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| dynamic models in biology ellner: Dynamic Models in Biology Stephen P. Ellner, John Guckenheimer, 2011-09-19 From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering. |
| dynamic models in biology ellner: An Introduction to Undergraduate Research in Computational and Mathematical Biology Hannah Callender Highlander, Alex Capaldi, Carrie Diaz Eaton, 2020-02-17 Speaking directly to the growing importance of research experience in undergraduate mathematics programs, this volume offers suggestions for undergraduate-appropriate research projects in mathematical and computational biology for students and their faculty mentors. The aim of each chapter is twofold: for faculty, to alleviate the challenges of identifying accessible topics and advising students through the research process; for students, to provide sufficient background, additional references, and context to excite students in these areas and to enable them to successfully undertake these problems in their research. Some of the topics discussed include: • Oscillatory behaviors present in real-world applications, from seasonal outbreaks of childhood diseases to action potentials in neurons • Simulating bacterial growth, competition, and resistance with agent-based models and laboratory experiments • Network structure and the dynamics of biological systems • Using neural networks to identify bird species from birdsong samples • Modeling fluid flow induced by the motion of pulmonary cilia Aimed at undergraduate mathematics faculty and advanced undergraduate students, this unique guide will be a valuable resource for generating fruitful research collaborations between students and faculty. |
| dynamic models in biology ellner: A Course in Mathematical Biology Gerda de Vries, Thomas Hillen, Mark Lewis, Johannes M?ller, Birgitt Sch?nfisch, 2006-07-01 This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?. |
| dynamic models in biology ellner: Computational Neuroendocrinology Duncan J. MacGregor, Gareth Leng, 2016-03-03 Neuroendocrinology with its well defined functions, inputs, and outputs, is one of the most fertile grounds for computational modeling in neuroscience. But modeling is often seen as something of a dark art. This book aims to display the power of modeling approaches in neuroendocrinology, and to showcase its potential for understanding these complex systems. A recurring theme in neuroendocrinology is rhythms. How are rhythms generated, and what purpose do they serve? Are these two questions inextricably intertwined? This book is written for innocents, presuming no math beyond high school or computing beyond calculators. It seeks to lead the curious into the thinking of the modeler, providing the tools to the reader to understand models, and even develop their own, giving life to paper diagrams. The diverse chapters, from ion channels to networks, systems, and hormonal rhythms, each tell the story of a model serving to join the hard won dots of experimentation, mapping a new understanding, and revealing hidden knowledge. • Written by a team of internationally renowned researchers • Both print and enhanced e-book versions are available • Illustrated in full colour throughout This is the fourth volume in a new Series ‘Masterclass in Neuroendocrinology’ , a co- publication between Wiley and the INF (International Neuroendocrine Federation) that aims to illustrate highest standards and encourage the use of the latest technologies in basic and clinical research and hopes to provide inspiration for further exploration into the exciting field of neuroendocrinology. Series Editors: John A. Russell, University of Edinburgh, UK and William E. Armstrong, The University of Tennessee, USA • Written by a team of internationally renowned researchers • Both print and enhanced e-book versions are available • Illustrated in full colour throughout This is the fourth volume in a new Series ‘Masterclass in Neuroendocrinology’ , a co- publication between Wiley and the INF (International Neuroendocrine Federation) that aims to illustrate highest standards and encourage the use of the latest technologies in basic and clinical research and hopes to provide inspiration for further exploration into the exciting field of neuroendocrinology. Series Editors: John A. Russell, University of Edinburgh, UK and William E. Armstrong, The University of Tennessee, USA |
| dynamic models in biology ellner: Mathematical Methods in Biology J. David Logan, William Wolesensky, 2009-08-17 A one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciences Highlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals the growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory. The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic. In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLAB®, but can also be replicated using other software packages, including R, Mathematica®, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study. Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics. |
