural networks, these flexible internal states are
{\em high-dimensional} attractors of the circuit dynamics,
that still allow the circuit state to absorb new
information from online input streams. In this way one
arrives at novel models for working memory, integration of
evidence, and reward expectation in cortical circuits. We
show that they are applicable to circuits of
conductance-based Hodgkin-Huxley (HH) neurons with high
levels of noise that reflect experimental data on in-vivo
conditions. },
year = {2006},
volume = {18},
pages = {835--842},
publisher = {MIT Press},
editor = {Y. Weiss and B. Schoelkopf and J. Platt}
}
@Article{MaassETAL:06a,
author = {W. Maass and P. Joshi and E. D. Sontag},
title = {Computational aspects of feedback in neural circuits},
journal = {PLoS Computational Biology},
year = 2007,
volume = {3},
number = {1},
pages = {e165, 1--20}
}
@Article{MaassETAL:07,
author = {H. Jaeger and W. Maass and J. Principe},
title = {Introduction to the Special Issue on Echo State Networks
and Liquid State Machines},
journal = {Neural Networks},
year = {2007},
volume = {20},
number = {3},
pages = {287--289},
note = {}
}
@Article{MaassETAL:81,
author = {W. Maass and A. Shore and M. Stob},
journal = {Israel J. Math.},
pages = {210--224},
title = {Splitting properties and jump classes},
volume = {39},
year = {1981}
}
@InProceedings{MaassETAL:87,
author = {W. Maass and G. Schnitger and E. Szemeredi},
booktitle = {Proceedings of the 19th Annual ACM Symposium on Theory of
Computing},
pages = {94--100},
title = {Two tapes are better than one for off-line Turing
machines},
year = {1987}
}
@InProceedings{MaassETAL:91,
author = {W. Maass and G. Schnitger and E. Sontag},
booktitle = {Proc. of the 32nd Annual IEEE Symposium on Foundations of
Computer Science 1991},
pages = {767-776},
title = {On the computational power of sigmoid versus boolean
threshold circuits},
year = {1991}
}
@InCollection{MaassETAL:91a,
author = {W. Maass and G. Schnitger and E. Sontag},
title = {On the computational power of sigmoid versus boolean
threshold circuits},
booktitle = {Theoretical Advances in Neural Computation and Learning},
pages = {127--151},
publisher = {Kluwer Academic Publishers (Boston)},
year = {1994},
editor = {V.~P.~Roychowdhury and K.~Y.~Siu and A.~Orlitsky}
}
@Article{MaassETAL:93,
author = {W. Maass and G. Schnitger and E. Szemeredi and G. Turan},
journal = {Computational Complexity},
pages = {392--401},
title = {Two tapes versus one for off-line {T}uring machines},
volume = {3},
year = {1993}
}
@InProceedings{MaassLegenstein:01,
author = {R. A. Legenstein and W. Maass},
title = {Foundations for a circuit complexity theory of sensory
processing},
booktitle = {Proc. of NIPS 2000, Advances in Neural Information
Processing Systems},
editor = {T. K. Leen and T. G. Dietterich and V. Tresp},
year = {2001},
volume = {13},
pages = {259--265},
publisher = {MIT Press},
address = {Cambridge},
htmlnote = {The poster presented at NIPS is available as gzipped Postscript.},
abstract = {We introduce {\em total wire length} as salient complexity
measure for an analysis of the circuit complexity of
sensory processing in biological neural systems and
neuromorphic engineering. Furthermore we introduce a set of
basic computational problems that apparently need to be
solved by circuits for translation- and scale-invariant
sensory processing. Finally we exhibit a number of circuit
design strategies for these new benchmark functions that
can be implemented within realistic complexity bounds, in
particular with linear or almost linear total wire length.}
}
@Article{MaassLegenstein:01a,
author = {R. A. Legenstein and W. Maass},
title = {Wire Length as a Circuit Complexity Measure},
journal = {Journal of Computer and System Sciences},
year = {2005},
volume = {70},
pages = {53--72},
abstract = { We introduce {\em wire length} as a salient complexity
measure for analyzing the circuit complexity of sensory
processing in biological neural systems. This new
complexity measure is applied in this paper to two basic
computational problems that arise in translation- and
scale-invariant pattern recognition, and hence appear to be
useful as benchmark problems for sensory processing. We
present new circuit design strategies for these benchmark
problems that can be implemented within realistic
complexity bounds, in particular with linear or almost
linear wire length. Finally we derive some general bounds
which provide information about the relationship between
new complexity measure wire length and traditional circuit
complexity measures.}
}
@Article{MaassLegenstein:01c,
author = {R. A. Legenstein and W. Maass},
title = {Neural circuits for pattern recognition with small total
wire length},
journal = {Theoretical Computer Science},
volume = {287},
pages = {239--249},
year = {2002},
abstract = {One of the most basic pattern recognition problems is
whether a certain local feature occurs in some linear array
to the left of some other local feature. We construct in
this article circuits that solve this problem with an
asymptotically optimal number of threshold gates.
Furthermore it is shown that much fewer threshold gates are
needed if one employs in addition a small number of
winner-take-all gates. In either case the circuits that are
constructed have linear or almost linear total wire length,
and are therefore not unrealistic from the point of view of
physical implementations.}
}
@Article{MaassLegenstein:01d,
author = {R. A. Legenstein and W. Maass},
title = {Optimizing the Layout of a Balanced Tree},
journal = {Technical Report},
year = {2001},
abstract = { It is shown that the total wire length of layouts of a
balanced binary tree on a 2-dimensional grid can be reduced
by 33% if one does not choose the obvious ``symmetric''
layout strategy. Furthermore it is shown that the more
efficient layout strategy that is presented in this article
is optimal, not only for binary trees but for m-ary trees
with any m >= 2.}
}
@Article{MaassMarkram:00,
author = {W. Maass and H. Markram},
title = {Synapses as dynamic memory buffers},
journal = {Neural Networks},
volume = {15},
pages = {155--161},
year = {2002}
}
@Article{MaassMarkram:02,
author = {W. Maass and H. Markram},
title = {On the Computational Power of Recurrent Circuits of
Spiking Neurons},
journal = {Journal of Computer and System Sciences},
year = {2004},
volume = {69},
number = {4},
pages = {593--616}
}
@InCollection{MaassMarkram:02a,
author = {W. Maass and H. Markram},
title = {Temporal Integration in Recurrent Microcircuits},
booktitle = {The Handbook
of Brain Theory and Neural Networks},
publisher = {MIT Press (Cambridge)},
year = {2003},
editor = {M. A. Arbib},
edition = {2nd},
pages = {1159--1163}
}
@InProceedings{MaassMarkram:04,
author = {W. Maass and H. Markram},
title = {Theory of the Computational Function of Microcircuit
Dynamics},
booktitle = {The Interface between Neurons and Global Brain Function},
editor = {S. Grillner and A. M. Graybiel},
year = {2006},
pages = {371--390},
chapter = {18},
publisher = {MIT Press},
series = {Dahlem Workshop Report 93}
}
@Article{MaassNatschlaeger:97a,
author = {W. Maass and T. Natschlaeger},
title = {Networks of Spiking Neurons can Emulate Arbitrary
{H}opfield nets in Temporal Coding},
journal = {Network: Computation in Neural Systems},
year = 1997,
volume = 8,
number = 4,
pages = {355--371},
keywords = {spiking neurons, hopfield net, temporal coding},
userlabel = {4},
abstract = {A theoretical model for analog computation with temporal
coding is introduced and tested through simulations in
GENESIS. It turns out that the use of multiple synapses
yields very noise robust mechanisms for analog computations
with temporal coding in networks of detailed compartmental
neuron models. One arrives in this way at a method for
emulating arbitrary Hopfield nets with spiking neurons in
temporal coding, yielding new models for associative recall
of spatio-temporal firing patterns. A corresponding layered
architecture yields a refinement of the synfire-chain model
that can assume a fairly large set of different firing
patterns for different inputs.}
}
@InProceedings{MaassNatschlaeger:98,
author = {W. Maass and T. Natschlaeger},
title = {Associative Memory with Networks of Spiking Neurons in
Temporal Coding},
booktitle = {Neuromorphic Systems: Engineering Silicon from
Neurobiology},
editor = {L. S. Smith and A. Hamilton},
year = 1998,
publisher = {World Scientific},
pages = {21--32},
keywords = {spiking neurons, hopfield net, temporal coding},
abstract = {A theoretical model for analog computation with temporal
coding is introduced and tested through simulations in
GENESIS. It turns out that the use of multiple synapses
yields very noise robust mechanisms for analog computations
with temporal coding in networks of detailed compartmental
neuron models. One arrives in this way at a method for
emulating arbitrary Hopfield nets with spiking neurons in
temporal coding, yielding new models for associative recall
of spatio-temporal firing patterns.}
}
@InProceedings{MaassNatschlaeger:98b,
author = {W. Maass and T. Natschlaeger},
title = {Emulation of {H}opfield Networks with Spiking Neurons in
Temporal Coding},
booktitle = {Computational Neuroscience: Trends in Research},
editor = {J. M. Bower},
year = 1998,
publisher = {Plenum Press},
pages = {221--226},
keywords = {spiking neurons, hopfield net, temporal coding},
abstract = {A theoretical model for analog computation with temporal
coding is introduced and tested through simulations in
GENESIS. It turns out that the use of multiple synapses
yields very noise robust mechanisms for analog computations
with temporal coding in networks of detailed compartmental
neuron models. One arrives in this way at a method for
emulating arbitrary Hopfield nets with spiking neurons in
temporal coding, yielding new models for associative recall
of spatio-temporal firing patterns. A corresponding layered
architecture yields a refinement of the synfire-chain model
that can assume a fairly large set of different firing
patterns for different inputs.}
}
@Article{MaassNatschlaeger:99,
author = {W. Maass and T. Natschlaeger},
title = {A model for Fast Analog Computation Based on Unreliable
Synapses},
journal = {Neural Computation},
year = 2000,
pages = {1679--1704},
volume = {12},
number = {7},
keywords = {unreliable synapses, universal function approximation,
fast analog computation, time series, hebbian learning,
space rate coding, population activity},
abstract = {We investigate through theoretical analysis and computer
simulations the consequences of unreliable synapses for
fast analog computations in networks of spiking neurons,
with analog variables encoded by the current firing
activities of pools of spiking neurons. Our results suggest
that the known unreliability of synaptic transmission may
be viewed as a useful tool for analog computing, rather
than as a ``bug'' in neuronal hardware. We also investigate
computations on time series and Hebbian learning in this
context of space-rate coding.}
}
@InProceedings{MaassOrponen:97,
author = {W. Maass and P. Orponen},
booktitle = {Advances in Neural Information Processing Systems},
editor = {M. Mozer and M. I. Jordan and T. Petsche},
pages = {218--224},
publisher = {MIT Press (Cambridge)},
title = {On the effect of analog noise in discrete-time analog
computations},
volume = {9},
year = {1997}
}
@Article{MaassOrponen:97j,
author = {W. Maass and P. Orponen},
title = {On the effect of analog noise in discrete-time analog
computations},
journal = {Neural Computation},
year = 1998,
volume = 10,
pages = {1071--1095}
}
@InProceedings{MaassRuf:95,
author = {W. Maass and B. Ruf},
address = {Paris},
booktitle = {Proc. of the International Conference on Artificial Neural
Networks ICANN},
pages = {515--520},
publisher = {EC2\&Cie},
title = {On the Relevance of the Shape of Postsynaptic Potentials
for the Computational Power of Networks of Spiking
Neurons},
year = {1995},
keywords = {spiking neuron, postsynaptic potential, computational
complexity}
}
@Article{MaassRuf:97,
author = {W. Maass and B. Ruf},
journal = {Information and Computation},
title = {On computation with pulses},
year = {1999},
volume = {148},
pages = {202--218},
keywords = {spiking neuron, computational complexity, postsynaptic
potential}
}
@InProceedings{MaassSchmitt:97,
author = {W. Maass and M. Schmitt},
booktitle = {Proc. of the 10th Conference on Computational Learning
Theory 1997},
note = {See also Electronic Proc. of the Fifth International
Symposium on Artificial Intelligence and Mathematics
(http://rutcor.rutgers.edu/\~{}amai)},
pages = {54--61},
publisher = {ACM-Press (New York)},
title = {On the complexity of learning for a spiking neuron},
year = {1997}
}
@Article{MaassSchmitt:98,
author = {W. Maass and M. Schmitt},
journal = {Information and Computation},
title = {On the complexity of learning for spiking neurons with
temporal coding},
year = {1999},
volume = {153},
pages = {26--46}
}
@InProceedings{MaassSchnitger:86,
author = {W. Maass and G. Schnitger},
booktitle = {Proceedings of the Structure in Complexity Theory
Conference, Berkeley 1986},
pages = {249--264},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
title = {An optimal lower bound for {T}uring machines with one Work
Tape and Two-Way Input Tape},
year = {1986},
volume = {223}
}
@Article{MaassSchorr:87,
author = {W. Maass and A. Schorr},
journal = {SIAM J. Comput.},
pages = {195--202},
title = {Speed-up of {T}uring machines with one work tape and a
two-way input tape},
volume = {16},
year = {1987}
}
@InProceedings{MaassSlaman:89,
author = {W. Maass and T. A. Slaman},
booktitle = {Proceedings of the Logic Colloquium '88, Padova, Italy},
editor = {Ferro and Bonotto and Valentini and Zanardo},
pages = {79-89},
publisher = {Elsevier Science Publishers (North-Holland)},
title = {Some problems and results in the theory of actually
computable functions},
year = {1989}
}
@InProceedings{MaassSlaman:89a,
author = {W. Maass and T. A. Slaman},
booktitle = {Proceedings of the 4th Annual Conference on Structure in
Complexity Theory},
pages = {231--239},
publisher = {IEEE Computer Society Press (Washington)},
title = {The complexity types of computable sets (extended
abstract)},
year = {1989}
}
@InProceedings{MaassSlaman:89b,
author = {W. Maass and T. A. Slaman},
booktitle = {Proceedings of the 7th International Conference on
Fundamentals of Computation Theory},
pages = {318--326},
publisher = {Springer (Berlin)},
series = {Lecture Notes in Computer Science},
title = {Extensional properties of sets of time bounded complexity
(extended abstract)},
volume = {380},
year = {1989}
}
@InProceedings{MaassSlaman:90,
author = {W. Maass and T. A. Slaman},
booktitle = {Proceedings of the 1989 Recursion Theory Week
Oberwolfach},
pages = {297--322},
publisher = {Springer (Berlin)},
title = {On the relationship between the complexity, the degree,
and the extension of a computable set},
year = {1990}
}
@InProceedings{MaassSlaman:91,
author = {W. Maass and T. A. Slaman},
booktitle = {Proceedings of a Workshop on Logic from Computer Science},
editor = {Y. N. Moschovakis},
pages = {359--372},
publisher = {Springer (Berlin)},
title = {Splitting and density for the recursive sets of a fixed
time complexity},
year = {1991}
}
@Article{MaassSlaman:92,
author = {W. Maass and T. A. Slaman},
journal = {J. Comput. Syst. Sci.},
note = {Invited paper for a special issue of the J. Comput. Syst.
Sci.},
pages = {168--192},
title = {The complexity types of computable sets},
volume = {44},
year = {1992}
}
@Article{MaassSontag:97,
author = {W. Maass and E. Sontag},
journal = {Neural Computation},
title = {Analog neural nets with {G}aussian or other common noise
distributions cannot recognize arbitrary regular
languages},
year = {1999},
volume = {11},
pages = {771--782}
}
@Article{MaassSontag:99a,
author = {W. Maass and E. D. Sontag},
title = {Neural systems as nonlinear filters},
journal = {Neural Computation},
volume = {12},
number = {8},
year = {2000},
pages = {1743--1772}
}
@InProceedings{MaassSontag:99b,
author = {W. Maass and E. D. Sontag},
title = {A precise characterization of the class of languages
recognized by neural nets under {G}aussian and other common
noise distributions},
booktitle = {Advances in Neural Information Processing Systems},
year = 1999,
volume = {11},
pages = {281--287},
editor = {M.~S.~Kearns and S.~S.~Solla and D.~A.~Cohn},
publisher = {MIT Press (Cambridge)}
}
@Article{MaassStob:83,
author = {W. Maass and M. Stob},
journal = {Ann. of Pure and Applied Logic},
pages = {189--212},
title = {Intervals of the lattice of recursively enumerable sets
determined by major subsets},
volume = {24},
year = {1983}
}
@Article{MaassSutner:88,
author = {W. Maass and K. Sutner},
journal = {Acta Informatica},
pages = {93-122},
title = {Motion planning among time dependent abstacles},
volume = {26},
year = {1988}
}
@InProceedings{MaassTuran:89,
author = {W. Maass and G. Turan},
booktitle = {Proceedings of the 30th Annual IEEE Symposium on
Foundations of Computer Science},
pages = {262--267},
title = {On the complexity of learning from counterexamples
(extended abstract)},
year = {1989}
}
@InProceedings{MaassTuran:90,
author = {W. Maass and G. Turan},
booktitle = {Proceedings of the 31th Annual IEEE Symposium on
Foundations of Computer Science},
pages = {203--210},
title = {On the complexity of learning from counterexamples and
membership queries},
year = {1990}
}
@Article{MaassTuran:92,
author = {W. Maass and G. Turan},
journal = {Machine Learning},
note = {Invited paper for a special issue of Machine Learning},
pages = {107--145},
title = {Lower bound methods and separation results for on-line
learning models},
volume = {9},
year = {1992}
}
@InCollection{MaassTuran:94,
author = {W. Maass and G. Turan},
booktitle = {Computational Learning Theory and Natural Learning System:
Constraints and Prospects},
editor = {S. J. Hanson and G. A. Drastal and R. L. Rivest},
pages = {381--414},
publisher = {MIT Press (Cambridge)},
title = {How fast can a threshold gate learn},
year = {1994}
}
@Article{MaassTuran:94a,
author = {W. Maass and G. Turan},
journal = {Machine Learning},
pages = {251--269},
title = {Algorithms and lower bounds for on-line learning of
geometrical concepts},
volume = {14},
year = {1994}
}
@InProceedings{MaassTuran:95,
author = {W. Maass and G. Turan},
address = {Jerusalem},
booktitle = {Proc. of the 4th Bar-Ilan Symposium on Foundations of
Artificial Intelligence (BISFAI'95)},
title = {On learnability and predicate logic (extended abstract)},
year = {1995},
pages = {75--85}
}
@InProceedings{MaassWarmuth:95,
author = {W. Maass and M. Warmuth},
booktitle = {Proc. of the 12th International Machine Learning
Conference, Tahoe City, USA},
editor = {Morgan Kaufmann (San Francisco)},
pages = {378-386},
title = {Efficient learning with virtual threshold gates},
year = {1995}
}
@Article{MaassWarmuth:95j,
author = {W. Maass and M. Warmuth},
title = {Efficient learning with virtual threshold gates},
journal = {Information and Computation},
year = 1998,
volume = 141,
number = 1,
pages = {66--83}
}
@InCollection{MaassWeibel:97,
author = {W. Maass and P. Weibel},
booktitle = {{Jenseits von Kunst}},
editor = {P. Weibel},
pages = {745--747},
publisher = {Passagen Verlag},
title = {{I}st die {V}ertreibung der {V}ernunft reversibel?
{U}eberlegungen zu einem {W}issenschafts- und
{M}edienzentrum},
year = {1997}
}
@InProceedings{MaassZador:98,
author = {W. Maass and A. M. Zador},
booktitle = {Advances in Neural Processing Systems},
publisher = {MIT Press (Cambridge)},
title = {Dynamic stochastic synapses as computational units},
volume = {10},
pages = {194--200},
year = {1998}
}
@InCollection{MaassZador:98a,
author = {W. Maass and A. Zador},
booktitle = {Pulsed Neural Networks},
editor = {W. Maass and C. Bishop},
publisher = {MIT-Press (Cambridge)},
title = {Computing and learning with dynamic synapses},
year = {1998},
pages = {321-336}
}
@Article{MaassZador:98j,
author = {W. Maass and A. M. Zador},
title = {Dynamic stochastic synapses as computational units},
journal = {Neural Computation},
year = 1999,
volume = 11,
number = 4,
pages = {903--917}
}
@Article{MelamedETAL:03,
author = {O. Melamed and W. Gerstner and W. Maass and M. Tsodyks and
H. Markram},
title = {Coding and Learning of Behavioral Sequences},
abstract = {A major challenge to understanding behavior is how the
nervous system allows the learning of behavioral sequences
that can occur over arbitrary timescales, ranging from
milliseconds up to seconds, using a fixed millisecond
learning rule. This article describes some potential
solutions, and then focuses on a study by Mehta et al. that
could contribute towards solving this puzzle. They have
discovered that an experience-dependent asymmetric shape of
hippocampal receptive fields combined with oscillatory
inhibition can serve to map behavioral sequences on a fixed
timescale.},
journal = {Trends in Neurosciences},
volume = 27,
number = 1,
year = {2004},
pages = {11--14}
}
@Article{MontemurroETAL:08,
author = {M. A. Montemurro and M. J. Rasch and Y. Murayam and N. K.
Logothetis and S. Panzeri},
title = {Phase-of-Firing Coding of Natural Visual Stimuli in
Primary Visual Cortex},
journal = {Current Biology},
year = {2008},
volume = {18},
number = {},
pages = {375--380},
note = {},
abstract = {We investigated the hypothesis that neurons encode rich
naturalistic stimuli in terms of their spike times relative
to the phase of ongoing network fluctuations rather than
only in terms of their spike count. We recorded local field
potentials (LFPs) and multiunit spikes from the primary
visual cortex of anaesthetized macaques while binocularly
presenting a color movie. We found that both the spike
counts and the low-frequency LFP phase were reliably
modulated by the movie and thus conveyed information about
it. Moreover, movie periods eliciting higher firing rates
also elicited a higher reliability of LFP phase across
trials. To establish whether the LFP phase at which spikes
were emitted conveyed visual information that could not be
extracted by spike rates alone,wecompared the Shannon
information about the movie carried by spike counts to that
carried by the phase of firing. We found that at low LFP
frequencies, the phase of firing conveyed 54 \% additional
information beyond that conveyed by spike counts. The extra
information available in the phase of firing was crucial
for the disambiguation between stimuli eliciting high spike
rates of similar magnitude. Thus, phase coding may allow
primary cortical neurons to represent several effective
stimuli in an easily decodable format.}
}
@Article{MullerETAL:07,
author = {E. Muller and L. Buesing and J. Schemmel and K. Meier},
title = {Spike-frequency adapting neural ensembles: Beyond mean
adaptation and renewal theories},
journal = {Neural Computation},
year = {2007},
volume = {19},
number = {11},
note = {},
pages = {},
abstract = {}
}
@MastersThesis{Natschlaeger:96,
author = {T. Natschlaeger},
title = {{R}aum- zeitliche {S}trukturen von {B}erechnungen in
biologisch realistischen neuronalen {N}etzwerken},
school = {Technische Universitaet Graz},
year = 1996,
month = {February},
userlabel = {2},
keywords = {spiking neurons, hopfield net, temporal coding}
}
@InCollection{Natschlaeger:96a,
author = {T. Natschlaeger},
title = {{N}etzwerke von {S}piking {N}euronen: {D}ie dritte
{G}eneration von {M}odellen fuer neuronale {N}etzwerke},
booktitle = {Jenseits von Kunst},
publisher = {Passagen Verlag},
year = 1996,
htmlnote = {Online
version},
userlabel = 3,
keywords = {spiking neurons, hopfield net, CPG, central pattern
generator},
abstract = {Dieser Artikel beschreibt in allgemein verstaendlicher
Form einige Ergebnisse ueber Netzwerke von ``spiking''
Neuronen, die an unserem Institut erarbeitet wurden. Einer
kurzen Einfuehrung, die die biologischen Grundlagen
beleuchtet, folgt eine Erklaerung des Modells und inwiefern
sich dieses Modell von der ersten und zweiten Generation
von Modellen fuer neuronale Netzwerke unterscheidet. Daran
anschliessend werden einige Arbeiten, die von den
Mitarbeitern unseres Institutes durchgefuehrt wurden,
vorgestellt. Der Kernpunkt dieser Ergebnisse betrifft die
grosse Berechnungsstaerke dieser Netzwerkmodelle. In diesem
Uebersichtsartikel wird kein fundiertes a priori Wissen
ueber diese Art von Modellen von neuronalen Netzwerken
vorausgesetzt.}
}
@InCollection{Natschlaeger:98b,
author = {T. Natschlaeger},
title = {Networks of Spiking Neurons: A New Generation of Neural
Network Models},
booktitle = {Jenseits von Kunst},
publisher = {Passagen Verlag},
year = 1998,
htmlnote = {Online
version}
}
@PhDThesis{Natschlaeger:99,
author = {T. Natschlaeger},
title = {Efficient Computation in Networks of Spiking Neurons --
Simulations and Theory},
school = {Graz University of Technology},
year = 1999,
abstract = {One of the most prominent features of biological neural
systems is that individual neurons communicate via short
electrical pulses, the so called action potentials or
spikes. In this thesis we investigate possible mechanisms
which can in principle explain how complex computations in
spiking neural networks (SNN) can be performed very fast,
i. e. within a few 10 milliseconds. Some of these models
are based on the assumption that relevant information is
encoded by the timing of individual spikes (temporal
coding). We will also discuss a model which is based on a
population code and still is able to perform fast complex
computations. In their natural environment biological
neural systems have to process signals with a rich temporal
structure. Hence it is an interesting question how neural
systems process time series. In this context we explore
possible links between biophysical characteristics of
single neurons (refractory behavior, connectivity, time
course of postsynaptic potentials) and synapses
(unreliability, dynamics) on the one hand and possible
computations on times series on the other hand. Furthermore
we describe a general model of computation that exploits
dynamic synapses. This model provides a general framework
for understanding how neural systems process time-varying
signals. }
}
@InCollection{NatschlaegerETAL-SOM:01,
author = {T. Natschlaeger and B. Ruf and M. Schmitt},
title = {Unsupervised Learning and Self-Organization in Networks of
Spiking Neurons},
booktitle = {Self-Organizing Neural Networks. Recent Advances and
Applications},
publisher = {Springer-Verlag},
year = 2001,
editor = {U. Seiffert and L. C. Jain},
volume = 78,
series = {Springer Series on Studies in Fuzziness and Soft
Computing},
address = {Heidelberg},
note = {in press},
abstract = {One of the most prominent features of biological neural
systems is that individual neurons communicate via short
electrical pulses, the so-called action potentials or
spikes. In this chapter we investigate possible mechanisms
of unsupervised learning and self-organization in networks
of spiking neurons. After giving a brief introduction to
spiking neuron networks we describe a biologically
plausible algorithm for these networks to find clusters in
a high dimensional input space or a subspace of it. The
algorithm is shown to work even in a dynamically changing
environment. Furthermore, we study self-organizing maps of
spiking neurons showing that networks of spiking neurons
using temporal coding can achieve a topology preserving
behavior quite similar to that of Kohonen's self-organizing
map. For these networks a mechanism of competitive
computation is proposed that is based on action potential
timing. Thus, the winner in a population of competing
neurons can be determined locally and in generally faster
than in approaches which use rate coding. The models and
algorithms presented in this chapter establish further
steps toward more realistic descriptions of unsupervised
learning in biological neural systems.}
}
@InProceedings{NatschlaegerETAL:01,
author = {T. Natschlaeger and W. Maass and E. D. Sontag and A.
