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Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

Mathematics. --- Economics, Mathematical. --- System theory. --- Statistical physics. --- Systems Theory, Control. --- Nonlinear Dynamics. --- Mathematical Biology in General. --- Quantitative Finance. --- Mathematics --- Mathematical models. --- Study and teaching. --- Models, Mathematical --- Simulation methods --- Systems theory. --- Finance. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Mathematical and Computational Biology. --- Funding --- Funds --- Economics --- Currency question --- Biomathematics. --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Biology --- Physics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Methodology --- Statistical methods --- Philosophy

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Cardiovascular diseases have a major impact in Western countries. Mathematical models and numerical simulations can help the understanding of physiological and pathological processes, complementing the information provided to medical doctors by medical imaging and other non-invasive means, and opening the possibility of a better diagnosis and more in-depth surgical planning.This book offers a mathematically sound and up-to-date foundation to the training of researchers, and serves as a useful reference for the development of mathematical models and numerical simulation codes. It is structured into different chapters, written by recognized experts in the field, and however it features a common thread, with consistency of notation and expressions and systematic cross-referencing. Many fundamental issues are faced, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls; the different scales coupling local and systemic dynamics. All of these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and simulation techniques. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling how the cardiovascular system works.

Mathematics. --- Applications of Mathematics. --- Cardiology. --- Mathematical Biology in General. --- Physiological, Cellular and Medical Topics. --- Mathematical Modeling and Industrial Mathematics. --- Partial Differential Equations. --- Differential equations, partial. --- Biology --- Physiology --- Mathématiques --- Cardiologie --- Cardiovascular system --- Mathematical models. --- Blood -- Diseases. --- Blood flow -- Mathematical models. --- Blood flow. --- Cardiovascular System --- Cardiovascular Physiological Processes --- Blood Physiological Phenomena --- Blood Physiological Processes --- Models, Biological --- Cardiovascular Physiological Phenomena --- Rheology --- Anatomy --- Investigative Techniques --- Circulatory and Respiratory Physiological Phenomena --- Models, Theoretical --- Blood Circulation --- Hemorheology --- Hemodynamics --- Models, Cardiovascular --- Blood Vessels --- Phenomena and Processes --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Engineering & Applied Sciences --- Human Anatomy & Physiology --- Health & Biological Sciences --- Applied Mathematics --- Circulatory system --- Vascular system --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Mathematical and Computational Biology. --- Blood --- Circulation --- Animal physiology --- Animals --- Heart --- Internal medicine --- Math --- Science --- Partial differential equations --- Diseases --- Models, Mathematical --- Simulation methods --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis

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How is genetic variability shaped by natural selection, demographic factors, and random genetic drift? To approach this question, we introduce and analyze a number of probability models beginning with the basics, and ending at the frontiers of current research. Throughout the book, the theory is developed in close connection with examples from the biology literature that illustrate the use of these results. Along the way, there are many numerical examples and graphs to illustrate the conclusions. This is the second edition and is twice the size of the first one. The material on recombination and the stepping stone model have been greatly expanded, there are many results form the last five years, and two new chapters on diffusion processes develop that viewpoint. This book is written for mathematicians and for biologists alike. No previous knowledge of concepts from biology is assumed, and only a basic knowledge of probability, including some familiarity with Markov chains and Poisson processes. The book has been restructured into a large number of subsections and written in a theorem-proof style, to more clearly highlight the main results and allow readers to find the results they need and to skip the proofs if they desire. Rick Durrett received his Ph.D. in operations research from Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in 1985. He is the author of eight books and 160 research papers, most of which concern the use of probability models in genetics and ecology. He is the academic father of 39 Ph.D. students and was recently elected to the National Academy of Sciences.