| dynamic models in biology ellner: Evolutionary Equations with Applications in Natural Sciences Jacek Banasiak, Mustapha Mokhtar-Kharroubi, 2014-11-07 With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering. |
| dynamic models in biology ellner: Mathematical Immunology of Virus Infections Gennady Bocharov, Vitaly Volpert, Burkhard Ludewig, Andreas Meyerhans, 2018-06-12 This monograph concisely but thoroughly introduces the reader to the field of mathematical immunology. The book covers first basic principles of formulating a mathematical model, and an outline on data-driven parameter estimation and model selection. The authors then introduce the modeling of experimental and human infections and provide the reader with helpful exercises. The target audience primarily comprises researchers and graduate students in the field of mathematical biology who wish to be concisely introduced into mathematical immunology. |
| dynamic models in biology ellner: Physical Biology of the Cell Rob Phillips, Jane Kondev, Julie Theriot, Hernan Garcia, 2012-10-29 Physical Biology of the Cell is a textbook for a first course in physical biology or biophysics for undergraduate or graduate students. It maps the huge and complex landscape of cell and molecular biology from the distinct perspective of physical biology. As a key organizing principle, the proximity of topics is based on the physical concepts that |
| dynamic models in biology ellner: Multiple Time Scale Dynamics Christian Kuehn, 2015-02-25 This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective. |
| dynamic models in biology ellner: The Physics of Living Processes Thomas Andrew Waigh, 2014-10-20 This full-colour undergraduate textbook, based on a two semester course, presents the fundamentals of biological physics, introducing essential modern topics that include cells, polymers, polyelectrolytes, membranes, liquid crystals, phase transitions, self-assembly, photonics, fluid mechanics, motility, chemical kinetics, enzyme kinetics, systems biology, nerves, physiology, the senses, and the brain. The comprehensive coverage, featuring in-depth explanations of recent rapid developments, demonstrates this to be one of the most diverse of modern scientific disciplines. The Physics of Living Processes: A Mesoscopic Approach is comprised of five principal sections: • Building Blocks • Soft Condensed Matter Techniques in Biology • Experimental Techniques • Systems Biology • Spikes, Brains and the Senses The unique focus is predominantly on the mesoscale — structures on length scales between those of atoms and the macroscopic behaviour of whole organisms. The connections between molecules and their emergent biological phenomena provide a novel integrated perspective on biological physics, making this an important text across a variety of scientific disciplines including biophysics, physics, physical chemistry, chemical engineering and bioengineering. An extensive set of worked tutorial questions are included, which will equip the reader with a range of new physical tools to approach problems in the life sciences from medicine, pharmaceutical science and agriculture. |
| dynamic models in biology ellner: Computer Methods Part B , 2009-11-05 The combination of faster, more advanced computers and more quantitatively oriented biomedical researchers has recently yielded new and more precise methods for the analysis of biomedical data. These better analyses have enhanced the conclusions that can be drawn from biomedical data, and they have changed the way that experiments are designed and performed. This volume, along with previous and forthcoming Computer Methods volumes for the Methods in Enzymology serial, aims to inform biomedical researchers about recent applications of modern data analysis and simulation methods as applied to biomedical research. - Presents step-by-step computer methods and discusses the techniques in detail to enable their implementation in solving a wide range of problems - Informs biomedical researchers of the modern data analysis methods that have developed alongside computer hardware - Presents methods at the nuts and bolts level to identify and resolve a problem and analyze what the results mean |
| dynamic models in biology ellner: Mathematics as a Laboratory Tool John Milton, Toru Ohira, 2021-08-11 The second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students. The focus is on dynamics and the effects of time delays and stochastic perturbations (“noise”) on the regulation provided by feedback control systems. The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology. The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations. Every effort has been made to ensure that the material is accessible to those with a background in calculus. The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools. Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem. |
