Vincenzo Capasso

Jacek Banasiak

Jacek Miekisz

Miroslaw Lachowicz

The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to biology and medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory, and game theory.

From Microscopic to Macroscopic

Multiscale Problems in the Life Sciences

Misha Gromov

Annick Harel-Bellan

Nadya Morozova

Linda Louise Pritchard

Pattern Formation in Morphogenesis is a rich source of interesting and challenging mathematical problems. The volume aims at showing how a combination of new discoveries in developmental biology and associated modelling and computational techniques has stimulated or may stimulate relevant advances in the field. Finally it aims at facilitating the process of unfolding a mutual recognition between Biologists and Mathematicians of their complementary skills, to the point where the resulting synergy generates new and novel discoveries. It offers an interdisciplinary interaction space between biologists from embryology, genetics and molecular biology who present their own work in the perspective of the advancement of their specific fields, and mathematicians who propose solutions based on the knowledge grasped from biologists.

Problems and Mathematical Issues

Pattern Formation in Morphogenesis

David Bakstein

This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. Balancing theory and applications, the authors use stochastic methods and concrete examples to model real-world problems from engineering, biomathematics, biotechnology, and finance. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. The book will be of interest to students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, physics, and engineering.

Theory, Models, and Applications to Finance, Biology, and Medicine

An Introduction to Continuous-Time Stochastic Processes

Giovanni Russo

Giuseppe Nicosia

Vittorio Romano

This book presents a collection of papers emphasizing applications of mathematical models and methods to real-world problems of relevance for industry, life science, environment, finance and so on. The biannual Conference of ECMI (the European Consortium of Mathematics in Industry) held in 2014 focused on various aspects of industrial and applied mathematics. The five main topics addressed at the conference were mathematical models in life science, material science and semiconductors, mathematical methods in the environment, design automation and industrial applications, and computational finance. Several other topics have been treated, such as, among others, optimization and inverse problems, education, numerical methods for stiff pdes, model reduction, imaging processing, multi physics simulation, mathematical models in textile industry. The conference, which brought together applied mathematicians and experts from industry, provided a unique opportunity to exchange ideas, problems and methodologies, bridging the gap between mathematics and industry and contributing to the advancement of science and technology. The conference has included a presentation of EU-Maths-In (European Network of Mathematics for Industry and Innovation), a recent joint initiative of ECMI and EMS. The proceedings from this conference represent a snapshot of the current activity in industrial mathematics in Europe, and are highly relevant to anybody interested in the latest applications of mathematics to industrial problems.

Progress in Industrial Mathematics at ECMI 2014

Jacques Periaux

This book consists of lecture notes of a summer school named after the late Jacques Louis Lions. The summer school was designed to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of socio-economic interest. This volume offers the reader a rare opportunity of being exposed to the presentation of real industrial and societal problems together with the relevant innovative methods used.

Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems

Ely Merzbach

B. Gail Ivanoff

Marco Dozzi

Robert Dalang

Thomas Mountford

The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, July 1-8, 2001

Topics in Spatial Stochastic Processes

Rossana Caselli

The design of more and more powerful computers, robots, flexible machine systems, etc. has increased the role of mathematicians in the field of high technology. To explore this role an International Workshop on the Mathematical Methods for Industrial Problems was held in Bari, Italy, 3--5 September 1988. The scope of the workshop was to exchange ideas and discuss problems encountered in the formulation, analysis and computer simulation of mathematical models of industrial processes. Problems of validation of models vs experimental data were also considered. This Proceedings volume contains the invited talks by lectures from universities and research centers involved in university--industry collaboration in the mathematical sciences. Also included are papers from experts from industries on mathematical problems arising in industry and the methods employed to solve them.

Proceedings of the International Workshop Held in Technopolis, Bari, Italy, September 3-5, 1988

Mathematical Methods for Industrial Problems

Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Vincenzo Capasso

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