Mathematics. --- Evolutionary Biology. --- Genetics and Population Dynamics. --- Mathematical Biology in General. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Probability Theory and Stochastic Processes. --- Evolution (Biology). --- Genetics --- Biology --- Distribution (Probability theory). --- Statistics. --- Mathématiques --- Evolution (Biologie) --- Distribution (Théorie des probabilités) --- Statistique --- Evolutionary genetics --Statistical methods. --- Nucleotide sequence --Statistical methods. --- Probabilities. --- Variation (Biology) --Statistical methods. --- Evolutionary genetics --- Nucleotide sequence --- Probabilities --- Variation (Biology) --- Probability --- Evolution, Molecular --- Base Sequence --- Models, Genetic --- Molecular Structure --- Mathematical Concepts --- Models, Biological --- Biological Evolution --- Molecular Sequence Data --- Statistics as Topic --- Genetic Structures --- Documentation --- Biological Processes --- Genetic Processes --- Models, Theoretical --- Health Care Evaluation Mechanisms --- Epidemiologic Methods --- Phenomena and Processes --- Biochemical Phenomena --- Genetic Phenomena --- Biological Phenomena --- Chemical Phenomena --- Quality of Health Care --- Investigative Techniques --- Information Services --- Public Health --- Environment and Public Health --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Information Science --- Health Care Quality, Access, and Evaluation --- Health Care --- Health & Biological Sciences --- Statistical methods --- Statistical methods. --- Biological variation --- Statistical inference --- Analysis, Nucleic acid sequence --- Analysis, Nucleotide sequence --- Base sequence (Nucleic acids) --- DNA sequence --- Nucleic acid sequence analysis --- Nucleotide sequence analysis --- RNA sequence --- Sequence, Nucleotide --- Genetic evolution --- Biochemistry. --- Evolutionary biology. --- Biomathematics. --- Biochemistry, general. --- Mathematical and Computational Biology. --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Heredity --- Mutation (Biology) --- Nucleic acids --- Nucleotides --- Sequence alignment (Bioinformatics) --- Evolution (Biology) --- Analysis --- Distribution (Probability theory. --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Biological chemistry --- Chemical composition of organisms --- Organisms --- Physiological chemistry --- Chemistry --- Medical sciences --- Animal evolution --- Animals --- Biological evolution --- Darwinism --- Evolutionary biology --- Evolutionary science --- Origin of species --- Evolution --- Biological fitness --- Homoplasy --- Natural selection --- Phylogeny --- Distribution functions --- Frequency distribution --- Characteristic functions --- Composition --- Statistics .

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This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.

