Veröffentlicht von De Gruyter

De Gruyter Series in Mathematics and Life Sciences

Herausgegeben von: Vitaly Volpert, Andrei Chtcheprov, Anna Marciniak-Czochra, Benoît Perthame, Olga Vasieva und Jean-Philippe Vert

ISSN: 2195-5530

The De Gruyter Series in Mathematics and Life Sciences is devoted to the publication of monographs in the field. They cover topics and methods in fields of current interest that use mathematical approaches to understand and explain, model and influence phenomena in all areas of life sciences. This includes, among others, theory and application of biological mathematical modeling, complex systems biology, bioinformatics, computational biomodeling stochastic modeling, biostatistics, computational evolutionary biology, comparative genomics, or structural bioinformatics. Also, new types of mathematical problems that arise from biological knowledge shall be covered.

eISSN: 2195-5549

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The De Gruyter Series in Mathematics and Life Sciences is devoted to the publication of monographs in the field. They cover topics and methods in fields of current interest that use mathematical approaches to understand and explain, model and influence phenomena in all areas of life sciences. This includes, among others, theory and application of biological mathematical modeling, complex systems biology, bioinformatics, computational biomodeling stochastic modeling, biostatistics, computational evolutionary biology, comparative genomics, or structural bioinformatics. Also, new types of mathematical problems shall be covered that arise from biological knowledge.

The main objectives is to make such expositions available to and accessible by an interdisciplinary, growing readership hailing from all disciplines involved. The volumes shall convey the context of the given topic and enable these readers to understand, apply and develop further mathematical methods to given problems in biology. For this reason, works with up to four authors are preferred over edited volumes.

Therefore, contributions which are on the borderline of mathematics and life sciences and which stimulate further research at the crossroads of these areas are particularly welcome. In addition, use of electronic media to demonstrate, visualize and model the methods presented are very welcome, especially when interwoven with the written text.

Editor-in-Chief Vitaly Volpert, CNRS, University of Lyon, FR, Editorial Board Andrey Chtcheprov, USA, Anna Marciniak-Czochra, Heidelberg University, GR, Benoît Perthame, Sorbonne-Université, FR, Olga Vasieva, UK, Jean-Philippe Vert, FR

Buch 2019

Singularities of Solutions to Chemotaxis Systems

Piotr Biler

Band 6 in dieser Reihe

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The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.

DOI:: https://doi.org/10.1515/9783110599534
ISBN:: 9783110599534
ISBN:: 9783110598629
ISBN:: 9783110597899
Fachgebiet:: Biologie
Fachgebiet:: Zellbiologie
Fachgebiet:: Mathematik
Fachgebiet:: Analysis
Fachgebiet:: Differentialgleichungen und dynamische Systeme
Verlag:: De Gruyter

Buch 2020

Electroencephalography and Magnetoencephalography

An Analytical-Numerical Approach

George Dassios, Athanassios S. Fokas

Band 7 in dieser Reihe

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Electroencephalography and magnetoencephalography are the two most efficient techniques to study the functional brain. This book completely aswers the fundamental mathematical question of uniqueness of the representations obtained using these techniques, and also covers many other concrete results for special geometric models of the brain, presenting the research of the authors and their groups in the last two decades.

DOI:: https://doi.org/10.1515/9783110547535
ISBN:: 9783110547535
ISBN:: 9783110545838
ISBN:: 9783110545784
Fachgebiet:: Mathematik
Fachgebiet:: Numerik und wissenschaftliches Rechnen
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2017

Radiation Risk Estimation

Based on Measurement Error Models

Sergii Masiuk, Alexander Kukush, Sergiy Shklyar, Mykola Chepurny, Illya Likhtarov

Band 5 in dieser Reihe

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This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies.

Contents:

Part I - Estimation in regression models with errors in covariates
Measurement error models
Linear models with classical error
Polynomial regression with known variance of classical error
Nonlinear and generalized linear models

Part II Radiation risk estimation under uncertainty in exposure doses
Overview of risk models realized in program package EPICURE
Estimation of radiation risk under classical or Berkson multiplicative error in exposure doses
Radiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accident
Elements of estimating equations theory
Consistency of efficient methods
Efficient SIMEX method as a combination of the SIMEX method and the corrected score method
Application of regression calibration in the model with additive error in exposure doses

DOI:: https://doi.org/10.1515/9783110433661
ISBN:: 9783110433661
ISBN:: 9783110441802
ISBN:: 9783110433470
Fachgebiet:: Medizin
Fachgebiet:: Klinische Medizin
Fachgebiet:: Radiologie
Fachgebiet:: Mathematik
Fachgebiet:: Wahrscheinlichkeitstheorie und Statistik
Fachgebiet:: Angewandte Mathematik
Fachgebiet:: Physik
Fachgebiet:: Kern- und Teilchenphysik
Verlag:: De Gruyter

Buch 2013

Complexity and Evolution of Dissipative Systems

An Analytical Approach

Sergey Vakulenko

Band 4 in dieser Reihe

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This book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems.

