"Doctoral thesis accepted by the University of Sheffield, Sheffield, UK."

SpringerLink Springer Engineering eBooks 2017 English+International

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Supervisor's Foreword; Acknowledgements; Contents; Acronyms; 1 Introduction; 1.1 Background; 1.2 Motivation; 1.3 Overview of the Book; References; 2 Time Encoding and Decoding in Bandlimited and Shift-Invariant Spaces; 2.1 Introduction; 2.2 Nonuniform Sampling and Reconstruction of Bandlimited Functions; 2.3 Time Encoding and Decoding in Bandlimited Spaces; 2.3.1 The Ideal IF Neuron; 2.3.2 The Ideal IF Neuron with Refractory Period; 2.3.3 The Leaky IF Neuron; 2.3.4 The Leaky IF Neuron with Random Threshold; 2.3.5 The Hodgkin-Huxley Neuron; 2.3.6 The Asynchronous Sigma-Delta Modulator.

2.4 Time Encoding and Decoding in Shift-Invariant Spaces2.5 Conclusions; References; 3 A Novel Framework for Reconstructing Bandlimited Signals Encoded by Integrate-and-Fire Neurons; 3.1 Introduction; 3.2 A New Method of Reconstructing Functions from Local Averages; 3.3 Direct Reconstruction Algorithms for Inputs Encoded with Ideal IF Neurons; 3.4 The Integrate-and-Fire Neuron as a Uniform Sampler; 3.5 Fast Indirect Reconstruction Algorithms for Inputs Encoded with Ideal IF Neurons; 3.6 Numerical Study; 3.6.1 Numerical Study for Algorithm 3.1; 3.6.2 Numerical Study for Algorithm 3.2.

3.6.3 Error Evaluation for the Interpolation Step of the Proposed Algorithms3.7 Conclusions; References; 4 A Novel Reconstruction Framework in Shift-Invariant Spaces for Signals Encoded with Integrate-and-Fire Neurons; 4.1 Introduction; 4.2 A New Non-iterative Method for Reconstructing Signals in Shift-Invariant Spaces from Spike Trains Generated with IF-TEMs; 4.3 Direct Reconstruction Algorithms for Inputs Encoded with Ideal IF Neurons; 4.4 Fast Indirect Reconstruction Algorithms for Inputs Encoded with Ideal IF Neurons; 4.5 Numerical Study.

4.5.1 Comparative Numerical Study of the Iterative Algorithms4.5.2 Comparative Numerical Study of the Non-iterative Algorithms; 4.6 Conclusions; References; 5 A New Approach to the Identification of Sensory Processing Circuits Based on Spiking Neuron Data; 5.1 Introduction; 5.2 Identification of Spiking Neural Circuits; 5.2.1 Identification of [Linear Filter]-[Ideal IF] Circuits; 5.2.2 Identification Methods for Different Circuit Structures; 5.3 The NARMAX Identification Methodology; 5.3.1 An Overview of the NARMAX Model; 5.3.2 The Orthogonal Least Squares Estimator.

5.3.3 The Orthogonal Forward Regression Algorithm5.3.4 The Generalised Frequency Response Functions; 5.4 A New Method for the Identification of [Nonlinear Filter]-[Ideal IF] Circuits; 5.4.1 Problem Statement; 5.4.2 Numerical Study; 5.5 A New Methodology for the Identification of [Linear Filter]-[Leaky IF] Circuits; 5.5.1 Problem Statement; 5.5.2 Numerical Study; 5.6 Conclusions; References; 6 A New Method for Implementing Linear Filters in the Spike Domain; 6.1 Introduction; 6.2 Problem Statement; 6.3 Direct Computation of Spike Times; 6.4 Numerical Study; 6.5 Conclusions; References.

This work is motivated by the ongoing open question of how information in the outside world is represented and processed by the brain. Consequently, several novel methods are developed. A new mathematical formulation is proposed for the encoding and decoding of analog signals using integrate-and-fire neuron models. Based on this formulation, a novel algorithm, significantly faster than the state-of-the-art method, is proposed for reconstructing the input of the neuron. Two new identification methods are proposed for neural circuits comprising a filter in series with a spiking neuron model. These methods reduce the number of assumptions made by the state-of-the-art identification framework, allowing for a wider range of models of sensory processing circuits to be inferred directly from input-output observations. A third contribution is an algorithm that computes the spike time sequence generated by an integrate-and-fire neuron model in response to the output of a linear filter, given the input of the filter encoded with the same neuron model.