51-7 --- 51:37 --- 51:37 Mathematics-:-Opvoeding en onderwijs --(algemeen) --- Mathematics-:-Opvoeding en onderwijs --(algemeen) --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Neurosciences informatiques --- Differential Equations. --- Mathematical Biology in General. --- Ordinary Differential Equations. --- Computational Mathematics and Numerical Analysis. --- Computer Appl. in Life Sciences. --- Models, Neurological --- Nerve Net --- Mathematical Modeling and Industrial Mathematics. --- Muscle Contraction --- Musculoskeletal Physiological Processes --- Musculoskeletal Physiological Phenomena --- Experimental Model --- Experimental Models --- Mathematical Model --- Model, Experimental --- Models (Theoretical) --- Models, Experimental --- Models, Theoretic --- Theoretical Study --- Mathematical Models --- Model (Theoretical) --- Model, Mathematical --- Model, Theoretical --- Studies, Theoretical --- Study, Theoretical --- Theoretical Model --- Theoretical Models --- Theoretical Studies --- Nervous Systems --- System, Nervous --- Systems, Nervous --- Computer mathematics --- Metabolic Phenomenon --- Metabolic Process --- Metabolism Concepts --- Metabolism Phenomena --- Process, Metabolic --- Processes, Metabolic --- Anabolism --- Catabolism --- Metabolic Concepts --- Metabolic Processes --- Concept, Metabolic --- Concept, Metabolism --- Concepts, Metabolic --- Concepts, Metabolism --- Metabolic Concept --- Metabolism Concept --- Phenomena, Metabolic --- Phenomena, Metabolism --- Phenomenon, Metabolic --- Musculoskeletal Physiologic Process --- Musculoskeletal Physiological Concepts --- Musculoskeletal Physiological Phenomenon --- Physiology, Musculoskeletal --- Musculoskeletal Physiologic Processes --- Musculoskeletal Physiological Process --- Musculoskeletal Physiology --- Concept, Musculoskeletal Physiological --- Concepts, Musculoskeletal Physiological --- Musculoskeletal Physiological Concept --- Phenomena, Musculoskeletal Physiological --- Phenomenon, Musculoskeletal Physiological --- Physiologic Process, Musculoskeletal --- Physiologic Processes, Musculoskeletal --- Process, Musculoskeletal Physiologic --- Process, Musculoskeletal Physiological --- Processes, Musculoskeletal Physiologic --- Processes, Musculoskeletal Physiological --- Active Ion Transport --- Facilitated Ion Transport --- Passive Ion Transport --- Antiport --- Ion Cotransport --- Ion Exchange, Intracellular --- Symport --- Uniport --- Cotransport, Ion --- Exchange, Intracellular Ion --- Intracellular Ion Exchange --- Ion Transport, Active --- Ion Transport, Facilitated --- Ion Transport, Passive --- Transport, Active Ion --- Transport, Ion --- Second Messengers --- Intracellular Second Messengers --- Intracellular Second Messenger --- Messenger, Second --- Messengers, Intracellular Second --- Messengers, Second --- Second Messenger --- Second Messenger System --- Second Messenger, Intracellular --- Second Messengers, Intracellular --- System, Second Messenger --- Systems, Second Messenger --- Calcium Puffs --- Calcium Sparks --- Calcium Spikes --- Calcium Oscillations --- Calcium Waves --- Calcium Oscillation --- Calcium Puff --- Calcium Signalings --- Calcium Spark --- Calcium Spike --- Calcium Wave --- Oscillation, Calcium --- Oscillations, Calcium --- Puff, Calcium --- Puffs, Calcium --- Signaling, Calcium --- Signalings, Calcium --- Spark, Calcium --- Sparks, Calcium --- Spike, Calcium --- Spikes, Calcium --- Wave, Calcium --- Waves, Calcium --- Muscular Contraction --- Inotropism --- Contraction, Muscle --- Contraction, Muscular --- Contractions, Muscle --- Contractions, Muscular --- Inotropisms --- Muscle Contractions --- Muscular Contractions --- Calculus of Variations and Optimal Control; Optimization. --- Physiological, Cellular and Medical Topics. --- Cell Cycle --- Processes, Cell Growth --- Cell Division Cycle --- Cell Cycles --- Cell Division Cycles --- Cycle, Cell --- Cycle, Cell Division --- Cycles, Cell --- Cycles, Cell Division --- Division Cycle, Cell --- Division Cycles, Cell --- Cell Multiplication --- Cell Number Growth --- Cell Growth in Number --- Cellular Proliferation --- Growth, Cell Number --- Multiplication, Cell --- Number Growth, Cell --- Proliferation, Cell --- Proliferation, Cellular --- Mathematics. --- Cell biology. --- Mathematical models. --- Biomathematics. --- Mathematical and Computational Biology. --- Cell Biology. --- Differential equations. --- Partial differential equations. --- Calculus of variations. --- Partial Differential Equations. --- Bioinformatics. --- Computational biology. --- Neurobiology. --- Computer mathematics. --- Ecology --- Evolution (Biology) --- Phylogeny --- Population genetics --- Animal phylogeny --- Animals --- Phylogenetics --- Phylogeny (Zoology) --- Biology --- Mathematical models --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc --- Math --- Science --- Mathematics --- Models, Mathematical --- Simulation methods --- Cell biology --- Cellular biology --- Cells --- Cytologists --- Neurosciences --- Discrete mathematics --- Electronic data processing --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Bioinformatics --- Bio-informatics --- Biological informatics --- Information science --- Computational biology --- Systems biology --- Data processing --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Cellular signal transduction. --- Calcium --- Physiological effect. --- Computational neuroscience. --- Differential equations, partial. --- Mathematical optimization. --- Physiology --- Computer science --- Data processing. --- Cytology. --- Animal physiology --- Anatomy --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- System analysis --- Cell proliferation. --- Cell cycle. --- Cancer cells. --- Pathology, Cellular --- Mitotic cycle --- Nuclear cycle (Cytology) --- Biological rhythms --- Cell renewal --- Cellular proliferation --- Cell cycle --- Cell division --- Cell populations --- Growth --- Neural circuitry --- Auditory pathways. --- Cellular signal transduction --- Physiological transport --- Physiological effect --- Metabolism --- Bioinformatics . --- Computational biology . --- Calcium - Physiological effect.