Zador},
title = {Processing of Time Series by Neural Circuits with
Biologically Realistic Synaptic Dynamics},
booktitle = {Advances in Neural Information Processing Systems 2000
({NIPS '2000})},
editor = {Todd K. Leen and Thomas G. Dietterich and Volker Tresp},
year = 2001,
volume = 13,
pages = {145--151},
address = {Cambridge},
publisher = {MIT Press},
abstract = {Experimental data show that biological synapses behave
quite differently from the symbolic synapses in common
artificial neural network models. Biological synapses are
dynamic, i.e., their weight changes on a short time scale
by several hundred percent in dependence of the past input
to the synapse. In this article we explore the consequences
that this synaptic dynamics entails for the computational
power of feedforward neural networks. It turns out that
even with just a single hidden layer such networks can
approximate a surprisingly large class of nonlinear
filters: all filters that can be characterized by Volterra
series. This result is robust with regard to various
changes in the model for synaptic dynamics. Furthermore we
show that simple gradient descent suffices to approximate a
given quadratic filter by a rather small neural system with
dynamic synapses. We demonstrate that with this approach
the nonlinear filter considered in (Back and Tsoi 93) can
be approximated even better than by their model.},
htmlnote = {The poster presented at NIPS is available as Acrobat PDF file.}
}
@Article{NatschlaegerETAL:01a,
author = {T. Natschlaeger and W. Maass and A. Zador},
title = {Efficient Temporal Processing with Biologically Realistic
Dynamic Synapses},
journal = {Network: Computation in Neural Systems},
year = 2001,
pages = {75--87},
volume = 12,
abstract = {Experimental data show that biological synapses behave
quite differently from the symbolic synapses in common
artificial neural network models. Biological synapses are
dynamic, i.e., their ``weight'' changes on a short time
scale by several hundred percent in dependence of the past
input to the synapse. Here we describe a general model of
computation that exploits dynamic synapses, and use a
backpropagation-like algorithm to adjust the synaptic
parameters. We show that such gradient descent suffices to
approximate a given quadratic filter by a rather small
neural system with dynamic synapses. We demonstrate that
with this approach the nonlinear filter considered in (Back
and Tsoi, 1993) can be approximated slightly better than by
their model. Our numerical results are complemented by
theoretical analysis which show that even with just a
single hidden layer such networks can approximate a
surprisingly large class of nonlinear filters: all filters
that can be characterized by Volterra series. This result
is robust with regard to various changes in the model for
synaptic dynamics. }
}
@Article{NatschlaegerETAL:02,
author = {T. Natschlaeger and W. Maass and H. Markram},
title = {The "Liquid Computer": A Novel Strategy for Real-Time
Computing on Time Series},
journal = {Special Issue on Foundations of Information Processing of
{TELEMATIK}},
year = {2002},
pages = {39--43},
volume = {8},
number = {1},
abstract = {We will discuss in this survey article a new framework for
analysing computations on time series and in particular on
spike trains, introduced in (Maass et. al. 2002). In
contrast to common computational models this new framework
does not require that information can be stored in some
stable states of a computational system. It has recently
been shown that such models where all events are transient
can be successfully applied to analyse computations in
neural systems and (independently) that the basic ideas can
also be used to solve engineering tasks such as the design
of nonlinear controllers. Using an illustrative example we
will develop the main ideas of the proposed model. This
illustrative example is generalized and cast into a
rigorous mathematical model: the Liquid State Machine. A
mathematical analysis shows that there are in principle no
computational limitations of liquid state machines in the
domain of time series computing. Finally we discuss several
successful applications of the framework in the area of
computational neuroscience and in the field of artificial
neural networks.}
}
@InCollection{NatschlaegerETAL:03,
author = {T. Natschlaeger and H. Markram and W. Maass},
title = {Computer Models and Analysis Tools for Neural
Microcircuits},
booktitle = {Neuroscience Databases. A Practical Guide},
publisher = {Kluwer Academic Publishers (Boston)},
year = {2003},
editor = {R. Koetter},
chapter = {9},
pages = {121--136},
abstract = {This chapter surveys web resources regarding computer
models and analysis tools for neural microcircuits. In
particular it describes the features of a new website
(www.lsm.tugraz.at) that facilitates the creation of
computer models for cortical neural microcircuits of
various sizes and levels of detail, as well as tools for
evaluating the computational power of these models in a
Matlabenvironment.}
}
@InCollection{NatschlaegerETAL:04,
author = {T. Natschlaeger and N. Bertschinger and R. Legenstein},
title = {At the Edge of Chaos: Real-time Computations and
Self-Organized Criticality in Recurrent Neural Networks},
booktitle = {Advances in Neural Information Processing Systems 17},
editor = {Lawrence K. Saul and Yair Weiss and {L\'{e}on} Bottou},
publisher = {MIT Press},
address = {Cambridge, MA},
pages = {145-152},
year = 2005,
abstract = {In this paper we analyze the relationship between the
computational capabilities of randomly connected networks
of threshold gates in the timeseries domain and their
dynamical properties. In particular we propose a complexity
measure which we find to assume its highest values near the
edge of chaos, i.e. the transition from ordered to chaotic
dynamics. Furthermore we show that the proposed complexity
measure predicts the computational capabilities very well:
only near the edge of chaos are such networks able to
perform complex computations on time series. Additionally a
simple synaptic scaling rule for self-organized criticality
is presented and analyzed.}
}
@Article{NatschlaegerMaass:01a,
author = {T. Natschlaeger and W. Maass},
title = {Computing the Optimally Fitted Spike Train for a Synapse},
journal = {Neural Computation},
year = 2001,
volume = 13,
number = 11,
pages = {2477--2494},
abstract = {Experimental data have shown that synapses are
heterogeneous: different synapses respond with different
sequences of amplitudes of postsynaptic responses to the
same spike train. Neither the role of synaptic dynamics
itself nor the role of the heterogeneity of synaptic
dynamics for computations in neural circuits is well
understood. We present in this article two computational
methods that make it feasible to compute for a given
synapse with known synaptic parameters the spike train that
is optimally fitted to the synapse in a certain sense. With
the help of these methods one can compute for example the
temporal pattern of a spike train (with a given number of
spikes) that produces the largest sum of postsynaptic
responses for a specific synapse. Several other
applications are also discussed. To our surprise we find
that most of these optimally fitted spike trains match
common firing patterns of specific types of neurons that
are discussed in the literature. Hence our analysis
provides a possible functional explanation for the
experimentally observed regularity in the combination of
specific types of synapses with specific types of neurons
in neural circuits. }
}
@InProceedings{NatschlaegerMaass:01b,
author = {T. Natschlaeger and W. Maass},
title = {Finding the Key to a Synapse},
booktitle = {Advances in Neural Information Processing Systems ({NIPS
'2000})},
editor = {Todd K. Leen and Thomas G. Dietterich and Volker Tresp},
year = 2001,
pages = {138--144},
volume = 13,
address = {Cambridge},
publisher = {MIT Press},
abstract = {Experimental data have shown that synapses are
heterogeneous: different synapses respond with different
sequences of amplitudes of postsynaptic responses to the
same presynaptic spike train. Neither the role of synaptic
dynamics itself nor the role of the heterogeneity of
synaptic dynamics for computations in neural circuits is
well understood. We present in this article methods that
make it feasible to compute for a given synapse with known
synaptic parameters the spike train that is optimally
fitted to the synapse, in the sense that it produces the
largest sum of postsynaptic responses. To our surprise we
find that most of these optimally fitted spike trains match
common firing patterns of specific types of neurons that
are discussed in the literature. Hence our analysis
provides a possible functional explanation for the
experimentally observed regularity in the combination of
specific types of synapses with specific types of neurons
in neural circuits.},
htmlnote = {The poster presented at NIPS is available as Acrobat PDF file.}
}
@InProceedings{NatschlaegerMaass:03,
author = {T. Natschlaeger and W. Maass},
title = {Information Dynamics and Emergent Computation in Recurrent
Circuits of Spiking Neurons},
booktitle = {Proc. of NIPS 2003, Advances in Neural Information
Processing Systems},
year = {2004},
volume = {16},
pages = {1255--1262},
editor = {S. Thrun and L. Saul and B. Schoelkopf},
publisher = {MIT Press},
address = {Cambridge},
abstract = {An efficient method using Bayesian and linear classifiers
is presented for analyzing the dynamics of information in
high dimensional circuit states, and applied to investigate
emergent computation in generic cortical microcircuit
models. It is shown that such recurrent circuits of spiking
neurons have an inherent capability to carry out rapid
computations on complex spike patterns, merging information
contained in the order of spike arrival with previously
acquired context information.}
}
@Article{NatschlaegerMaass:04,
author = {T. Natschlaeger and W. Maass},
title = {Dynamics of Information and Emergent Computation in
Generic Neural Microcircuit Models},
journal = {Neural Networks},
volume = {18},
number = {10},
pages = {1301--1308},
year = {2005},
abstract = {Numerous methods have already been developed to estimate
the information contained in single spike trains. In this
article we explore efficient methods for estimating the
information contained in the simultaneous firing activity
of hundreds of neurons. Obviously such methods are needed
to analyze data from multi-unit recordings. We test these
methods on generic neural microcircuit models consisting of
800 neurons, and analyze the temporal dynamics of
information about preceding spike inputs in such circuits.
It turns out that information spreads with high speed in
such generic neural microcircuit models, thereby supporting
-- without the postulation of any additional neural or
synaptic mechanisms -- the possibility of ultra-rapid
computations on the first input spikes.}
}
@Article{NatschlaegerMaass:2001,
author = {T. Natschlaeger and W. Maass},
title = {Spiking Neurons and the Induction of Finite State
Machines},
journal = {Theoretical Computer Science: Special Issue on Natural
Computing},
volume = 287,
year = 2002,
pages = {251--265},
abstract = {We discuss in this short survey article some current
mathematical models from neurophysiology for the
computational units of biological neural systems: neurons
and synapses. These models are contrasted with the
computational units of common artificial neural network
models, which reflect the state of knowledge in
neurophysiology 50 years ago. We discuss the problem of
carrying out computations in circuits consisting of
biologically realistic computational units, focusing on the
biologically particularly relevant case of computations on
time series. Finite state machines are frequently used in
computer science as models for computations on time series.
One may argue that these models provide a reasonable common
conceptual basis for analyzing computations in computers
and biological neural systems, although the emphasis in
biological neural systems is shifted more towards
asynchronous computation on analog time series. In the
second half of this article some new computer experiments
and theoretical results are discussed, which address the
question whether a biological neural system can in
principle learn to behave like a given simple finite state
machine. }
}
@InProceedings{NatschlaegerMaass:99,
author = {T. Natschlaeger and W. Maass},
title = {Fast Analog Computation in Networks of Spiking Neurons
Using Unreliable Synapses},
booktitle = {{ESANN'99} Proceedings of the European Symposium on
Artificial Neural Networks},
year = 1999,
address = {Bruges, Belgium},
pages = {417--422},
keywords = {unreliable synapses, universal function approximation,
fast analog computation, time series, hebbian learning,
space rate coding, population activity},
abstract = {We investigate through theoretical analysis and computer
simulations the consequences of unreliable synapses for
fast analog computations in networks of spiking neurons,
with analog variables encoded by the firing activities of
pools of spiking neurons. Our results suggest that the
known unreliability of synaptic transmission may be viewed
as a useful tool for analog computing, rather than as a
``bug'' in neuronal hardware. We also investigate
computations on analog time series encoded by the firing
activities of pools of spiking neurons.}
}
@Article{NatschlaegerRuf:98a,
author = {T. Natschlaeger and B. Ruf},
title = {Spatial and temporal pattern analysis via spiking
neurons},
journal = {Network: Computation in Neural Systems},
year = 1998,
volume = 9,
number = 3,
pages = {319--332},
userlabel = 7,
keywords = {spiking neurons, RBF networks, clustering, hebbian
learning},
abstract = {Spiking neurons, receiving temporally encoded inputs, can
compute radial basis functions (RBFs) by storing the
relevant information in their delays. In this paper we show
how these delays can be learned using exclusively locally
available information (basically the time difference
between the pre- and postsynaptic spike). Our approach
gives rise to a biologically plausible algorithm for
finding clusters in a high dimensional input space with
networks of spiking neurons, even if the environment is
changing dynamically. Furthermore, we show that our
learning mechanism makes it possible that such RBF neurons
can perform some kind of feature extraction where they
recognize that only certain input coordinates carry
relevant information. Finally we demonstrate that this
model allows the recognition of temporal sequences even if
they are distorted in various ways.}
}
@InProceedings{NatschlaegerRuf:98b,
author = {T. Natschlaeger and B. Ruf},
title = {Online Clustering with Spiking Neurons Using Temporal
Coding},
booktitle = {Neuromorphic Systems: Engineering Silicon from
Neurobiology},
editor = {L. S. Smith and A. Hamilton},
year = 1998,
publisher = {World Scientific},
pages = {33--42},
userlabel = {6},
keywords = {spiking neurons, RBF networks, clustering, hebbian
learning},
abstract = {Spiking neurons, receiving temporally encoded inputs, can
compute radial basis functions in a biologically realistic
way. They store the relevant information in their delays.
In this paper we show how these delays can be learned using
exclusively locally available information (basically the
time difference between the pre- and postsynaptic spike).
Our approach gives rise to a biologically plausible
algorithm for finding clusters in a high dimensional input
space with networks of spiking neurons, even if the
environment is changing dynamically.}
}
@Article{NatschlaegerRuf:99c,
author = {T. Natschlaeger and B. Ruf},
title = {Pattern Analysis with Spiking Neurons using Delay Coding},
journal = {Neurocomputing},
year = 1999,
pages = {463-469},
volume = {26-27},
number = {1-3},
keywords = {spiking neurons, RBF networks, clustering, hebbian
learning},
abstract = {Spiking neurons, receiving temporally encoded inputs, can
compute radial basis functions (RBFs) by storing the
relevant information in their delays. These delays can be
learned using exclusively locally available information
(basically the time difference between the pre- and
postsynaptic spike). Our approach gives rise to a
biologically plausible algorithm for finding clusters in a
high dimensional input space. Furthermore, we show that our
learning mechanism makes it possible that such RBF neurons
can perform some kind of feature extraction. Finally we
demonstrate that this model allows the recognition of
temporal sequences even if they are distorted in various
ways.}
}
@Article{NatschlaegerSchmitt:96,
author = {T. Natschlaeger and M. Schmitt},
title = {Exact {VC}-{D}imension of Boolean Monomials},
journal = {Information Processing Letters},
year = 1996,
volume = 59,
pages = {19--20},
userlabel = {1},
keywords = {monome, VC-dimension, combinatorial problems,
computational complexity, learnability },
abstract = {We show that the Vapnik-Chervonenkis dimension of Boolean
monomials over $n$ variables is at most $n$ for all $n <
2$. It follows that the VC-dimension is determined exactly
and is, except for $n=1$, equal to the VC-dimension of the
proper subclass of monotone monomials.}
}
@Article{NesslerETAL:08,
author = {B. Nessler and M. Pfeiffer and W. Maass},
title = {Hebbian learning of {B}ayes optimal decisions},
journal = {In Proc. of NIPS 2008: Advances in Neural Information
Processing Systems},
year = {2009},
volume = {21},
number = {},
pages = {},
note = {MIT Press},
abstract = {When we perceive our environment, make a decision, or take
an action, our brain has to deal with multiple sources of
uncertainty. The Bayesian framework of statistical
estimation provides computational methods for dealing
optimally with uncertainty. Bayesian inference however is
algorithmically quite complex, and learning of Bayesian
inference involves the storage and updating of probability
tables or other data structures that are hard to implement
in neural networks. Hence it is unclear how our nervous
system could acquire the capability to approximate optimal
Bayesian inference and action selection. This article shows
that the simplest and experimentally best supported type of
synaptic plasticity, Hebbian learning, can in principle
achieve this. Even inference in complex Bayesian networks
can be approximated by Hebbian learning in combination with
population coding and lateral inhibition
(``Winner-Take-All'') in cortical microcircuits that
produce a sparse encoding of complex sensory stimuli. We
also show that a corresponding reward-modulated Hebbian
plasticity rule provides a principled framework for
understanding how Bayesian inference could support fast
reinforcement learning in the brain. In particular we show
that recent experimental results by Yang and Shadlen on
reinforcement learning of probabilistic inference in
primates can be modeled in this way.}
}
@InProceedings{NesslerETAL:10,
author = {B. Nessler and M. Pfeiffer and W. Maass},
title = {{STDP} enables spiking neurons to detect hidden causes of
their inputs},
booktitle = {Proc. of NIPS 2009: Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2010},
volume = {22},
pages = {1357--1365},
abstract = {The principles by which spiking neurons contribute to the
astounding computational power of generic cortical
microcircuits, and how spike-timing-dependent plasticity
(STDP) of synaptic weights could generate and maintain this
computational function, are unknown. We show here that
STDP, in conjunction with a stochastic soft winner-take-all
(WTA) circuit, induces spiking neurons to generate through
their synaptic weights implicit internal models for
subclasses (or “causes”) of the high-dimensional spike
patterns of hundreds of pre-synaptic neurons. Hence these
neurons will fire after learning whenever the current input
best matches their internal model. The resulting
computational function of soft WTA circuits, a common
network motif of cortical microcircuits, could therefore be
a drastic dimensionality reduction of information streams,
together with the autonomous creation of internal models
for the probability distributions of their input patterns.
We show that the autonomous generation and maintenance of
this computational function can be explained on the basis
of rigorous mathematical principles. In particular, we show
that STDP is able to approximate a stochastic online
Expectation-Maximization (EM) algorithm for modeling the
input data. A corresponding result is shown for Hebbian
learning in artificial neural networks.}
}
@InProceedings{NeumannETAL:07,
author = {G. Neumann and M. Pfeiffer and W. Maass},
booktitle = {Proceedings of the 18th European Conference on Machine
Learning (ECML) and the 11th European Conference on
Principles and Practice of Knowledge Discovery in Databases
(PKDD) 2007, Warsaw (Poland)},
title = {Efficient Continuous-Time Reinforcement Learning with
Adaptive State Graphs},
publisher = {Springer (Berlin)},
year = {2007},
pages = {},
note = {in press},
abstract = {We present a new reinforcement learning approach for
deterministic continuous control problems in environments
with unknown, arbitrary reward functions. The difficulty of
finding solution trajectories for such problems can be
reduced by incorporating limited prior knowledge of the
approximative local system dynamics. The presented
algorithm builds an adaptive state graph of sample points
within the continuous state space. The nodes of the graph
are generated by an efficient principled exploration scheme
that directs the agent towards promising regions, while
maintaining good online performance. Global solution
trajectories are formed as combinations of local
controllers that connect nodes of the graph, thereby
naturally allowing continuous actions and continuous time
steps. We demonstrate our approach on various movement
planning tasks in continuous domains.}
}
@InProceedings{NeumannETAL:09,
author = {G. Neumann and W. Maass and J. Peters},
title = {Learning Complex Motions by Sequencing Simpler Motion
Templates},
booktitle = {Proc. of the Int. Conf. on Machine Learning (ICML 2009),
Montreal},
year = {2009},
volume = {},
number = {},
pages = {},
note = {in press},
abstract = {Abstraction of complex, longer motor tasks into simpler
elemental movements enables humans and animals to exhibit
motor skills which have not yet been matched by robots.
Humans intuitively decompose complex motions into smaller,
simpler segments. For example when describing simple
movements like drawing a triangle with a pen, we can easily
name the basic steps of this movement. Surprisingly, such
abstractions have rarely been used in artificial motor
skill learning algorithms. These algorithms typically
choose a new action (such as a torque or a force) at a very
fast time-scale. As a result, both policy and temporal
credit assignment problem become unnecessarily complex -
often beyond the reach of current machine learning methods.
We introduce a new framework for temporal abstractions in
reinforcement learning (RL), i.e. RL with motion templates.
We present a new algorithm for this framework which can
learn high-quality policies by making only few abstract
decisions. }
}
@Article{NikolicETAL:06,
author = {D. Nikolic and S. Haeusler and W. Singer and W. Maass},
title = {Temporal dynamics of informational contents carried by
neurons in the primary visual cortex},
journal = {submitted for publication},
year = 2006
}
@Article{NikolicETAL:07,
author = {D. Nikolic and S. Haeusler and W. Singer and W. Maass},
title = {Distributed fading memory for stimulus properties in the
primary visual},
journal = {submitted for publication},
year = {2009},
volume = {},
number = {},
pages = {},
abstract = {}
}
@InProceedings{NikolicETAL:07a,
author = {D. Nikoli\'{c} and S. Haeusler and W. Singer and W. Maass},
title = {Temporal dynamics of information content carried by
neurons in the primary visual cortex},
booktitle = {Proc. of NIPS 2006, Advances in Neural Information
Processing Systems},
editor = {},
publisher = {MIT Press},
year = {2007},
volume = {19},
pages = {1041--1048},
abstract = {We use multi-electrode recordings from cat primary visual
cortex and investigate whether a simple linear classifier
ca n extract information about the presented stimuli. We
find that information is extractable and that it even las
ts for several hundred milliseconds after the stimulus has
b een removed. In a fast sequence of stimulus presentation,
information about both new and old stimuli is present
simultaneously and nonlinear relations between these
stimuli can be extracted. These results suggest nonlinear
properties of cortical representat ions. The implications
of these properties for the nonlinear brain theory are
discussed.}
}
@Article{NikolicETAL:09,
author = {D. Nikolic and S. Haeusler and W. Singer and W. Maass},
title = {Distributed fading memory for stimulus properties in the
primary visual cortex},
journal = {PLoS Biology},
year = {2009},
volume = {7},
number = {12},
pages = {1--19},
abstract = {It is currently not known how distributed neuronal
responses in early visual areas carry stimulus-related
information. We made multi-electrode recordings from cat
primary visual cortex and applied methods from machine
learning in order to analyze the temporal evolution of
stimulus-related information in the spiking activity of
large ensembles of around 100 neurons. We used sequences of
up to three different visual stimuli (letters) presented
for 100 ms and with intervals of 100 ms or larger. Most of
the information about visual stimuli extractable by
sophisticated methods of machine learning, i.e. support
vector machines with non-linear kernel functions, was also
extractable by simple linear classification such as can be
achieved by individual neurons. New stimuli did not erase
information about previous stimuli. The responses to the
most recent stimulus contained about equal amounts of
information about both this and the preceding stimulus.
This information was encoded both in the discharge rates
(response amplitudes) of the ensemble of neurons and, when
using short time-constants for integration (e.g., 20 ms),
in the precise timing of individual spikes (<= $~20$ ms),
and persisted for several 100 ms beyond the offset of
stimuli. The results indicate that the network from which
we recorded is endowed with fading memory and is capable of
performing online computations utilizing information about
temporally sequential stimuli. This result challenges
models assuming frame-by-frame analyses of sequential
inputs.},
note = {}
}
@Article{PecevskiETAL:07,
author = {R. Brette and D. Pecevski},
title = {Simulation of networks of spiking neurons: a review of
tools and strategies},
journal = {J. Computer Neuroscience},
year = {2007},
volume = {23},
number = {3},
pages = {349--398},
abstract = {}
}
@Article{PecevskiETAL:09,
author = {D. Pecevski and T. Natschlaeger and K. Schuch},
title = {{PCSIM}: A Parallel Simulation Environment for Neural
Circuits Fully Integrated with {P}ython},
journal = {Frontiers in Neuroinformatics},
year = {2009},
volume = {3},
number = {},
pages = {},
note = {doi:10.3389/neuro.11.011.2009},
abstract = {The {P}arallel {C}ircuit {SIM}ulator ({PCSIM}) is a
software package for simulation of neural circuits. It is
primarily designed for distributed simulation of large
scale networks of spiking point neurons. Although its
computational core is written in {C}++, {PCSIM}'s primary
interface is implemented in the {P}ython programming
language, which is a powerful programming environment and
allows the user to easily integrate the neural circuit
simulator with data analysis and visualization tools to
manage the full neural modeling life cycle. The main focus
of this paper is to describe {PCSIM}'s full integration
into {P}ython and the benefits thereof. In particular we
will investigate how the automatically generated
bidirectional interface and {PCSIM}'s object-oriented
modular framework enable the user to adopt a hybrid
modeling approach: using and extending {PCSIM}'s
functionality either employing pure {P}ython or {C}++ and
thus combining the advantages of both worlds. Furthermore,
we describe several supplementary {PCSIM} packages written
in pure {P}ython and tailored towards setting up and
analyzing neural simulations.}
}
@TechReport{PecevskiETAL:11,
author = {D. Pecevski and L. B\"using and W. Maass},
title = {Networks of spiking neurons are able to carry out
probabilistic inference in general graphical models through
their inherent stochastic dynamics},
institution = {Graz University of Technology},
year = {2011}
}
@Article{PecevskiETAL:11a,
author = {D. Pecevski and L. B\"using and W. Maass},
title = {Probabilistic Inference in General Graphical Models
through Sampling in Stochastic Networks of Spiking
Neurons},
journal = {PLoS Computational Biology},
year = {2011},
pages = {e1002294},
volume = {7},
number = {12},
abstract = {An important open problem of computational neuroscience is
the generic organization of computations in networks of
neurons in the brain. We show here through rigorous
theoretical analysis that inherent stochastic features of
spiking neurons, in combination with simple nonlinear
computational operations in specific network motifs and
dendritic arbors, enable networks of spiking neurons to
carry out probabilistic inference through sampling in
general graphical models. In particular, it enables them to
carry out probabilistic inference in Bayesian networks with
converging arrows (“explaining away”) and with undirected
loops, that occur in many real-world tasks. Ubiquitous
stochastic features of networks of spiking neurons, such as
trial-to-trial variability and spontaneous activity, are
necessary ingredients of the underlying computational
organization. We demonstrate through computer simulations
that this approach can be scaled up to neural emulations of
probabilistic inference in fairly large graphical models,
yielding some of the most complex computations that have
been carried out so far in networks of spiking neurons.},
note = {}
}
@InProceedings{PfeifferETAL:06,
author = {M. Pfeiffer and A. R. Saffari A. A. and A. Juffinger},
title = {Predicting Text Relevance from Sequential Reading
Behavior},
booktitle = {Proceedings of the NIPS 2005 Workshop on Machine Learning
for Implicit Feedback and User Modeling},
year = {2006},
editor = {K. Puolamaeki and S. Kaski},
pages = {25--30},
address = {Otaniemi, Finland},
month = {May},
organization = {Helsinki University of Technology}
}
@Article{PfeifferETAL:09,
author = {M. Pfeiffer and B. Nessler and W. Maass and R. J.
Douglas},
title = {Reward-modulated {H}ebbian Learning of Optimal Decision
Making},
journal = {Neural Computation},
year = {2009},
pages = {},
volume = {}
}
@Article{PfeifferETAL:09b,
author = {M. Pfeiffer and B. Nessler and W. Maass},
title = {{STDP} approximates Expectation Maximization in networks
of spiking neurons with lateral inhibition},
journal = {in preparation},
year = {2009},
pages = {},
volume = {}
}
@Article{PfeifferETAL:09c,
author = {M. Pfeiffer and B. Nessler and R. Douglas and W. Maass},
title = {Reward-modulated {H}ebbian {L}earning of {D}ecision
{M}aking},
journal = {Neural Computation},
year = {2010},
volume = {22},
pages = {1399--1444},
abstract = {We introduce a framework for decision making in which the
learning of decision making is reduced to its simplest
andbiologically most plausible form: Hebbian learning on a
linear neuron. We cast our Bayesian-Hebb learning rule as
reinforcement learning in which certain decisions are
rewarded and prove that each synaptic weight will on
average converge exponentially fast to the log-odd of
receiving a reward when its pre- and postsynaptic neurons
are active. In our simple architecture, a particular action
is selected from the set of candidate actions by a
winner-takeall operation. The global reward assigned to
this action then modulates the update of each synapse.
Apart from this global reward signal, our reward-modulated
Bayesian Hebb rule is a pure Hebb update that depends only
on the coactivation of the pre- and postsynaptic neurons,
not on theweighted sum of all presynaptic inputs to the
postsynaptic neuron as in the perceptron learning rule or
the Rescorla-Wagner rule. This simple approach to
action-selection learning requires that information about
sensory inputs be presented to the Bayesian decision stage
in a suitably preprocessed form resulting from other
adaptive processes (acting on a larger timescale) that
detect salient dependencies among input features. Hence our
proposed framework for fast learning of decisions also
provides interesting new hypotheses regarding neural nodes
and computational goals of cortical areas that provide
input to the final decision stage.}
}
@PhDThesis{Rasch:08,
author = {M. Rasch},
title = {Analysis of neural signals: Interdependence, information
coding, and relation to network models},
school = {Graz University of Technology, Institute for Theoretical
Computer Science},
year = {2008}
}
@TechReport{RaschETAL:06,
author = {M. Rasch and S. Haeusler and Z. Kisvarday and W. Maass and
N. Logothetis},
title = {Comparison of a detailed model for area {V}1 with
simultaneous recordings from {LGN} and {V}1},
institution = {Technische Universitaet Graz and MPI Tuebingen},
year = {2006}
}
@TechReport{RaschETAL:06b,
author = {M. Rasch and A. Gretton and Y. Murayama and W. Maass and
N. Logothetis},
title = {Interaction of local field potential and spiking activity
in area {V}1},
institution = {Technische Universitaet Graz and MPI Tuebingen},
year = {2006}
}
@Article{RaschETAL:07,
author = {M. J. Rasch and A. Gretton and Y. Murayama and W. Maass
and N. K. Logothetis},
title = {Inferring spike trains from local field potentials},
journal = {Journal of Neurophysiology},
year = {2008},
volume = {99},
number = {},
pages = {1461--1476},
note = {},
abstract = {We investigated whether it is possible to infer spike
trains solely on the basis of the underling local field
potentials ({LFP}s). Employing support vector machines and
linear regression models, we found that in the primary
visual cortex ({V}1) of monkeys, spikes can indeed be
inferred from {LFP}s, at least with moderate success.
Although there is a considerable degree of variation across
electrodes, the low-frequency structure in spike trains (in
the 100 ms range) can be inferred with reasonable accuracy,
whereas exact spike positions are not reliably predicted.
Two kinds of features of the {LFP} are exploited for
prediction: the frequency power of bands in the high
$\gamma$-range (40-90 {H}z), and information contained in
low-frequency oscillations (<10 {H}z), where both phase and
power modulations are informative. Information analysis
revealed that both features code (mainly) independent
aspects of the spike-to-{LFP} relationship, with the
low-frequency {LFP} phase coding for temporally clustered
spiking activity. Although both features and prediction
quality are similar during semi-natural movie stimuli and
spontaneous activity, prediction performance during
spontaneous activity degrades much more slowly with
increasing electrode distance. The general trend of data
obtained with anesthetized animals is qualitatively
mirrored in that of a more limited data set recorded in
{V}1 of awake monkeys. In contrast to the cortical field
potentials, thalamic {LFP}s (e.g. {LFP}s derived from
recordings in d{LGN}) hold no useful information for
predicting spiking activity.}
}
@Article{RaschETAL:09,
author = {M. J. Rasch and K. Schuch and N. K. Logothetis and W.
