Math Everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry. Dedicated to the 60th Birthday of Vincenzo Capasso PDF
Preview Math Everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry. Dedicated to the 60th Birthday of Vincenzo Capasso
MathEverywhere G. Aletti M. Burger A. Micheletti D. Morale Editors Math Everywhere Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry. Dedicated to the 60th Birthday of Vincenzo Capasso ABC GiacomoAletti MartinBurger AlessandraMicheletti InstitutfürNumerischeund DanielaMorale AngewandteMathematik WestfälischeWilhelms-UniversitätMünster ADAMSS&DepartmentofMathematics Einsteinstraße62 UniversityofMilano 48149Münster,Germany ViaC.Saldini50 E-mail:[email protected] 20133Milano,Italy E-mail:[email protected] [email protected] [email protected] Mathematics Subject Classification (2000): 35Kxx, 60D05, 28A75, 62M30, 62G05, 60G17,60H10,65C30,92B05 LibraryofCongressControlNumber:2006933717 ISBN-10 3-540-44445-9SpringerBerlinHeidelbergNewYork ISBN-13 978-3-540-44445-9SpringerBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsare liableforprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia springer.com (cid:1)c Springer-VerlagBerlinHeidelberg2007 Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:bytheauthorsandtechbooksusingaSpringerLATEXmacropackage Coverdesign:design&productionGmbH,Heidelberg Printedonacid-freepaper SPIN:11862000 46/techbooks 543210 “Do you really want to mathematize everything?” Jacques-Louis Lions Preface The title of the book is a perfect way to synthesize the point of view of Vin- cenzo Capasso (VK) about the role played by mathematics in nature and all human activities, as mentioned by Willi Ja¨ger in the Introduction. As VK mentioned in one of his speeches, “it is important that our scientific com- munity appreciates the importance of theory and mathematics to face the enormouschallengeswhicharisefromtheemergingfieldsofBiologyandMedi- cine, Industry and Economics to improve the quality of Life.” His enthusiasm and new ideas have brought him in this challenging mission. By transferring methods and tools from one field to another, by learning novel mathemat- ical methods and ideas from the observation of real world phenomena and behavior, and by approaching real industrial problems, he has accepted to play a fundamental role in both the Italian and European community in the establishment and reinforcement of communication channels between Acad- emia (methods) and Industry (applications), being himself a driving force of the scientific and technological progress that we are observing in our daily life. This books collects the proceedings of the workshop Math Everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and In- dustry which took place in Milano, Italy in the period September 4–6, 2005, and was organized in honor of the 60th birthday of Vincenzo Capasso (VK). It has been a successful meeting involving many prestigious scientists, in par- ticular mathematicians from all over the world who have discussed, in a very friendly and relaxed atmosphere, relevant innovative mathematical methods which have been developed to solve mathematically complex systems arisen in connection with real industrial, economic and social problems. The main featureofthemeetinghasbeenthevarietyofthethemesdiscussedbothfrom themathematicalandtheappliedpointofview,atanimpressivelyhighscien- tificlevel.IthasreflectedthewidespectrumofscientificinterestsofVincenzo Capasso, which have been ranging from the first papers on the mathematical foundations of Quantum Mechanics in the early 70s, through his fundamen- tal work on reaction-diffusion systems, including the qualitative behaviour, VIII Preface control problems and stochasticity of epidemic systems, published in many papers and a very cited book “Mathematical structures of epidemic systems” (an editorial success of the Lecture Notes in Biomathematics, published by Springer), up to the most recent work on time-and-space structured systems with evolving stochastic geometries. In this work, in which he has involved a numberofstudents/collaboratorsfromvariousuniversitiesinEurope,aseries of open problems have been faced including the strong coupling of evolu- tion equations for the (stochastic) geometries with the evolution equations of the underlying fields, at different scales. He has opened new mathematical problems at the interface of geometric measure theory, stochastic geometry, stochastic analysis, and statistics for evolution problems regarding densities, concentrations, i.e. relevant quantities describing the phenomena from an ap- plied point of view, so to match one of the most important goals in VK’s research, being useful to the applied sciences. Alongtheselines,theoreticallyorientedpapershavebeenpresentedinthe field of reaction-diffusion systems, control theory, stochastic geometry, multi- parameter stochastic processes and stochastic interacting particles. TheworkshophasbeenamirrorofVK’slivelyexperience:frombeingthe PresidentofESMTB,theEuropeanSocietyforMathematicalandTheoretical BiologyandthePresidentofECMI,theEuropeanConsortiumofMathematics in Industry; by establishing at first MIRIAM, the Milan Research Centre for Industrial and Applied Mathematics, and more recently ADAMSS, the InterdisciplinaryCentreforMathematicalModelling,StatisticalAnalysis,and ComputationalSimulationforScientificandTechnologicalInnovation,aiming at a daily interaction between Mathematics and all other research areas, to further innovation in Industry, Finance, Medicine, public services, etc., in collaboration with a number of other centres, universities and public research bodies,companies,organicallylinkedwithsimilaractivitiesatcommonlevels of excellence in Europe, and