From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems. We have called attention to four aspects: (i) A choice has to be made about the kind of equations one extracts from the predominantly verbal arguments about the basic assumptions, and subsequently uses as a starting point for a rigorous mathematical analysis. Though differential equations are easy to formulate (different mechanisms don't interact in infinites­ imal time intervals and so end up as separate terms in the equations) they may be hard to interpret rigorously as infinitesimal generators. Integral equations constitute an attractive alternative. (ii) The ability of physiologically structured population models to increase our un­ derstanding of the relation between mechanisms at the i-level and phenomena at the p-level will depend strongly on the development of dynamical systems lab facilities which are applicable to this class of models. (iii) Physiologically structured population models are ideally suited for the for­ mulation of evolutionary questions. Apart from the special case of age (see Charlesworth 1980, Yodzis 1989, Caswell 1989, and the references given there) hardly any theory exists at the moment. This will, hopefully, change rapidly in the coming years. Again the development of appropriate software may turn out to be crucial.

Computational Genome Analysis: An Introduction presents the foundations of key problems in computational molecular biology and bioinformatics. It focuses on computational and statistical principles applied to genomes, and introduces the mathematics and statistics that are crucial for understanding these applications. The book is appropriate for a one-semester course for advanced undergraduate or beginning graduate students, and it can also introduce computational biology to computer scientists, mathematicians, or biologists who are extending their interests into this exciting field.

This book gathers papers presented at the Workshop on Computational Diffusion MRI, CDMRI 2020, held under the auspices of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), which took place virtually on October 8th, 2020, having originally been planned to take place in Lima, Peru.

In this monograph, new combinatorial and computational approaches in the study of RNA structures are presented which enhance both mathematics and computational biology. It begins with an introductory chapter, which motivates and sets the background of this research. In the following chapter, all the concepts are systematically developed. The reader will find * integration of more than forty research papers covering topics like, RSK-algorithm, reflection principle, singularity analysis and random graph theory * systematic presentation of the theory of pseudo-knotted RNA structures including their generating function, uniform generation as well as central and discrete limit theorems * computational biology of pseudo-knotted RNA structures, including dynamic programming paradigms and a new folding algorithm * analysis of neutral networks of pseudo knotted RNA structures and their random graph theory, including neutral paths, giant components and connectivity All algorithms presented are freely available through springer.com and implemented in C. A proofs section at the end contains the necessary technicalities. This book will serve graduate students and researchers in the fields of discrete mathematics, mathematical and computational biology. It is suitable as a textbook for a graduate course in mathematical and computational biology.

This two-volume set LNCS 10954 and LNCS 10955 constitutes - in conjunction with the volume LNAI 10956 - the refereed proceedings of the 14th International Conference on Intelligent Computing, ICIC 2018, held in Wuhan, China, in August 2018. The 275 full papers and 72 short papers of the three proceedings volumes were carefully reviewed and selected from 632 submissions.

Arguably the most intricate dynamic object in the universe, the human brain is an unsounded source of wonder for the scienti?c community. The primary aim of this book is to provide both students and established - vestigators in the growing area of neuroscience with an appreciation of the roles that mathematics may play in helping to understand this en- maticorgan. Alongwithdiscussionsofresultsobtainedbytheneuroscience community, emphasis is placed on suggesting fruitful research problems for those planning to embark on mathematical studies in neuroscience. To make the overall perspectives understandable to philosophers and psychologists, essential features of the discussions are presented in ordinary English, with more detailed mathematical comments in appendices and footnotes. Although it attempts to maintain both clarity and biological relevance, this is not a text on the anatomy of nerve systems; thus readers should bring some knowledge of neurophysiology through other courses, associated studies, or laboratory research. It is a guiding theme throughout the book that the brain is organized into several quite di?erent levels of dynamic activity. As will be seen, these levels are hierarchically structured, beginning with the molecular dynamics ofintrinsicmembraneproteinsandproceedingupward,throughtheswit- ing properties of active membrane patches and synapses, the emergence of impulses on active ?bers, overall properties of individual neurons, and the growth of functional assemblies of interacting neurons, to the global - namics of a brain. At each level of description, reality turns di?erent facets of her mystery to us, and diverse phenomena make their contributions to the brain’s collective behavior.

