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Probabilistic Spiking Neuronal Nets Neuromathematics for the Computer Era /

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, suc...

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Bibliographische Detailangaben
Hauptverfasser: Galves, Antonio (VerfasserIn), Löcherbach, Eva (VerfasserIn), Pouzat, Christophe (VerfasserIn)
Körperschaft: SpringerLink (Online service)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing : Imprint: Springer, 2024.
Ausgabe:1st ed. 2024.
Schriftenreihe:Lecture Notes on Mathematical Modelling in the Life Sciences,
Schlagworte:
Biomathematics.
Probabilities.
Stochastic processes.
Mathematical statistics.
Neural circuitry.
Mathematical and Computational Biology.
Probability Theory.
Stochastic Processes.
Mathematical Statistics.
Neural Circuits.
Online-Zugang:https://doi.org/10.1007/978-3-031-68409-8
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Inhaltsangabe:
  • 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.

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