Maass},
title = {Statistical characterization of the spike response to
natural stimuli in monkey area {V}1 and in a detailed model
for a patch of {V}1},
journal = {submitted},
year = {2009},
pages = {},
volume = {}
}
@Article{RaschETAL:10,
author = {M. J. Rasch and K. Schuch and N. K. Logothetis and W.
Maass},
title = {Statistical Comparision of Spike Responses to Natural
Stimuli in Monkey Area {V}1 With Simulated Responses of a
Detailed Laminar Network Model for a Patch of {V}1},
journal = {J Neurophysiol},
year = {2011},
pages = {757--778},
volume = {105},
abstract = {A major goal of computational neuroscience is the creation
of computer models for cortical areas whose response to
sensory stimuli resembles that of cortical areas in vivo in
important aspects. It is seldom considered whether the
simulated spiking activity is realistic (in a statistical
sense) in response to natural stimuli. Because certain
statistical properties of spike responses were suggested to
facilitate computations in the cortex, acquiring a
realistic firing regimen in cortical network models might
be a prerequisite for analyzing their computational
functions. We present a characterization and comparison of
the statistical response properties of the primary visual
cortex (V1) in vivo and in silico in response to natural
stimuli. We recorded from multiple electrodes in area V1 of
4 macaque monkeys and developed a large state-of-the-art
network model for a 5 x 5-mm patch of V1 composed of 35,000
neurons and 3.9 million synapses that integrates previously
published anatomical and physiological details. By
quantitative comparison of the model response to the
"statistical fingerprint" of responses in vivo, we find
that our model for a patch of V1 responds to the same movie
in a way which matches the statistical structure of the
recorded data surprisingly well. The deviation between the
firing regimen of the model and the in vivo data are on the
same level as deviations among monkeys and sessions. This
suggests that, despite strong simplifications and
abstractions of cortical network models, they are
nevertheless capable of generating realistic spiking
activity. To reach a realistic firing state, it was not
only necessary to include both N-methyl- D-aspartate and
GABAB synaptic conductances in our model, but also to
markedly increase the strength of excitatory synapses onto
inhibitory neurons (more than 2-fold) in comparison to
literature values, hinting at the importance to carefully
adjust the effect of inhibition for achieving realistic
dynamics in current network models.},
htmlnote = {(Commentary by W.S. Anderson and B. Kreiman in Current
Biology 2011 PDF)}
}
@TechReport{RaschKisvarday:06,
author = {M. Rasch and Z. Kisvarday},
title = {Design of stimuli for investigating spatial integration of
information in optical recordings},
institution = {Technische Universitaet Graz and University of Debrecen},
year = {2006}
}
@MastersThesis{Ruf:93,
author = {B. Ruf},
note = {(in German)},
school = {Rheinisch-Westfaelische Technische Hochschule Aachen,
Germany},
title = {Sequentielle und parallele {L}ernverfahren fuer
{B}oltzmann-{M}aschinen},
year = {1993},
keywords = {boltzmann machine, learning algorithm}
}
@InProceedings{Ruf:94,
author = {B. Ruf},
address = {Brussels},
booktitle = {Proc. of the 2nd european symposium on artificial neural
networks},
editor = {M. Verleysen},
pages = {109--116},
title = {A stop criterion for the Boltzmann machine learning
algorithm},
year = {1994},
keywords = {boltzmann machine, learning}
}
@InProceedings{Ruf:96,
author = {B. Ruf},
booktitle = {Workshop on Neural Networks Dynamics and Pattern
Recognition, Toulouse},
pages = {25--26},
publisher = {Onera, Centre d'Etudes et de Recherches de Toulouse},
title = {Pattern Recognition with Networks of Spiking Neurons},
year = {1996},
keywords = {spiking neurons, pattern recognition, temporal coding}
}
@InProceedings{Ruf:97,
author = {B. Ruf},
booktitle = {Biological and artificial computation: From neuroscience
to technology},
editor = {J. Mira and R. Moreno-Diaz and J. Cabestany},
pages = {265--272},
publisher = {Springer, Berlin},
series = {Lecture Notes in Computer Science},
title = {Computing functions with spiking neurons in temporal
coding},
volume = {1240},
year = {1997},
keywords = {spiking neuron, linear function, temporal coding,
approximation}
}
@PhDThesis{Ruf:98a,
author = {B. Ruf},
school = {TU Graz},
title = {Computing and learning with spiking neurons - theory and
simulations},
year = {1998}
}
@InProceedings{Ruf:98b,
author = {B. Ruf},
booktitle = {Proc. of the VI-Dynn 98 conference},
editor = {T. Lindblad},
publisher = {Spie},
title = {Networks of spiking neurons can compute linear functions
using action potential timing},
year = {1998}
}
@Article{RufSchmitt:97,
author = {B. Ruf and M. Schmitt},
journal = {Neural Processing Letters},
number = {1},
pages = {9--18},
title = {Learning temporally encoded patterns in networks of
spiking neurons},
volume = {5},
year = {1997},
keywords = {spiking neuron, temporal coding, hebbian learning}
}
@InProceedings{RufSchmitt:97a,
author = {B. Ruf and M. Schmitt},
booktitle = {Biological and artificial computation: From neuroscience
to technology},
editor = {J. Mira and R. Moreno-Diaz and J. Cabestany},
pages = {380--389},
publisher = {Springer, Berlin},
series = {Lecture Notes in Computer Science},
title = {Hebbian Learning in Networks of Spiking Neurons Using
Temporal Coding},
volume = {1240},
year = {1997},
keywords = {spiking neuron, hebbian learning, temporal coding}
}
@InProceedings{RufSchmitt:97b,
author = {B. Ruf and M. Schmitt},
booktitle = {Proc. of the 7th International Conference on Artificial
Neural Networks},
editor = {W. Gerstner and A. Germond and M. Hasler and J. Nicoud},
pages = {361--366},
publisher = {Springer, Berlin},
series = {Lecture Notes in Computer Science},
title = {Unsupervised learning in networks of spiking neurons using
temporal coding},
volume = {1327},
year = {1997},
keywords = {unsupervised learning, self organizing map, spiking
neuron}
}
@Article{RufSchmitt:97d,
author = {B. Ruf and M. Schmitt},
booktitle = {Proc. of the 7th International Conference on Artificial
Neural Networks},
journal = {IEEE Transactions on Neural Networks},
pages = {575--578},
title = {Self-organization of spiking neurons using action
potential timing},
volume = {9:3},
year = {1998},
keywords = {unsupervised learning, self organizing map, spiking
neuron}
}
@InProceedings{RufSchmitt:98,
author = {B. Ruf and M. Schmitt},
booktitle = {Computational Neuroscience: Trends in Research 1998 (to
appear)},
editor = {J. Bower},
publisher = {Plenum Press},
title = {Self-organizing maps of spiking neurons using temporal
coding},
year = {1998},
keywords = {unsupervised learning, spiking neuron, self-organizing
map}
}
@MastersThesis{Schwaighofer00,
author = {Schwaighofer, A.},
title = {Fingerprint Matching with Spectral Features},
school = {Institute for Theoretical Computer Science, Graz
University of Technology, Austria},
year = 2000,
month = may,
abstract = {The underlying purpose of this thesis is to investigate
methods of fingerprint recognition which employ principles
from the field of machine learning, and that do not require
much image pre-processing. Fingerprint images are
represented by features derived from their spectrum. The
features are to a certain extent invariant with respect to
translation and rotation. The features are chosen such that
the two classes of identical and different fingerprints are
best separated. The features are used in different
classification methods, namely nearest neighbour
classifier, MLP and SVM, with specifically adapted training
methods. The resulting matchers are compared. In addition,
a pre-matcher based on these features is constructed,
together with figures to describe its characteristics. This
thesis makes two major contributions: The spectral features
are optimised such that a low-dimensional representation
with high discriminative power is obtained. Secondly, the
proposed pre-matching system drastically reduces both the
error rates and the overall runtime, while the pre-matcher
itself requires only little computational effort.},
aschwaig_label= 1
}
@PhDThesis{Schwaighofer_thesis,
author = {Schwaighofer, Anton},
title = {Kernel Systems for Regression and Graphical Modelling},
school = {Institute for Theoretical Computer Science, Graz
University of Technology, Austria},
year = 2003,
month = {October},
aschwaig_label= 12
}
@Article{SteimerETAL:09,
author = {A. Steimer and W. Maass and R. Douglas},
title = {Belief-propagation in networks of spiking neurons},
journal = {Neural Computation},
year = {2009},
volume = {21},
number = {},
pages = {2502--2523},
abstract = {From a theoretical point of view, statistical inference is
an attractive model of brain operation. However, it is
unclear how to implement these inferential processes in
neuronal networks. We offer a solution to this problem by
showing in detailed simulations how the Belief-Propagation
algorithm on a factor graph can be embedded in a network of
spiking neurons. We use pools of spiking neurons as the
function nodes of the factor graph. Each pool gathers
'messages' in the form of population activities from its
input nodes and combines them through its network dynamics.
The various output messages to be transmitted over the
edges of the graph are each computed by a group of readout
neurons that feed in their respective destination pools. We
use this approach to implement two examples of factor
graphs. The first example is drawn from coding theory. It
models the transmission of signals through an unreliable
channel and demonstrates the principles and generality of
our network approach. The second, more applied example, is
of a psychophysical mechanism in which visual cues are used
to resolve hypotheses about the interpretation of an
object's shape and illumination. These two examples, and
also a statistical analysis, all demonstrate good agreement
between the performance of our networks and the direct
numerical evaluation of beliefpropagation.}
}
@Article{SteinbauerETAL:02,
author = {G. Steinbauer and R. Koholka and W. Maass},
title = {A very short story about autonomous robots},
journal = {Special Issue on Foundations of Information Processing of
{TELEMATIK}},
year = {2002},
volume = {8},
number = {1},
pages = {26--29}
}
@Article{SussilloETAL:07,
author = {D. Sussillo and T. Toyoizumi and W. Maass},
title = {Self-tuning of neural circuits through short-term synaptic
plasticity},
journal = {Journal of Neurophysiology},
year = {2007},
volume = {97},
pages = {4079--4095},
abstract = {Circuits of neurons in the cortex have a remarkable
capability to maintain functional and dynamic stability in
spite of changes in the level of external inputs, synaptic
plasticity and changes in the circuit structure that occur
during development and adult learning. The source of this
characteristic stability of cortical circuits has remained
a mystery, especially since even stronglysimplified models
of such circuits do not exhibit similar stability
properties. One simplification that is usually made in such
models is that the empirically found nonlinear and diverse
inherent short term dynamics (paired-pulse facilitation and
depression) of biological synapses is replaced by static
and uniform linear synapse models. We show in this article
that this is a mistake, since the complex and diverse
nonlinear dynamics of biological synapses supports the
implementation of powerful control principles that endow
circuits of spiking neurons with almost in-vivo like
stability properties.}
}
@InProceedings{ToescherETAL:08,
author = {Andreas Toescher and Michael Jahrer and Robert
Legenstein},
title = {Improved Neighborhood-Based Algorithms for Large-Scale
Recommender Systems},
note = {in press},
pages = {},
booktitle = {KDD-Cup and Workshop},
publisher = {ACM},
year = 2008,
abstract = {Neighborhood-based algorithms are frequently used modules
of recommender systems. Usually, the choice of the
similarity measure used for evaluation of neighborhood
relationships is crucial for the success of such
approaches. In this article we propose a way to calculate
similarities by formulating a regression problem which
enables us to extract the similarities from the data in a
problem-specific way. Another popular approach for
recommender systems is regularized matrix factorization
(RMF). We present an algorithm -- neighborhood-aware matrix
factorization -- which efficiently includes neighborhood
information in a RMF model. This leads to increased
prediction accuracy. The proposed methods are tested on the
Netflix dataset.}
}
@Article{UchizawaETAL:06,
author = {K. Uchizawa and R. Douglas and W. Maass},
title = {On the Computational Power of Threshold Circuits with
Sparse Activity},
journal = {Neural Computation},
year = 2006,
volume = 18,
number = 12,
pages = {2994--3008},
abstract = {Circuits composed of threshold gates (McCulloch-Pitts
neurons, or perceptrons) are simplified models of neural
circuits with the advantage that they are theoretically
more tractable than their biological counterparts. However,
when such threshold circuits are designed to perform a
specific computational task they usually differ in one
important respect from computations in the brain: they
require very high activity. On average every second
threshold gate fires (sets a ``1'' as output) during a
computation. By contrast, the activity of neurons in the
brain is much more sparse, with only about 1\% of neurons
firing. This mismatch between threshold and neuronal
circuits is due to the particular complexity measures
(circuit size and circuit depth) that have been minimized
in previous threshold circuit constructions. In this
article we investigate a new complexity measure for
threshold circuits, {\em energy complexity}, whose
minimization yields computations with sparse activity. We
prove that all computations by threshold circuits of
polynomial size with entropy $O(\log n)$ can be
restructured so that their energy complexity is reduced to
a level near the {\em entropy of circuit states}. This
entropy of circuit states is a novel circuit complexity
measure, which is of interest not only in the context of
threshold circuits, but for circuit complexity in general.
As an example of how this measure can be applied we show
that any polynomial size threshold circuit with entropy
$O(\log n)$ can be simulated by a polynomial size threshold
circuit of depth 3.
Our results demonstrate that the structure of circuits
which result from a minimization of their energy complexity
is quite different from the structure which results from a
minimization of previously considered complexity measures,
and potentially closer to the structure of neural circuits
in the nervous system. In particular, different pathways
are activated in these circuits for different classes of
inputs. This article shows that such circuits with sparse
activity have a surprisingly large computational power.}
}
@InProceedings{UchizawaETAL:06a,
author = {K. Uchizawa and R. Douglas and W. Maass},
booktitle = {Proceedings of the 33rd International Colloquium on
Automata, Languages and Programming, ICALP (1) 2006,
Venice, Italy, July 10-14, 2006, Part I},
title = {Energy Complexity and Entropy of Threshold Circuits},
year = {2006},
volume = {4051},
pages = {631--642},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
editor = {M. Bugliesi and B. Preneel and V. Sassone and I. Wegener},
abstract = {Circuits composed of threshold gates (McCulloch-Pitts
neurons, or perceptrons) are simplified models of neural
circuits with the advantage that they are theoretically
more tractable than their biological counterparts. However,
when such threshold circuits are designed to perform a
specific computational task they usually differ in one
important respect from computations in the brain: they
require very high activity. On average every second
threshold gate fires (sets a ``1'' as output) during a
computation. By contrast, the activity of neurons in the
brain is much more sparse, with only about 1\% of neurons
firing. This mismatch between threshold and neuronal
circuits is due to the particular complexity measures
(circuit size and circuit depth) that have been minimized
in previous threshold circuit constructions. In this
article we investigate a new complexity measure for
threshold circuits, {\em energy complexity}, whose
minimization yields computations with sparse activity. We
prove that all computations by threshold circuits of
polynomial size with entropy $O(\log n)$ can be
restructured so that their energy complexity is reduced to
a level near the {\em entropy of circuit states}. This
entropy of circuit states is a novel circuit complexity
measure, which is of interest not only in the context of
threshold circuits, but for circuit complexity in general.
As an example of how this measure can be applied we show
that any polynomial size threshold circuit with entropy
$O(\log n)$ can be simulated by a polynomial size threshold
circuit of depth 3.}
}
@TechReport{WinterETAL:06,
author = {M. Winter and H. Bischof and M. Rasch and W. Maass},
title = {Results and open problems regarding the role of local
feature descriptors for image classification in computer
vision, and image representations in primary visual
cortex},
institution = {Technische Universitaet Graz},
year = {2006}
}
@InProceedings{a-aagt-88,
author = {F. Aurenhammer},
title = {Algorithmic aspects of {G}ale transforms (abstract)},
booktitle = {Proc. $13^{th}$ 3-Ann. Int'l Symp. Mathematical
Programming},
pages = 176,
year = 1988,
address = {Tokyo, Japan}
}
@Article{a-caecc-87,
author = {F. Aurenhammer},
title = {A criterion for the affine equivalence of cell complexes
in {$R^d$} and convex polyhedra in {$R^{d+1}$}},
journal = {Discrete \& Computational Geometry},
year = 1987,
volume = 2,
number = 1,
pages = {49--64},
note = {[IIG-Report-Series 205, TU Graz, Austria, 1985]},
abstract = {A criterion is gives that decides, for a convex tiling $C$
of $R^d$, whether $C$ is the projection of the faces in the
boundary of some convex polyhedron $P$ in $R^{d+1}$. Its
applicability is restricted neither by the properties nor
by the dimension of $C$. It turns out to be simpler than
other criteria and allows the easy examination of various
classes of cell complexes. In addition, the criterion is
constructive, that is, it can be used to construct $P$
provided it exists.}
}
@PhDThesis{a-ccphn-97,
author = {O. Aichholzer},
title = {Combinatorial \& Computational Properties of the Hypercube
- New Results on Covering, Slicing, Clustering and
Searching on the Hypercube},
school = {IGI-TU Graz, Austria},
year = 1997,
abstract = { The central topic of this thesis is the $d$-dimensional
hypercube ($d$-cube). Despite of its simple definition, the
$d$-cube has been an object of study from various points of
view. The contributions of this thesis are twofold. In the
combinatorial part we investigate the structure of
hyperplanes intersecting the $d$-cube: How many and which
types of hyperplanes can be spanned by vertices of the
$d$-cube? What is the minimum number of skew hyperplanes
that cover all the vertices of the $d$-cube? What is the
best arrangement of slicing hyperplanes to linearly
separate all neighbours on the $d$-cube? Such results are
then used e.g. for determining the maximal number of facets
a 5-dimensional $0/1$-polytope can achieve. In the second
part of the thesis we consider algorithmical properties of
the $d$-cube. We first obtain efficient clustering methods
for objects represented as binary strings of fixed length
$d$, including various agglomerative hierarchical methods
like single linkage and complete linkage. Utilizing these
hierarchical structures we derive a new efficient approach
to the ${0,1}$-string searching problem, where for a given
set of binary strings of fixed length $d$ and a query
string one asks for the most similar string in this set.
Motivation for investigating these problems stems, among
other areas, from coding theory, communication theory, and
learning theory.}
}
@Article{a-cgeqr-01,
author = {F. Aurenhammer},
title = {Computational geometry -- some easy questions and their
recent solutions},
journal = {J. Universal Computer Science},
year = 2001,
volume = 7,
pages = {338--354},
note = {Special Issue.},
abstract = {We address three basic questions in computational geometry
which can be phrased in simple terms but have only recently
received (more or less) satisfactory answers: point set
enumeration, optimum triangulation, and polygon
decomposition.}
}
@TechReport{a-ch-96,
author = {O. Aichholzer},
title = {Clustering the Hypercube},
institution = {SFB 'Optimierung und Kontrolle', TU Graz, Austria},
year = 1996,
type = {SFB-Report},
number = {F003-93},
abstract = {In this paper we consider various clustering methods for
objects represented as binary strings of fixed length $d$.
The dissimilarity of two given objects is the number of
disagreeing bits, that is, their Hamming distance.
Clustering these objects can be seen as clustering a subset
of the vertices of a $d$-dimensional hypercube, and thus is
a geometric problem in d dimensions. We give algorithms for
various agglomerative hierarchical methods (including
single linkage and complete linkage) as well as for
two-clusterings and divisive methods.\\ We only present
linear space algorithms since for most practical
applications the number of objects to be clustered is
usually to large for non-linear space solutions to be
practicable. All algorithms are easy to implement and the
constants in their asymptotic runtime are small. We give
experimental results for all cluster methods considered,
and for uniformly distributed hypercube vertices as well as
for specially chosen sets. These experiments indicate that
our algorithms work well in practice.}
}
@InProceedings{a-e0ssb-98,
author = {O. Aichholzer},
title = {Efficient $\{0,1\}$-String Searching Based on
Pre-clustering},
booktitle = {Proc. $14^{th}$ European Workshop on Computational
Geometry CG '98},
pages = {11--13},
year = 1998,
address = {Barcelona, Spain},
note = {[SFB Report F003-94, TU Graz, Austria, 1996]},
abstract = {In this paper we consider the ${0,1}$-string searching
problem. For a given set $S$ of binary strings of fixed
length $d$ and a query string $q$ one asks for the most
similar string in $S$. Thereby the dissimilarity of two
given strings is the number of disagreeing bits, that is,
their Hamming distance. We present an efficient
${0,1}$-string searching algorithm based on hierarchical
pre-clustering. To this end we give several useful
observations on the inter- and intra-cluster distances.\\
The presented algorithms are easy to implement and we give
exhaustive experimental results for uniformly distributed
sets as well as for specially chosen strings. These
experiments indicate that our algorithms work well in
practice.}
}
@InCollection{a-ep0pd-00,
author = {O. Aichholzer},
title = {Extremal Properties of 0/1-Polytopes of Dimension 5},
booktitle = {Polytopes - Combinatorics and Computation},
publisher = {Birkhaeuser},
year = 2000,
editor = {G. Ziegler and G. Kalai},
pages = {111--130},
note = {[SFB-Report F003-132, TU Graz, Austria, 1998]},
htmlnote = {You can also investigate
0/1-polytopes by e-mail!},
abstract = {In this paper we consider polytopes whose vertex
coordinates are $0$ or $1$, so called $0/1$-polytopes. For
the first time we give a complete enumeration of all
$0/1$-polytopes of dimension $5$, which enables us to
investigate various of their combinatorial extremal
properties.\\ For example we show that the maximum number
of facets of a five-dimensional $0/1$-polytope is $40$,
answering an open question of Ziegler. Based on the
complete enumeration for dimension $5$ we obtain new
results for $2$-neighbourly $0/1$-polytopes for higher
dimensions.}
}
@InProceedings{a-gcvtp-93,
author = {F. Aurenhammer},
title = {Geometric clustering and {V}oronoi-type partitions},
booktitle = {$16^{th}$ IFIP Conf. System Modelling and Optimization},
year = 1993,
pages = {93-94},
address = {Compiegne, France}
}
@Article{a-gefsi-95,
author = {F. Aurenhammer},
title = {Guest editor's foreword of the special issue on
computational geometry},
journal = {Int'l Journal of Computational Geometry \& Applications},
year = 1995,
volume = {5},
pages = {1}
}
@TechReport{a-gpd-83,
author = {F. Aurenhammer},
title = {On the generality of power diagrams},
institution = {TU Graz, Austria},
year = 1983,
type = {IIG Report},
number = {F126},
abstract = {A set $s = \{ x \mid ^2 = r^2 \}$ in Euclidean space
is called a sphere with center $z$ and positive radius $r$.
For an arbitrary point $x$, $^2 = r^2$ is the power of
$x$ with respect to $s$. Extending these concepts to
imaginary radii, they are exploited to show the equivalence
of two types of cell complexes: those that can be obtained
by projection of convex polyhedra, and those that come from
projecting levels in arrangement of hyperplanes. As a
consequence, higher-order Voronoi diagrams can be
constructed by determining a convex hull.}
}
@InProceedings{a-gv-85,
author = {F. Aurenhammer},
title = {Gewichtete {V}oronoidiagramme},
booktitle = {Workshop on Computational Geometry CG '85},
year = 1985,
address = {Karlsruhe, Germany}
}
@PhDThesis{a-gvdgd-84,
author = {F. Aurenhammer},
title = {Gewichtete {V}oronoi {D}iagramme: {G}eometrische {D}eutung
und {K}onstruktions-{A}lgorithmen},
school = {IIG-TU Graz, Austria},
year = 1984,
note = {Report B53},
abstract = {Das oft als Computational Geometry bezeichnete Teilgebiet
der Computerwissenschaften beschaeftigt sich mit der
algorithmischen Loesung elementargeometrischer Probleme.
