De Gruyter Series in Mathematics and Life Sciences

The publication of this book is motivated by the need to present the latest research & advancements in the fields of Fluid/Solid Mechanics, Nonlinear Dynamics, and Differential Equations in Applied Mathematics. This book gathers the work of leading experts, offering cutting-edge findings addressing existing challenges in the field. It covers a broad spectrum of topics, including advanced computational methods/mathematical modeling/different Mathematical methods & their applications in many scientific disciplines like predicting the nature and behavior of physical systems in engineering. These problems often require solving differential equations governing fluid flow, heat transfer, and structural deformation, often simultaneously, among other topics. Each chapter delves into specific problems, showcasing interdisciplinary approaches & demonstrating the practical impact of mathematical research on real-world issues. This book is a great resource for scholars, professionals, and researchers as it offers a comprehensive overview of cutting-edge methodologies & innovative solutions. It aims to stimulate additional investigation, promote interdisciplinary collaboration & make substantial contributions to advancing knowledge.

Information about the author:

Fateh Mebarek-Oudina received his PhD in 2010. He has published more than 120 papers in reputed international journals. Currently, he works as a full professor at Skikda University in Algeria and regularly serves as a reviewer for more than 250 international journals. He is ranked in the Top 2% Scientists Worldwide (2020, 2021, 2022, 2023) by Stanford University. His research work is focused on heat and mass transfer, MHD, mathematical simulation and modelling, biofluids, nanofluids, hybrid nanofluids, ternary nanofluids, microfluidics, and computational fluid dynamics.

Information abiout the book:

Mathematical modeling presented in the book is designed to help engineers understand physical systems, including magnetohydrodynamic effects on the non-Newtonian fluid flow and multiphase flow. Special attention will be given to heat transfer and entropy generation analysis on hybrid nanofluids. The process of entropy generation for nanofluid flows through porous channels will also be discussed and analyzed by means of a theoretical approach and CFD modeling. Some applications to blood-mediated gold-silver nanoparticles will be presented with detailed numerical examples. The book is designed to facilitate a more profound understanding for engineers of adopting CFD models to natural manufacturing environments. Overall, the primary objective of the book is to present mathematical modeling with CFD applications to simulate real-world engineering, industrial, and medical science problems to expose various analytical and numerical techniques and, at the same time, extend to expose researchers and academicians to the recent advancement in these diverse fields.

This book aims to engage “Young Science – Talented & Ambitious” for a lasting collaboration to advance holistic mathematical modeling of “how the body works” in variant surroundings. The book sets road signs to mathematics in body’s vital, physical, and cognitive functions, as well as to factors of health impact in person’s environmental and social settings. It showcases selected current research in mathematical and biological theory, mathematical models at molecular, organism, and population levels as well as engineering, imaging, and data sciences methodologies, including bio-informatics and machine learning applications. For overarching theory, evaluation of surrogate structures with category theory, multi-scale whole-body dynamics by separation of functional organization from cellular material as well as mathematical axioms matching classic principles of philosophy in traditional Chinese medicine are introduced. Interested are systems-oriented researchers in all sciences related to human health who seek new profile-shaping challenges in transdisciplinary collaboration.

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.

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.

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.

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.

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

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.

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.

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.