Presents a discrete in time-space universal map of relative dynamics that is used to unfold an extensive catalogue of dynamic events not previously discussed in mathematical or social science literature. With emphasis on the chaotic dynamics that may ensue, the book describes the evolution on the basis of temporal and locational advantages. It explains nonlinear discrete time dynamic maps primarily through numerical simulations. These very rich qualitative dynamics are linked to evolution processes in socio-spatial systems. Important features include: The analytical properties of the one-stock, two- and three-location map; the numerical results from the one- and two-stock, two- and three-location dynamics; and the demonstration of the map's potential applicability in the social sciences through simulating population dynamics of the U.S. Regions over a two-century period. In addition, this book includes new findings: the Hopf equivalent discrete time dynamics bifurcation; the Feigenbaum slope-sequences; the presence of strange local attractors and containers; switching of extreme states; the presence of different types of turbulence; local and global turbulence. Intended for researchers and advanced graduate students in applied mathematics and an interest in dynamics and chaos. Mathematical social scientists in many other fields will also find this book useful.

During the past decade, geneticists have constructed detailed maps of the human genome and cloned scores of Mendelian disease genes. They now stand on the threshold of sequencing the genome in its entirety. The unprecedented insights into human disease and evolution offered by mapping and sequencing will transform medicine and agriculture. This revolution depends vitally on the contributions of applied mathematicians, statisticians, and computer scientists. Mathematical and Statistical Methods for Genetic Analysis is written to equip graduate students in the mathematical sciences to understand and model the epidemiological and experimental data encountered in genetics research. Mathematical, statistical, and computational principles relevant to this task are developed hand in hand with applications to gene mapping, risk prediction, and the testing of epidemiological hypotheses. The book includes many topics currently accessible only in journal articles, including pedigree analysis algorithms, Markov chain Monte Carlo methods, reconstruction of evolutionary trees, radiation hybrid mapping, and models of recombination. Exercise sets are included.

This two-volume set LNCS 10954 and LNCS 10955 constitutes - in conjunction with the volume LNAI 10956 - the refereed proceedings of the 14th International Conference on Intelligent Computing, ICIC 2018, held in Wuhan, China, in August 2018. The 275 full papers and 72 short papers of the three proceedings volumes were carefully reviewed and selected from 632 submissions.

Food webs hold a central place in ecology. They describe which organisms feed on which others in natural habitats. This book describes recently discovered empirical regularities in real food webs: it proposes a novel theory unifying many of these regularities, as well as extensive empirical data. After a general introduction, reviewing the empirical and theoretical discoveries about food webs, the second portion of the book shows that community food webs obey several striking phenomenological regularities. Some of these unify, regardless of habitat. Others differentiate, showing that habitat significantly influences structure. The third portion of the book presents a theoretical analysis of some of the unifying empirical regularities. The fourth portion of the book presents 113 community food webs. Collected from scattered sources and carefully edited, they are the empirical basis for the results in the volume. The largest available set of data on community food webs provides a valuable foundation for future studies of community food webs. The book is intended for graduate students, teachers and researchers primarily in ecology. The theoretical portions of the book provide materials useful to teachers of applied combinatorics, in particular, random graphs. Researchers in random graphs will find here unsolved mathematical problems.

This two-volume set LNCS 10954 and LNCS 10955 constitutes - in conjunction with the volume LNAI 10956 - the refereed proceedings of the 14th International Conference on Intelligent Computing, ICIC 2018, held in Wuhan, China, in August 2018. The 275 full papers and 72 short papers of the three proceedings volumes were carefully reviewed and selected from 632 submissions.

This book gathers the proceedings of MEDICON 2019 – the XV Mediterranean Conference on Medical and Biological Engineering and Computing – which was held in September 26-28, 2019, in Coimbra, Portugal. A special emphasis has been given to practical findings, techniques and methods, aimed at fostering an effective patient empowerment, i.e. to position the patient at the heart of the health system and encourages them to be actively involved in managing their own healthcare needs. The book reports on research and development in electrical engineering, computing, data science and instrumentation, and on many topics at the interface between those disciplines. It provides academics and professionals with extensive knowledge on cutting-edge techniques and tools for detection, prevention, treatment and management of diseases. A special emphasis is given to effective advances, as well as new directions and challenges towards improving healthcare through holistic patient empowerment.

This book gathers papers presented at the Workshop on Computational Diffusion MRI, CDMRI 2020, held under the auspices of the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI), which took place virtually on October 8th, 2020, having originally been planned to take place in Lima, Peru.

With the availability of high speed computers and advances in computational techniques, the application of mathematical modeling to biological systems is expanding. This comprehensive and richly illustrated volume provides up-to-date, wide-ranging material on the mathematical modeling of kidney physiology, including clinical data analysis and practice exercises. Basic concepts and modeling techniques introduced in this volume can be applied to other areas (or organs) of physiology.