Einen Schwerpunkt in der Computational Geometry bildet die
Untersuchung von Abstandsproblemen. In diesem Zusammenhang
spielt das Voronoi Diagramm einer endlichen Punktmenge eine
zentrale Rolle. Die vorliegende Arbeit ist eine
geometrische und algorithmische Studie sogenannter
gewichteter Voronoi Diagramme. Diese Diagramme leiten sich
aus dem Original durch Ersetzen des Euklidabstandes durch
individuell gewichtete Abstaende her. Das
Anwendungsspektrum solcher Konzepte umfasst die
Wissenschaften Geographie, Oekonomie, Biologie, Mathematik,
Physik und Chemie. Die Hauptergebnisse dieser Arbeit sind
die Erforschung der Verwandtschaft gewichteter Diagramme zu
anderen geometrischen Objekten (konvexe Huellen,
Zellkomplexe und Arrangements) mit Hilfe geometrischer
Transformationen, und der Entwurf effizienter Algorithmen
fuer ihre Konstruktion. Ein Teil der Resultate wurde
bereits in Schnelldruckserien und wissenschaftlichen
Journalen veroeffentlicht.}
}
@MastersThesis{a-hhkq-92,
author = {O. Aichholzer},
title = {{H}yperebenen in {H}yperkuben - {E}ine {K}lassifizierung
und {Q}uantifizierung},
school = {IGI-TU Graz, Austria},
year = 1992,
abstract = {In dieser Arbeit werden affine Hyperebenen in
hoeherdimensionalen Raeumen behandelt, die den
$n$-dimensionalen Hyperkubus schneiden. Dabei konzentriert
sich die Untersuchung auf folgende Fragestellung: Wieviele
und welche Arten von Hyperebenen gibt es, die durch
Eckpunkte des Hyperkubus eindeutig festgelegt sind? Neben
der Betrachtung, wieviele solcher Hyperebenen existieren,
wird eine Klassifizierung nach verschiedenen Kriterien wie
Symmetrie, Parallelitaet zu den Koordinatenachsen, Anzahl
der geschnittenen Eckpunkte etc. untersucht. Die Arbeit
enthaelt sowohl eine vollstaendige enumerative Berechnung
aller relevanten Werte bis einschliesslich der achten
Dimension, als auch die theoretische Herleitung allgemein
gueltiger Saetze ueber solche Hyperebenen. Die Beitraege
dieser Arbeit fallen in das Gebiet der geometrischen
Kombinatorik und finden sowohl in der Codierungs- und
Lerntheorie als auch in der linearen Optimierung sowie im
VLSI-Design Anwendung.}
}
@Article{a-iadbu-88,
author = {F. Aurenhammer},
title = {Improved algorithms for discs and balls using power
diagrams},
journal = {Journal of Algorithms},
year = 1988,
volume = 9,
number = 2,
pages = {151--161},
note = {[IIG-Report-Series 209, TU Graz, Austria, 1985]},
abstract = {The properties of a particular generalization of Voronoi
diagrams called power diagrams are exploited to obtain new
and improved algorithms for union, intersection, and
measure problems for discs and balls.}
}
@InProceedings{a-jschc-87,
author = {F. Aurenhammer},
title = {{J}ordan sorting via convex hulls of certain non-simple
polygons},
booktitle = {Proc. $3^{rd}$ Ann. ACM Symp. Computational Geometry},
pages = {21--29},
year = 1987,
address = {Waterloo, Canada}
}
@Article{a-lai-97,
author = {P. Auer},
title = {On Learning from Ambiguous Information},
journal = {Periodica Polytechnica Electrical Engineering},
year = {1998},
volume = {42},
number = {1},
pages = {115-122}
}
@Article{a-lcpd-88,
author = {F. Aurenhammer},
title = {Linear combinations from power domains},
journal = {Geometriae Dedicata},
year = 1988,
volume = 28,
pages = {45--52},
note = {[IIG-Report-Series 243, TU Graz, Austria, 1987]},
abstract = {The well-known concept of power domains defined via
subsets of a finite set $S$ of weighted points in $R^d$ is
exploited to obtain various linear combinations among the
points in $S$. This generalizes a result of Sibson who
considered the special case of singleton subsets and
unweighted points.}
}
@InProceedings{a-lpt-95,
author = {O. Aichholzer},
title = {Local properties of triangulations},
booktitle = {Proc. $11^{th}$ European Workshop on Computational
Geometry CG '95},
pages = {27--30},
year = 1995,
address = {Hagenberg/Linz, Austria},
abstract = {In this paper we study local properties of two well known
triangulations of a planar point set $S$, both of which are
defined in a non-local way. The first one is the greedy
triangulation (GT) that is defined procedurally: it can be
obtained by starting with the empty set and at each step
adding the shortest compatible edge between two points of
$S$, where a compatible edge is defined to be an edge that
does not cross any of the previously inserted edges. The
other triangulation we deal with is the minimum-weight
triangulation (MWT) which minimizes the sum of the length
of the edges among all possible triangulations of $S$. We
present several results on exclusion- and inclusion-regions
for these two triangulations.}
}
@InProceedings{a-ndrcv-86,
author = {F. Aurenhammer},
title = {A new duality result concerning {V}oronoi diagrams},
booktitle = {Proc. $13^{th}$ Ann. ICALP, Lecture Notes in Computer
Science},
pages = {21--32},
year = 1986,
volume = 226,
address = {Rennes, France},
publisher = {Springer Verlag},
abstract = {A new duality between order-$k$ Voronoi diagrams in $E^d$
and convex hulls in $E^{d+1}$ is established. It implies a
reasonably simple algorithm for computing the order-$k$
Voronoi diagram for $n$ points in the palne in $O(k^2 n
\log n)$ time and optimal $O(k(n-k))$ space.}
}
@Article{a-ndrcv-90,
author = {F. Aurenhammer},
title = {A new duality result concerning {V}oronoi diagrams},
journal = {Discrete \& Computational Geometry},
year = 1990,
volume = 5,
number = 3,
pages = {243--254},
note = {[IIG-Report-Series 216, TU Graz, Austria, 1985]},
abstract = {A new duality between order-$k$ Voronoi diagrams in $E^d$
and convex hulls in $E^{d+1}$ is established. It implies a
reasonably simple algorithm for computing the order-$k$
Voronoi diagram for $n$ points in the palne in $O(k^2 n
\log n)$ time and optimal $O(k(n-k))$ space.}
}
@Article{a-odwvd-86,
author = {F. Aurenhammer},
title = {The one-dimensional weighted {V}oronoi diagram},
journal = {Information Processing Letters},
year = 1986,
volume = 22,
number = 3,
pages = {119--123},
note = {[IIG-Report-Series F110, TU Graz, Austria, 1983]}
}
@Article{a-olsts-88a,
author = {F. Aurenhammer},
title = {On-line sorting of twisted sequences in linear time},
journal = {BIT},
year = 1988,
volume = 28,
pages = {194--204},
note = {[IIG-Report-Series 232, TU Graz, Austria, 1987]},
abstract = {A sequence of real numbers is called twisted if it can be
produced from the sorted sequence by repeatedly reversing
the order of consecutive subsequences. It is shown that
twisted sequences constitute a class of exponentially many
members each of which can be recognized and sorted, by a
simple on-line algorithm, in linear time.}
}
@InProceedings{a-olsts-88b,
author = {F. Aurenhammer},
title = {On-line sorting of twisted sequences in linear time},
booktitle = {$2^{nd}$ Workshop on Computational Geometry and Discrete
Algorithms},
year = 1988,
address = {Osaka, Japan}
}
@Article{a-pdpaa-87,
author = {F. Aurenhammer},
title = {Power diagrams: properties, algorithms, and applications},
journal = {SIAM Journal on Computing},
year = 1987,
volume = 16,
number = 1,
pages = {78--96},
note = {[IIG-Report-Series F120, TU Graz, Austria, 1983]},
abstract = {The power $pow(x,s)$ of a point $x$ with respect to a
sphere $s$ in Euclidean $d$-space $E^d$ is given by
$d^2(x,z)-r^2$, where $d$ denotes the Euclidean distance
function, and $z$ and $r$ are the center and the radius of
$s$. The power diagram of a finite set $S$ of spheres in
$E^d$ is a cell complex that associates each $s \in S$ with
the convex domain $\{x \in E^d \mid pow(x,s) < pow(x,t),
\mbox{for all} t \in S - \{s\} \}$. The close relationship
to convex hulls and arrangements of hyperplanes is
investigated and exploited. Efficient algorithms that
compute the power diagram and its order-$k$ modifications
are obtained. Among the applications of these results are
algorithms for detecting $k$-sets, for union and
intersection problems for cones and paraboloids, and for
constructing weighted Voronoi diagrams and Voronoi diagrams
for spheres. Upper space bounds for these geometric
problems are derived.}
}
@InProceedings{a-pgdtf-05,
author = {F. Aurenhammer},
title = {Pre-triangulations: A generalization of {D}elaunay
triangulations and flips},
booktitle = {$2^{nd}$ Intern. Symp. on Voronoi Diagrams in Science and
Engineering},
pages = {235},
year = 2005,
address = {Hanyang University, Seoul, Korea},
note = {(plenar talk)}
}
@InProceedings{a-psd-03,
author = {F. Aurenhammer},
title = {Pseudo-simplices and their derivation},
booktitle = {Voronoi Conference on Analytic Number Theory and Spatial
Tesselations},
pages = {11},
year = 2003,
address = {Inst. Math. National Academy of Sciences, Kiev, Ukraine}
}
@InProceedings{a-pt-97,
author = {O. Aichholzer},
title = {The Path of a Triangulation},
booktitle = {Proc. $13^{th}$ European Workshop on Computational
Geometry CG '97},
pages = {1--3},
year = 1997,
address = {Wuerzburg, Germany},
htmlnote = {For an implementation see my page on triangulation
counting.},
abstract = {For a planar point set $S$ let $T$ be a triangulation of
$S$ and $l$ a line properly intersecting $T$. We show that
there always exists a unique path in $T$ with certain
properties with respect to $l$. This path is then
generalized to (non triangulated) point sets restricted to
the interior of simple polygons. This so-called
triangulation path enables us to treat several
triangulation problems on planar point sets in a divide \&
conquer-like manner. For example, we give the first
algorithm for counting triangulations of a planar point set
which is observed to run in time sublinear in the number of
triangulations. Moreover, the triangulation path proves to
be useful for the computation of optimal triangulations.}
}
@InProceedings{a-pt-99,
author = {O. Aichholzer},
title = {The Path of a Triangulation},
booktitle = {Proc. $15^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {14--23},
year = 1999,
address = {Miami Beach, Florida, USA},
htmlnote = {For an implementation see my page on triangulation
counting.},
abstract = {For a planar point set $S$ let $T$ be a triangulation of
$S$ and $l$ a line properly intersecting $T$. We show that
there always exists a unique path in $T$ with certain
properties with respect to $l$. This path is then
generalized to (non triangulated) point sets restricted to
the interior of simple polygons. This so-called
triangulation path enables us to treat several
triangulation problems on planar point sets in a divide \&
conquer-like manner. For example, we give the first
algorithm for counting triangulations of a planar point set
which is observed to run in time sublinear in the number of
triangulations. Moreover, the triangulation path proves to
be useful for the computation of optimal triangulations.}
}
@Article{a-rbgtv-90,
author = {F. Aurenhammer},
title = {A relationship between {G}ale transforms and {V}oronoi
diagrams},
journal = {Discrete Applied Mathematics},
year = 1990,
volume = 28,
pages = {83--91},
note = {[IIG-Report-Series 247, TU Graz, Austria, 1988]},
abstract = {Gale transforms and Voronoi diagrams for finite point sets
in $R^d$ are two structures well known in discrete and
computational geometry. It is shown that they are related
in the sense that Gale transforms of a point set can be
computed from (generalizations of) its Voronoi diagram.}
}
@Article{a-rpccc-87,
author = {F. Aurenhammer},
title = {Recognizing polytopical cell complexes and constructing
projection polyhedra},
journal = {Journal of Symbolic Computation},
year = 1987,
volume = 3,
number = 3,
pages = {249--255},
note = {[IIG-Report-Series 203, TU Graz, Austria, 1985]},
abstract = {A simple cell complex $C$ in Euclidean $d$-space $E^d$ is
a covering of $E^d$ by finitely many convex $j$-dimensional
polyhedra (the $j$-faces of $C$), each of which is in the
closure of exactly $d-j+1$ $d$-faces of $C$. An algorithm
that recognises when $C$ is the projection of the set of
faces bounding some convex polyhedron $P(C)$ in $E^{d+1}$,
and that constructs $P(C)$ provided its existence is
outlined. The method is optimal at least for $d=2$. No
complexity results were previously known for both problems.
The results have applications in statics, to the
recognition of Voronoi diagrams, and to planar point
location.}
}
@InProceedings{a-srlfa-99,
author = {P. Auer},
title = {An Improved On-line Algorithm for Learning Linear
Evaluation Functions},
booktitle = {Proc. 13th Ann. Conf. Computational Learning Theory},
pages = {118--125},
year = {2000},
publisher = {Morgan Kaufmann}
}
@InProceedings{a-tnnb-98,
author = {P. Auer},
title = {Some thoughts on Boosting and Neural Networks},
booktitle = {Beitraege zum 3.~Cottbuser Workshop `Aspekte des
Neuronalen Lernens' CoWAN'98},
editor = {L. Cromme and T. Kolb and H. Koch},
optvolume = {},
optnumber = {},
optseries = {},
year = {1998},
optorganization={},
publisher = {Shaker Verlag},
address = {Cottbus, Germany},
month = {October},
pages = {11--28},
note = {Invited paper}
}
@Article{a-ucbeeto-2002,
author = {P. Auer},
title = {Using Confidence Bounds for Exploitation-Exploration
Trade-offs},
journal = {J. Machine Learning Research},
year = {2002},
volume = {3(Nov)},
pages = {397--422},
note = {A preliminary version has appeared in {\em Proc. of the
41th Annual Symposium on Foundations of Computer Science}}
}
@InProceedings{a-ugtcg-88,
author = {F. Aurenhammer},
title = {Using {G}ale transforms in computational geometry},
booktitle = {Proc. $4^{th}$ Workshop on Computational Geometry CG '88,
Lecture Notes in Computer Science},
pages = {202--216},
year = 1988,
volume = 333,
address = {Wuerzburg, Germany},
publisher = {Springer Verlag},
abstract = {Let $P$ denote a set of $n \geq d+1$ points in $d$-space
$R^d$. A Gale transform of $P$ assigns to each point in $P$
a vector in space $R^{d+1}$ such that the resulting
$n$-tuple of vectors reflects all affinely invariant
properties of $P$. First utilized by Gale in the 1950s,
Gale transforms have been recognized as a powerful tool in
combinatorial geometry. This paper introduces Gale
transforms to computational geometry. It offers a direct
algorithm for their construction and sketches applications
to convex hull and visibility problems. An application to
scene analysis is worked out in some more detail.}
}
@Article{a-ugtcg-91,
author = {F. Aurenhammer},
title = {Using {G}ale transforms in computational geometry},
journal = {Mathematical Programming},
year = 1991,
volume = {B 52},
pages = {179--190},
note = {Special Issue. [IIG-Report-Series 248, TU Graz, Austria,
1988]},
abstract = {Let $P$ denote a set of $n \geq d+1$ points in $d$-space
$R^d$. A Gale transform of $P$ assigns to each point in $P$
a vector in space $R^{d+1}$ such that the resulting
$n$-tuple of vectors reflects all affinely invariant
properties of $P$. First utilized by Gale in the 1950s,
Gale transforms have been recognized as a powerful tool in
combinatorial geometry. This paper introduces Gale
transforms to computational geometry. It offers a direct
algorithm for their construction and addresses applications
to convex hull and visibility problems. An application to
scene analysis is worked out in detail.}
}
@InProceedings{a-uucbol-00,
author = {P. Auer},
title = {Using Upper Confidence Bounds for Online Learning},
booktitle = {Proceedings of the 41th Annual Symposium on Foundations of
Computer Science},
pages = {270--293},
year = {2000},
publisher = {IEEE Computer Society}
}
@Article{a-vdsfg-91a,
author = {F. Aurenhammer},
title = {{V}oronoi diagrams -- a survey of a fundamental geometric
data structure},
journal = {ACM Computing Surveys},
year = 1991,
volume = 23,
number = 3,
pages = {345--405},
note = {{H}abilitationsschrift. [Report B 90-09, FU Berlin,
Germany, 1990]},
abstract = {This paper presents a survey of the Voronoi diagram, one
of the most fundamental data structures in computational
geometry. It demonstrates the importance and usefulness of
the Voronoi diagram in a wide variety of fields inside and
outside computer science and surveys the history of its
development. The paper puts particular emphasis on the
unified exposition of its mathematical and algorithmic
properties. Finally, the paper provides the first
comprehensive bibliography on Voronoi diagrams and related
structures.}
}
@Article{a-vdsfg-91b,
author = {F. Aurenhammer},
title = {{V}oronoi diagrams -- a survey of a fundamental geometric
data structure},
journal = {bit acm computing surveys '91 (Japanese translation),
Kyoritsu Shuppan Co., Ltd.},
year = 1993,
pages = {131--185}
}
@Article{a-wsdaq-02,
author = {P. Auer},
title = {Why Students Don't Ask Questions},
journal = {TELEMATIK},
year = {2002},
pages = {21--23},
volume = {8},
number = {1},
note = {Special Issue on Foundations of Information Processing for
the 21st Century},
optannote = {}
}
@Article{a-wsfsd-07,
author = {F. Aurenhammer},
title = {Weighted skeletons and fixed-share decomposition},
journal = {Computational Geometry: Theory and Applications},
year = {2007},
volume = {40},
pages = {93-101},
abstract = {We introduce the concept of weighted skeleton of a polygon
and present various decomposition and optimality results
for this skeletal structure when the underlying polygon is
convex.}
}
@InProceedings{aa-chh-94,
author = {O. Aichholzer and F. Aurenhammer},
title = {Classifying hyperplanes in hypercubes},
booktitle = {Proc. $10^{th}$ European Workshop on Computational
Geometry CG '94},
pages = {53--57},
year = 1994,
address = {Santander, Spain},
abstract = {We consider hyperplanes spanned by vertices of the unit
$d$-cube. We classify these hyperplanes by parallelism to
coordinate axes, by symmetry of the $d$-cube vertices they
avoid, as well as by so-called hull-honesty. (Hull-honest
hyperplanes are those whose intersection figure with the
$d$-cube coincides with the convex hull of the $d$-cube
vertices they contain; they do not cut $d$-cube edges
properly.) We describe relationships between these classes,
and give the exact number of hull-honest hyperplanes, in
general dimensions. An experimental enumeration of all
spanned hyperplanes up to dimension eight showed us the
intrinsic difficulty of developing a general enumeration
scheme. Motivation for considering such hyperplanes stems
from coding theory, from linear programming, and from the
theory of machine learning.}
}
@Article{aa-chh-96,
author = {O. Aichholzer and F. Aurenhammer},
title = {Classifying hyperplanes in hypercubes},
journal = {SIAM Journal on Discrete Mathematics},
year = 1996,
volume = 9,
number = 2,
pages = {225--232},
note = {[IIG-Report-Series 408, TU Graz, Austria, 1995]},
abstract = {We consider hyperplanes spanned by vertices of the unit
$d$-cube. We classify these hyperplanes by parallelism to
coordinate axes, by symmetry of the $d$-cube vertices they
avoid, as well as by so-called hull-honesty. (Hull-honest
hyperplanes are those whose intersection figure with the
$d$-cube coincides with the convex hull of the $d$-cube
vertices they contain; they do not cut $d$-cube edges
properly.) We describe relationships between these classes,
and give the exact number of hull-honest hyperplanes, in
general dimensions. An experimental enumeration of all
spanned hyperplanes up to dimension eight showed us the
intrinsic difficulty of developing a general enumeration
scheme. Motivation for considering such hyperplanes stems
from coding theory, from linear programming, and from the
theory of machine learning.}
}
@InProceedings{aa-ssgpf-96,
author = {O. Aichholzer and F. Aurenhammer},
title = {Straight skeletons for general polygonal figures},
booktitle = {Proc. $2^{nd}$ Ann. Int'l. Computing and Combinatorics
Conf. COCOON'96, Lecture Notes in Computer Science},
pages = {117--126},
year = 1996,
volume = 1090,
address = {Hong Kong},
publisher = {Springer Verlag},
note = {[IIG-Report-Series 423, TU Graz, Austria, 1995]},
abstract = {A novel type of skeleton for general polygonal figures,
the straight skeleton $S(G)$ of a planar straight line
graph $G$, is introduced and discussed. Exact bounds on the
size of $S(G)$ are derived. The straight line structure of
$S(G)$ and its lower combinatorial complexity may make
$S(G)$ preferable to the widely used Voronoi diagram (or
medial axis) of $G$ in several applications. We explain why
$S(G)$ has no Voronoi diagram based interpretation and why
standard construction techniques fail to work. A simple
$O(n)$ space algorithm for constructing $S(G)$ is proposed.
The worst-case running time is $O(n^3 \log n)$, but the
algorithm can be expected to be practically efficient, and
it is easy to implement. We also show that the concept of
$S(G)$ is flexible enough to allow an individual weighting
of the edges and vertices of $G$, without changes in the
maximal size of $S(G)$, or in the method of construction.
Apart from offering an alternative to Voronoi-type
skeletons, these generalizations of $S(G)$ have
applications to the reconstruction of a geographical
terrain from a given river map, and to the construction of
a polygonal roof above a given layout of ground walls.}
}
@InCollection{aa-ssgpf-98,
author = {O. Aichholzer and F. Aurenhammer},
title = {Straight skeletons for general polygonal figures in the
plane},
booktitle = {Voronoi's Impact on Modern Sciences II},
pages = {7--21},
publisher = {Proc. Institute of Mathematics of the National Academy of
Sciences of Ukraine},
year = 1998,
editor = {A.M. Samoilenko},
volume = 21,
address = {Kiev, Ukraine},
abstract = {A novel type of skeleton for general polygonal figures,
the straight skeleton $S(G)$ of a planar straight line
graph $G$, is introduced and discussed. Exact bounds on the
size of $S(G)$ are derived. The straight line structure of
$S(G)$ and its lower combinatorial complexity may make
$S(G)$ preferable to the widely used Voronoi diagram (or
medial axis) of $G$ in several applications. We explain why
$S(G)$ has no Voronoi diagram based interpretation and why
standard construction techniques fail to work. A simple
$O(n)$ space algorithm for constructing $S(G)$ is proposed.
The worst-case running time is $O(n^3 \log n)$, but the
algorithm can be expected to be practically efficient, and
it is easy to implement. We also show that the concept of
$S(G)$ is flexible enough to allow an individual weighting
of the edges and vertices of $G$, without changes in the
maximal size of $S(G)$, or in the method of construction.
Apart from offering an alternative to Voronoi-type
skeletons, these generalizations of $S(G)$ have
applications to the reconstruction of a geographical
terrain from a given river map, and to the construction of
a polygonal roof above a given layout of ground walls.}
}
@Article{aa-vdcgf-02,
author = {O. Aichholzer and F. Aurenhammer},
title = {Voronoi Diagrams - Computational Geometry's Favorite},
journal = {Special Issue on Foundations of Information Processing of
{TELEMATIK}},
pages = {7--11},
volume = 1,
year = {2002},
address = {Graz, Austria}
}
@InProceedings{aaacjr-at-10,
author = {O. Aichholzer and W. Aigner and F. Aurenhammer and K.
\v{C}ech Dobi\.a\v{s}ov\.a and B. J\"uttler and G. Rote},
title = {Arc triangulations},
booktitle = {Proc. $26^{th}$ European Workshop on Computational
Geometry EuroCG '2010},
pages = {17--20},
year = 2010,
address = {Dortmund, Germany},
abstract = {An important objective in the choice of a triangulation of
a given point set is that the smallest angle becomes as
large as possible. In the straight line case, it is known
that the Delaunay triangulation is optimal in this respect.
We propose and study the concept of a circular arc
triangulation, a simple and effective alternative that
offers flexibility for additionally enlarging small angles.
We show that angle optimization and related questions lead
to linear programming problems that can be formulated as
simple graph-theoretic problems, and we define flipping
operations in arc triangles. Moreover, special classes of
arc triangulations are considered, for applications in
finite element methods and graph drawing.}
}
@InProceedings{aaacjr-twca-11,
author = {O. Aichholzer and W. Aigner and F. Aurenhammer and K.
\v{C}ech Dobi\.a\v{s}ov\.a and B. J\"uttler and G. Rote},
title = {Triangulations with circular arcs},
booktitle = {Proc. $19^{th}$ Int. Symposium on Graph Drawing, Springer
LNCS},
volume = 7034,
pages = {296--307},
year = 2011,
address = {Eindhoven, Netherlands},
abstract = {An important objective in the choice of a triangulation is
that the smallest angle becomes as large as possible. In
the straight line case, it is known that the Delaunay
triangulation is optimal in this respect. We propose and
study the concept of a circular arc triangulation---a
simple and effective alternative that offers flexibility
for additionally enlarging small angles---and discuss its
applications in graph drawing.}
}
@Article{aaag-ntsp-95,
author = {O. Aichholzer and D. Alberts and F. Aurenhammer and B.
Gaertner},
title = {A novel type of skeleton for polygons},
journal = {Journal of Universal Computer Science},
year = 1995,
volume = 1,
number = 12,
pages = {752--761},
htmlnote = {Click here for the Online
Version},
note = {[IIG-Report-Series 424, TU Graz, Austria, 1995]},
abstract = {A new internal structure for simple polygons, the straight
skeleton, is introduced and discussed. It is composed of
pieces of angular bisectores which partition the interior
of a given $n$-gon $P$ in a tree-like fashion into $n$
monotone polygons. Its straight-line structure and its
lower combinatorial complexity may make the straight
skeleton preferable to the widely used medial axis of a
polygon. As a seemingly unrelated application, the straight
skeleton provides a canonical way of constructing a
polygonal roof above a general layout of ground walls.}
}
@InProceedings{aaag-sssp-95,
author = {O. Aichholzer and D. Alberts and F. Aurenhammer and B.
Gaertner},
title = {Straight skeletons of simple polygons},
booktitle = {Proc. $4^{th}$ Int. Symp. of LIESMARS},
pages = {114--124},
year = 1995,
address = {Wuhan, P. R. China},
abstract = {A new internal structure for simple polygons, the straight
skeleton, is introduced and discussed. It is a tree and
partitions the interior of a given $n$-gon $P$ into $n$
monotone polygons, one for each edge of $P$. Its
straight-line structure and its lower combinatorial
complexity may make the straight skeleton $S(P)$ preferable
to the widely used medial axis of $P$. We show that $S(P)$
has no Voronoi diagram structure and give an $O(n r \log
n)$ time and $O(n)$ space construction algorithm, where $r$
counts the reflex vertices of $P$. As a seemingly unrelated
application, the straight skeleton provides a canonical way
of constructing a roof of given slope above a polygonal
layout of ground walls.}
}
@InProceedings{aaahjpr-dcvdr-09,
author = {O. Aichholzer and W. Aigner and F. Aurenhammer and T.
Hackl and B. J\"uttler and E. Pilgerstorfer and M. Rabl},
title = {Divide-and conquer for {V}oronoi diagrams revisited},
booktitle = {Proc. $25^{th}$ Ann. ACM Symp. Computational Geometry},
address = {Aarhus, Denmark},
pages = {189--197},
year = 2009,
abstract = {We show how to divide the edge graph of a Voronoi diagram
into a tree that corresponds to the medial axis of an
(augmented) planar domain. Division into base cases is then
possible, which, in the bottom-up phase, can be merged by
trivial concatenation. The resulting construction
algorithm---similar to Delaunay triangulation methods---is
not bisector-based and merely computes dual links between
the sites, its atomic steps being inclusion tests for sites
in circles. This guarantees computational simplicity and
numerical stability. Moreover, no part of the Voronoi
diagram, once constructed, has to be discarded again. The
algorithm works for polygonal and curved objects as sites
and, in particular, for circular arcs which allows its
extension to general free-form objects by Voronoi diagram
preserving and data saving biarc approximations. The
algorithm is randomized, with expected runtime $O(n\logn)$
under certain assumptions on the input data. Experiments
substantiate an efficient behavior even when these
assumptions are not met. Applications to offset
computations and motion planning for general objects are
described.}
}
@Article{aaahjpr-dcvdr-10,
author = {O. Aichholzer and W. Aigner and F. Aurenhammer and T.
Hackl and B. J\"uttler and E. Pilgerstorfer and M. Rabl},
title = {Divide-and conquer for {V}oronoi diagrams revisited},
journal = {Computational Geometry: Theory and Applications},
volume = {43},
pages = {688-699},
year = 2010,
abstract = {We show how to divide the edge graph of a Voronoi diagram
into a tree that corresponds to the medial axis of an
(augmented) planar domain. Division into base cases is then
possible, which, in the bottom-up phase, can be merged by
trivial concatenation. The resulting construction
algorithm---similar to Delaunay triangulation methods---is
not bisector-based and merely computes dual links between
the sites, its atomic steps being inclusion tests for sites
in circles. This guarantees computational simplicity and
numerical stability. Moreover, no part of the Voronoi
diagram, once constructed, has to be discarded again. The
algorithm works for polygonal and curved objects as sites
and, in particular, for circular arcs which allows its
extension to general free-form objects by Voronoi diagram
preserving and data saving biarc approximations. The
algorithm is randomized, with expected runtime $O(n\logn)$
under certain assumptions on the input data. Experiments
substantiate an efficient behavior even when these
assumptions are not met. Applications to offset
computations and motion planning for general objects are
described.}
}
@InProceedings{aaahjpr1-dcvdr-09,
author = {O. Aichholzer and W. Aigner and F. Aurenhammer and T.
Hackl and B. J\"uttler and E. Pilgerstorfer and M. Rabl},
title = {Divide-and conquer for {V}oronoi diagrams revisited},
booktitle = {Proc. $25^{th}$ European Workshop on Computational
Geometry EuroCG'09},
address = {Brussels, Belgium},
pages = {293--296},
year = 2009,
abstract = {We propose a simple and practical divide-and-conquer
algorithm for constructing planar Voronoi diagrams. The
novel aspect of the algorithm is its emphasis on the
top-down phase, which makes it applicable to sites of
general shape.}
}
@Article{aaahjr-macpffs-08,
author = {O. Aichholzer and W. Aigner and F. Aurenhammer and T.
Hackl and B. Juettler and M. Rabl},
title = {Medial axis computation for planar free-form shapes},
journal = {Computer Aided Design},
year = 2009,
volume = 41,
pages = {339--349},
note = {Special Issue},
abstract = {We present a simple, efficient, and stable method for
computing---with any desired precision---the medial axis of
simply connected planar domains. The domain boundaries are
assumed to be given as polynomial spline curves. Our
approach combines known results from the field of geometric
approximation theory with a new algorithm from the field of
computational geometry. Challenging steps are (1) the
approximation of the boundary spline such that the medial
axis is geometrically stable, and (2) the efficient
decomposition of the domain into base cases where the
medial axis can be computed directly and exactly. We solve
these problems via spiral biarc approximation and a
randomized divide \& conquer algorithm.}
}
@InProceedings{aaaj-emactsrplm-11,
author = {O. Aichholzer and W. Aigner and F. Aurenhammer and B.
J\"uttler},
title = {Exact medial axis computation for triangulated solids with
respect to piecewise linear metrics},
booktitle = {Proc. Int. Conf. Curves and Surfaces, Springer LNCS},
address = {Avignon, France},
year = 2011,
volume = 6920,
pages = {1--27},
abstract = {We propose a novel approach for the medial axis
approximation of triangulated solids by using a polyhedral
unit ball $B$ instead of the standard Euclidean unit ball.
By this means, we compute the exact medial axis
$MA(\Omega)$ of a triangulated solid $\Omega$ with respect
to a piecewise linear (quasi-)metric $d_B$. The obtained
representation of $\Omega$ by the medial axis transform
$MAT(\Omega)$ allows for a convenient computation of the
trimmed offset of $\Omega$ with respect to $d_B$. All
calculations are performed within the field of rational
numbers, resulting in a robust and efficient implementation
of our approach. Adapting the properties of $B$ provides an
easy way to control the level of details captured by the
medial axis, making use of the implicit pruning at flat
boundary features.}
}
@InProceedings{aabekm-nesca-00,
author = {O. Aichholzer and F. Aurenhammer and B. Brandtstaetter and
T. Ebner and H. Krasser and C. Magele},
title = {Niching evolution strategy with cluster algorithms},
booktitle = {$9^{th}$ Biennial IEEE Conf. Electromagnetic Field
Computations},
year = 2000,
address = {Milwaukee, Wisconsin, USA},
abstract = {In most real world optimization problems one tries to
determine the global among some or even numerous local
solutions within the feasible region of parameters. On the
other hand, it could be worth to investigate some of the
local solutions as well. Therefore, a most desirable
behaviour would be, if the optimization strategy behaves
globally and yields additional information about local
minima detected on the way to the global solution. In this
paper a clustering algorithm has been implemented into an
Higher Order Evolution Strategy in order to achieve these
goals.}
}
@Article{aabk-ptsnt-03,
author = {O. Aichholzer and F. Aurenhammer and P. Brass and H.
Krasser},
title = {Pseudo-Triangulations from Surfaces and a Novel Type of
Edge Flip},
journal = {SIAM Journal on Computing},
volume = {32},
year = {2003},
pages = {1621--1653},
abstract = {We prove that planar pseudo-triangulations have
realizations as polyhedral surfaces in three-space. Two
main implications are presented: The spatial embedding
leads to a novel flip operation that allows for a drastical
reduction of flip distances, especially between (full)
triangulations. Moreover, several key results for
triangulations, like flipping to optimality, (constrained)
Delaunayhood, and a convex polytope representation, are
extended to pseudo-triangulations in a natural way.},
address = {Graz, Austria}
}
@InProceedings{aabk-sept-03,
author = {O. Aichholzer and F. Aurenhammer and P. Brass and H.
