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112
A Practical Bayesian Framework for Backprop Networks
 Neural Computation
, 1991
"... A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures ..."
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Cited by 399 (20 self)
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A quantitative and practical Bayesian framework is described for learning of mappings in feedforward networks. The framework makes possible: (1) objective comparisons between solutions using alternative network architectures
The structure of multineuron firing patterns in primate retina
 Petrusca D, Sher A, Litke AM & Chichilnisky EJ
, 2006
"... Synchronized firing among neurons has been proposed to constitute an elementary aspect of the neural code in sensory and motor systems. However, it remains unclear how synchronized firing affects the largescale patterns of activity and redundancy of visual signals in a complete population of neuron ..."
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Cited by 54 (7 self)
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Synchronized firing among neurons has been proposed to constitute an elementary aspect of the neural code in sensory and motor systems. However, it remains unclear how synchronized firing affects the largescale patterns of activity and redundancy of visual signals in a complete population of neurons. We recorded simultaneously from hundreds of retinal ganglion cells in primate retina, and examined synchronized firing in completely sampled populations of �50–100 ONparasol cells, which form a major projection to the magnocellular layers of the lateral geniculate nucleus. Synchronized firing in pairs of cells was a subset of a much larger pattern of activity that exhibited local, isotropic spatial properties. However, a simple model based solely on interactions between adjacent cells reproduced 99 % of the spatial structure and scale of synchronized firing. No more than 20 % of the variability in firing of an individual cell was predictable from the activity of its neighbors. These results held both for spontaneous firing and in the presence of independent visual modulation of the firing of each cell. In sum, largescale synchronized firing in the entire population of ONparasol cells appears to reflect simple neighbor interactions, rather than a unique visual signal or a highly redundant coding scheme.
A Review of Parametric Modelling Techniques for EEG Analysis
 Med. Eng. Phys
, 1996
"... This tutorial provides an introduction to the use of parametric modelling techniques for time series analysis, and in particular the application of autoregressive modelling to the analysis of physiological signals such as the human electroencephalogram. The concept of signal stationarity is consider ..."
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Cited by 33 (15 self)
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This tutorial provides an introduction to the use of parametric modelling techniques for time series analysis, and in particular the application of autoregressive modelling to the analysis of physiological signals such as the human electroencephalogram. The concept of signal stationarity is considered and, in the light of this, both adaptive models, and nonadaptive models employing fixed or adaptive segmentation, are discussed. For nonadaptive autoregressive models, the YuleWalker equations are derived and the popular LevinsonDurbin and Burg algorithms are introduced. The interpretation of an autoregressive model as a recursive digital filter and its use in spectral estimation are considered, and the important issues of model stability and model complexity are discussed. Keywords: autoregressive modelling, biomedical signal processing, human sleep EEG 1 INTRODUCTION Parametric modelling is a technique for time series analysis in which a mathematical model is fitted to a sample...
Drawing With Constraints
 The Visual Computer
, 1994
"... The success of constraintbased approaches to drawing has been limited by difficulty in creating constraints, solving them, and presenting them to users. In this paper, we discuss techniques used in the Briar drawing program to address all of these issues. Briar¼s approach separates the problem of i ..."
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Cited by 22 (1 self)
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The success of constraintbased approaches to drawing has been limited by difficulty in creating constraints, solving them, and presenting them to users. In this paper, we discuss techniques used in the Briar drawing program to address all of these issues. Briar¼s approach separates the problem of initially establishing constraints from that of maintaining them during subsequent editing. We describe how nonconstraint based drawing tools can be augmented to specify constraints in addition to positions. These constraints are then maintained as the user drags the model, allowing the user to explore configurations consistent with the constraints. Visual methods are provided for displaying and editing the constraints.
Low Entropy Coding with Unsupervised Neural Networks
"... ed on visual and speech data. The ability of the network to automatically generate wavelet codes from natural images is demonstrated. These bear a close resemblance to 2D Gabor functions, which have previously been used to describe physiological receptive fields, and as a means of producing compact ..."
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Cited by 20 (0 self)
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ed on visual and speech data. The ability of the network to automatically generate wavelet codes from natural images is demonstrated. These bear a close resemblance to 2D Gabor functions, which have previously been used to describe physiological receptive fields, and as a means of producing compact image representations. Keywords: neural networks, unsupervised learning, selforganisation, feature extraction, information theory, redundancy reduction, sparse coding, imaging models, occlusion, image coding, speech coding. Declaration This dissertation is the result of my own original work, except where reference is made to the work of others. No part of it has been submitted for any other university degree or diploma. Its length, including captions, footnotes, appendix and bibliography, is approximately 58000 words. Acknowledgements I would like first and foremost to thank Richard Prager, my supervisor, fo
Neural Maps and Topographic Vector Quantization
, 1999
"... Neural maps combine the representation of data by codebook vectors, like a vector quantizer, with the property of topography, like a continuous function. While the quantization error is simple to compute and to compare between different maps, topography of a map is difficult to define and to quantif ..."