elsewhere. HererecentworksinBiomathematicsandMathematicalMedicinearepre- sented: Structured Populations and interacting Individuals, Tumour Cords, Vascular Cancer, Vasculogenesis, Epidemics Models, Competition Models, Glucose-Insulin Homeostasis, Pattern Formation in Butterflies, Quiescent States,ReactionDiffusionSystem,andNeutronLifetimeEstimationaresome of the main subjects investigated nowadays in the field. Furthermore in the industrial applications problems on the kinetics of nucleation and growth processes, crystallization phenomena and optimizing batch processes in the chemicalindustryhavebeeninvestigated.Finallyalsotheproblemofoptimal marketing in economics is presented here. It is worth to mention here that the opening lecture and the closing lec- ture have been delivered by Grace Yang and Willi Ja¨ger, respectively. Grace Yang has always been quoted by VK as his most influential scientific advisor, especially for introducing himself scientifically in one of the most prestigious SchoolsofMathematicalStatistics,theoneleadbyJerzyNeymanandLucien LeCam, whom, thanks to her, he had the chance to meet and discuss with. Preface IX Indeed his first relevant paper in probability was on the the asymptotics of the Neyman-Scott model of epidemics, a pioneering model of stochastic point processes;itwaswrittenbyanenthusiasticandbrilliantyoungscientistunder the guidance of Grace, first during the Summer School on Biomathematics at the Scuola Normale Superiore in Pisa (1972), and later at the Department of Mathematics of the University of Maryland (1973). Willi Ja¨ger has not only strongly influenced VK scientifically, by stimulating and encouraging him to face hard mathematical problems in the general area of nonlinear multiscale systems,butasWilliJa¨gerhasreported,theyhavedeeplysharedsuchaview of Mathematics Everywhere, supported by a genuine interest in facing chal- lenging problems in biomedicine of great relevance for the quality of life of humanbeings,bymeansofdifferentmathematicalmethodsandoftencreating problem-driven new ones. With elation we are happy to state that everyone has very much enjoyed the very warm atmosphere, and the fantastic richness of scientific ideas that have pervaded the whole meeting. X Preface Here we would like to thank VK, for sharing with us his enthusiasm and thisideaofamathematicsasatoolforachallengingmission.Yourenthusiasm and happiness of being a mathematician, but first of all a human being have soaked in our being scientists. Thanks! Milano, Linz, Giacomo Aletti July 2006 Martin Burger Alessandra Micheletti Daniela Morale Contents List of Contributors ...........................................XV Introduction Willi Ja¨ger...................................................... 1 Part I Deterministic and Stochastic Systems Coupled Dynamics and Quiescent Phases Karl P. Hadeler, Thomas Hillen ................................... 7 Long Time Behavior of a System of Stochastic Differential Equations Modelling Aggregation Vincenzo Capasso, Daniela Morale, Matteo Ortisi .................... 25 Invariant Density Estimation for Multidimensional Diffusions Annamaria Bianchi .............................................. 39 First Contact Distribution Function Estimation for a Partially Observed Dynamic Germ-Grain Model with Renewal Dropping Process Marcello De Giosa ............................................... 51 An Extension of the Kolmogorov-Avrami Formula to Inhomogeneous Birth-and-Growth Processes Martin Burger, Vincenzo Capasso, Alessandra Micheletti.............. 63 On the Generalized Geometric Densities of Random Closed Sets. An Application to Growth Processes Vincenzo Capasso, Elena Villa .................................... 77 The Multiparameter Fractional Brownian Motion Erick Herbin, Ely Merzbach ....................................... 93 XII Contents Filtering of Multiparameter Processes: Theory and Applications Alberto Carabar´ın-Aguirre, B. Gail Ivanoff, Adriana Jordan ..........103 IFSM Representation of Brownian Motion with Applications to Simulation Stefano Maria Iacus, Davide La Torre ..............................115 Iterated Function Systems on Multifunctions Davide La Torre, Franklin Mendivil, Edward R. Vrscay ...............125 Part II Mathematical Problems in Biology, Medicine and Ecology Stochastic Modeling and Estimation in a Neutron Lifetime Experiment Grace L. Yang, Kevin J. Coakley...................................141 The Transport of Specific Monoclonal Antibodies in Tumour Cords Alessandro Bertuzzi, Antonio Fasano, Alberto Gandolfi, Carmela Sinisgalli........................................................151 Structural Adaptation in Normal and Cancerous Vasculature Philip K. Maini, Toma´s Alarco´n, Helen M. Byrne, Markus R. Owen, James Murphy...................................................165 Approximation of 2D and 3D Models of Chemotactic Cell Movement in Vasculogenesis Fausto Cavalli, Andrea Gamba, Giovanni Naldi, Matteo Semplice ......179 Homogenization Closure For A Two-Dimensional Effective Model Describing Fluid-Structure Interaction in Blood Flow Andro Mikeli´c, Sunˇcica Cˇani´c .....................................193 Pattern Formation in Butterfly Wings: Experiments and Models Toshio Sekimura .................................................207 Stabilization for a Reaction-Diffusion System in Epidemiology Sebastian Ani¸ta..................................................219 Global Stability of Equilibria for a Metapopulation S–I–S Model Francesca Arrigoni, Andrea Pugliese ...............................229 State Feedback Control of the Glucose-Insulin System Pasquale Palumbo, Andrea De Gaetano .............................241
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