Krasser},
title = {Spatial Embedding of Pseudo-Triangulations},
booktitle = {Proc. $19^{th}$ Ann. ACM Symp. Computational Geometry},
address = {San Diego, California, USA},
pages = {144--153},
year = 2003,
abstract = {We show that pseudo-triangulations have natural embeddings
in three-space. As a consequence, various concepts for
triangulations, like flipping to optimality, (constrained)
Delaunayhood, and a polytope representation carry over to
pseudo-triangulations.}
}
@InProceedings{aabkmmr-eshc-01,
author = {O. Aichholzer and F. Aurenhammer and B. Brandtstaetter and
H. Krasser and C. Magele and M. Muehlmann and W. Renhart},
title = {Evolution trategy and ierarchical lustering},
booktitle = {$13^{th}$ COMPUMAG Conference on the Computation of
Electromagnetic Fields},
year = 2001,
address = {Lyon-Evian, France},
abstract = {Multi-objective optimization problems, in general, exhibit
several local optima besides a global one. A desirable
feature of any optimization strategy would therefore be to
supply the user with as many information as possible about
local optima on the way to the global solution. In this
paper a hierarchical clustering algorithm implemented into
a higher order Evolution Strategy is applied to achieve
these goals.}
}
@Article{aackrtx-tin-96,
author = {O. Aichholzer and F. Aurenhammer and S.-W. Cheng and N.
Katoh and G. Rote and M. Taschwer and Y.-F. Xu},
title = {Triangulations intersect nicely},
journal = {Discrete \& Computational Geometry},
year = 1996,
volume = 16,
pages = {339--359},
note = {Special Issue. [SFB Report F003-030, TU Graz, Austria,
1995]},
abstract = {We show that there is a matching between the edges of any
two triangulations of a planar point set such that an edge
of one triangulation is matched either to the identical
edge in the other triangulation or to an edge that crosses
it. This theorem also holds for the triangles of the
triangulations and in general independence systems. As an
application, we give some lower bounds for the minimum
weight triangulation which can be computed in polynomial
time by matching and network flow techniques. We exhibit an
easy-to-recognize class of point sets for which the
minimum-weight triangulation coincides with the greedy
triangulation.}
}
@InProceedings{aaclmp-vddsd-97,
author = {O. Aichholzer and F. Aurenhammer and D.Z. Chen and D.T.
Lee and A. Mukhopadhyay and E. Papadopoulou},
title = {{V}oronoi diagrams for direction-sensitive distances
(communication)},
booktitle = {Proc. $13^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {418--420},
year = 1997,
address = {Nice, France},
note = {[SFB Report F003-098, TU Graz, Austria, 1996]},
abstract = {On a tilted plane $T$ in three-space, direction-sensitive
distances are defined as the Euclidean distance plus a
multiple of the signed difference in height. These
direction-sensitive distances, called skew distances
generalize the Euclidean distance and may model realistic
environments more closely than the Euclidean distance.
Various Voronoi diagrams and related problems under this
kind of distances are investigated. A relationship to
convex distance functions and to Euclidean Voronoi diagrams
for planar circles is shown, and is exploited for a
geometric analysis and a plane-sweep construction of
Voronoi diagrams on $T$. Several optimal algorithms based
on the direction-sensitive distances on $T$ are presented.
For example, an output-sensitive algorithm is developed for
computing the skew distance Voronoi diagram with $n$ sites
on $T$, in $O(n \log h)$ time and $O(n)$ space, where $h$
is the number of sites which have non-empty Voronoi regions
($1 \leq h \leq n$). $O(n \log n)$ time and $O(n)$ space
algorithms are also given for several other problems under
skew distances, including the all nearest neighbors and the
layers of Voronoi diagram. These algorithms have certain
features different from their 'ordinary' counterparts based
on the Euclidean distance.}
}
@Article{aaclp-svd-99,
author = {O. Aichholzer and F. Aurenhammer and D.Z. Chen and D.T.
Lee and E. Papadopoulou},
title = {Skew {V}oronoi diagrams},
journal = {Int'l. Journal of Computational Geometry \& Applications},
year = 1999,
volume = 9,
pages = {235--247},
htmlnote = {Click here for Figures
and Animations of Skew Voronoi Diagrams},
abstract = {On a tilted plane $T$ in three-space, {\em skew
distances\/} are defined as the Euclidean distance plus a
multiple of the signed difference in height. Skew distances
may model realistic environ\-ments more closely than the
Euclidean distance. Voro\-noi diagrams and related problems
under this kind of distances are investigated. A
relationship to convex distance functions and to Euclidean
Voronoi diagrams for planar circles is shown, and is
exploited for a geometric analysis and a plane-sweep
construction of Voronoi diagrams on $T$. An
output-sensitive algorithm running in time $O(n \log h)$ is
developed, where $n$ and $h$ is the number of sites and
non-empty Voronoi regions, respectively. The all nearest
neighbors problem for skew distances, which has certain
features different from its Euclidean counterpart, is
solved in $O(n \log n)$ time.}
}
@Article{aadhru-okcp-11,
author = {O. Aichholzer and F. Aurenhammer and E.D. Demaine and F.
Hurtado and P. Ramos and J. Urrutia},
title = {On $k$-convex polygons},
journal = {Computational Geometry: Theory and Applications},
year = 2012,
volume = 45,
pages = {73--87},
abstract = {We introduce the notion of $k$-convexity and explore
polygons in the plane that have this property. Polygons
which are $k$-convex can be triangulated with fast yet
simple algorithms. However, recognizing them is a 3SUM-hard
problem. We give a characterization of 2-convex polygons, a
particularly interesting class, and show how to recognize
them in $O(n \log n)$ time. A description of their shape is
given as well, which leads to Erd\"os-Szekeres type results
regarding subconfigurations of their vertex sets. Finally,
we introduce the concept of generalized geometric
permutations, and show that their number can be exponential
in the number of 2-convex objects considered.}
}
@InProceedings{aadhtv-09,
author = {O. Aichholzer and F. Aurenhammer and O. Devillers and T.
Hackl and M. Teillaud and B. Vogtenhuber},
title = {Lower and upper bounds on the number of empty cylinders
and ellipsoids},
booktitle = {Proc. $25^{th}$ European Workshop on Computational
Geometry EuroCG'09},
address = {Brussels, Belgium},
pages = {139--141},
year = 2009
}
@InProceedings{aaghhhkrv-mefpp-05,
author = {O. Aichholzer and F. Aurenhammer and P. Gonzalez-Nava and
T. Hackl and C. Huemer and F. Hurtado and H. Krasser and S.
Ray and B. Vogtenhuber},
title = {Matching edges and faces in polygonal partitions},
booktitle = {Proc. $17^{th}$ Canadian Conference on Computational
Geometry CCCG '05},
pages = {123--126},
year = 2005,
address = {Windsor, Ontario},
abstract = {We define general Laman (count) conditions for edges and
faces of polygonal partitions in the plane. Several
well-known classes, including $k$-regular partitions,
$k$-angulations, and rank-$k$ pseudo-triangulations, are
shown to fulfill such conditions. As a consequence,
non-trivial perfect matchings exist between the edge sets
(or face sets) of two such structures when they live on the
same point set. We also describe a link to spanning tree
decompositions that applies to quadrangulations and certain
pseudo-triangulations.}
}
@Article{aaghhhkrv-mefpp-07,
author = {O. Aichholzer and F. Aurenhammer and P. Gonzalez-Nava and
T. Hackl and C. Huemer and F. Hurtado and H. Krasser and S.
Ray and B. Vogtenhuber},
title = {Matching edges and faces in polygonal partitions},
journal = {Computational Geometry: Theory and Applications},
year = {2008},
volume = 39,
pages = {134--141},
abstract = {We define general Laman (count) conditions for edges and
faces of polygonal partitions in the plane. Several
well-known classes, including $k$-regular partitions,
$k$-angulations, and rank-$k$ pseudo-triangulations, are
shown to fulfill such conditions. As a consequence,
non-trivial perfect matchings exist between the edge sets
(or face sets) of two such structures when they live on the
same point set. We also describe a link to spanning tree
decompositions that applies to quadrangulations and certain
pseudo-triangulations.}
}
@InProceedings{aah-eoncs-00,
author = {O. Aichholzer and F. Aurenhammer and F. Hurtado},
title = {Edge Operations on Non-Crossing Spanning Trees},
booktitle = {Proc. $16^{th}$ European Workshop on Computational
Geometry CG '2000},
pages = {121--125},
year = 2000,
address = {Eilat, Israel},
htmlnote = {You can download our MST-Tool.}
,
abstract = {Let $S$ be a set of $n$ points in the Euclidean plane.
Consider the set ${\cal T}_S$ of all non-crossing spanning
trees of $S$. A {\em tree graph\/} ${\cal TG}_{\tt op}(S)$
is the graph that has ${\cal T}_S$ as its vertex set and
that connects vertex (tree) $T$ to vertex $T'$ iff $T' =
{\tt op}(T)$, where ${\tt op}$ is some operation that
exchanges two tree edges following a specific rule. The
existence of a path between two vertices in ${\cal TG}_{\tt
op}(S)$ means transformability of the corresponding trees
into each other by repeated application of the operation
${\tt op}$. The length of a shortest path corresponds to
the distance between the two trees with respect to the
operation ${\tt op}$. Distances of this kind provide a
measure of similarity between trees. We prove new results
on ${\cal TG}_{\tt op}(S)$ for two classical operations
${\tt op}$, namely the (improving and crossing-free) {\em
edge move\/} and the (crossing-free) {\em edge slide\/}.
Applications to morphing of trees and to the continuous
deformation of sets of line segments seem reasonable. Our
results mainly rely on a fact of interest in its own right:
Let $MST(S)$ and $DT(S)$ be the minimum spanning tree and
the Delaunay triangulation of $S$, respectively. Then any
pair $(T,\Delta)$, for $T \in {\cal T}_S$ and $\Delta$
being $T's$ constrained Delaunay triangulation, can be
transformed into the pair $(MST(S),DT(S))$ via a canonical
tree/triangulation sequence.}
}
@InProceedings{aah-fps-01a,
author = {O. Aichholzer and L.S. Alboul and F. Hurtado},
title = {On Flips in Polyhedral Surfaces},
booktitle = {Proc. $17^{th}$ European Workshop on Computational
Geometry CG '2001},
pages = {27--30},
year = 2001,
address = {Berlin, Germany},
htmlnote = {See also our interactive
web-page.},
abstract = {Let $V$ be a finite point set in 3D-space, and let ${\cal
S}(V)$ be the set of triangulated polyhedral surfaces
homeomorphic to a sphere and with vertex set $V$. Let $abc$
and $cbd$ be two adjacent triangles belonging to a surface
$S\in {\cal S}(V)$; the {\sl flip} of the edge $bc$ would
replace these two triangles by the triangles $abd$ and
$adc$. The flip operation is only considered when it does
not produce a self--intersecting surface. In this paper we
show that given two surfaces $S_1, S_2\in {\cal S}(V)$, it
is possible that there is no sequence of flips transforming
$S_1$ into $S_2$, even in the case that $V$ consists of
points in convex position.}
}
@Article{aah-fps-01b,
author = {O. Aichholzer and L.S. Alboul and F. Hurtado},
title = {On Flips in Polyhedral Surfaces},
journal = {International Journal of Foundations of Computer Science
(IJFCS), special issue on Volume and Surface
Triangulations},
year = 2002,
volume = 13,
number = 2,
pages = {303--311},
abstract = {Let $V$ be a finite point set in 3-space, and let ${\cal
S}(V)$ be the set of triangulated polyhedral surfaces
homeomorphic to a sphere and with vertex set $V$. Let $abc$
and $cbd$ be two adjacent triangles belonging to a surface
$S\in {\cal S}(V)$; the {\sl flip} of the edge $bc$ would
replace these two triangles by the triangles $abd$ and
$adc$. The flip operation is only considered when it does
not produce a self--intersecting surface. In this paper we
show that given two surfaces $S_1, S_2\in {\cal S}(V)$, it
is possible that there is no sequence of flips transforming
$S_1$ into $S_2$, even in the case that $V$ consists of
points in convex position.}
}
@Article{aah-nrms-99,
author = {O. Aichholzer and F. Aurenhammer and R. Hainz},
title = {New results on {MWT} subgraphs},
journal = {Information Processing Letters},
year = 1999,
volume = 69,
pages = {215--219},
note = {[SFB Report F003-140, TU Graz, Austria, 1998]},
abstract = {Let $P$ be a polygon in the plane. We disprove the
conjecture that the so-called LMT-skeleton coincides with
the intersection of all locally minimal triangulations,
$LMT(P)$, even for convex polygons $P$. We introduce an
improved LMT-skeleton algorithm which, for any simple
polygon $P$, exactly computes $LMT(P)$, and thus a larger
subgraph of the minimum-weight triangulation $MWT(P)$. The
algorithm achieves the same in the general point set case
provided the connectedness of the improved LMT-skeleton,
which is given in allmost all practical instances. We
further observe that the $\beta$-skeleton of $P$ is a
subset of $MWT(P)$ for all values $\beta >
\sqrt{\frac{4}{3}}$ provided $P$ is convex or near-convex.
This gives evidence for the tightness of this bound in the
general point set case.}
}
@InProceedings{aah-ptlc-06,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl},
title = {Pre-triangulations and liftable complexes},
booktitle = {$22^{nd}$ Ann. ACM Symp. Computational Geometry},
year = 2006,
pages = {282--291},
address = {Sedona, Arizona, USA},
abstract = {We introduce and discuss the concept of
pre-triangulations, a relaxation of triangulations that
goes beyond the well-established class of
pseudo-triangulations.}
}
@Article{aah-ptlc-07,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl},
title = {Pre-triangulations and liftable complexes},
journal = {Discrete \& Computational Geometry},
volume = 38,
year = 2007,
pages = {701--725},
abstract = {We introduce the concept of pre-triangulations, a
relaxation of triangulations that goes beyond the
frequently used concept of pseudo-triangulations.
Pre-triangulations turn out to be more natural than
pseudo-triangulations in certain cases. We show that
pre-triangulations arise in three different contexts: In
the characterization of polygonal complexes that are
liftable to three-space in a strong sense, in flip
sequences for general polygonal complexes, and as graphs of
maximal locally convex functions.}
}
@Article{aah-sstft-00,
author = {O. Aichholzer and F. Aurenhammer and F. Hurtado},
title = {Sequences of spanning trees and a fixed tree theorem},
year = 2002,
journal = {Computational Geometry: Theory and Applications},
volume = {21},
number = {1--2},
pages = {3--20},
note = {Special Issue. [Report MA2-IR-00-00026, Universitat
Polite\'cnica de Catalunya, Barcelona, Spain, 2000]},
htmlnote = {You can also download the nice program MST-Tool
we used to check and visualize some of the presented
results!},
abstract = {Let ${\cal T}_S$ be the set of all crossing-free spanning
trees of a planar $n$-point set $S$. We prove that ${\cal
T}_S$ contains, for each of its members $T$, a
length-decreasing sequence of trees $T_o,\ldots,T_k$ such
that $T_o=T$, $T_k=MST(S)$, $T_i$ does not cross $T_{i-1}$
for $i=1,\ldots,k$, and $k=O(\log n)$. Here $MST(S)$
denotes the Euclidean minimum spanning tree of the point
set $S$. As an implication, the number of length-improving
and planar edge moves needed to transform a tree $T \in
{\cal T}_S$ into $MST(S)$ is only $O(n\log n)$. Moreover,
it is possible to transform any two trees in ${\cal T}_S$
into each other by means of a local and constant-size edge
slide operation. Applications of these results to morphing
of simple polygons are possible by using a crossing-free
spanning tree as a skeleton description of a polygon.}
}
@Article{aahh-ccps-06,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and C.
Huemer},
title = {Connecting colored point sets},
journal = {Discrete Applied Mathematics},
volume = 155,
year = 2007,
pages = {271--278},
abstract = {We study the following Ramsey-type problem. Let \mbox{$S =
B \cup R$} be a two-colored set of $n$ points in the plane.
We show how to construct, in \mbox{$O(n \log n)$} time, a
crossing-free spanning tree $T(R)$ for~$R$, and a
crossing-free spanning tree $T(B)$ for~$B$, such that both
the number of crossings between $T(R)$ and $T(B)$ and the
diameters of~$T(R)$ and $T(B)$ are kept small. The
algorithm is conceptually simple and is implementable
without using any non-trivial data structure. This improves
over a previous method in Tokunaga~\cite{T} that is less
efficient in implementation and does not guarantee a
diameter bound.}
}
@InProceedings{aahhpv-3cpt,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and C.
Huemer and A. Pilz and B. Vogtenhuber},
title = {3-colorability of pseudo-triangulations},
booktitle = {Proc. $26^{th}$ European Workshop on Computational
Geometry EuroCG'10},
address = {Dortmund, Germany},
pages = {21--24},
year = 2010,
abstract = {Deciding $3$-colorability for general plane graphs is
known to be an NP-complete problem. However, for certain
classes of plane graphs, like triangulations, polynomial
time algorithms exist. We consider the family of
pseudo-triangulations (a generalization of triangulations)
and prove NP-completeness for this class, even if the
maximum face-degree is bounded to four, or pointed
pseudo-triangulations with maximum face degree five are
considered. As a complementary result, we show that for
pointed pseudo-triangulations with maximum face-degree
four, a $3$-coloring always exists and can be found in
linear time.}
}
@InProceedings{aahjos-csacbr-07,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and B.
Juettler and M. Oberneder and Z. Sir},
title = {Computational and Structural Advantages of Circular
Boundary Representation},
booktitle = {Proc. 10th Int. Workshop on Algorithms and Data
Structures, WADS'07, Springer LNCS 4619},
year = 2007,
address = {Halifax, Canada},
pages = {374-385},
abstract = {Boundary approximation of planar shapes by circular arcs
has quantitive and qualitative advantages compared to using
straight-line segments. We demonstrate this by way of three
basic and frequent computations on shapes -- convex hull,
decomposition, and medial axis. In particular, we propose a
novel medial axis algorithm that beats existing methods in
simplicity and practicality, and at the same time
guarantees convergence to the medial axis of the original
shape. }
}
@Article{aahjos-csacbr-10,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and B.
Juettler and M. Oberneder and Z. Sir},
title = {Computational and Structural Advantages of Circular
Boundary Representation},
journal = {Int'l Journal of Computational Geometry \& Applications},
volume = 21,
year = 2011,
pages = {47--69},
abstract = {Boundary approximation of planar shapes by circular arcs
has quantitive and qualitative advantages compared to using
straight-line segments. We demonstrate this by way of three
basic and frequent computations on shapes -- convex hull,
decomposition, and medial axis. In particular, we propose a
novel medial axis algorithm that beats existing methods in
simplicity and practicality, and at the same time
guarantees convergence to the medial axis of the original
shape.}
}
@InProceedings{aahk-tct-01,
author = {O. Aichholzer and F. Aurenhammer and F. Hurtado and H.
Krasser},
title = {Towards Compatible Triangulations},
booktitle = {Proc. $7^{th}$ Ann. Int'l. Computing and Combinatorics
Conf. COCOON'01, Lecture Notes in Computer Science},
pages = {101--110},
year = 2001,
volume = {2108},
address = {Guilin, China},
editor = {Jie Wang},
publisher = {Springer Verlag},
abstract = {We state the following conjecture: any two planar
$n$-point sets (that agree on the number of convex hull
points) can be triangulated in a compatible manner, i.e.,
such that the resulting two planar graphs are isomorphic.
The conjecture is proved true for point sets with at most
three interior points. We further exhibit a class of point
sets which can be triangulated compatibly with any other
set (that satisfies the obvious size and hull
restrictions). Finally, we prove that adding a small number
of Steiner points (the number of interior points minus two)
always allows for compatible triangulations.}
}
@Article{aahk-tct-01b,
author = {O. Aichholzer and F. Aurenhammer and F. Hurtado and H.
Krasser},
title = {Towards Compatible Triangulations},
year = 2003,
journal = {Theoretical Computer Science},
note = {Special Issue},
volume = {296},
pages = {3--13},
publisher = {Elsevier},
abstract = {We state the following conjecture: any two planar
$n$-point sets (that agree on the number of convex hull
points) can be triangulated in a compatible manner, i.e.,
such that the resulting two triangulations are
topologically equivalent. The conjecture is proved true for
point sets with at most three interior points. We further
exhibit a class of point sets which can be triangulated
compatibly with any other set that satisfies the obvious
size and hull restrictions. Finally, we prove that adding a
small number of extraneous points (the number of interior
points minus two) always allows for compatible
triangulations.}
}
@InProceedings{aahk-tspt-05,
author = {O. Aichholzer and F. Aurenhammer and C. Huemer and H.
Krasser},
title = {Transforming spanning trees and pseudo-triangulations},
booktitle = {Proc. $21^{st}$ European Workshop on Computational
Geometry EuroCG '05},
pages = {81--84},
year = 2005,
address = {Eindhoven, The Netherlands},
abstract = {Let $T_{S}$ be the set of all crossing-free straight line
spanning trees of a planar $n$-point set~$S$. Consider the
graph ${\cal T}_S$ where two members $T$ and $T'$ of
$T_{S}$ are adjacent if $T$ intersects $T'$ only in points
of~$S$ or in common edges. We prove that the diameter
of~${\cal T}_S$ is $O(\log k)$, where $k$ denotes the
number of convex layers of $S$. Based on this result, we
show that the flip graph~${\cal P}_S$ of
pseudo-triangulations of~$S$ (where two
pseudo-triangulations are adjacent if they differ in
exactly one edge -- either by replacement or by removal)
has a dia\-meter of $O(n \log k)$. This sharpens a known
$O(n \log n)$ bound. Let~${\cal \widehat{P}}_S$ be the
induced subgraph of pointed pseudo-triangulations of~${\cal
P}_S$. We present an example showing that the distance
between two nodes in~${\cal \widehat{P}}_S$ is strictly
larger than the distance between the corresponding nodes
in~${\cal P}_S$.}
}
@Article{aahk-tspt-06,
author = {O. Aichholzer and F. Aurenhammer and C. Huemer and H.
Krasser},
title = {Transforming spanning trees and pseudo-triangulations},
journal = {Information Processing Letters},
pages = {19--22},
volume = {97},
year = 2006,
abstract = {Let $T_{S}$ be the set of all crossing-free straight line
spanning trees of a planar $n$-point set~$S$. Consider the
graph ${\cal T}_S$ where two members $T$ and $T'$ of
$T_{S}$ are adjacent if $T$ intersects $T'$ only in points
of~$S$ or in common edges. We prove that the diameter
of~${\cal T}_S$ is $O(\log k)$, where $k$ denotes the
number of convex layers of $S$. Based on this result, we
show that the flip graph~${\cal P}_S$ of
pseudo-triangulations of~$S$ (where two
pseudo-triangulations are adjacent if they differ in
exactly one edge -- either by replacement or by removal)
has a dia\-meter of $O(n \log k)$. This sharpens a known
$O(n \log n)$ bound. Let~${\cal \widehat{P}}_S$ be the
induced subgraph of pointed pseudo-triangulations of~${\cal
P}_S$. We present an example showing that the distance
between two nodes in~${\cal \widehat{P}}_S$ is strictly
larger than the distance between the corresponding nodes
in~${\cal P}_S$.}
}
@InProceedings{aahkpp-abtob-07,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and B.
Kornberger and M. Peternell and H. Pottmann},
title = {Approximating boundary-triangulated objects with balls},
booktitle = {Proc. 23rd European Workshop on Computational Geometry,
EWCG'07},
year = 2007,
address = {Graz, Austria},
pages = {130--133},
abstract = {We compute a set of balls that approximates a given 3D
object, and we derive small additive bounds for the
overhead in balls with respect to the minimal solution with
the same quality. The algorithm has been implemented and
tested using the CGAL library.}
}
@InProceedings{aahkprsv-spia-08,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and B.
Kornberger and S. Plantinga and G. Rote and A. Sturm and G.
Vegter},
title = {Seed polytopes for incremental approximation},
booktitle = {Proc. $24^{th}$ European Workshop on Computational
Geometry EuroCG '08},
year = 2008,
pages = {13--16},
address = {Nancy, France},
abstract = {Approximating a three-dimensional object in order to
simplify its handling is a classical topic in computational
geometry and related fields. A typical approach is based on
incremental approximation algorithms, which start with a
small and topologically correct polytope representation
(the seed polytope) of a given sample point cloud or input
mesh. In addition, a correspondence between the faces of
the polytope and the respective regions of the object
boundary is needed to guarantee correctness.
We construct such a polytope by first computing a
simplified though still homotopy equivalent medial axis
transform of the input object. Then, we inflate this medial
axis to a polytope of small size. Since our approximation
maintains topology, the simplified medial axis transform is
also useful for skin surfaces and envelope surfaces.}
}
@InProceedings{aahlrss-swe-05,
author = {B. Aronov and F. Aurenhammer and F. Hurtado and S.
Langerman and D. Rappaport and S. Smorodinsky and C.
Seara},
title = {Small weak epsilon nets},
booktitle = {Proc. $17^{th}$ Canadian Conference on Computational
Geometry CCCG '05},
pages = {51--54},
year = 2005,
address = {Windsor, Ontario},
abstract = {Let S be a family of sets in the plane. Let 0 <
epsilon(S,i) < 1 denote the minimum real number such that
for any finite point set P there exists a set Q of i points
that is a weak epsilon(S,i)-net for P with respect to S. We
derice upper and lower bounds on epsilon(S,i) for small
integers i and when S is the family of all convex sets, or
the family of all axis-parallel rectangles.}
}
@Article{aahlrss-swe-07,
author = {B. Aronov and F. Aurenhammer and F. Hurtado and S.
Langerman and D. Rappaport and S. Smorodinsky and C.
Seara},
title = {Small weak epsilon nets},
journal = {Computational Geometry: Theory and Applications},
year = 2009,
volume = 42,
pages = {455--462},
note = {Special Issue},
abstract = {Let S be a family of sets in the plane. Let 0 <
epsilon(S,i) < 1 denote the minimum real number such that
for any finite point set P there exists a set Q of i points
that is a weak epsilon(S,i)-net for P with respect to S. We
derice upper and lower bounds on epsilon(S,i) for small
integers i and when S is the family of all convex sets, or
the family of all axis-parallel rectangles.}
}
@InProceedings{aahru-tcp-09,
author = {O. Aichholzer and F. Aurenhammer and F. Hurtado and P.A.
Ramos and J. Urrutia},
title = {Two-convex polygons},
booktitle = {Proc. $25^{th}$ European Workshop on Computational
Geometry EuroCG'09},
address = {Brussels, Belgium},
pages = {117--120},
year = 2009,
abstract = {We introduce a notion of k-convexity and explore some
properties of polygons that have this property. In
particular, 2-convex polygons can be recognized in
\mbox{$O(n \log n)$} time, and k-convex polygons can be
triangulated in $O(kn)$ time.}
}
@Article{aahs-mwpt-08,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and B.
Speckmann},
title = {On minimum weight pseudo-triangulations},
journal = {Computational Geometry: Theory and Applications},
year = 2009,
volume = 42,
pages = {627--631},
abstract = {In this note we discuss some structural properties of
minimum weight pseudo-triangulations.}
}
@InProceedings{aahs-pmwpt-07,
author = {O. Aichholzer and F. Aurenhammer and T. Hackl and B.
Speckmann},
title = {On (pointed) minimum weight pseudo-triangulations},
booktitle = {Proc. $19^{th}$ Canadian Conference on Computational
Geometry CCCG '07},
year = 2007,
address = {Ottawa, Canada},
pages = {209-212},
abstract = {In this note we discuss some structural properties of
minimum weight (pointed) pseudo-triangulations.}
}
@InProceedings{aahv-gcepslg-06,
author = {O. Aichholzer and F. Aurenhammer and C. Huemer and B.
Vogtenhuber},
title = {Gray code enumeration of plane straight-line graphs},
booktitle = {Proc. $22^{nd}$ European Workshop on Computational
Geometry EuroCG '06},
year = 2006,
pages = {71--74},
address = {Delphi, Greece},
abstract = {We develop Gray code enumeration schemes for geometric
graphs in the plane. The considered graph classes include
plane straight-line graphs, plane spanning trees, and
connected plane straight-line graphs. Previous results were
restricted to the case where the underlying vertex set is
in convex position.}
}
@Article{aahv-gcepslg-07,
author = {O. Aichholzer and F. Aurenhammer and C. Huemer and B.
Vogtenhuber},
title = {Gray code enumeration of plane straight-line graphs},
journal = {Graphs and Combinatorics},
year = 2007,
volume = 23,
pages = {467--479},
abstract = {We develop Gray code enumeration schemes for geometric
graphs in the plane. The considered graph classes include
plane straight-line graphs, plane spanning trees, and
connected plane straight-line graphs. Previous results were
restricted to the case where the underlying vertex set is
in convex position.}
}
@InProceedings{aaiklr-gsac-98a,
author = {O. Aichholzer and F. Aurenhammer and C. Icking and R.
