LEADER 03637nam 2200613Ia 450 001 9910438153203321 005 20200520144314.0 010 $a3-642-32157-7 024 7 $a10.1007/978-3-642-32157-3 035 $a(CKB)3400000000102754 035 $a(SSID)ssj0000788856 035 $a(PQKBManifestationID)11510540 035 $a(PQKBTitleCode)TC0000788856 035 $a(PQKBWorkID)10828737 035 $a(PQKB)10419527 035 $a(DE-He213)978-3-642-32157-3 035 $a(MiAaPQ)EBC3070874 035 $a(PPN)168321114 035 $a(EXLCZ)993400000000102754 100 $a20120917d2013 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 00$aStochastic biomathematical models $ewith applications to neuronal modeling /$fMostafa Bachar, Jerry Batzel, Susanne Ditlevsen, editors 205 $a1st ed. 2013. 210 $aBerlin ;$aNew York $cSpringer$dc2013 215 $a1 online resource (XVI, 206 p. 34 illus., 13 illus. in color.) 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v2058.$aMathematical biosciences subseries 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-32156-9 320 $aIncludes bibliographical references and index. 327 $a1 Introduction to stochastic models in biology -- 2 One-dimensional homogeneous diffusions -- 3 A brief introduction to large deviations theory -- 4 Some numerical methods for rare events simulation and analysis -- 5 Stochastic Integrate and Fire models: a review on mathematical methods and their applications -- 6 Stochastic partial differential equations in Neurobiology: linear and nonlinear models for spiking neurons -- 7 Deterministic and stochastic FitzHugh-Nagumo systems -- 8 Stochastic modeling of spreading cortical depression. 330 $aStochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2058. 410 0$aLecture notes in mathematics (Springer-Verlag).$pMathematical biosciences subseries. 606 $aNeurons$xMathematical models 606 $aStochastic models 606 $aComputational neuroscience 615 0$aNeurons$xMathematical models. 615 0$aStochastic models. 615 0$aComputational neuroscience. 676 $a612.8/1046015118 701 $aBachar$b Mostafa$01757727 701 $aBatzel$b Jerry J$01757728 701 $aDitlevsen$b Susanne$01757729 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438153203321 996 $aStochastic biomathematical models$94195676 997 $aUNINA