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Cited by 20 (4 self)
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Neural maps combine the representation of data by codebook vectors, like a vector quantizer, with the property of topography, like a continuous function. While the quantization error is simple to compute and to compare between different maps, topography of a map is difficult to define and to quantify. Yet, topography of a neural map is an advantageous property, e.g. in the presence of noise in a transmission channel, in data visualization, and in numerous other applications. In this paper we review some conceptual aspects of definitions of topography, and some recently proposed measures to quantify topography. We apply the measures first to neural maps trained on synthetic data sets, and check the measures for properties like reproducability, scalability, systematic dependence of the value of the measure on the topology of the map etc. We then test the measures on maps generated for four realworld data sets, a chaotic time series, speech data, and two sets of image data. The measures ...
Numerical Relativity: A review
, 2001
"... Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected ..."
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Cited by 18 (1 self)
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Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss (some) future prospects.
Exact simulation of integrateandfire models with synaptic conductances
 Neural Comp
, 2006
"... Computational neuroscience relies heavily on the simulation of large networks of neuron models. There are essentially two simulation strategies: 1) using an approximation method (e.g. RungeKutta) with spike times binned to the time step; 2) calculating spike times exactly in an eventdriven fashion ..."
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Cited by 14 (1 self)
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Computational neuroscience relies heavily on the simulation of large networks of neuron models. There are essentially two simulation strategies: 1) using an approximation method (e.g. RungeKutta) with spike times binned to the time step; 2) calculating spike times exactly in an eventdriven fashion. In large networks, the computation time of the best algorithm for either strategy scales linearly with the number of synapses, but each strategy has its own assets and constraints: approximation methods can be applied to any model but are inexact; exact simulation avoids numerical artefacts but is limited to simple models. Previous work has focused on improving the accuracy of approximation methods. In this paper we extend the range of models that can be simulated exactly to a more realistic model, namely an integrateandfire model with exponential synaptic conductances.
Settings in social networks: A measurement model
 Sociological Methodology
, 2003
"... A class of statistical models is proposed which aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model builds on two assumptions. The observed network is assumed to be generated by hierarchically nested latent transitive ..."
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Cited by 12 (1 self)
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A class of statistical models is proposed which aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model builds on two assumptions. The observed network is assumed to be generated by hierarchically nested latent transitive structures, expressed by ultrametrics. It is assumed that expected tie strength decreases with ultrametric distance. The approach could be described as modelbased clustering with an ultrametric space as the underlying metric to capture the dependence in the observations. Maximum likelihood methods as well as Bayesian methods are applied for statistical inference. Both approaches are implemented using Markov chain Monte Carlo methods. 1.
Calculation Of The Gi/g/1 WaitingTime Distribution And Its Cumulants From Pollaczek's Formulas
"... The steadystate waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steadystate waiting time in the GI/G/1 queue is characterized by Spitzer's (1956) formula. However, earlier, Pollaczek (1952) derived an eq ..."
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Cited by 9 (5 self)
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The steadystate waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steadystate waiting time in the GI/G/1 queue is characterized by Spitzer's (1956) formula. However, earlier, Pollaczek (1952) derived an equivalent contourintegral expression for the Laplace transform of the GI/G/1 steadystate waiting time. Since Spitzer's formula is easier to understand probabilistically, it is better known today, but it is not so easy to apply directly except in special cases. In contrast, we show that it is easy to compute the GI/G/1 waitingtime distribution and its cumulants (and thus its moments) from Pollaczek's formulas. For the waitingtime tail probabilities, we use numerical transform inversion, numerically integrating the Pollaczek contour integral to obtain the transform values. For the cumulants and the probability of having to wait, we directly integrate the Pollazcek contour integrals numerically. The resulting algorithm is evidently the first for a GI/G/1 queue in which neither the transform of the interarrivaltime distribution nor the transform of the servicetime transform distribution need be rational. The algorithm can even be applied to longtail distributions, i.e., distributions with some infinite moments. To treat these distributions, we approximate them by suitable exponentiallydamped versions of these distributions. Overall, the algorithm is remarkably simple compared to alternative algorithms requiring more structure.