LEADER 03965nam 22006495 450 001 9910495195503321 005 20251113201156.0 010 $a3-030-72162-0 024 7 $a10.1007/978-3-030-72162-6 035 $a(CKB)4100000011984432 035 $a(MiAaPQ)EBC6682762 035 $a(Au-PeEL)EBL6682762 035 $a(OCoLC)1261380181 035 $a(PPN)269149260 035 $a(DE-He213)978-3-030-72162-6 035 $a(EXLCZ)994100000011984432 100 $a20210722d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on Optimal Transport /$fby Luigi Ambrosio, Elia Brué, Daniele Semola 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (250 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v130 311 08$a3-030-72161-2 320 $aIncludes bibliographical references. 327 $a1 Lecture 1: Preliminary notions and the Monge problem -- 2 Lecture 2: The Kantorovich problem -- 3 Lecture 3: The Kantorovich - Rubinstein duality -- 4 Lecture 4: Necessary and sufficient optimality conditions -- 5 Lecture 5: Existence of optimal maps and applications -- 6 Lecture 6: A proof of the Isoperimetric inequality and stability in Optimal Transport -- 7 Lecture 7: The Monge-Ampére equation and Optimal Transport on Riemannian manifolds -- 8 Lecture 8: The metric side of Optimal Transport -- 9 Lecture 9: Analysis on metric spaces and the dynamic formulation of Optimal Transport -- 10 Lecture 10: Wasserstein geodesics, nonbranching and curvature -- 11 Lecture 11: Gradient flows: an introduction -- 12 Lecture 12: Gradient flows: the Brézis-Komura theorem -- 13 Lecture 13: Examples of gradient flows in PDEs -- 14 Lecture 14: Gradient flows: the EDE and EDI formulations -- 15 Lecture 15: Semicontinuity and convexity of energies in the Wasserstein space -- 16 Lecture 16: The Continuity Equation and the Hopf-Lax semigroup -- 17 Lecture 17: The Benamou-Brenier formula -- 18 Lecture 18: An introduction to Otto?s calculus -- 19 Lecture 19: Heat flow, Optimal Transport and Ricci curvature. 330 $aThis textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v130 606 $aMathematical analysis 606 $aMathematical optimization 606 $aCalculus of variations 606 $aMeasure theory 606 $aAnalysis 606 $aCalculus of Variations and Optimization 606 $aMeasure and Integration 615 0$aMathematical analysis. 615 0$aMathematical optimization. 615 0$aCalculus of variations. 615 0$aMeasure theory. 615 14$aAnalysis. 615 24$aCalculus of Variations and Optimization. 615 24$aMeasure and Integration. 676 $a519.6 700 $aAmbrosio$b Luigi$044009 702 $aBrue?$b Elia 702 $aSemola$b Daniele 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910495195503321 996 $aLectures on Optimal Transport$92175022 997 $aUNINA LEADER 05438nam 22007935 450 001 9910483251403321 005 20251226200551.0 010 $a3-540-68894-3 024 7 $a10.1007/978-3-540-68894-5 035 $a(CKB)1000000000440610 035 $a(SSID)ssj0000317714 035 $a(PQKBManifestationID)11245535 035 $a(PQKBTitleCode)TC0000317714 035 $a(PQKBWorkID)10294610 035 $a(PQKB)10486603 035 $a(DE-He213)978-3-540-68894-5 035 $a(MiAaPQ)EBC3068574 035 $a(PPN)127048294 035 $a(BIP)23624697 035 $a(EXLCZ)991000000000440610 100 $a20100301d2008 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFormal Methods for Computational Systems Biology $e8th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2008 Bertinoro, Italy, June 2-7, 2008 /$fedited by Marco Bernardo, Pierpaolo Degano, Gianluigi Zavattaro 205 $a1st ed. 2008. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2008. 215 $a1 online resource (X, 527 p.) 225 1 $aProgramming and Software Engineering,$x2945-9168 ;$v5016 300 $aLectures. 311 08$a3-540-68892-7 320 $aIncludes bibliographical references and index. 327 $aRegular Lectures -- Sensitivity Analysis of Stochastic Models of Bistable Biochemical Reactions -- Pathway Logic -- Formal Cell Biology in Biocham -- Hierarchical Modeling for Computational Biology -- Simulation Methods in Systems Biology -- Membrane Computing as a Modeling Framework. Cellular Systems Case Studies -- Petri Nets for Systems and Synthetic Biology -- Process Algebras in Systems Biology -- The BlenX Language: A Tutorial -- BISCA Talks -- Cells in Silico: A Holistic Approach -- The Calculus of Looping Sequences -- Hybrid Systems and Biology -- ?@: A ?-Based Process Calculus for the Implementation of Compartmentalised Bio-inspired Calculi -- A Gentle Introduction to Stochastic (Poly)Automata Collectives and the (Bio)Chemical Ground Form. 330 $aThis volume presents the set of papers accompanying the lectures of the eighth International School on Formal Methods for the Design of Computer, Com- nication, and Software Systems (SFM). Thisseriesofschoolsaddressestheuseofformalmethodsincomputerscience asaprominentapproachtotherigorousdesignofcomputer, communication, and software systems. The main aim of the SFM series is to o'er a good spectrum of current research in foundations as well as applications of formal methods, which can be of help for graduate students and young researchers who intend to approach the ?eld. SFM 2008 was devoted to formal techniques for computational systems - ology and covered several aspects of the ?eld, including computational models, calculi and logics for biological systems, and veri'cation and simulation me- ods. Theschoolfeatured not onlyregularlectures, but also talksgivenby people involvedinthe ItalianresearchprojectonBio-InspiredSystems andCalculiwith Applications (BISCA). The ?rst partof this volume comprises nine papers basedon regularlectures. The paper by Degasperi and Gilmore describes the application of sensitivity analysistechniques to stochastic simulation algorithms. Talcott's paper presents pathway logic, an approach to modeling and analysis of biological processes based on rewriting logic. Fages and Soliman study reaction graphs and acti- tion/inhibition graphs used by biologists through formal methods originating from programming theory. The paper by Maus, John, R] ohl, and Uhrmacher d- cusses categories, abstraction hierarchies, and composition hierarchies playing a role in modeling and simulation for computational biology. Gillespie's paper - views the theory of stochastic chemical kinetics and several simulation methods that are based on that theory. 410 0$aProgramming and Software Engineering,$x2945-9168 ;$v5016 606 $aSoftware engineering 606 $aCompilers (Computer programs) 606 $aComputer science 606 $aComputers, Special purpose 606 $aComputer networks 606 $aSoftware Engineering 606 $aCompilers and Interpreters 606 $aComputer Science Logic and Foundations of Programming 606 $aSpecial Purpose and Application-Based Systems 606 $aComputer Communication Networks 615 0$aSoftware engineering. 615 0$aCompilers (Computer programs). 615 0$aComputer science. 615 0$aComputers, Special purpose. 615 0$aComputer networks. 615 14$aSoftware Engineering. 615 24$aCompilers and Interpreters. 615 24$aComputer Science Logic and Foundations of Programming. 615 24$aSpecial Purpose and Application-Based Systems. 615 24$aComputer Communication Networks. 676 $a005.1 701 $aBernardo$b Marco$01754236 701 $aDegano$b Pierpaolo$f1950-$01750376 701 $aZavattaro$b Gianluigi$01754873 712 12$aInternational School on Formal Methods for the Design of Computer, Communication, and Software Systems. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483251403321 996 $aFormal methods for computational systems biology$94193279 997 $aUNINA