Probabilistic Spiking Neuronal Nets : Neuromathematics for the Computer Era / by Antonio Galves, Eva Löcherbach, Christophe Pouzat.

Format:

Book

Author/Creator:

Galves, Antonio.

Contributor:

Löcherbach, Eva.

Pouzat, Christophe.

Series:

Lecture Notes on Mathematical Modelling in the Life Sciences, 2193-4797

Language:

English

Subjects (All):

Biomathematics.

Probabilities.

Stochastic processes.

Mathematical statistics.

Neural circuitry.

Mathematical and Computational Biology.

Probability Theory.

Stochastic Processes.

Mathematical Statistics.

Neural Circuits.

Local Subjects:

Mathematical and Computational Biology.

Probability Theory.

Stochastic Processes.

Mathematical Statistics.

Neural Circuits.

Physical Description:

1 online resource (203 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2024.

Summary:

This book provides a self-contained introduction to a new class of stochastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a stochastic process with a memory of variable length. Several mathematical tools are put to use, such as Markov chains, stochastic chains having memory of variable length, point processes having stochastic intensity, Hawkes processes, random graphs, mean field limits, perfect sampling algorithms, the Context algorithm, and statistical model selection. The book’s focus on mathematically tractable objects distinguishes it from other texts on theoretical neuroscience. The biological complexity of neurons is not ignored, but reduced to some of its main features, such as the intrinsic randomness of neuronal dynamics. This reduction in complexity aims at explaining and reproducing statistical regularities and collective phenomena that are observed in experimental data, an approach that leads to mathematically rigorous results. With an emphasis on a constructive and algorithmic point of view, this book is directed towards mathematicians interested in learning about stochastic network models and their neurobiological underpinning, and neuroscientists interested in learning how to build and prove results with mathematical models that relate to actual experimental settings.

Contents:

A Neurophysiology Primer for Mathematicians

A Discrete Time Stochastic Neural Network Model

Mean Field Limits for Discrete Time Stochastic Neural Network Models

But Time is Continuous!

Models without Reset: Hawkes Processes

What is a Stationary State in a Potentially Infinite System?

Statistical Estimation of the Interaction Graph

Mean Field Limits and Short-Term Synaptic Facilitation in Continuous Time Models

A Non-Exhaustive List of Some Open Questions

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

Appendix F

References

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783031684098

3031684095

OCLC:

1461997489