Klein and E. Langetepe and G. Rote},
title = {Generalized self-approaching curves},
booktitle = {Proc. $14^{th}$ European Workshop on Computational
Geometry CG '98},
pages = {15--18},
year = 1998,
address = {Barcelona, Spain},
abstract = {We consider all planar oriented curves that have the
following property. For each point $B$ on the curve, the
rest of the curve lies inside a wedge of angle $\varphi$
with apex in $B$, where $\varphi < \Pi$ is fixed. This
property restrains the curve's meandering. we provide an
upper bound $c(\varphi)$ for the length of such a curve,
divided by the distance between its endpoints, and prove
this bound to be tight. A main step is in proving that the
curve's length cannot exceed the perimeter of its convex
hull, divided by $1+\cos(\varphi)$.}
}
@InProceedings{aaiklr-gsac-98b,
author = {O. Aichholzer and F. Aurenhammer and C. Icking and R.
Klein and E. Langetepe and G. Rote},
title = {Generalized self-approaching curves},
booktitle = {Proc. $9^{th}$ Int. Symp. Algorithms and Computation
ISAAC'98, Lecture Notes in Computer Science},
pages = {317--326},
year = 1998,
volume = 1533,
address = {Taejon, Korea},
publisher = {Springer Verlag},
abstract = {We consider all planar oriented curves that have the
following property depending on a fixed angle $\varphi$.
For each point $B$ on the curve, the rest of the curve lies
inside a wedge of angle $\varphi$ with apex in $B$. This
property restrains the curve's meandering, and for $\varphi
\leq \Pi/2$ this means that a point running along the curve
always gets closer to all points on the remaining part. For
all $\varphi < \Pi$, we provide an upper bound $c(\varphi)$
for the length of such a curve, divided by the distance
between its endpoints, and prove this bound to be tight. A
main step is in proving that the curve's length cannot
exceed the perimeter of its convex hull, divided by
$1+\cos(\varphi)$.}
}
@Article{aaiklr-vsac-00,
author = {O. Aichholzer and F. Aurenhammer and C. Icking and R.
Klein and E. Langetepe and G. Rote},
title = {Generalized self-approaching curves},
journal = {Discrete Applied Mathematics},
year = 2001,
note = {Special Issue. [SFB-Report F003-134, TU Graz, Austria,
1998]},
pages = {3--24},
volume = {109},
number = {1-2},
abstract = {We consider all planar oriented curves that have the
following property depending on a fixed angle $\varphi$.
For each point $B$ on the curve, the rest of the curve lies
inside a wedge of angle $\varphi$ with apex in $B$. This
property restrains the curve's meandering, and for $\varphi
\leq \Pi/2$ this means that a point running along the curve
always gets closer to all points on the remaining part. For
all $\varphi < \Pi$, we provide an upper bound $c(\varphi)$
for the length of such a curve, divided by the distance
between its endpoints, and prove this bound to be tight. A
main step is in proving that the curve's length cannot
exceed the perimeter of its convex hull, divided by
$1+\cos(\varphi)$.}
}
@InProceedings{aak-aptnl-03,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {Adapting (Pseudo)-Triangulations with a Near-Linear Number
of Edge Flips},
booktitle = {Lecture Notes in Computer Science 2748, Proc. 8th
International Workshop on Algorithms and Data Structures
(WADS)},
volume = {2748},
pages = {12--24},
year = 2003,
abstract = {We provide two results on flip distances in
pseudo-triangulations -- for minimum pseudo-triangulations
when using traditional flips operations, as well as for
triangulations when a novel and natural edge flip operation
is included into the repertoire of admissible flips. The
obtained flip distance lengths are $O(n \log^2 n)$ and $O(n
\log n)$, respectively. Our results partially rely on new
partitioning results for pseudo-triangulations which may be
of separate interest.}
}
@InProceedings{aak-cncg-02,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {On the Crossing Number of Complete Graphs},
year = 2002,
booktitle = {Proc. $18^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {19--24},
address = {Barcelona, Spain},
htmlnote = {See also our crossing
number homepage.},
abstract = {Let $\overline{cr}(G)$ denote the rectilinear crossing
number of a graph $G$. We determine
$\overline{cr}(K_{11})=102$ and
$\overline{cr}(K_{12})=153$. Despite the remarkable hunt
for crossing numbers of the complete graph~$K_n$ --
initiated by R.~Guy in the 1960s -- these quantities have
been unknown for $n>10$ to~date. Our solution mainly relies
on a tailor-made method for enumerating all inequivalent
sets of points (so-called order types) of size $11$. Based
on these findings, we establish new upper and lower bounds
on $\overline{cr}(K_{n})$ for general~$n$. Specific values
for $n \leq 45$ are given, along with significantly
improved asymptotic values. The asymptotic lower bound is
immediate from the fact $\overline{cr}(K_{11})=102$,
whereas the upper bound stems from a novel construction of
drawings with few crossings. The construction is shown to
be optimal within its frame. The tantalizing question of
determining $\overline{cr}(K_{13})$ is left open. The
latest ra(n)ge is $\{221,223,225,227,229\}$; our conjecture
is $\overline{cr}(K_{13}) = 229$.}
}
@InProceedings{aak-cncg-02b,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {On the Crossing Number of Complete Graphs - Extended
Abstract},
year = 2002,
booktitle = {Proc. $18^{th}$ European Workshop on Computationl Geometry
CG '02 Warszawa},
pages = {90-92},
address = {Warszawa, Poland},
htmlnote = {See also our crossing
number homepage.},
abstract = {Let $\overline{cr}(G)$ denote the rectilinear crossing
number of a graph $G$. We determine
$\overline{cr}(K_{11})=102$ and
$\overline{cr}(K_{12})=153$. Despite the remarkable hunt
for crossing numbers of the complete graph~$K_n$ --
initiated by R.~Guy in the 1960s -- these quantities have
been unknown for $n>10$ to~date. Our solution mainly relies
on a tailor-made method for enumerating all inequivalent
sets of points (so-called order types) of size $11$. Based
on these findings, we establish new upper and lower bounds
on $\overline{cr}(K_{n})$ for general~$n$. Specific values
for $n \leq 45$ are given, along with significantly
improved asymptotic values. The asymptotic lower bound is
immediate from the fact $\overline{cr}(K_{11})=102$,
whereas the upper bound stems from a novel construction of
drawings with few crossings. The construction is shown to
be optimal within its frame. The tantalizing question of
determining $\overline{cr}(K_{13})$ is left open. The
latest ra(n)ge is $\{221,223,225,227,229\}$; our conjecture
is $\overline{cr}(K_{13}) = 229$.}
}
@Article{aak-cncg-06,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {On the Crossing Number of Complete Graphs},
year = 2006,
journal = {Computing},
pages = {165--176},
volume = {76},
htmlnote = {See also our crossing
number homepage.},
abstract = {Let $\overline{cr}(G)$ denote the rectilinear crossing
number of a graph~$G$. We determine
$\overline{cr}(K_{11})=102$ and
$\overline{cr}(K_{12})=153$. Despite the remarkable hunt
for crossing numbers of the complete graph~$K_n$ --
initiated by R.~Guy in the 1960s -- these quantities have
been unknown for \mbox{$n>10$} to~date. Our solution mainly
relies on a tailor-made method for enumerating all
inequivalent sets of points (order types) of size~$11$.
Based on these findings, we establish a new upper bound on
$\overline{cr}(K_{n})$ for general~$n$. The bound stems
from a novel construction of drawings of $K_{n}$ with few
crossings.}
}
@InProceedings{aak-ctps-01,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {On Compatible Triangulations of Point Sets},
booktitle = {Proc. $17^{th}$ European Workshop on Computational
Geometry CG '2001},
pages = {23--26},
year = 2001,
address = {Berlin, Germany},
abstract = {Two conjectures on compatible triangulations for planar
point sets are stated and proven for small sets and for
special sets of arbitrary size.}
}
@InProceedings{aak-eotsp-01,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {Enumerating Order Types for Small Point Sets with
Applications},
booktitle = {Proc. $17^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {11--18},
year = 2001,
address = {Medford, Massachusetts, USA},
htmlnote = {See also our order
type homepage.},
abstract = {Order types are a means to characterize the combinatorial
properties of a finite point configuration. In particular,
the crossing properties of all straight-line segments
spanned by a planar $n$-point set are reflected by its
order type. We establish a complete and reliable data base
for all possible order types of size $n=10$ or less. The
data base includes a realizing point set for each order
type in small integer grid representation. To our
knowledge, no such project has been carried out before. We
substantiate the usefulness of our data base by applying it
to several problems in computational and combinatorial
geometry. Problems concerning triangulations, simple
polygonalizations, complete geometric graphs, and $k$-sets
are addressed. This list of possible applications is not
meant to be exhaustive. We believe our data base to be of
value to many researchers who wish to examine their
conjectures on small point configurations. }
}
@Article{aak-eotsp-01a,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {Enumerating Order Types for Small Point Sets with
Applications},
journal = {Order},
pages = {265--281},
volume = 19,
year = {2002},
htmlnote = {See also our order
type homepage.},
abstract = {Order types are a means to characterize the combinatorial
properties of a finite point configuration. In particular,
the crossing properties of all straight-line segments
spanned by a planar $n$-point set are reflected by its
order type. We establish a complete and reliable data base
for all possible order types of size $n=10$ or less. The
data base includes a realizing point set for each order
type in small integer grid representation. To our
knowledge, no such project has been carried out before. We
substantiate the usefulness of our data base by applying it
to several problems in computational and combinatorial
geometry. Problems concerning triangulations, simple
polygonalizations, complete geometric graphs, and $k$-sets
are addressed. This list of possible applications is not
meant to be exhaustive. We believe our data base to be of
value to many researchers who wish to examine their
conjectures on small point configurations. }
}
@Article{aak-pc-02,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {Points and Combinatorics},
journal = {Special Issue on Foundations of Information Processing of
{TELEMATIK}},
pages = {12--17},
volume = 1,
year = {2002},
address = {Graz, Austria}
}
@TechReport{aak-prcn-01,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser},
title = {Progress on rectilinear crossing numbers},
institution = {IGI-TU Graz, Austria},
year = 2002,
abstract = {Let $\overline{cr}(G)$ denote the rectilinear crossing
number of a graph $G$. We show $\overline{cr}(K_{11})=102$
and $\overline{cr}(K_{12})=153$. Despite the remarkable
hunt for the crossing number of the complete graph $K_n$,
initiated by R. Guy in the 1960s, these quantities have
been unknown for $n>10$ to date. We also establish new
upper and lower bounds on $\overline{cr}(K_{n})$ for $13
\leq n \leq 20$, along with an improved general lower bound
for $\overline{cr}(K_{n})$. The results mainly rely on
recent methods developed by the authors for exhaustively
enumerating all combinatorially inequivalent sets of points
(so-called order types). },
htmlnote = {See also our crossing
number homepage.}
}
@InProceedings{aakprsv-rsro-09,
author = {O. Aichholzer and F. Aurenhammer and B. Kornberger and S.
Plantinga and G. Rote and A. Sturm and G. Vegter},
title = {Recovering structure from $r$-sampled objects},
booktitle = {Eurographics Symposium on Geometry Processing, Computer
Graphics Forum},
volume = {28},
year = 2009,
address = {Berlin, Germany},
pages = {1349-1360},
note = {Special Issue}
}
@InProceedings{aaks-cmpt-02,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser and B.
Speckmann},
title = {Convexity Minimizes Pseudo-Triangulations},
booktitle = {Proc. $14th$ Annual Canadian Conference on Computational
Geometry CCCG 2002},
pages = {158--161},
year = 2002,
address = {Lethbridge, Alberta, Canada},
abstract = {For standard triangulations it is not known which sets of
points have the fewest or the most triangulations. In
contrast, we show that sets of points in convex position
minimize the number of minimum pseudo-triangulations. This
adds to the common belief that minimum
pseudo-triangulations are more tractable in many
respects.}
}
@Article{aaks-cmpt-03,
author = {O. Aichholzer and F. Aurenhammer and H. Krasser and B.
Speckmann},
title = {Convexity Minimizes Pseudo-Triangulations},
journal = {Computational Geometry: Theory and Applications},
volume = {28},
pages = {3--10},
year = 2004,
abstract = {The number of minimum pseudo-triangulations is minimized
for point sets in convex position.}
}
@InProceedings{aap-qpssc-02,
author = {O. Aichholzer and F. Aurenhammer and B. Palop},
title = {Quickest Paths, Straight Skeletons, and the City {V}oronoi
Diagram},
year = 2002,
booktitle = {Proc. $18^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {151--159},
address = {Barcelona, Spain},
abstract = {The city Voronoi diagram is induced by quickest paths, in
the $L_1$~plane speeded up by an isothetic transportation
network. We investigate the rich geometric and algorithmic
properties of city Voronoi diagrams, and report on their
use in processing quickest-path queries.\\ In doing so, we
revisit the fact that not every Voronoi-type diagram has
interpretations in both the distance model and the
wavefront model. Especially, straight skeletons are a
relevant example where an interpretation in the former
model is lacking. We clarify the relation between these
models, and further draw a connection to the
bisector-defined abstract Voronoi diagram model, with the
particular goal of computing the city Voronoi diagram
efficiently. }
}
@Article{aap-qpssc-03,
author = {O. Aichholzer and F. Aurenhammer and B. Palop},
title = {Quickest Paths, Straight Skeletons, and the City {V}oronoi
Diagram},
journal = {Discrete \& Computational Geometry},
volume = 31,
number = 1,
pages = {17--35},
year = {2004},
abstract = {The city Voronoi diagram is induced by quickest paths, in
the $L_1$~plane speeded up by an isothetic transportation
network. We investigate the rich geometric and algorithmic
properties of city Voronoi diagrams, and report on their
use in processing quickest-path queries.\\ In doing so, we
revisit the fact that not every Voronoi-type diagram has
interpretations in both the distance model and the
wavefront model. Especially, straight skeletons are a
relevant example where an interpretation in the former
model is lacking. We clarify the relation between these
models, and further draw a connection to the
bisector-defined abstract Voronoi diagram model, with the
particular goal of computing the city Voronoi diagram
efficiently. }
}
@InProceedings{aar-msrp-94a,
author = {O. Aichholzer and H. Alt and G. Rote},
title = {Matching Shapes with a Reference Point},
booktitle = {Proc. $10^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {85--92},
year = 1994,
address = {Stony Brook, New York, USA},
abstract = {For two given point sets, we present a very simple (almost
trivial) algorithm to translate one set so that the
Hausdorff distance between the two sets is not larger than
a constant factor times the minimum Hausdorff distance
which can be achieved in this way. The algorithm just
matches the so-called Steiner points of the two sets.\\ The
focus of our paper is the general study of reference points
(like the Steiner point) and their properties with respect
to shape matching.\\ For more general transformations than
just translations, our method eliminates several degrees of
freedom from the problem and thus yields good matchings
with improved time bounds.}
}
@InProceedings{aar-msrp-94b,
author = {O. Aichholzer and H. Alt and G. Rote},
title = {Matching Shapes with a Reference Point},
booktitle = {Proc. $10^{th}$ European Workshop on Computational
Geometry CG '94},
pages = {81--84},
year = 1994,
address = {Santander, Spain},
abstract = {For two given point sets, we present a very simple (almost
trivial) algorithm to translate one set so that the
Hausdorff distance between the two sets is not larger than
a constant factor times the minimum Hausdorff distance
which can be achieved in this way. The algorithm just
matches the so-called Steiner points of the two sets.\\ The
focus of our paper is the general study of reference points
(like the Steiner point) and their properties with respect
to shape matching.\\ For more general transformations than
just translations, our method eliminates several degrees of
freedom from the problem and thus yields good matchings
with improved time bounds.}
}
@Article{aar-msrp-97,
author = {O. Aichholzer and H. Alt and G. Rote},
title = {Matching Shapes with a Reference Point},
journal = {Int'l Journal of Computational Geometry \& Applications},
year = 1997,
volume = 7,
number = 4,
pages = {349--363},
abstract = {For two given point sets, we present a very simple (almost
trivial) algorithm to translate one set so that the
Hausdorff distance between the two sets is not larger than
a constant factor times the minimum Hausdorff distance
which can be achieved in this way. The algorithm just
matches the so-called Steiner points of the two sets.\\ The
focus of our paper is the general study of reference points
(like the Steiner point) and their properties with respect
to shape matching.\\ For more general transformations than
just translations, our method eliminates several degrees of
freedom from the problem and thus yields good matchings
with improved time bounds.}
}
@TechReport{aar-ogosa-95,
author = {O. Aichholzer and F. Aurenhammer and G. Rote},
title = {Optimal graph orientation with storage applications},
institution = {SFB 'Optimierung und Kontrolle', TU Graz, Austria},
year = 1995,
type = {SFB-Report},
number = {F003-51},
abstract = {We show that the edges of a graph with maximum edge
density $d$ can always be oriented such that each vertex
has in-degree at most $d$. Hence, for arbitrary graphs,
edges can always be assigned to incident vertices as
uniformly as possible. For example, in-degree 3 is achieved
for planar graphs. This immediately gives a space-optimal
data structure that answers edge membership queries in a
maximum edge density-$d$ graph in $O(\log d)$ time.}
}
@InProceedings{aart-tin-95,
author = {O. Aichholzer and F. Aurenhammer and G. Rote and M.
Taschwer},
title = {Triangulations intersect nicely},
booktitle = {Proc. $11^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {220--229},
year = 1995,
address = {Vancouver, Canada},
abstract = {We prove that two different triangulations of the same
planar point set always intersect in a systematic manner,
concerning both their edges and their triangles. As a
consequence, improved lower bounds on the weight of a
triangulation are obtained by solving an assignment
problem. The new bounds cover the previously known bounds
and can be computed in polynomial time. As a by-product, an
easy-to-recognize class of point sets is exhibited where
the minimum-weight triangulation coincides with the greedy
triangulation.}
}
@InProceedings{aarx-clgta-96,
author = {O. Aichholzer and F. Aurenhammer and G. Rote and Y.-F.
Xu},
title = {Constant-level greedy triangulations approximate the {MWT}
well},
booktitle = {Proc. $2^{nd}$ Int'l. Symp. Operations Research \&
Applications ISORA'96, Lecture Notes in Operations
Research},
pages = {309--318},
year = 1996,
editor = {Du, Zhang, Cheng},
volume = 2,
address = {Guilin, P. R. China},
publisher = {World Publishing Corporation},
abstract = {The well-known greedy triangulation $GT(S)$ of a finite
point set $S$ is obtained by inserting compatible edges in
increasing length order, where an edge is compatible if it
does not cross previously inserted ones. Exploiting the
concept of so-called light edges, we introduce a definition
of $GT(S)$ that does not rely on the length ordering of the
edges. Rather, it provides a decomposition of $GT(S)$ into
levels, and the number of levels allows us to bound the
total edge length of $GT(S)$. In particular, we show
$|GT(S)| \leq 3 \cdot 2^{k+1} |MWT(S)|$, where $k$ is the
number of levels and $MWT(S)$ is the minimum-weight
triangulation of $S$.}
}
@Article{aarx-clgta-99,
author = {O. Aichholzer and F. Aurenhammer and G. Rote and Y.-F.
Xu},
title = {Constant-level greedy triangulations approximate the {MWT}
well},
journal = {Journal of Combinatorial Optimization},
year = 1999,
volume = 2,
pages = {361--369},
note = {[SFB-Report F003-050, TU Graz, Austria, 1995]},
abstract = {The well-known greedy triangulation $GT(S)$ of a finite
point set $S$ is obtained by inserting compatible edges in
increasing length order, where an edge is compatible if it
does not cross previously inserted ones. Exploiting the
concept of so-called light edges, we introduce a definition
of $GT(S)$ that does not rely on the length ordering of the
edges. Rather, it provides a decomposition of $GT(S)$ into
levels, and the number of levels allows us to bound the
total edge length of $GT(S)$. In particular, we show
$|GT(S)| \leq 3 \cdot 2^{k+1} |MWT(S)|$, where $k$ is the
number of levels and $MWT(S)$ is the minimum-weight
triangulation of $S$.}
}
@InProceedings{aarx-ngta-96,
author = {O. Aichholzer and F. Aurenhammer and G. Rote and Y.-F.
Xu},
title = {New greedy triangulation algorithms},
booktitle = {Proc. $12^{th}$ European Workshop on Computational
Geometry CG '96},
pages = {11--14},
year = 1996,
address = {Muenster, Germany},
abstract = {The classical greedy triangulation (GT) of a set $S$ of
$n$ points in the plane is the triangulation obtained by
starting with the empty set (of edges) and at each step
adding the shortest compatible edge between two of the
points of $S$, where a compatible edge is defined to be an
edge that crosses none of the previously added edges. In
this paper we use the greedy method as a general concept to
compute a triangulation of a planar point set. We use
either edges or triangles as basic objects. Furthermore we
give different variants to compute the weight of the
objects, either in a static or dynamic way, leading to a
total of $156$ different greedy triangulation algorithms.
We investigate these algorithms in their quality of
approximating the MWT.}
}
@Article{aaw-afa-02,
author = {O. Aichholzer and F. Aurenhammer and T. Werner},
title = {Algorithmic Fun - {A}balone},
journal = {Special Issue on Foundations of Information Processing of
{TELEMATIK}},
pages = {4--6},
year = {2002},
volume = 1,
address = {Graz, Austria}
}
@InProceedings{abdhkkrsu-ggt-03,
author = {O. Aichholzer and D. Bremner and E.D. Demaine and F.
Hurtado and E. Kranakis and H. Krasser and S. Ramaswami and
S. Sethia and J. Urrutia},
title = {Geometric Games on Triangulations},
booktitle = {Proc. $19^{th}$ European Workshop on Computationl Geometry
CG '03 Bonn },
pages = {89--92},
year = 2003,
address = {Bonn, Germany},
abstract = {We analyze several perfect-information combinatorial games
played on planar triangulations. We describe main broad
categories of these games and provide in various situations
polynomial-time algorithms to determine who wins a given
game under optimal play, and ideally, to find a winning
strategy. Relations to relevant existing combinatorial
games, such as Kayles, are also shown.}
}
@InProceedings{abdhkkrsu-pwt-02,
author = {O. Aichholzer and D. Bremner and E.D. Demaine and F.
Hurtado and E. Kranakis and H. Krasser and S. Ramaswami and
S. Sethia and J. Urrutia},
title = {Playing with Triangulations},
booktitle = {Proc. Japan Conference on Discrete and Computational
Geometry JCDCG 2002},
pages = {46--54},
year = 2002,
address = {Tokyo, Japan},
abstract = {We analyze several perfect-information combinatorial games
played on planar triangulations. We describe main broad
categories of these games and provide in various situations
polynomial-time algorithms to determine who wins a given
game under optimal play, and ideally, to find a winning
strategy. Relations to relevant existing combinatorial
games, such as Kayles, are also shown.}
}
@InProceedings{abdhkkrsu-pwt-03,
author = {O. Aichholzer and D. Bremner and E.D. Demaine and F.
Hurtado and E. Kranakis and H. Krasser and S. Ramaswami and
S. Sethia and J. Urrutia},
title = {Playing with Triangulations},
booktitle = {Lecture Notes in Computer Science 2866, Japanese
Conference, JCDCG 2002},
pages = {22--37},
year = 2003,
abstract = {We analyze several perfect-information combinatorial games
played on planar triangulations. We introduce three broad
categories of such games constructing, transforming and
marking triangulations. In various situations, we develop
polynomial-time algorithms to determine who wins a given
game under optimal play, and to find a winning strategy.
Along the way we show connections to existing combinatorial
games, such as Kayles.}
}
@InProceedings{abdmss-lpuof-01,
author = {O. Aichholzer and D. Bremner and E.D. Demaine and D.
Meijer and V. Sacrist\'{a}n and M. Soss},
title = {Long Proteins with Unique Optimal Foldings in the H-P
Model},
booktitle = {Proc. $17^{th}$ European Workshop on Computational
Geometry CG '2001},
pages = {59--62},
year = 2001,
address = {Berlin, Germany},
abstract = {We explore a problem suggested by Brian Hayes in 1998:
what proteins in the two-dimensional
hydrophilic-hydrophobic (H-P) model have {\it unique}
optimal foldings? In particular, we prove that there are
closed chains of monomers (amino acids) with this property
for all (even) lengths; and that there are open monomer
chains with this property fo all lengths divisible by four.
Along the way, we prove and conjecture several results
about bonds in the H-P model.}
}
@Article{abdmss-lpuof-02,
author = {O. Aichholzer and D. Bremner and E.D. Demaine and D.
Meijer and V. Sacrist\'{a}n and M. Soss},
title = {Long Proteins with Unique Optimal Foldings in the H-P
Model},
journal = {Computational Geometry: Theory and Applications},
year = 2003,
pages = {139--159},
volume = {25},
abstract = {It is widely accepted that (1) the natural or folded state
of proteins is a global energy minimum, and (2) in most
cases proteins fold to a unique state determined by their
amino acid sequence. The H-P (hydrophobic-hydrophilic)
model is a simple combinatorial model designed to answer
qualitative questions about the protein folding process. In
this paper we consider a problem suggested by Brian Hayes
in 1998: what proteins in the two-dimensional H-P model
have \emph{unique} optimal (minimum energy) foldings? In
particular, we prove that there are closed chains of
monomers (amino acids) with this property for all (even)
lengths; and that there are open monomer chains with this
property for all lengths divisible by four.}
}
@Article{acbfs-nsmabp-2002,
author = {P. Auer and N. Cesa-Bianchi and Y. Freund and R. E.
Schapire },
title = {The Nonstochastic Multiarmed Bandit Problem},
journal = {SIAM Journal on Computing},
year = {2002},
volume = {32},
number = {1},
pages = {48--77},
note = {A preliminary version has appeared in {\em Proceedings of
the 36th Annual Symposium on Foundations of Computer
Science}}
}
@Article{acbg-ascolla-2003,
author = {P. Auer and N. Cesa-Bianchi and C. Gentile},
title = {Adaptive and Self-Confident On-Line Learning Algorithms},
journal = {JCSS},
year = {2002},
volume = {64},
number = {1},
pages = {48--75},
note = {A preliminary version has appeared in {\em Proc. 13th Ann.
Conf. Computational Learning Theory}}
}
@InProceedings{acddemoprt-fp-00a,
author = {O. Aichholzer and C. Cort\'{e}s and E.D. Demaine and V.
Dujmovi\'{c} and J. Erickson and H. Meijer and M. Overmars
and B. Palop and S. Ramaswami and G.T. Toussaint},
title = {Flipturning Polygons},
booktitle = {Proc. Japan Conference on Discrete and Computational
Geometry JCDCG 2000},
year = 2000,
address = {Tokay University, Tokyo, Japan},
htmlnote = {See also Jeff'shomepage
about this paper.},
abstract = {A flipturn is an operation that transforms a nonconvex
simple polygon into another simple polygon, by rotating a
concavity 180 degrees around the midpoint of its bounding
convex hull edge. Joss and Shannon proved in 1973 that a
sequence of flipturns eventually transforms any simple
polygon into a convex polygon. This paper describes several
new results about such flipturn sequences. We show that any
orthogonal polygon is convexified after at most $n-5$
arbitrary flipturns, or at most $5(n-4)/6$ well-chosen
flipturns, improving the previously best upper bound of
$(n-1)!/2$. We also show that any simple polygon can be
convexified by at most $n^2-4n+1$ flipturns, generalizing
earlier results of Ahn et al. These bounds depend
critically on how degenerate cases are handled; we
carefully explore several possibilities. We describe how to
maintain both a simple polygon and its convex hull in
$O(\log^4 n)$ time per flipturn, using a data structure of
size $O(n)$. We show that although flipturn sequences for
the same polygon can have very different lengths, the shape
and position of the final convex polygon is the same for
all sequences and can be computed in $O(n \log n)$ time.
Finally, we demonstrate that finding the longest
convexifying flipturn sequence of a simple polygon is
NP-hard.}
}
@Article{acddemoprt-fp-00b,
author = {O. Aichholzer and C. Cort\'{e}s and E.D. Demaine and V.
Dujmovi\'{c} and J. Erickson and H. Meijer and M. Overmars
and B. Palop and S. Ramaswami and G.T. Toussaint},
title = {Flipturning Polygons},
journal = {Discrete \& Computational Geometry},
year = 2002,
pages = {231--253},
volume = {28},
note = {[Report UU-CS-2000-31, Universiteit Utrecht, The
Netherlands, 2000]},
htmlnote = {See also Jeff'shomepage
about this paper.},
abstract = {A flipturn is an operation that transforms a nonconvex
simple polygon into another simple polygon, by rotating a
concavity 180 degrees around the midpoint of its bounding
convex hull edge. Joss and Shannon proved in 1973 that a
sequence of flipturns eventually transforms any simple
polygon into a convex polygon. This paper describes several
new results about such flipturn sequences. We show that any
orthogonal polygon is convexified after at most $n-5$
arbitrary flipturns, or at most $5(n-4)/6$ well-chosen
flipturns, improving the previously best upper bound of
$(n-1)!/2$. We also show that any simple polygon can be
convexified by at most $n^2-4n+1$ flipturns, generalizing
earlier results of Ahn et al. These bounds depend
critically on how degenerate cases are handled; we
carefully explore several possibilities. We describe how to
maintain both a simple polygon and its convex hull in
$O(\log^4 n)$ time per flipturn, using a data structure of
size $O(n)$. We show that although flipturn sequences for
the same polygon can have very different lengths, the shape
and position of the final convex polygon is the same for
all sequences and can be computed in $O(n \log n)$ time.