| dynamic models in biology ellner: Molecular Mechanisms that Orchestrate the Assembly of Antigen Receptor Loci , 2015-11-16 Molecular Mechanisms That Orchestrate the Assembly of Antigen Receptor Loci, the latest volume in the Advances in Immunology series focuses on the generation of an effective immune response to invading pathogens As B and T lymphocytes are characterized by the expression of antigen receptors that specifically recognize determinants expressed on pathogens, this volume discusses how antigen receptors are synthesized in B and T lymphocytes. - Focuses on the generation of an effective immune response to invading pathogens - Contains contributions from leading authorities - Informs and updates on all the latest developments in the field of immunology |
| dynamic models in biology ellner: Dynamical Modeling of Biological Systems Stilianos Louca, 2023-06-07 This book introduces concepts and practical tools for dynamical mathematical modeling of biological systems. Dynamical models describe the behavior of a system over time as a result of internal feedback loops and external forcing, based on mathematically formulated dynamical laws, similarly to how Newton's laws describe the movement of celestial bodies. Dynamical models are increasingly popular in biology, as they tend to be more powerful than static regression models. This book is meant for undergraduate and graduate students in physics, applied mathematics and data science with an interest in biology, as well as students in biology with a strong interest in mathematical methods. The book covers deterministic models (for example differential equations), stochastic models (for example Markov chains and autoregressive models) and model-independent aspects of time series analysis. Plenty of examples and exercises are included, often taken or inspired from the scientific literature, and covering a broad range of topics such as neuroscience, cell biology, genetics, evolution, ecology, microbiology, physiology, epidemiology and conservation. The book delivers generic modeling techniques used across a wide range of situations in biology, and hence readers from other scientific disciplines will find that much of the material is also applicable in their own field. Proofs of most mathematical statements are included for the interested reader, but are not essential for a practical understanding of the material. The book introduces the popular scientific programming language MATLAB as a tool for simulating models, fitting models to data, and visualizing data and model predictions. The material taught is current as of MATLAB version 2022b. The material is taught in a sufficiently general way that also permits the use of alternative programming languages. |
| dynamic models in biology ellner: Encyclopedia of Bioinformatics and Computational Biology , 2018-08-21 Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics, Three Volume Set combines elements of computer science, information technology, mathematics, statistics and biotechnology, providing the methodology and in silico solutions to mine biological data and processes. The book covers Theory, Topics and Applications, with a special focus on Integrative –omics and Systems Biology. The theoretical, methodological underpinnings of BCB, including phylogeny are covered, as are more current areas of focus, such as translational bioinformatics, cheminformatics, and environmental informatics. Finally, Applications provide guidance for commonly asked questions. This major reference work spans basic and cutting-edge methodologies authored by leaders in the field, providing an invaluable resource for students, scientists, professionals in research institutes, and a broad swath of researchers in biotechnology and the biomedical and pharmaceutical industries. Brings together information from computer science, information technology, mathematics, statistics and biotechnology Written and reviewed by leading experts in the field, providing a unique and authoritative resource Focuses on the main theoretical and methodological concepts before expanding on specific topics and applications Includes interactive images, multimedia tools and crosslinking to further resources and databases |
| dynamic models in biology ellner: Landscape Ecology in Theory and Practice Monica G. Turner, Robert H. Gardner, 2015-10-29 This work provides in-depth analysis of the origins of landscape ecology and its close alignment with the understanding of scale, the causes of landscape pattern, and the interactions of spatial pattern with a variety of ecological processes. The text covers the quantitative approaches that are applied widely in landscape studies, with emphasis on their appropriate use and interpretation. The field of landscape ecology has grown rapidly during this period, its concepts and methods have matured, and the published literature has increased exponentially. Landscape research has enhanced understanding of the causes and consequences of spatial heterogeneity and how these vary with scale, and they have influenced the management of natural and human-dominated landscapes. Landscape ecology is now considered mainstream, and the approaches are widely used in many branches of ecology and are applied not only in terrestrial settings but also in aquatic and marine systems. In response to these rapid developments, an updated edition of Landscape Ecology in Theory and Practice provides a synthetic overview of landscape ecology, including its development, the methods and techniques that are employed, the major questions addressed, and the insights that have been gained.” |
