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

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 non--adaptive models employing fixed or adaptive segmentation, are discussed. For non--adaptive autoregressive models, the Yule--Walker equations are derived and the popular Levinson--Durbin 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...

The success of constraint-based 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 non-constraint- 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.

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 real-world data sets, a chaotic time series, speech data, and two sets of image data. The measures ...

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 2-D 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, self-organisation, 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

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.

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. Runge-Kutta) with spike times binned to the time step; 2) calculating spike times exactly in an event-driven 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 integrate-and-fire model with exponential synaptic conductances.

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 model-based 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.

The steady-state 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 steady-state waiting time in the GI/G/1 queue is characterized by Spitzer's (1956) formula. However, earlier, Pollaczek (1952) derived an equivalent contour-integral expression for the Laplace transform of the GI/G/1 steady-state 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 waiting-time distribution and its cumulants (and thus its moments) from Pollaczek's formulas. For the waiting-time 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 interarrival-time distribution nor the transform of the service-time transform distribution need be rational. The algorithm can even be applied to long-tail distributions, i.e., distributions with some infinite moments. To treat these distributions, we approximate them by suitable exponentially-damped versions of these distributions. Overall, the algorithm is remarkably simple compared to alternative algorithms requiring more structure.

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