Finally, we demonstrate that finding the longest
convexifying flipturn sequence of a simple polygon is
NP-hard.}
}
@Article{acf-ftamabp-02,
author = {P. Auer and N. Cesa-Bianchi and P. Fischer},
title = {Finite Time Analysis of the Multiarmed Bandit Problem},
journal = {Machine Learning},
year = {2002},
volume = {47},
number = {2/3},
pages = {235--256},
note = {A preliminary version has appeared in {\em Proc. of the
15th International Conference on Machine Learning}}
}
@InProceedings{acf-ftamabp-99,
author = {P. Auer and N. Cesa-Bianchi and P. Fischer},
title = {Finite Time Analysis of the Multiarmed Bandit Problem},
booktitle = {IT Workshop on Decision, Estimation, Classification and
Imaging},
year = {1999},
optorganization={},
optpublisher = {},
address = {Santa Fe},
month = {Feb}
}
@InProceedings{adehost-rcp-00a,
author = {O. Aichholzer and E.D. Demaine and J. Erickson and F.
Hurtado and M. Overmars and M.A. Soss and G.T. Toussaint},
title = {Reconfiguring Convex Polygons},
booktitle = {Proc. $12th$ Annual Canadian Conference on Computational
Geometry CCCG 2000},
pages = {17--20},
year = 2000,
address = {Fredericton, New Brunswick, Canada},
abstract = {We prove that there is a motion from any convex polygon to
any convex polygon with the same counterclockwise sequence
of edge lengths, that preserves the lengths of the edges,
and keeps the polygon convex at all times. Furthermore, the
motion is ``direct'' (avoiding any intermediate canonical
configuration like a subdivided triangle) in the sense that
each angle changes monotonically throughout the motion. In
contrast, we show that it is impossible to achieve such a
result with each vertex-to-vertex distance changing
monotonically.}
}
@Article{adehost-rcp-00b,
author = {O. Aichholzer and E.D. Demaine and J. Erickson and F.
Hurtado and M. Overmars and M.A. Soss and G.T. Toussaint},
title = {Reconfiguring Convex Polygons},
journal = {Computational Geometry: Theory and Applications},
year = 2001,
pages = {85--95},
volume = 20,
note = {[Report UU-CS-2000-30, Universiteit Utrecht, The
Netherlands, 2000]},
abstract = {We prove that there is a motion from any convex polygon to
any convex polygon with the same counterclockwise sequence
of edge lengths, that preserves the lengths of the edges,
and keeps the polygon convex at all times. Furthermore, the
motion is ``direct'' (avoiding any intermediate canonical
configuration like a subdivided triangle) in the sense that
each angle changes monotonically throughout the motion. In
contrast, we show that it is impossible to achieve such a
result with each vertex-to-vertex distance changing
monotonically. We also demonstrate that there is a motion
between any two such polygons using three-dimensional moves
known as pivots, although the complexity of the motion
cannot be bounded as a function of the number of vertices
in the polygon.}
}
@Article{adk-flsvd-06,
author = {F. Aurenhammer and R.L.S.Drysdale and H. Krasser},
title = {Farthest line segment {V}oronoi diagrams},
journal = {Information Processing Letters},
year = 2006,
pages = {220--225},
volume = {100},
abstract = {The farthest line segment Voronoi diagram shows properties
different from both the closest-segment Voronoi diagram and
the farthest-point Voronoi diagram. Surprisingly, this
structure did not receive attention in the computational
geometry literature. We analyze its combinatorial and
topological properties and outline an $O(n \log n)$ time
construction algorithm that is easy to implement. No
restrictions are placed upon the~$n$ input line segments;
they are allowed to touch or cross.}
}
@TechReport{adr-sltgt-95,
author = {O. Aichholzer and R.L.S. Drysdale and G. Rote},
title = {A Simple Linear Time Greedy Triangulation Algorithm for
Uniformly Distributed Points},
institution = {TU Graz, Austria},
year = 1995,
type = {IIG-Report-Series},
number = {408},
note = {Presented at the Workshop on Computational Geometry, Army
MSI Cornell, Stony Brook, 1994},
abstract = {The greedy triangulation (GT) of a set $S$ of $n$ points
in the plane is the triangulation obtained by starting with
the empty set and at each step adding the shortest
compatible edge between two of the points, where a
compatible edge is defined to be an edge that crosses none
of the previously added edges. In this paper we present a
simple, practical algorithm that computes the greedy
triangulation in expected time $O(n)$ and space $O(n)$, for
$n$ points drawn independently from a uniform distribution
over some fixed convex shape.\\ This algorithm is an
improvement of the $O(n \log n)$ algorithm of Dickerson,
Drysdale, McElfresh, and Welzl. It uses their basic
approach, but generates only $O(n)$ plausible greedy edges
instead of $O(n \log n)$. It uses some ideas similar to
those presented in Levcopoulos and Lingas's $O(n)$ expected
time algorithm. Since we use more knowledge about the
structure of a random point set and its greedy
triangulation, our algorithm needs only elementary data
structures and simple bucketing techniques. Thus it is a
good deal simpler to explain and to implement than the
algorithm of Levcopoulos and Lingas. }
}
@InProceedings{ads-ccq-08,
author = {F. Aurenhammer and M. Demuth and T. Schiffer},
title = {Computing convex quadrangulations},
booktitle = {Proc. 5th Ann. Int. Symp. Voronoi Diagrams in Science and
Engineering, Voronoi's Impact on Modern Science},
year = 2008,
address = {Kiev, Ukraine},
volume = 4,
pages = {32--43},
abstract = {We use projected Delaunay tetrahedra and a maximum
independent set approach to compute large subsets of convex
quadrangulations on a given set of points in the plane. The
new method improves over the popular pairing method based
on triangulating the point set.}
}
@Article{sad-ccq-11,
author = {T. Schiffer and F. Aurenhammer and M. Demuth},
title = {Computing convex quadrangulations},
journal = {Discrete Applied Mathematics},
year = 2011,
volume = {x},
pages = {xxx--yyy},
abstract = {We use projected Delaunay tetrahedra and a maximum
independent set approach to compute large subsets of convex
quadrangulations on a given set of points in the plane. The
new method improves over the popular pairing method based
on triangulating the point set.}
}
@Article{ae-oacwv-84,
author = {F. Aurenhammer and H. Edelsbrunner},
title = {An optimal algorithm for constructing the weighted
{V}oronoi diagram in the plane},
journal = {Pattern Recognition},
year = 1984,
volume = 17,
number = 2,
pages = {251--257},
note = {[IIG-Report-Series F109, TU Graz, Austria, 1983]},
abstract = {Let $S$ denote a set of $n$ points in the plane such that
each point $p$ has assigned a positive weight $w(p)$ which
expresses its capability to influence its neighborhood. In
this sense, the weighted distance of an arbitrary point $x$
from $p$ is gived by $d_e(x,p)/w(p)$, where $d_e$ denotes
the Euclidean distance function. The weighted Voronoi
diagram for $S$ is a subdivision of the plane such that
each point $p$ in $S$ is associated with a region
consisting of all points $x$ in the plane for which $p$ is
a weighted nearest point of $S$. An algorithm which
constructs the weighted Voronoi diagram for $S$ in $O(n^2)$
time is outlined in this paper. The method is optimal as
the diagram can consist of $\Theta(n^2)$ faces, edges, and
vertices.}
}
@Article{afisw-fiepc-94,
author = {F. Aurenhammer and M. Formann and R. Idury and A.
Schaeffer and F. Wagner},
title = {Faster isometric embedding in products of complete
graphs},
journal = {Discrete Applied Mathematics},
year = 1994,
volume = 52,
pages = {17--28},
note = {[Report B-90-06, FU Berlin, Germany, 1990]},
abstract = {An isometric embedding of a connected graph $G$ into a
cartesian product of complete graphs is equivalent to a
labeling of each vertex of $G$ by a string of fixed length
such that the distance in $G$ between two vertices is equal
to the Hamming distance between their labels. We give a
simple $O(D(m,n)+n^{2})$-time algorithm for deciding if $G$
admits such an embedding, and for labeling $G$ if one
exists, where $D(m,n)$ is the time needed to compute the
all-pairs distance matrix of a graph with $m$ edges and $n$
vertices. If the distance matrix is part of the input, our
algorithm runs in $O(n^{2})$ time. We also show that an
$n$-vertex subgraph of $(K_{a})^{d}$, the cartesian product
of $d$ equal-sized complete graphs, cannot have more than
$\frac{a-1}{2}n\log_a n$ edges. With this result our
algorithm can be used to decide whether a graph $G$ is an
$a$-ary Hamming graph in $O(n^2\log n)$ time (for fixed
$a$).}
}
@InProceedings{ag-asola-00,
author = {P. Auer and C. Gentile},
title = {Adaptive and Self-Confident On-Line Learning Algorithms},
booktitle = {Proc. 13th Ann. Conf. Computational Learning Theory},
year = {2000},
pages = {107--117},
publisher = {Morgan Kaufmann}
}
@InProceedings{ah-ceceg-89,
author = {F. Aurenhammer and J. Hagauer},
title = {Computing equivalence classes among the edges of a graph
with applications},
booktitle = {Proc. Int'l Conf. Algebraic Graph Theory},
year = 1989,
pages = {11},
address = {Leibnitz, Austria},
abstract = {For two edges $e=(x,y)$ and $e'=(x',y')$ of a connected
graph $G=(V,E)$ let $e \Theta e'$ iff $d(x,x') + d(y,y')
\neq d(x,y') + d(x',y)$. Here $d(x,y)$ denotes the length
of a shortest path in $G$ joining vertices $x$ and $y$. An
algorithm is presented that computes the equivalence
classes induced on $E$ by the transitive closure
$\hat{\Theta}$ of $\Theta$ in time $O(|V||E|)$ and space
$O(|V|^2)$. Finding the equivalence classes of
$\hat{\Theta}$ is the primary step of several graph algorithms.}
}
@Article{ah-ceceg-92,
author = {F. Aurenhammer and J. Hagauer},
title = {Computing equivalence classes among the edges of a graph
with applications},
journal = {Discrete Mathematics},
year = 1992,
volume = 109,
pages = {3--12},
note = {Special Issue. [IIG-Report-Series 271, TU Graz, Austria,
1989]},
abstract = {For two edges $e=(x,y)$ and $e'=(x',y')$ of a connected
graph $G=(V,E)$ let $e \Theta e'$ iff $d(x,x') + d(y,y')
\neq d(x,y') + d(x',y)$. Here $d(x,y)$ denotes the length
of a shortest path in $G$ joining vertices $x$ and $y$. An
algorithm is presented that computes the equivalence
classes induced on $E$ by the transitive closure
$\hat{\Theta}$ of $\Theta$ in time $O(|V||E|)$ and space
$O(|V|^2)$. Finding the equivalence classes of
$\hat{\Theta}$ is the primary step of several graph algorithms.}
}
@InProceedings{ah-fmmrr-93,
author = {O. Aichholzer and H. Hassler},
title = {A fast method for modulus reduction in Residue Number
System},
booktitle = {Proc. epp'93},
pages = {41--54},
year = 1993,
address = {Vienna, Austria},
note = {[IIG-Report-Series 312, TU Graz, Austria, 1991]},
abstract = {Over the last three decades there has been considerable
interest in the implementation of digital computer elements
using hardware based on the residue number system. We
propose a technique to compute a residue in this number
system using a parallel network. Our technique enables
scaling, to. We improve a former result of $O(n)$ cycles to
$O(\log n)$, where $n$ is the number of moduli. The
hardware expense is the same, $O(n^2)$. Further advantages
are that scaling factors can be chosen almost freely
allowing scaling with radix $2$. Negative numbers are
covered as well, requiring no additional effort.
Applications are RSA encryption and scaling.}
}
@InProceedings{ah-rbhgo-91,
author = {F. Aurenhammer and J. Hagauer},
title = {Recognizing binary {H}amming graphs in {$O(n^{2} \log n)$}
time},
booktitle = {Proc. $16^{th}$ Int'l Workshop on Graph-Theoretical
Concepts in Computer Science, Lecture Notes in Computer
Science},
pages = {90--98},
year = 1991,
volume = 484,
address = {Berlin, Germany},
publisher = {Springer Verlag},
abstract = {A graph $G$ is called a binary Hamming graph if each
vertex of $G$ can be assigned a binary address of fixed
length such that the Hamming distance between two addresses
equals the length of a shortest path between the
corresponding vertices. It is shown that $O(n^2 \log n)$
time suffices for deciding whether a given $n$-vertex graph
$G$ is a binary Hamming graph, and for computing a valid
addressing scheme for $G$ provided its existence. This is
not far from being optimal as $n$ addresses of length $n-1$
have to be computed in the worst case.}
}
@Article{ah-rbhgo-95,
author = {F. Aurenhammer and J. Hagauer},
title = {Recognizing binary {H}amming graphs in {$O(n^{2} \log n)$}
time},
journal = {Mathematical Systems Theory},
year = 1995,
volume = 28,
pages = {387--395},
note = {[IIG-Report-Series 273, TU Graz, Austria, 1989]},
abstract = {A graph $G$ is called a binary Hamming graph if each
vertex of $G$ can be assigned a binary address of fixed
length such that the Hamming distance between two addresses
equals the length of a shortest path between the
corresponding vertices. It is shown that $O(n^2 \log n)$
time suffices for deciding whether a given $n$-vertex graph
$G$ is a binary Hamming graph, and for computing a valid
addressing scheme for $G$ provided its existence. This is
not far from being optimal as $n$ addresses of length $n-1$
have to be computed in the worst case.}
}
@InProceedings{aha-lsp-92,
author = {F. Aurenhammer and F. Hoffmann and B. Aronov},
title = {Least-squares partitioning},
booktitle = {Proc. $8^{th}$ European Workshop on Computational Geometry
CG '92},
pages = {55--57},
year = 1992,
address = {Utrecht, the Netherlands}
}
@InProceedings{aha-mttls-92,
author = {F. Aurenhammer and F. Hoffmann and B. Aronov},
title = {{M}inkowski-type theorems and least-squares partitioning},
booktitle = {Proc. $8^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {350--357},
year = 1992,
address = {Berlin, Germany},
note = {[Report B-92-09, FU Berlin, Germany, 1992]},
abstract = {The power diagram of $n$ weighted sites partitions a given
$m$-point set into clusters, one cluster for each region of
the diagram. In this way, an assignment of points to sites
is induced. We show the equivalence of such assignments to
constrained Euclidean least-squares assignments. As a
corollary, there always exists a power diagram whose
regions partition a given $d$-dimensional $m$-point set
into clusters of prescribed sizes, no matter where the
sites are placed. Another consequence is that least-squares
assignments can be computed by finding suitable weights for
the sites. In the plane, this takes roughly $O(n^2m)$ time
and optimal space $O(m)$, which improves on previous
methods. We further show that a constrained least-squares
assignment can be computed by solving a particular linear
program in $n+1$ dimensions. This leads to an algorithm for
iteratively improving the weights. Aside from the obvious
application, least-squares assignments are shown to be
useful in solving a certain transportation problem, and in
finding least-squares fittings where translation and
scaling are allowed. Finally, we extend the concept of a
constrained least-squares assignment to continuous point
sets, thereby obtaining results on power diagrams with
prescribed region volumes that are related to Minkowski's
theorem for convex polytopes.}
}
@Article{aha-mttls-98,
author = {F. Aurenhammer and F. Hoffmann and B. Aronov},
title = {{M}inkowski-type theorems and least-squares clustering},
journal = {Algorithmica},
year = 1998,
volume = 20,
pages = {61--76},
note = {[SFB Report F003-075, TU Graz, Austria, 1996]},
abstract = {Dissecting Euclidean $d$-space with the power diagram of
$n$ weighted point sites partitions a given $m$-point set
into clusters, one cluster for each region of the diagram.
In this manner, an assignment of points to sites is
induced. We show the equivalence of such assignments to
constrained Euclidean least-squares assignments. As a
corollary, there always exists a power diagram whose
regions partition a given $d$-dimensional $m$-point set
into clusters of prescribed sizes, no matter where the
sites are placed. Another consequence is that constrained
least-squares assignments can be computed by finding
suitable weights for the sites. In the plane, this takes
roughly $O(n^2m)$ time and optimal space $O(m)$, which
improves on previous methods. We further show that a
constrained least-squares assignment can be computed by
solving a specially structured linear program in $n+1$
dimensions. This leads to an algorithm for iteratively
improving the weights, based on the gradient-descent
method. Besides having the obvious optimization property,
least-squares assignments are shown to be useful in solving
a certain transportation problem, and in finding a
least-squares fitting of two point sets where translation
and scaling are allowed. Finally, we extend the concept of
a constrained least-squares assignment to continuous
distributions of points, thereby obtaining existence
results for power diagrams with prescribed region volumes.
These results are related to Minkowski's theorem for convex
polytopes. The aforementioned iterative method for
approximating the desired power diagram applies to
continuous distributions as well.}
}
@Article{ahi-cgflc-92,
author = {F. Aurenhammer and J. Hagauer and W. Imrich},
title = {{C}artesian graph factorization at logarithmic cost per
edge},
journal = {Computational Complexity},
year = 1992,
volume = 2,
pages = {331--349},
abstract = {Let $G$ be a connected graph with $n$ vertices and $m$
edges. We develop an algorithm that finds the prime factors
of $G$ with respect to Cartesian multiplication in $O(m
\log n)$ time and $O(m)$ space. This shows that factoring
$G$ is at most as costly as sorting its edges. The
algorithm gains its efficiency and practicality from using
only basic properties of product graphs and simple data
structures.}
}
@InProceedings{ahi-fcpgl-90,
author = {F. Aurenhammer and J. Hagauer and W. Imrich},
title = {Factoring {C}artesian-product graphs at logarithmic cost
per edge},
booktitle = {Proc. MPS Conf. Integer Programming and Combinatorial
Optimization IPCO'90},
pages = {29--44},
year = 1990,
address = {Waterloo, Canada},
note = {[IIG-Report-Series 287, TU Graz, Austria, 1990]},
abstract = {Let $G$ be a connected graph with $n$ vertices and $m$
edges. We develop an algorithm that finds the prime factors
of $G$ with respect to Cartesian multiplication in $O(m
\log n)$ time and $O(m)$ space. This shows that factoring
$G$ is at most as costly as sorting its edges. The
algorithm gains its efficiency and practicality from using
only basic properties of product graphs and simple data
structures.}
}
@InProceedings{ahk-twpst-04,
author = {O. Aichholzer and C. Huemer and H. Krasser},
title = {Triangulations Without Pointed Spanning Trees - Extended
Abstract},
booktitle = {Proc. $20^{th}$ European Workshop on Computational
Geometry EWCG '04},
year = 2004,
pages = {221--224},
address = {Sevilla, Spain},
abstract = {Problem $50$ in the Open Problems Project~\cite{OPP} asks
whether any triangulation on a point set in the plane
contains a pointed spanning tree as a subgraph. We provide
a counterexample. As a consequence we show that there exist
triangulations which require a linear number of edge flips
to become Hamiltonian. }
}
@Article{ahn-lbntp-04,
author = {O. Aichholzer and F. Hurtado and M. Noy},
title = {A Lower Bound on the Number of Triangulations of Planar
Point Sets},
year = 2004,
journal = {Computational Geometry: Theory and Applications},
volume = {29},
number = {2},
pages = {135--145},
htmlnote = {See also the Counting
Triangulations - Olympics.},
abstract = {We show that the number of straight-edge triangulations
exhibited by any set of $n$ points in general position in
the plane is bounded from below by $\Omega(2.33^n)$.}
}
@InProceedings{ahn-ntepp-01,
author = {O. Aichholzer and F. Hurtado and M. Noy},
title = {On the Number of Triangulations Every Planar Point Set
Must Have},
booktitle = {Proc. $13th$ Annual Canadian Conference on Computational
Geometry CCCG 2001},
pages = {13--16},
year = 2001,
address = {Waterloo, Ontario, Canada},
htmlnote = {See also the Counting
Triangulations - Olympics.},
abstract = {We show that the number of straight line triangulations
exhibited by any set of $n$ points in general position in
the plane is bounded from below by
$\Omega((2+\varepsilon)^n)$ for some $\varepsilon > 0$. To
the knowledge of the authors this is the first non-trivial
lower bound.}
}
@InProceedings{ahst-dbcpt-03,
author = {O. Aichholzer and M. Hoffmann and B. Speckmann and C. D.
T\'oth},
title = {Degree Bounds for Constrained Pseudo-Triangulations},
booktitle = {Proc. $15th$ Annual Canadian Conference on Computational
Geometry CCCG 2003},
pages = {155--158},
year = 2003,
address = {Halifax, Nova Scotia, Canada},
abstract = {We introduce the concept of a constrained pointed
pseudo-triangulation $\mathcal{T}_G$ of a point set $S$
with respect to a pointed planar straight line graph $G =
(S, E)$. For the case that $G$ forms a simple polygon $P$
with vertex set $S$ we give tight bounds on the vertex
degree of $\mathcal{T}_G$. }
}
@InProceedings{ai-gravd-87,
author = {F. Aurenhammer and H. Imai},
title = {Geometric relations among {V}oronoi diagrams},
booktitle = {Proc. $4^{th}$ Ann. STACS, Lecture Notes in Computer
Science},
pages = {53--65},
year = 1987,
volume = 247,
address = {Passau, Germany},
publisher = {Springer Verlag},
abstract = {Two general classes of Voronoi diagrams are introduced
and, along with their modifications to higher order, are
shown to be geometrically related. This geometric
background, on the one hand, serves to analyze the size and
the combinatorial structure, and on the other hand, implies
general and efficient methods of construction, for various
important types of Voronoi diagrams considered in the
literature.}
}
@Article{ai-grvd-88,
author = {F. Aurenhammer and H. Imai},
title = {Geometric relations among {V}oronoi diagrams},
journal = {Geometriae Dedicata},
year = 1988,
volume = 27,
pages = {65--75},
note = {[IIG-Report-Series 228, TU Graz, Austria, 1986]},
abstract = {Two general classes of Voronoi diagrams are introduced
and, along with their modifications to higher order, are
shown to be geometrically related. This geometric
background, on the one hand, serves to analyze the size and
the combinatorial structure, and on the other hand, implies
general and efficient methods of construction, for various
important types of Voronoi diagrams considered in the
literature.}
}
@Article{ak-psclcf-06,
author = {F. Aurenhammer and H. Krasser},
title = {Pseudo-simplicial complexes from maximal locally convex
functions},
journal = {Discrete \& Computional Geometry},
year = 2006,
pages = {201--221},
volume = 35,
abstract = {We introduce and discuss pseudo-simplicial complexes
in~$R^d$ as generalizations of pseudo-triangulations
in~$R^2$. Our approach is based on the concept of maximal
locally convex functions on polytopal domains.}
}
@InProceedings{ak-psotd-01,
author = {O. Aichholzer and H. Krasser},
title = {The Point Set Order Type Data Base: A Collection of
Applications and Results},
booktitle = {Proc. $13th$ Annual Canadian Conference on Computational
Geometry CCCG 2001},
pages = {17--20},
year = 2001,
address = {Waterloo, Ontario, Canada},
htmlnote = {See also our order
type homepage.},
abstract = {Order types are a common tool to provide the combinatorial
structure of point sets in the plane. For many problems in
combinatorial and computational geometry only the order
type of the underlying point set has to be considered.
Recently a complete order type data base of $n$-point sets
has been developed for $n\leq 10$, which gives a way to
examine the combinatorial properties of all possible point
sets for fixed size $n$. Based on this result we present
applications and results for problems concerning
intersection properties, convexity, crossing-free straight
line graphs, and others, thus confirming or disproving
several conjectures on these topics. Besides providing
concrete results the aim of this work is to stimulate
further research by revealing structural relations of
extreme examples for $17$ geometrical and combinatorial
problems.}
}
@InProceedings{ak-ptc-05,
author = {F. Aurenhammer and H. Krasser},
title = {Pseudo-tetrahedral complexes},
booktitle = {Proc. $21^{st}$ European Workshop on Computational
Geometry EuroCG '05},
pages = {85--88},
year = 2005,
address = {Eindhoven, The Netherlands},
abstract = {Pseudo-triangulations are interesting and flexible
generalizations of triangulations that have found their
place in computational geometry. Unlike triangulations,
pseudo-triangulations eluded a meaningful generalization to
higher dimensions so far. In this paper, we define
pseudo-simplices and pseudo-simplicial complexes in d-space
in a way consistent to pseudo-triangulations in the plane.
Flip operations in pseudo-complexes are specified, as
combinations of flips in pseudo-triangulations, and of
bistellar flips in simplicial complexes. Our results are
based on the concept of maximal locally convex functions on
polyhedral domains, that allows us to unify several
well-known structures, namely pseudo-triangulations,
constrained Delaunay triangulations, and regular simplicial
complexes.}
}
@InCollection{ak-vd-00,
author = {F. Aurenhammer and R. Klein},
title = {{V}oronoi diagrams},
booktitle = {Handbook of Computational Geometry, Chapter V},
pages = {201--290},
publisher = {Elsevier Science Publishing},
year = 2000,
editor = {J. Sack and G. Urrutia},
note = {[SFB Report F003-092, TU Graz, Austria, 1996]},
abstract = {The topic of this chapter -- Voronoi diagrams -- differs
from other areas of computational geometry, in that its
origin dates back to the 17th century. In his book on the
principles of philosophy, R.~Descartes' illustrations show
a decomposition of space into convex regions, whose
underlying idea seems to be that of a Voronoi diagram. This
concept has independently emerged, and proven useful, in
various fields of science. Different names particular to
the respective field have been used, such as {\em medial
axis transform\/} in biology and physiology, {\em
Wigner-Seitz zones\/} in chemistry and physics, {\em
domains of action\/} in crystallography, and {\em Thiessen
polygons\/} in metereology and geography. The
mathematicians Dirichlet and Voronoi were the first to
formally introduce this concept. The resulting structure
has been called {\em Dirichlet tessellation\/} or {\em
Voronoi diagram\/}, which has become its standard name
today. Voronoi was the first to consider the {\em dual\/}
of this structure, where any two point sites are connected
whose regions have a boundary in common. Later, Delaunay
obtained the same by defining that two point sites are
connected if and only if they lie on a circle whose
interior contains no other point site. After him, the dual
of the Voronoi diagram has been denoted {\em Delaunay
tessellation\/} or {\em Delaunay triangulation\/}. Besides
its applications in other fields of science, the Voronoi
diagram and its dual can be used for solving numerous, and
surprisingly different, geometric problems. Moreover, these
structures are very appealing, and a lot of research has
been devoted to their study (about one out of 16 papers in
computational geometry), ever since Shamos and Hoey
introduced them to the field. Within one chapter, we cannot
review all known results and applications. Instead, we are
trying to highlight the intrinsic potential of Voronoi
diagrams, that lies in its structural properties, in the
existence of efficient algorithms for its construction, and
in its adaptability.}
}
@Article{akkox-autmp-00a,
author = {F. Aurenhammer and N. Katoh and H. Kojima and M. Ohsaki
and Y.-F. Xu},
title = {Approximating uniform triangular meshes in polygons},
journal = {Theoretical Computer Science},
year = 2002,
volume = 289,
pages = {879--895},
note = {Special Issue. [SFB Report F003-159, TU Graz, Austria,
1999]},
abstract = {We consider the problem of triangulating a convex polygon
using $n$ Steiner points under the following optimality
criteria: (1) minimizing the overall edge length ratio, (2)
minimizing the maximum edge length, and (3) minimizing the
maximum triangle perimeter. We establish a relation of
these problems to a certain extreme packing problem. Based
on this relationship, we develop a heuristic producing
constant approximations for all the optimality criteria
above (provided $n$ is chosen sufficiently large). That is,
the produced triangular mesh is {\em uniform} in these
respects. The method is easy to implement and runs in
$O(n^2 \log n)$ time and $O(n)$ space. The observed runtime
is much less. Moreover, for criterion (1) the method works
-- within the same complexity and approximation bounds --
for {\em arbitrary} polygons with possible holes, and for
criteria (2) and (3) it does so for a large subclass.}
}
@InProceedings{akkox-autmp-00b,
author = {F. Aurenhammer and N. Katoh and H. Kojima and M. Ohsaki
and Y.-F. Xu},
title = {Approximating uniform triangular meshes in polygons},
booktitle = {Proc. $6^{th}$ Ann. Intl. Computing and Combinatorics
Conference, Lecture Notes in Computer Science},
pages = {23--33},
year = 2000,
volume = {1558},
address = {Sydney, Australia},
publisher = {Springer Verlag},
abstract = {We consider the problem of triangulating a convex polygon
using $n$ Steiner points under the following optimality
criteria: (1) minimizing the overall edge length ratio, (2)
minimizing the maximum edge length, and (3) minimizing the
maximum triangle perimeter. We establish a relation of
these problems to a certain extreme packing problem. Based
on this relationship, we develop a heuristic producing
constant approximations for all the optimality criteria
above (provided $n$ is chosen sufficiently large). That is,
the produced triangular mesh is {\em uniform} in these
respects. The method is easy to implement and runs in
$O(n^2 \log n)$ time and $O(n)$ space. The observed runtime
is much less. Moreover, for criterion (1) the method works
-- within the same complexity and approximation bounds --
for {\em arbitrary} polygons with possible holes, and for
criteria (2) and (3) it does so for a large subclass.}
}
@Article{aksb-isve-2002,
author = {K. Andrews and W. Kienreich and V. Sabol and J. Becker and
G. Droschl and F. Kappe and M. Granitzer and P. Auer and K.
Tochtermann},
title = {The {InfoSky} visual explorer: exploiting hierarchical
structure and document similarities},
journal = {Information Visualization},
year = {2002},
volume = {1},
pages = {166--181}
}
@InProceedings{aoss-nptcp-03,
author = {O. Aichholzer and D. Orden and F. Santos and B.
