Jacek Miekisz's Books

From Genetics to Mathematics

By: Miros?aw Lachowicz,Jacek Miekisz

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This volume contains pedagogical and elementary introductions to genetics for mathematicians and physicists as well as to mathematical models and techniques of population dynamics. It also offers a physicist's perspective on modeling biological processes. Each chapter starts with an overview followed by the recent results obtained by authors. Lectures are self-contained and are devoted to various phenomena such as the evolution of the genetic code and genomes, age-structured populations, demography, sympatric speciation, the Penna model, LotkaVolterra and other predator-prey models, evolutionary models of ecosystems, extinctions of species, and the origin and development of language. Authors analyze their models from the computational and mathematical points of view.

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Page Count

242

Publisher

World Scientific

Published Date

ISBN 10

9812837248

ISBN 13

9789812837240

Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz

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Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz

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.

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Page Count

340

Publisher

Springer

Published Date

ISBN 10

3540783628

ISBN 13

9783540783626

Methods of Small Parameter in Mathematical Biology

By: Jacek Banasiak,Mirosław Lachowicz

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Methods of Small Parameter in Mathematical Biology

By: Jacek Banasiak,Mirosław Lachowicz

This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools the authors describe allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.

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Page Count

295

Publisher

Springer Science & Business

Published Date

ISBN 10

3319051407

ISBN 13

9783319051406

Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz

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Multiscale Problems in the Life Sciences

From Microscopic to Macroscopic

By: Jacek Banasiak,Vincenzo Capasso,Miroslaw Lachowicz,Jacek Miekisz

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Solve jigsaw puzzle

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Page Count

330

Publisher

Springer

Published Date

ISBN 10

3540783601

ISBN 13

9783540783602

Book's by Jacek Miekisz

From Genetics to Mathematics

From Genetics to Mathematics

Multiscale Problems in the Life Sciences

Multiscale Problems in the Life Sciences

Methods of Small Parameter in Mathematical Biology

Methods of Small Parameter in Mathematical Biology

Multiscale Problems in the Life Sciences

Multiscale Problems in the Life Sciences

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