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001 978-3-031-68409-8
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020 _a9783031684098
_9978-3-031-68409-8
024 7 _a10.1007/978-3-031-68409-8
_2doi
050 4 _aQH323.5
050 4 _aQH324.2-324.25
072 7 _aPBW
_2bicssc
072 7 _aPSA
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPSAX
_2thema
100 1 _aGalves, Antonio.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986180
245 1 0 _aProbabilistic Spiking Neuronal Nets
_h[electronic resource] :
_bNeuromathematics for the Computer Era /
_cby Antonio Galves, Eva Löcherbach, Christophe Pouzat.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXV, 199 p. 26 illus., 11 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes on Mathematical Modelling in the Life Sciences,
_x2193-4797
505 0 _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.
520 _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.
650 0 _aBiomathematics.
_970325
650 0 _aProbabilities.
_965724
650 0 _aStochastic processes.
_976770
650 0 _aMathematical statistics.
_967233
650 0 _aNeural circuitry.
_986181
650 1 4 _aMathematical and Computational Biology.
_970327
650 2 4 _aProbability Theory.
_967428
650 2 4 _aStochastic Processes.
_976770
650 2 4 _aMathematical Statistics.
_967233
650 2 4 _aNeural Circuits.
_986182
700 1 _aLöcherbach, Eva.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986183
700 1 _aPouzat, Christophe.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_986184
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031684081
776 0 8 _iPrinted edition:
_z9783031684104
830 0 _aLecture Notes on Mathematical Modelling in the Life Sciences,
_x2193-4797
_986185
856 4 0 _uhttps://doi.org/10.1007/978-3-031-68409-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c64272
_d64272