Reconstruction, identification and implementation methods for spiking neural circuits

• Main Author: Florescu, Dorian (Author)
• Format: Electronic eBook
• Language: English
• Published: Cham, Switzerland : Springer, 2017.
• Series: Springer theses.
• Subjects: Neural circuitry.; elektronické knihy; electronic books
• ISBN: 9783319570815; 9783319570808
• Physical Description: 1 online resource (xiv, 139 pages) : illustrations (some color)

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-fir...

Table of Contents:

• 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.