LEADER 00921nam--2200325---450- 001 990003334270203316 005 20091015112817.0 035 $a000333427 035 $aUSA01000333427 035 $a(ALEPH)000333427USA01 035 $a000333427 100 $a20091015d1962----km-y0itay50------ba 101 $aeng 102 $aUS 105 $a||||||||001yy 200 1 $aLinear programming$fG. Hadley 210 $aReading$cAddison-Wesley Publishing company$dcopyr. 1962 215 $aXII, 520 p.$cill.$d22 cm 606 0 $aProgrammazione a numeri interi 676 $a519.77 700 1$aHADLEY,$bG.$0462707 801 0$aIT$bsalbc$gISBD 912 $a990003334270203316 951 $a519.77 HAD$b23997/CBS$c519.77$d00328940 959 $aBK 969 $aSCI 979 $aRSIAV6$b90$c20091015$lUSA01$h1126 979 $aRSIAV6$b90$c20091015$lUSA01$h1128 996 $aLinear programming$9188260 997 $aUNISA LEADER 01293nam--2200397---450- 001 990002025400203316 005 20120105095941.0 010 $a88-371-1097-9 035 $a000202540 035 $aUSA01000202540 035 $a(ALEPH)000202540USA01 035 $a000202540 100 $a20040924d1999----km-y0itay50------ba 101 0 $aita 102 $aIT 105 $ay|||||||001yy 200 1 $aElementi di didattica della matematica$fBruno D'Amore$gpremessa di Colette Laborde 210 $aBologna$cPitagora$d1999 215 $aXV, 454 p.$d25 cm 225 2 $aComplementi di matematica per l'indirizzo didattico$v6 410 0$12001$aComplementi di matematica per l'indirizzo didattico$v6 606 0 $aMatematica$xInsegnamento$2BNCF 676 $a510.71 700 1$aD'AMORE,$bBruno$f<1946- > $046064 702 1$aLABORDE,$bColette 801 0$aIT$bsalbc$gISBD 912 $a990002025400203316 951 $aII.4. 1573$b234642 L.M.$cII.4.$d00269892 951 $aII.4. 1573 a$b234643 L.M.$cII.4.$d00269893 959 $aBK 969 $aUMA 979 $aMARIA$b10$c20040924$lUSA01$h1135 979 $aMARIA$b10$c20040929$lUSA01$h1143 979 $aANNAMARIA$b90$c20120105$lUSA01$h0959 996 $aElementi di didattica della matematica$91041690 997 $aUNISA LEADER 04794nam 22005295 450 001 9910903789103321 005 20260121160030.0 010 $a3-031-75270-8 024 7 $a10.1007/978-3-031-75270-4 035 $a(CKB)36527794700041 035 $a(DE-He213)978-3-031-75270-4 035 $a(EXLCZ)9936527794700041 100 $a20241102d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIndividual-Based Models and Their Limits /$fby Ryszard Rudnicki, Rados?aw Wieczorek 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (VIII, 126 p. 12 illus.) 225 1 $aSpringerBriefs in Mathematical Methods,$x2365-0834 311 08$a3-031-75269-4 327 $a- 1. Models -- 2. Limit Passages -- 3. Central Limit-type Theorems -- 4. Selected Superprocesses -- 5. Phenotype Models -- 6. Modelling of Phytoplankton Dynamics -- 7. Chemotaxis Models. 330 $aIndividual-based models (IBM) describe a population as a collection of different organisms whose local interactions determine the behaviour of the entire population. The individual description is convenient for computer simulations and the determination of various model parameters, and appropriate limit passages lead to the transport equations used in classical population dynamics models. The aim of this book is to provide a brief mathematical introduction to IBMs and their application to selected biological topics. The book is divided into seven chapters. In the first chapter we give a general description of IBMs and we present examples of models to illustrate their possible applications. Examples of applications include age, size and phenotype models, coagulation-fragmentation process, and models of genome evolution. The second chapter contains some theoretical results concerning limit passages from IBMs to phenotype and age-structured models. The rate of this convergence formulated as functional central limit theorems is presented in Chapter 3. As a result of the limit passage can be a superprocess, i.e., a stochastic process with values in a space of measures. Chapter 4 presented examples of such passages: from the branching Brownian motion to the Dawson--Watanabe superprocess and from the Moran's model of genetic drift with mutations to the Fleming--Viot superprocess. The next three chapters are devoted to models, in which we directly participated in the study. In Chapter 5 we study IBMs phenotype models and their limit passages. We show that random mating stabilises the distribution of traits, while assortative mating can lead to a polymorphic population. Formation of aggregates of phytoplankton and their movement is studied in Chapter 6. We present two types of models based on: fragmentation-coagulation processes; and diffusion with chemical signals leading to advanced superprocesses. Chapter 7 is devoted to rather advanced models with chemotaxis used to description of retinal angiogenesis and cell proliferations. The book is complemented by two appendices in which we have collected information about stochastic processes and various spaces we have used. The book is dedicated both to mathematicians and biologists. The first group will find here new biological models which leads to interesting and often new mathematical questions. Biologists can observe how to include seemingly different biological processes into a unified mathematical theory and deduce from this theory interesting biological conclusions. Apart from the sections on superprocesses, where quite advanced mathematical issues arise, such as stochastic partial equations, we try to keep the required mathematical and biological background to a minimum so that the topics are accessible to students. 410 0$aSpringerBriefs in Mathematical Methods,$x2365-0834 606 $aMathematics 606 $aBiomathematics 606 $aApplications of Mathematics 606 $aMathematical and Computational Biology 606 $aBiologia de poblacions$2thub 606 $aModels matemātics$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematics. 615 0$aBiomathematics. 615 14$aApplications of Mathematics. 615 24$aMathematical and Computational Biology. 615 7$aBiologia de poblacions 615 7$aModels matemātics 676 $a519 700 $aRudnicki$b Ryszard$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767382 702 $aWieczorek$b Rados?aw$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910903789103321 996 $aIndividual-Based Models and Their Limits$94529856 997 $aUNINA