LEADER 04493nam 22007815 450 001 9910897987203321 005 20260121123403.0 010 $a9783031684098 010 $a3031684095 024 7 $a10.1007/978-3-031-68409-8 035 $a(MiAaPQ)EBC31731481 035 $a(Au-PeEL)EBL31731481 035 $a(CKB)36364867700041 035 $a(DE-He213)978-3-031-68409-8 035 $a(OCoLC)1461997489 035 $a(EXLCZ)9936364867700041 100 $a20241017d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProbabilistic Spiking Neuronal Nets $eNeuromathematics for the Computer Era /$fby Antonio Galves, Eva Löcherbach, Christophe Pouzat 205 $a1st ed. 2024. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024. 215 $a1 online resource (203 pages) 225 1 $aLecture Notes on Mathematical Modelling in the Life Sciences,$x2193-4797 311 08$a9783031684081 311 08$a3031684087 327 $aA 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. 330 $aThis book provides a self-contained introduction to a new class of stochastic models for systems of spiking neurons. These systems have a large number of interacting components, each one evolving as a stochastic process with a memory of variable length. Several mathematical tools are put to use, such as Markov chains, stochastic chains having memory of variable length, point processes having stochastic intensity, Hawkes processes, random graphs, mean field limits, perfect sampling algorithms, the Context algorithm, and statistical model selection. The book?s focus on mathematically tractable objects distinguishes it from other texts on theoretical neuroscience. The biological complexity of neurons is not ignored, but reduced to some of its main features, such as the intrinsic randomness of neuronal dynamics. This reduction in complexity aims at explaining and reproducing statistical regularities and collective phenomena that are observed in experimental data, an approach that leads to mathematically rigorous results. With an emphasis on a constructive and algorithmic point of view, this book is directed towards mathematicians interested in learning about stochastic network models and their neurobiological underpinning, and neuroscientists interested in learning how to build and prove results with mathematical models that relate to actual experimental settings. 410 0$aLecture Notes on Mathematical Modelling in the Life Sciences,$x2193-4797 606 $aBiomathematics 606 $aProbabilities 606 $aStochastic processes 606 $aMathematical statistics 606 $aNeural circuitry 606 $aMathematical and Computational Biology 606 $aProbability Theory 606 $aStochastic Processes 606 $aMathematical Statistics 606 $aNeural Circuits 606 $aSistemes estocāstics$2thub 606 $aXarxes neuronals (Informātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aBiomathematics. 615 0$aProbabilities. 615 0$aStochastic processes. 615 0$aMathematical statistics. 615 0$aNeural circuitry. 615 14$aMathematical and Computational Biology. 615 24$aProbability Theory. 615 24$aStochastic Processes. 615 24$aMathematical Statistics. 615 24$aNeural Circuits. 615 7$aSistemes estocāstics 615 7$aXarxes neuronals (Informātica) 676 $a570.285 700 $aGalves$b Antonio$01767074 701 $aLöcherbach$b Eva$01767075 701 $aPouzat$b Christophe$01767076 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910897987203321 996 $aProbabilistic Spiking Neuronal Nets$94211918 997 $aUNINA