ThisvolumecelebratestheeightiethbirthdayofJosephB. Keller. The authors who contributed to this volume belong to what can be called the “Keller school of applied mathematics. ” They are former students, postdoctoral fellows and visiting scientists who have collaborated with Joe (some of them still do) during his long career. They all look at Joe as their ultimate (role) model. JoeKeller’sdistinguishedcareerhasbeendividedbetweentheCourant Institute of Mathematical Sciences at New York University, where he received all his degrees (his PhD adviser being the great R. Courant himself) and served as a professor for 30 years, and Stanford University, where he has been since 1978. The appended photos highlight some scenes from the old days. Those who know Joe Keller’s work have been always amazed by its diversity and breadth. It is considered a well-known truth that there is not a single important area in applied mathematics or physics which Keller did not contribute to. This can be appreciated, for example, by glancing through his list of publication included in this volume. App- priately, the papers in this book, written with Joe’s inspiration, cover a variety of application areas; together they span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to ?nance, waves, - croorganisms, shocks, DNA, ?ames, contact, optics, ?uids, bubbles and jets. Joe’s activity includes many more areas, which unfortunately are not represented here.

The International Statistical Institute was founded in 1885 and is therefore one of the world's oldest international scientific societies. The field of statistics is still expanding rapidly and possesses a rich variety of applications in many areas of human activity such as science, government, business, industry, and everyday affairs. In consequence, the celebration of the Institute's centenary in 1985 is of considerable interest not only to statisticians but also more widely to the international scientific community. As part of its centennial celebration planning the Institute decided to publish a volume of papers representing the immensely wide range of interests encompassed by statistics in its international context, viewed both from a historical and from a contemporary standpoint. We were fortunate in securing the services of Anthony Atkinson and Stephen Fienberg as Editors of this volume: they have worked hard over a period of several years to put together a most fascinating collection of papers. On behalf of the Institute it is my pleasant duty to thank them and the authors for their contributions. J. DURBIN, President International Statistical Institute Preface The papers in this volume were prepared to help celebrate the centenary of the International Statistical Institute. During the lSI's first 100 years statistics has matured, both as a scientific discipline and as a profession, in ways that the lSI's founders could not possibly have imagined.

The dynamics of infectious diseases represents one of the oldest and ri- est areas of mathematical biology. From the classical work of Hamer (1906) and Ross (1911) to the spate of more modern developments associated with Anderson and May, Dietz, Hethcote, Castillo-Chavez and others, the subject has grown dramatically both in volume and in importance. Given the pace of development, the subject has become more and more di?use, and the need to provide a framework for organizing the diversity of mathematical approaches has become clear. Enzo Capasso, who has been a major contributor to the mathematical theory, has done that in the present volume, providing a system for organizing and analyzing a wide range of models, depending on the str- ture of the interaction matrix. The ?rst class, the quasi-monotone or positive feedback systems, can be analyzed e?ectively through the use of comparison theorems, that is the theory of order-preserving dynamical systems; the s- ond, the skew-symmetrizable systems, rely on Lyapunov methods. Capasso develops the general mathematical theory, and considers a broad range of - amples that can be treated within one or the other framework. In so doing, he has provided the ?rst steps towards the uni?cation of the subject, and made an invaluable contribution to the Lecture Notes in Biomathematics. Simon A. Levin Princeton, January 1993 Author’s Preface to Second Printing In the Preface to the First Printing of this volume I wrote: \ . .

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.

MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.

The emphasis of this book lies in the teaching of mathematical modeling rather than simply presenting models. To this end the book starts with the simple discrete exponential growth model as a building block, and successively refines it. This involves adding variable growth rates, multiple variables, fitting growth rates to data, including random elements, testing exactness of fit, using computer simulations and moving to a continuous setting. No advanced knowledge is assumed of the reader, making this book suitable for elementary modeling courses. The book can also be used to supplement courses in linear algebra, differential equations, probability theory and statistics.