Speckmann},
title = {On the Number of Pseudo-Triangulations of Certain Point
Sets},
booktitle = {Proc. $15th$ Annual Canadian Conference on Computational
Geometry CCCG 2003},
pages = {141--144},
year = 2003,
address = {Halifax, Nova Scotia, Canada},
abstract = {We compute the exact number of pseudo-triangulations for
two prominent point sets, namely the so-called double
circle and the double chain. We also derive a new
asymptotic lower bound for the maximal number of
pseudo-triangulations which lies significantly above the
related bound for triangulations. }
}
@InProceedings{aoss-nptcp-04,
author = {O. Aichholzer and D. Orden and F. Santos and B.
Speckmann},
title = {On the Number of Pseudo-Triangulations of Certain Point
Sets},
booktitle = {Proc. $20^{th}$ European Workshop on Computational
Geometry EWCG '04},
year = 2004,
pages = {119--122},
address = {Sevilla, Spain},
abstract = {We compute the exact number of pseudo-triangulations for
two prominent point sets, namely the so-called double
circle and the double chain. We also derive a new
asymptotic lower bound for the maximal number of
pseudo-triangulations which lies significantly above the
related bound for triangulations. }
}
@InProceedings{appw-vdos-07,
author = {F. Aurenhammer and M. Peternell and H. Pottmann and J.
Wallner},
title = {Voronoi Diagrams for Oriented Spheres},
booktitle = {Proc. 4th Int. Symp. on Voronoi Diagrams in Science and
Engineering, ISVD'07},
year = 2007,
pages = {33--37},
address = {Pontypridd, UK},
abstract = {We consider finite sets of oriented spheres in (k-1)-space
and, by interpreting such spheres as points in k-space,
study the Voronoi diagrams they induce for several variants
of distance between spheres. We give bounds on the
combinatorial complexity of these diagrams in the plane and
in 3-space, and derive properties useful for constructing
them. Our results are motivated by applications to special
relativity theory.}
}
@InProceedings{ar-qdbsb-04,
author = {O. Aichholzer and K. Reinhardt},
title = {A quadratic distance bound on sliding between
crossing-free spanning trees - Extended Abstract},
booktitle = {Proc. $20^{th}$ European Workshop on Computational
Geometry EWCG '04},
year = 2004,
pages = {13--16},
address = {Sevilla, Spain},
abstract = {Let $S$ be a set of $n$ points in the plane and let
${\mathcal T}_S$ be the set of all crossing-free spanning
trees of $S$. We show that any two trees in ${\mathcal
T}_S$ can be transformed into each other by $O(n^2)$ local
and constant-size edge slide operations. No polynomial
upper bound for this task has been known, but in~\cite{AAH}
a bound of $O(n^2 \log n)$ operations was conjectured.}
}
@InProceedings{arss-zppt-03,
author = {O. Aichholzer and G. Rote and B. Speckmann and I.
Streinu},
title = {The Zigzag Path of a Pseudo-Triangulation},
booktitle = {Lecture Notes in Computer Science 2748, Proc. 8th
International Workshop on Algorithms and Data Structures
(WADS)},
volume = {2748},
pages = {377--389},
year = 2003,
abstract = {We define the zigzag path of a pseudo-triangulation, a
concept generalizing the path of a triangulation of a point
set. The pseudo-tri\-an\-gu\-la\-tion zigzag path allows us
to use divide-and-conquer type of approaches for suitable
(i.e., decomposable) problems on
pseudo-tri\-an\-gu\-la\-tions. For this we provide an
algorithm that enumerates all pseudo-triangulation zigzag
paths (of all pseudo-triangulations of a given point set
with respect to a given line) in $O(n^2)$ time per path and
$O(n^2)$ space, where $n$ is the number of points. We
illustrate applications of our scheme which include a novel
algorithm to count the number of pseudo-triangulations of a
point set. }
}
@InProceedings{as-fvd-90,
author = {F. Aurenhammer and G. Stoeckl},
title = {Fenster - {V}oronoi {D}iagramme ({A}bstract)},
booktitle = {Tagungsband DMV Jubilaeumstagung},
pages = 52,
year = 1990,
address = {Bremen, Germany},
abstract = {In the peeper's Voronoi diagram for $n$ sites, any point
in the plane belongs to the region of the closest site
visible from it. Visibility is constrained to a segment on
a line avoiding the convex hull of the sites. We show that
the peeper's Voronoi diagram attains a size of
$\Theta(n^{2})$ in the worst case, and that it can be
computed in $O(n^{2})$ time and space.}
}
@Article{as-pvd-91,
author = {F. Aurenhammer and G. Stoeckl},
title = {On the peeper's {V}oronoi diagram},
journal = {SIGACT News},
year = 1991,
volume = 22,
number = 4,
pages = {50--59},
note = {[IIG-Report-Series 264, TU Graz, Austria, 1988]},
abstract = {In the peeper's Voronoi diagram for $n$ sites, any point
in the plane belongs to the region of the closest site
visible from it. Visibility is constrained to a segment on
a line avoiding the convex hull of the sites. We show that
the peeper's Voronoi diagram attains a size of
$\Theta(n^{2})$ in the worst case, and that it can be
computed in $O(n^{2})$ time and space.}
}
@InProceedings{as-solri-91,
author = {F. Aurenhammer and O. Schwarzkopf},
title = {A simple on-line randomized incremental algorithm for
computing higher order {V}oronoi diagrams},
booktitle = {Proc. $7^{th}$ Ann. ACM Symp. Computational Geometry},
pages = {142--151},
year = 1991,
address = {North Conway, U.S.A.},
abstract = {We present a simple algorithm for maintaining order-$k$
Voronoi diagrams in the plane. By using a duality transform
that is of interest in its own right, we show that the
insertion or deletion of a site involves little more than
the construction of a single convex hull in three-space. In
particular, the order-$k$ Voronoi diagram for $n$ sites can
be computed in time $O(nk^{2} \log n + nk \log^{3} n)$ and
optimal space $O(k(n-k))$ by an on-line randomized
incremental algorithm. The time bound can be improved by a
logarithmic factor without losing much simplicity. For $k
\geq \log^{2} n$, this is optimal for a randomized
incremental construction; we show that the expected number
of structural changes during the construction is $\Theta
(nk^{2})$. Finally, by going back to primal space, we
obtain a dynamic data structure that supports $k$-nearest
neighbor queries, insertions, and deletions in a planar set
of sites. The structure promises easy implementation,
exhibits a satisfactory expected performance, and occupies
no more storage than the current order-$k$ Voronoi diagram.}
}
@Article{as-solri-92,
author = {F. Aurenhammer and O. Schwarzkopf},
title = {A simple on-line randomized incremental algorithm for
computing higher order {V}oronoi diagrams},
journal = {Int'l Journal of Computational Geometry \& Applications},
year = 1992,
volume = 2,
pages = {363--381},
note = {Special Issue. [Report B 91-02, FU Berlin, Germany,
1991]},
abstract = {We present a simple algorithm for maintaining order-$k$
Voronoi diagrams in the plane. By using a duality transform
that is of interest in its own right, we show that the
insertion or deletion of a site involves little more than
the construction of a single convex hull in three-space. In
particular, the order-$k$ Voronoi diagram for $n$ sites can
be computed in time $O(nk^{2} \log n + nk \log^{3} n)$ and
optimal space $O(k(n-k))$ by an on-line randomized
incremental algorithm. The time bound can be improved by a
logarithmic factor without losing much simplicity. For $k
\geq \log^{2} n$, this is optimal for a randomized
incremental construction; we show that the expected number
of structural changes during the construction is $\Theta
(nk^{2})$. Finally, by going back to primal space, we
obtain a dynamic data structure that supports $k$-nearest
neighbor queries, insertions, and deletions in a planar set
of sites. The structure promises easy implementation,
exhibits a satisfactory expected performance, and occupies
no more storage than the current order-$k$ Voronoi diagram.}
}
@InProceedings{as-sslro-92a,
author = {F. Aurenhammer and G. Stoeckl},
title = {Searching for segments with largest relative overlap},
booktitle = {Proc. $15^{th}$ IFIP Conf. System Modelling and
Optimization, Lecture Notes in Control and Information
Sciences},
pages = {77--84},
year = 1992,
volume = 180,
address = {Zuerich, Switzerland},
publisher = {Springer Verlag},
abstract = {Let $S$ be a set of $n$ possibly intersecting line
segments on the $x$-axis. A data structure is developed
that -- for an arbitrary query segment $\sigma$ -- reports
in $O(\log)$ time a segment in $S$ which yields the largest
relative overlap with $\sigma$. The structure needs $O(n
\log)$ time and $O(n)$ space for construction. These bounds
are asymptotically optimal.}
}
@Article{as-sslro-92b,
author = {F. Aurenhammer and G. Stoeckl},
title = {Searching for segments with largest relative overlap},
journal = {Information Processing Letters},
year = 1992,
volume = 41,
pages = {103--108},
note = {[Report B 91-10, FU Berlin, Germany, 1991]},
abstract = {Let $S$ be a set of $n$ possibly intersecting line
segments on the $x$-axis. A data structure is developed
that -- for an arbitrary query segment $\sigma$ -- reports
in $O(\log)$ time a segment in $S$ which yields the largest
relative overlap with $\sigma$. The structure needs $O(n
\log)$ time and $O(n)$ space for construction. These bounds
are asymptotically optimal.}
}
@InProceedings{ass-ppt-02,
author = {O. Aichholzer and B. Speckmann and I. Streinu},
title = {The Path of a Pseudo-Triangulation},
booktitle = {Abstracts of the DIMACS Workshop on Computational Geometry
2002},
pages = {2},
year = 2002,
address = {Piscataway (NJ), USA},
abstract = {We define the path of a pseudo-triangulation, a data
structure generalizing the path of a triangulation of a
point set. This structure allows us to use
divide-and-conquer type of approaches for suitable (i.e.
decomposable) problems on pseudo-triangulations. We
illustrate this method by presenting a novel algorithm that
counts the number of pseudo-triangulations of a point
set.}
}
@InProceedings{asw-popfp-91,
author = {F. Aurenhammer and G. Stoeckl and E. Welzl},
title = {The post-office problem for fuzzy point sets},
booktitle = {Proc. $7^{th}$ Workshop on Computational Geometry CG '91,
Lecture Notes in Computer Science},
pages = {1--11},
year = 1991,
volume = 553,
address = {Bern, Switzerland},
publisher = {Springer Verlag},
note = {[Report B 91-07, FU Berlin, Germany, 1991]},
abstract = {The post-office problem for $n$ point sites in the plane
(determine which site is closest to a later specified query
point) is generalized to the situation when the residence
of each site is uncertain and it is described via uniform
distribution within a disk. Two probabilistic concepts of
neighborhood, -- expected closest site and probably closest
site -- are discussed and the resulting Voronoi diagrams
are investigated from a combinatorial and computational
point of view.}
}
@InCollection{ax-ot-07,
author = {F. Aurenhammer and Y.-F.Xu},
title = {Optimal triangulations},
booktitle = {Encyclopedia of Optimization, Second Edition},
publisher = {Springer},
editor = {C.A.Floudas, P.M.Pardalos},
year = 2008,
pages = {2757--2764},
abstract = {A {\em triangulation} of a given set $S$ of $n$ points in
the plane is a maximal set of non-crossing line segments
spanned by $S$. The problem of automatically generating
{\em optimal triangulations} for a point set $S$ has been a
subject of research since decades. As the number of
different triangulations of $S$ is an exponential function
of $n$, enumerating all possible triangulations and
selecting an optimal one (exhaustive search) is too
time-consuming even for small $n$. In fact, constructing
optimal triangulations in polynomial time is a challenging
task. Results on optimizing {\em combinatorial} properties
of triangulations, such as their degree or connectivity,
are rare. Most optimization criteria for which efficient
algorithms are known concern {\em geometric} properties of
the edges and triangles. The present survey article is
devoted to this topic.}
}
@InCollection{ax-ot-99,
author = {F. Aurenhammer and Y.-F.Xu},
title = {Optimal triangulations},
booktitle = {Encyclopedia of Optimization},
publisher = {Kluwer Academic Publishing},
editor = {C.A.Floudas, P.M.Pardalos},
year = 2000,
pages = {160--166},
volume = 4,
note = {[SFB Report F003-099, Tu Graz, Austria, 1998]},
abstract = {A {\em triangulation} of a given set $S$ of $n$ points in
the Euclidean plane is a maximal set of non-crossing line
segments spanned by $S$. The problem of automatically
generating {\em optimal triangulations} for a point set $S$
has been a subject of research since decades. As the number
of different triangulations of $S$ is an exponential
function of $n$, enumerating all possible triangulations
and selecting an optimal one (exhaustive search) is too
time-consuming even for small $n$. In fact, constructing
optimal triangulations in polynomial time is a challenging
task. Results on optimizing {\em combinatorial} properties
of triangulations, such as their degree or connectivity,
are rare. Most optimization criteria for which efficient
algorithms are known concern {\em geometric} properties of
the edges and triangles. The present survey article is
devoted to this topic.}
}
@InProceedings{cikm02_collabfiltering,
author = {Yu, Kai and Xu, Xiaowei and Schwaighofer, Anton and Tresp,
Volker and Kriegel, Hans-Peter},
title = {Removing Redundancy and Inconsistency in Memory-based
Collaborative Filtering},
booktitle = {Proceedings of the 11th International Conference on
Information and Knowledge Management CIKM02},
year = 2002,
publisher = {ACM},
pages = {52--59},
abstract = {The application range of memory-based collaborative
filtering (CF) is limited due to CF's high memory
consumption and long runtime. The approach presented in
this paper removes redundant and inconsistent instances
(users) from the data. Our work shows that a satisfactory
accuracy can be achieved by using only a small portion of
the original data set, thereby alleviating the storage and
runtime cost of the CF algorithm. In our approach, we
consider instance selection as the problem of selecting
informative data that increase the \textit{a posteriori}
probability of the optimal model. We evaluate the empirical
performance of our approach on two realworld data sets and
attain very promising results. Data size and prediction
time are significantly reduced, while the prediction
accuracy is on a par with results achieved by using the
complete database.},
aschwaig_label= 9
}
@InProceedings{dap-ssbi-10,
author = {M. Demuth and F. Aurenhammer and A. Pinz},
title = {Straight skeletons for binary shapes},
booktitle = {$3^{rd}$ Workshop on non-rigid shape analysis and
deformable image alignment (NORDIA'10)},
year = 2010,
address = {San Francisco, USA},
abstract = {This paper reviews the concept of straight skeletons,
which is well known in computational geometry, and applies
it to binary shapes that are used in vision-based shape and
object recognition. We devise a novel algorithm for
computing discrete straight skeletons from binary input
images, which is based on a polygonal approximation of the
input shape and a hybrid method that combines continuous
and discrete geometry. In our experiments, we analyze the
potential of straight skeletons in shape recognition, by
comparing their performance with medial-axis based shock
graphs on the Kimia shape databases. Our discrete straight
skeleton algorithm is not only outperforming typical
skeleton algorithms in terms of computational complexity,
it also delivers surprisingly good results in its
straightforward application to shape recognition.}
}
@InProceedings{haa-nrmwt-97,
author = {R. Hainz and O. Aichholzer and F. Aurenhammer},
title = {New results on minimum-weight triangulations and the {LMT}
skeleton},
booktitle = {Proc. $13^{th}$ European Workshop on Computational
Geometry CG '97},
pages = {4--6},
year = 1997,
address = {Wuerzburg, Germany},
abstract = {Let $P$ be a simple polygon in the plane and let $MWT(P)$
be a minimum-weight triangulation of $P$. We prove that the
$\beta$-skeleton of $P$ is a subset of $MWT(P)$ for all
values $\beta$ > $\sqrt{\frac{4}{3}}$ provided $P$ is
convex or near-convex. This settles the question of
tightness of this bound for a special case and gives
evidence for its validity in the general point set case.\\
We further disprove the conjecture that the so-called
$LMT$-skeleton coincides with the intersection of all
locally minimal triangulations, $LMT(P)$, even for convex
polygons $P$. We introduce an improved $LMT$-skeleton
algorithm which, for simple polygons $P$, exactly computes
$LMT(P)$, and thus a larger subgraph of $MWT(P)$. The
algorithm achieves the same in the general point set case
provided the connectedness of the improved $LMT$-skeleton,
which is given in allmost all practical instances.}
}
@InProceedings{icann01_bcsvm,
author = {Schwaighofer, A. and Tresp, V.},
title = {The {B}ayesian Committee Support Vector Machine},
booktitle = {Artificial Neural Networks -- ICANN 2001},
editor = {Dorffner, G. and Bischof, H. and Hornik, K.},
series = lncs # {2130},
pages = {411--417},
year = 2001,
publisher = {Springer Verlag},
abstract = {Empirical evidence indicates that the training time for
the support vector machine (SVM) scales to the square of
the number of training data points. In this paper, we
introduce the Bayesian committee support vector machine
(BC-SVM) and achieve an algorithm for training the SVM
which scales linearly in the number of training data
points. We verify the good performance of the BC-SVM using
several data sets.},
aschwaig_label= 2
}
@InProceedings{icann01_kernels,
author = {Tresp, V. and Schwaighofer, A.},
title = {Scalable Kernel Systems},
booktitle = {Artificial Neural Networks -- ICANN 2001},
year = 2001,
editor = {Dorffner, G. and Bischof, H. and Hornik, K.},
series = lncs # {2130},
pages = {285--291},
publisher = {Springer Verlag},
abstract = {Kernel-based systems are currently very popular approaches
to supervised learning. Unfortunately, the computational
load for training kernel-based systems increases
drastically with the number of training data points.
Recently, a number of approximate methods for scaling
kernel-based systems to large data sets have been
introduced. In this paper we investigate the relationship
between three of those approaches and compare their
performances experimentally.},
aschwaig_label= 3
}
@MastersThesis{k-ktep-99,
author = {H. Krasser},
title = {Kompatible Triangulierungen ebener Punktmengen},
note = {(in German)},
school = {Institute for Theoretical Computer Science, Graz
University of Technology, Austria},
year = 1999,
month = {June},
keywords = {computational geometry, triangulations, compatible,
isomorphic},
abstract = {Triangulations are very important in computational
geometry, since a lot of algorithms make use of this data
structure. The subject of this thesis is the special
problem of compatible triangulations. The original
motivation to investigate this problem comes from
cartography. Two point sets in the plane are called
compatible if isomorphic triangulations exist. First the
structure of the convex hulls of compatible triangulations
is analyzed in the case of edge-compatibility. Then it is
shown that triangle-compatibility simplifies the situation.
A connection to lambda-matrices is also given. If two point
sets have the same lambda-matrices then every triangulation
of one point set admits a compatible triangulation of the
other point set. At last the main conjecture on compatible
triangulations, namely that every two point sets of same
cardinality in general position that have an identical
number of points on the convex hulls admit compatible
triangulations, is proved for some special cases. }
}
@PhDThesis{k-otpsp-03,
author = {H. Krasser},
title = {Order Types of Point Sets in the Plane},
school = {Institute for Theoretical Computer Science, Graz
University of Technology, Austria},
year = 2003,
month = {October},
keywords = {computational geometry, combinatorial geometry, order
types, point sets, pseudoline arrangements, rectilinear
crossing number, triangulation, pseudo-triangulation},
abstract = {Order types are a means to characterize the combinatorial
properties of a finite point set in the plane. In
particular, the crossing properties of all straight-line
segments spanned by a point configuration are reflected by
its order type. We establish a complete and reliable data
base for all different order types of size up to $11$. To
the best of our knowledge, such a project has not been
carried out before, not even for point sets of smaller
size. We discuss several applications of this data base and
related techniques to prominent problems in computational
and combinatorial geometry. These include problems on
crossing-free graphs like triangulations or simple
polygonalizations, but also general crossing problems like
the rectilinear crossing number.}
}
@InProceedings{nips02_approxgp,
author = {Schwaighofer, Anton and Tresp, Volker},
title = {Transductive and Inductive Methods for Approximate
{G}aussian Process Regression},
booktitle = nips # { 15},
year = 2003,
editor = {Becker, Suzanna and Thrun, Sebastian and Obermayer,
Klaus},
publisher = {MIT Press},
abstract = {Gaussian process regression allows a simple analytical
treatment of exact Bayesian inference and has been found to
provide good performance, yet scales badly with the number
of training data. In this paper we compare several
approaches towards scaling Gaussian processes regression to
large data sets: the subset of representers method, the
reduced rank approximation, online Gaussian processes, and
the Bayesian committee machine. Furthermore we provide
theoretical insight into some of our experimental results.
We found that subset of representers methods can give good
and particularly fast predictions for data sets with high
and medium noise levels. On complex low noise data sets,
the Bayesian committee machine achieves significantly
better accuracy, yet at a higher computational cost.},
aschwaig_label= 6
}
@InProceedings{nips02_rheuma,
author = {Schwaighofer, Anton and Tresp, Volker and Mayer, Peter and
Scheel, Alexander K. and Mueller, Gerhard A. },
title = {The {RA} Scanner: Prediction of Rheumatoid Joint
Inflammation Based on Laser Imaging},
booktitle = nips # { 15},
year = 2003,
editor = {Becker, Suzanna and Thrun, Sebastian and Obermayer,
Klaus},
publisher = {MIT Press},
abstract = {We describe the RA scanner, a novel system for the
examination of patients suffering from rheumatoid
arthritis. The RA scanner is based on a novel laser-based
imaging technique which is sensitive to the optical
characteristics of finger joint tissue. Based on the laser
images, finger joints are classified according to whether
the inflammatory status has improved or worsened. To
perform the classification task, various linear and
kernel-based systems were implemented and their
performances were compared. Special emphasis was put on
measures to reliably perform parameter tuning and
evaluation, since only a very small data set was available.
Based on the results presented in this paper, it was
concluded that the RA scanner permits a reliable
classification of pathological finger joints, thus paving
the way for a further development from prototype to product
stage.},
aschwaig_label= 7
}
@InProceedings{nips03_gplocation,
author = {Schwaighofer, Anton and Grigora{\c{s}}, Marian and Tresp,
Volker and Hoffmann, Clemens},
title = {{GPPS}: A {G}aussian Process Positioning System for
Cellular Networks},
booktitle = nips # { 16},
editor = {Thrun, Sebastian and Saul, Lawrence and Schoelkopf,
Bernhard},
year = 2004,
abstract = {In this article, we present a novel approach to solving
the localization problem in cellular networks. The goal is
to estimate a mobile user's position, based on measurements
of the signal strengths received from network base
stations. Our solution works by building Gaussian process
models for the distribution of signal strengths, as
obtained in a series of calibration measurements. In the
localization stage, the user's position can be estimated by
maximizing the likelihood of received signal strengths with
respect to the position. We investigate the accuracy of the
proposed approach on data obtained within a large indoor
cellular network.},
aschwaig_label= 13
}
@Article{omics_mining,
author = {Dejori, Mathaeus and Schwaighofer, Anton and Tresp, Volker
and Stetter, Martin},
title = {Mining Functional Modules in Genetic Networks with
Decomposable Graphical Models},
journal = {OMICS A Journal of Integrative Biology},
year = 2004,
note = {Accepted for publication},
aschwaig_label= 14
}
@Article{tbe_rheuma,
author = {Schwaighofer, A. and Tresp, V. and Mayer, P. and Scheel,
A. and Reuss-Borst, M. and Krause, A. and Mesecke-von
Rheinbaben, I. and Rost, H.},
title = {Prediction of Rheumatoid Joint Inflammation Based on Laser
Imaging Using Linear and Kernel-Based Classifiers},
journal = {IEEE Transactions on Biomedical Engineering},
year = 2002,
note = {Accepted for publication},
abstract = {We describe a novel system for the examination of patients
suffering from rheumatoid arthritis. Basis of this system
is a laser imaging technique which is sensitive to the
optical characteristics of finger joint tissue. From the
laser images acquired at baseline and followup, finger
joints can automatically be classified according to whether
the inflammatory status has improved or worsened. To
perform the classification task, various linear and
kernel-based systems were implemented and their
performances were compared. From the results presented in
this paper, we concluded that the laser-based imaging
permits a reliable classification of pathological finger
joints, making it a sensitive method for detecting
arthritic changes.},
aschwaig_label= 4
}
@TechReport{techrep_nystrom,
author = {Williams, Christopher K.I. and Rasmussen, Carl Edward and
Schwaighofer, Anton and Tresp, Volker},
title = {Observations on the {N}ystroem Method for {G}aussian
Process Prediction},
institution = {Available from the authors' web pages},
month = may,
year = 2002,
aschwaig_label= 8
}
@Article{telematik_fingerprint,
author = {Schwaighofer, Anton},
title = {Sorting it out: Machine Learning and Fingerprints},
journal = {Telematik},
year = 2002,
volume = 8,
number = 1,
pages = {18--20},
abstract = {Machine learning concepts can find applications in many
domains. We describe here one such application to the
problem of fingerprint verification. In biometric
verification using fingerprints, one often has to handle
large archives of fingerprint images. When verifying an
individual fingerprint, it is important to have a fast
method at hand that selects suitable candidate images out
of a large archive. We present an approach to sort a
fingerprint archive according to similarity with a given
fingerprint, inspired by an opto-electronic device called
the wedge-ring-detector.},
aschwaig_label= 5
}
@Article{tkde_collabfiltering,
author = {Yu, Kai and Schwaighofer, Anton and Tresp, Volker and Xu,
Xiaowei and Kriegel, Hans-Peter},
title = {Probabilistic Memory Based Collaborative Filtering:
Learning Individual and Social Preferences},
journal = {IEEE Transactions on Knowledge and Data Engineering
(Special issue on mining and searching the web)},
year = 2004,
volume = 16,
number = 1,
pages = {56--69},
abstract = {Memory-based collaborative filtering (CF) has been
extensively studied in the literature and has proven to be
successful in various types of personalized recommender
systems. In this paper we develop a probabilistic framework
for memory-based CF (PMCF). While this framework has clear
links with classical memory-based CF, it allows us to find
principled solutions to known problems of CF-based
recommender systems. In particular, we show that a
probabilistic active learning method can be used to
actively query the user, thereby solving the ``new user
problem'' . Furthermore, the probabilistic framework allows
us to reduce the computational cost of memory-based CF by
working on a carefully selected subset of user profiles,
while retaining high accuracy. We report experimental
results based on two real world data sets, which
demonstrate that our proposed PMCF framework allows an
accurate and efficient prediction of user preferences.},
aschwaig_label= 10
}
@InProceedings{uai03_collabensemble,
author = {Yu, Kai and Schwaighofer, Anton and Tresp, Volker and Ma,
Wei-Ying and Zhang, HongJiang},
title = {Collaborative Ensemble Learning: Combining Collaborative
and Content-Based Information Filtering via Hierarchical
{B}ayes},
booktitle = {Uncertainty in Artificial Intelligence: Proceedings of the
19th Conference (UAI-2003)},
editor = {Meek, Christopher and Kj{\ae}rulff, Uffe},
publisher = {Morgan Kaufmann},
year = 2003,
pages = {616--623},
abstract = {Collaborative filtering (CF) and content-based filtering
(CBF) have widely been used in information filtering
applications, both approaches having their individual
strengths and weaknesses. This paper proposes a novel
probabilistic framework to unify CF and CBF, named
collaborative ensemble learning. Based on content based
probabilistic models for each user's preferences (the CBF
idea), it combines a society of users' preferences to
predict an active user's preferences (the CF idea). While
retaining an intuitive explanation, the combination scheme
can be interpreted as a hierarchical Bayesian approach in
which a common prior distribution is learned from related
experiments. It does not require a global training stage
and thus can incrementally incorporate new data. We report
results based on two data sets, the Reuters-21578 text data
set and a data base of user opionions on art images. For
both data sets, collaborative ensemble achieved excellent
performance in terms of recommendation accuracy. In
addition to recommendation engines, collaborative ensemble
learning is applicable to problems typically solved via
classical hierarchical Bayes, like multisensor fusion and
multitask learning.},
aschwaig_label= 11
}