Format:
1 Online-Ressource (XV, 199 Seiten)
ISBN:
9783031684098
Series Statement:
Lecture notes on mathematical modelling in the life sciences
Content:
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.
Note:
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.
Additional Edition:
ISBN 9783031684081
Additional Edition:
ISBN 9783031684104
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031684081
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783031684104
Additional Edition:
Erscheint auch als Druck-Ausgabe Galves, Antonio, 1947 - 2023 Probabilistic spiking neuronal nets Cham, Switzerland : Springer Nature, 2024 ISBN 9783031684081
Language:
English
Keywords:
Nervennetz
;
Neurowissenschaften
;
Stochastisches Modell
;
Aktionspotenzial
;
Stochastischer Prozess
;
Mean-Field-Theorie
;
Zufallsgraph
DOI:
10.1007/978-3-031-68409-8
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