| dynamic models in biology ellner: Biophysical Tools for Biologists John J. Correia, H. William Detrich III, 2011-09-21 Driven in part by the development of genomics, proteomics, and bioinformatics as new disciplines, there has been a tremendous resurgence of interest in physical methods to investigate macromolecular structure and function in the context of living cells. This volume in Methods in Cell Biology is devoted to biophysical techniques in vitro and their applications to cellular biology. Biophysical Tools for Biologists covers methods-oriented chapters on fundamental as well as cutting-edge techniques in molecular and cellular biophysics. This book is directed toward the broad audience of cell biologists, biophysicists, pharmacologists, and molecular biologists who employ classical and modern biophysical technologies or wish to expand their expertise to include such approaches. It will also interest the biomedical and biotechnology communities for biophysical characterization of drug formulations prior to FDA approval. - Describes techniques in the context of important biological problems - Delineates critical steps and potential pitfalls for each method - Includes full-color plates to illustrate techniques |
| dynamic models in biology ellner: Technological Advancement in Instrumentation & Human Engineering Mohd Hasnun Arif Hassan, Mohd Hafizi Zohari, Kumaran Kadirgama, Nik Abdullah Nik Mohamed, Amir Aziz, 2022-08-10 This book (Technological Advancement in Instrumentation & Human Engineering) gathers selected papers submitted to the 6th International Conference on Mechanical Engineering Research in fields related to human engineering, ergonomics, vibration, instrumentation, Internet of Things and signal processing. This proceeding consists of papers in aforementioned related fields presented by researchers and scientists from universities, research institutes and industry showcasing their latest findings and discussions with an emphasis on innovations and developments in embracing the new norm, resulting from the COVID pandemic. |
| dynamic models in biology ellner: Transactions on Computational Collective Intelligence IX Ngoc Thanh Nguyen, 2013-02-12 These transactions publish research in computer-based methods of computational collective intelligence (CCI) and their applications in a wide range of fields such as the semantic Web, social networks and multiagent systems. TCCI strives to cover new methodological, theoretical, and practical aspects of CCI understood as the form of intelligence that emerges from the collaboration and competition of many individuals (artificial and/or natural). The application of multiple computational intelligence technologies such as fuzzy systems, evolutionary computation, neural systems, consensus theory, etc., aims to support human and other collective intelligence and to create new forms of CCI in natural and/or artificial systems. This ninth issue contains ten carefully selected and thoroughly revised contributions. |
| dynamic models in biology ellner: Mathematical Methods in Counterterrorism Nasrullah Memon, Jonathan David Farley, David L. Hicks, Torben Rosenorn, 2009-08-25 Terrorism is one of the serious threats to international peace and security that we face in this decade. No nation can consider itself immune from the dangers it poses, and no society can remain disengaged from the efforts to combat it. The termcounterterrorism refers to the techniques, strategies, and tactics used in the ?ght against terrorism. Counterterrorism efforts involve many segments of so- ety, especially governmental agencies including the police, military, and intelligence agencies (both domestic and international). The goal of counterterrorism efforts is to not only detect and prevent potential future acts but also to assist in the response to events that have already occurred. A terrorist cell usually forms very quietly and then grows in a pattern – sp- ning international borders, oceans, and hemispheres. Surprising to many, an eff- tive “weapon”, just as quiet – mathematics – can serve as a powerful tool to combat terrorism, providing the ability to connect the dots and reveal the organizational pattern of something so sinister. The events of 9/11 instantly changed perceptions of the wordsterrorist andn- work, especially in the United States. The international community was confronted with the need to tackle a threat which was not con?ned to a discreet physical - cation. This is a particular challenge to the standard instruments for projecting the legal authority of states and their power to uphold public safety. As demonstrated by the events of the 9/11 attack, we know that terrorist attacks can happen anywhere. |