DOI:: https://doi.org/10.1515/9783110268287
ISBN:: 978-3-11-026648-1
ISBN:: 978-3-11-026828-7
Fachgebiet:: Mathematik
Fachgebiet:: Diskrete Mathematik
Fachgebiet:: Angewandte Mathematik
Fachgebiet:: Physik
Fachgebiet:: Biophysik
Verlag:: De Gruyter

Buch 2013

Lotka-Volterra and Related Systems

Recent Developments in Population Dynamics

Shair Ahmad, Ivanka M. Stamova, Zhanyuan Hou, Benedetta Lisena, Marina Pireddu, Fabio Zanolin

Band 2 in dieser Reihe

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In recent years, there has been a tremendous amount of research activity in the general area of population dynamics, particularly the Lotka-Volterra system, which has been a rich source of mathematical ideas from both theoretical and application points of view.

In spite of the technological advances, many authors seem to be unaware of the bulk of the work that has been done in this area recently. This often leads to duplication of work and frustration to the authors as well as to the editors of various journals. This book is built out of lecture notes and consists of three chapters written by four mathematicians with overlapping expertise that cover a broad sector of the research in this area. Each chapter consists of carefully written introductory exposition, main breakthroughs, open questions and bibliographies.

The chapters present recent developments on topics involving the dynamic behavior of solutions and topics such as stability theory, permanence, persistence, extinction, existence of positive solutions for the Lotka-Volterra and related systems. This fills a void in the literature, by making available a source book of relevant information on the theory, methods and applications of an important area of research.

DOI:: https://doi.org/10.1515/9783110269840
ISBN:: 978-3-11-026951-2
ISBN:: 978-3-11-026984-0
Fachgebiet:: Biologie
Fachgebiet:: Ökologie
Fachgebiet:: Biologie, andere
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2012

Mathematics and Life Sciences

Alexandra V. Antoniouk, Roderick V. N. Melnik, Robert Anderssen, Andre Bouville, Helen M. Byrne, Mykola Chepurny, Maureen P. Edwards, Andrei V. Fursikov, Vassili N. Kolokoltsov, Natalia L. Komarova, Alexander A. Kovalevsky, Lina Kovgan, Alexander Kukush, János F. László, Illya Likhtarov, Anna Marciniak-Czochra, Sergii Masiuk, Taras A. Mel’nyk, Sergiy Pereverzyev Jr., Andrey V. Popov, Sergiy Shklyar, Vitaly A. Stepanenko, David Swigon, Nikolai Tarkhanov

Band 1 in dieser Reihe

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The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. The book provides also with a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important.

Many areas within life sciences are becoming increasingly quantitative and the progress in those areas will be more and more dependent on the successful development of advanced mathematical, statistical and modelling methodologies and techniques. The state-of-the-art developments in such methodologies and techniques are scattered throughout research journals and hardly accessible to the practitioners in those areas. This book identifies a number of frontier areas where such methodologies and techniques have recently been developed and are to be published here for the first time, bringing substantial potential benefit to a range of applications in life sciences. In addition, the book contains several state-of-the-art surveys at the interface of mathematics and life sciences that would benefit a larger interdisciplinary community.

It is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.

DOI:: https://doi.org/10.1515/9783110288537
ISBN:: 978-3-11-027372-4
ISBN:: 978-3-11-028853-7
Fachgebiet:: Biologie
Fachgebiet:: Biochemie
Fachgebiet:: Biologie, andere
Fachgebiet:: Mathematik
Fachgebiet:: Numerik und wissenschaftliches Rechnen
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2023

Volume 2 Fitness Landscape, Red Queen, Evolutionary Enigmas, and Applications to Virology

Igor M. Rouzine

Teil des mehrbändigen Werks Mathematical Modeling of Evolution

Band 8/2 in dieser Reihe

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This two-volume work focuses on the mathematical aspects of Darwinian evolution starting from the basic model of stochastic evolution of a single isolated locus in the presence of mutation to the multi–locus models of sexual and asexual populations. Volume 2 discusses the inference of fi tness landscape from DNA sequence data, discovery of the evolutionary roles of enygmatic traits, co-evolution of adversarial species, and various applications to virus evolution.

DOI:: https://doi.org/10.1515/9783110697384
ISBN:: 9783110697384
ISBN:: 9783110697469
ISBN:: 9783110697315
Fachgebiet:: Informatik
Fachgebiet:: Bioinformatik
Fachgebiet:: Biologie
Fachgebiet:: Mikrobiologie und Virologie
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Fachgebiet:: Physik
Fachgebiet:: Biophysik
Verlag:: De Gruyter

Buch 2020

Volume 1 One-Locus and Multi-Locus Theory and Recombination

Igor M. Rouzine

Teil des mehrbändigen Werks Mathematical Modeling of Evolution

Band 8/1 in dieser Reihe

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The book will benefit a reader with a background in physical sciences and applied mathematics interested in the mathematical models of genetic evolution. In the first chapter, we analyze several thought experiments based on a basic model of stochastic evolution of a single genomic site in the presence of the factors of random mutation, directional natural selection, and random genetic drift. In the second chapter, we present a more advanced theory for a large number of linked loci. In the third chapter, we include the effect of genetic recombination into account and find out the advantage of sexual reproduction for adaptation. These models are useful for the evolution of a broad range of asexual and sexual populations, including virus evolution in a host and a host population.

DOI:: https://doi.org/10.1515/9783110615456
ISBN:: 9783110615456
ISBN:: 9783110607895
ISBN:: 9783110608199
Fachgebiet:: Informatik
Fachgebiet:: Bioinformatik
Fachgebiet:: Biologie
Fachgebiet:: Mikrobiologie und Virologie
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Fachgebiet:: Physik
Fachgebiet:: Biophysik
Verlag:: De Gruyter