This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed. Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e.g. astrophysics, or for electrons on superfluid helium. The book brings together the research of the best international experts in seemingly very different disciplinary areas.

Biological Oscillators: Their Mathematical Analysis introduces the main features of the dynamic properties of biological oscillators and the mathematical techniques necessary for their investigation. It is not a comprehensive description of all known biological oscillators, since this would require a much bigger volume as well as a different type of expertise. Instead certain classes of biological oscillators are described, and then only in as much detail as required for the study of their dynamics. The opening chapter reviews fundamental mathematical concepts and techniques which will be used in the remainder of the book. These include phase plane techniques; asymptotic techniques of Krylov, Bogoliubov, and Mitopolski; and the describing function. Subsequent chapters discuss examples of biological oscillators; phase shifts and phase response curves; the entrainment of oscillators by external inputs; the dynamics of circadian oscillators; effects of changing environment on the dynamics of biological oscillators; the features peculiar to populations of interacting oscillators; and biological phenomena attributable to populations of oscillators.

An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.

As 1 review these pages, the last of them written in Summer 1978, some retrospec tive thoughts come to mind which put the whole business into better perspective for me and might aid the prospective reader in choosing how to approach this volume. The most conspicuous thought in my mind at present is the diversity of wholly independent explorations that came upon phase singularities, in one guise or another, during the past decade. My efforts to gather the published literature during the last phases of actually writing a whole book about them were almost equally divided between libraries of Biology, Chemistry, Engineering, Mathematics, Medicine, and Physics. A lot of what 1 call "gathering " was done somewhat in anticipation in the form of cönjecture, query, and prediction based on analogy between developments in different fields. The consequence throughout 1979 was that our long-suffering publisher re peatedly had to replace such material by citation of unexpected flurries of papers giving substantive demonstration. 1 trust that the authors of these many excellent reports, and especially of those I only found too late, will forgive the brevity of allusion I feIt compelled to observe in these substitutions. A residue of loose ends is largely collected in the index under "QUERIES. " It is c1ear to me already that the materials I began to gather several years ago represented only the first flickering of what turns out to be a substantial conflagration.

​ This volume brings together a unique collection of protocols that cover standard, novel, and specialized techniques. Cell Cycle Oscillators: Methods and Protocols guides readers through recent progress in the field from both holistic and reductionist perspectives, providing the latest developments in molecular biology techniques, biochemistry, and computational analysis used for studying oscillatory networks. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Authoritative and cutting-edge, Cell Cycle Oscillators: Methods and Protocols will serve as an invaluable reference to gain further insight into the complex and incompletely understood processes that are involved in the cell cycle and its regulation by oscillatory networks.

Recent years have seen spectacular advances in the field of circadian biology. These have attracted the interest of researchers in many fields, including endocrinology, neurosciences, cancer, and behavior. By integrating a circadian view within the fields of endocrinology and metabolism, researchers will be able to reveal many, yet-unsuspected aspects of how organisms cope with changes in the environment and subsequent control of homeostasis. This field is opening new avenues in our understanding of metabolism and endocrinology. A panel of the most distinguished investigators in the field gathered together to discuss the present state and the future of the field. The editors trust that this volume will be of use to those colleagues who will be picking up the challenge to unravel how the circadian clock can be targeted for the future development of specific pharmacological strategies toward a number of pathologies.

This book describes the fundamental process of senescence, and reviews a new concept developed by a number of research groups that is based on cellular senescence and its secretome. This concept provides a basic explanation of the main physiological and pathological features of senescence, and delineates possibilities for “treating” it. Following an introduction to the emerging medical landscape, the increasing incidence of a new epidemiological group (age-related “chronic non-transmissible diseases”), and the multiple origins of aging, the book explores and characterizes the senescent cell, which is linked to benign and pathological age-related manifestations. In turn, the closing chapters discuss how to “treat” or “prevent” the aging process, underscoring the central role of physical exercise and caloric reduction as compared to new senolytic approaches. Appendices are also provided, and address circadian rhythms, telomere shortening, diabetic cardiomyopathy, and senescence in plants and bacteria. Given its scope, the book will primarily be of interest to geriatricians, but will also appeal to a wider range of clinicians.