De Gruyter Series in Mathematics and Life Sciences – serie

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.

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 covariatesMeasurement error modelsLinear models with classical errorPolynomial regression with known variance of classical errorNonlinear and generalized linear models Part II Radiation risk estimation under uncertainty in exposure dosesOverview of risk models realized in program package EPICUREEstimation of radiation risk under classical or Berkson multiplicative error in exposure dosesRadiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accidentElements of estimating equations theoryConsistency of efficient methodsEfficient SIMEX method as a combination of the SIMEX method and the corrected score methodApplication of regression calibration in the model with additive error in exposure doses

The aim of this monograph is to initiate and facilitate a systematic study of the global asymptotic behavior of nonlinear nonautonomous difference equations. In addition to general classes of nonautonomous equations, a focus lies on some special classes including periodic and asymptotically autonomous equations. The authors' primary goal is to study global stability, in particular the extreme stability (path stability), as well as the global asymptotic stability in periodic equations. In addition, they explore the oscillatory character of solutions including semicycles analysis, boundednes and persistence, permanence, the existence and the character of solutions having special properties such as periodicity, unboundedness, or monotonicity. Special attention is placed on the notion of attenuance and resonance of periodic cycles and their generalizations. This monograph presents to the reader a broad spectrum of approaches to the mentioned problems and contains several important developments in this area with applications mainly to Mathematical Biology as well as to other disciplines. In the Appendix some issues about the dynamics of discontinuous population models and discontinuous difference equations are addressed. The reader is exposed to the frontiers of the discipline, including a variety of important open problems and conjectures that require immediate attention.

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.

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.

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.

This book presents a heterodox approach to studying cancer progression in an individual patient and assessment of the effects of treatment. The book combines methodological, mathematical, statistical and computational sides of cancer modeling with biomedical and clinical insights. Understanding cancer-related processes through mathematical modeling reveals unobservable aspects of the natural history of cancer and unexpected effects of treatment. The book also gives an unvarnished account of what stands in the way of winning the war on cancer.

This book presents life phenomena in terms of physics with an element of philosophy. It is written for university graduates and undegraduate students, who are yet to see that there is no clean cut between the different sciences. The physics concepts of nonlinearity, equilibrium, energy, entropy, system, and information are applied to the biological processes of metabolism, organism development and evolution.

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. You can find "BIOKYBERNETIKA II - Thermodynamics, Functional Physiology, Process Control, and Society Impact" here https://www.degruyterbrill.com/document/isbn/9783112216811/html

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.

The premise of this book is that by understanding the initial conditions at the origins of reality, we can comprehend how all of our observable physical systems (including chemical and biological systems) have emerged. The book focuses on familiar principles of quantum physics and provides very simple derivations of the Heisenberg Uncertainty Principle, Pauli's Exclusion Principle, Schrodinger's wave equation, Noether's theorem, and the Continuity Equation. Background is provided in group theory and symmetries. Using these concepts, the book explores the nature of vacuum, of fundamental constants and particles, and of physical laws. Building on these basic principles, the book explains the emergence of atoms, the natural elements, chemical reactions, and life. In the process, numerous paradoxes are encountered and solved.

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.