| dynamic models in biology ellner: Chaos and Dynamical Systems David P. Feldman, 2019-08-06 Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences. |
| dynamic models in biology ellner: Biomolecular Feedback Systems Domitilla Del Vecchio, Richard Murray, 2014-10-26 This book provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. It begins with modeling tools such as reaction-rate equations, reduced-order models, stochastic models, and specific models of important core processes. It then describes in detail the control and dynamical systems tools used to analyze these models. These include tools for analyzing stability of equilibria, limit cycles, robustness, and parameter uncertainty. Modeling and analysis techniques are then applied to design examples from both natural systems and synthetic biomolecular circuits. In addition, this comprehensive book addresses the problem of modular composition of synthetic circuits, the tools for analyzing the extent of modularity, and the design techniques for ensuring modular behavior. It also looks at design trade-offs, focusing on perturbations due to noise and competition for shared cellular resources. Featuring numerous exercises and illustrations throughout, Biomolecular Feedback Systems is the ideal textbook for advanced undergraduates and graduate students. For researchers, it can also serve as a self-contained reference on the feedback control techniques that can be applied to biomolecular systems. Provides a user-friendly introduction to essential concepts, tools, and applications Covers the most commonly used modeling methods Addresses the modular design problem for biomolecular systems Uses design examples from both natural systems and synthetic circuits Solutions manual (available only to professors at press.princeton.edu) An online illustration package is available to professors at press.princeton.edu |
| dynamic models in biology ellner: Examining Robustness and Vulnerability of Networked Systems S. Butenko, E.L. Pasiliao, V. Shylo, 2014-06-19 Modern critical infrastructure is characterized by complex, heterogeneous and dynamically evolving networks. But these can be vulnerable to component failure, and this is a problem which must be addressed by realistic mathematical models. This book presents papers from the NATO Advanced Research Workshop (ARW), Examining Robustness and Vulnerability of Critical Infrastructure Networks, held in Kiev, Ukraine, in June 2013. Contributions were from workshop participants as well as invited experts in the field, and cover topics including: mathematical models; probability-based risk measures; algorithms for the design and detection of robust structures; identification of critical network components and case studies. This book will be of interest to researchers, practitioners and graduate students in the fields of mathematics, computer science and engineering. |
| dynamic models in biology ellner: Computer-Aided Biodesign Across Scales Thomas E. Gorochowski, Fabio Parmeggiani, Jonathan Karr, Boyan Yordanov, 2021-08-05 |
| dynamic models in biology ellner: Trends in Applied Intelligent Systems Nicolás García-Pedrajas, Francisco Herrera, Colin Fyfe, José Manuel Benítez Sánchez, Moonis Ali, 2011-01-22 Annotation The three volume set LNAI 6096, LNAI 6097, and LNAI 6098 constitutes the thoroughly refereed conference proceedings of the 23rd International Conference on Industrial Engineering and Other Applications of Applied Intelligend Systems, IEA/AIE 2010, held in Cordoba, Spain, in June 2010. The total of 119 papers selected for the proceedings were carefully reviewed and selected from 297 submissions. |
| dynamic models in biology ellner: An Invitation to Applied Mathematics Carmen Chicone, 2016-09-24 An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. - Presents an integrated wealth of modeling, analysis, and numerical methods in one volume - Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM - Includes a rich set of applications, with more appealing problems and projects suggested |
| dynamic models in biology ellner: Ordinary Differential Equations: Basics and Beyond David G. Schaeffer, John W. Cain, 2016-11-10 This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom). |
| dynamic models in biology ellner: History of Mathematics Vagn Lundsgaard Hansen, Jeremy Gray, 2010-12-20 History of Mathematics is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on History of Mathematics discusses: Mathematics in Egypt and Mesopotamia; History of Trigonometryto 1550; Mathematics in Japan; The Mathematization of The Physical Sciences-Differential Equations of Nature; A Short History of Dynamical Systems Theory:1885-2007; Measure Theories and Ergodicity Problems; The Number Concept and Number Systems; Operations Research and Mathematical Programming: From War to Academia - A Joint Venture; Elementary Mathematics From An Advanced Standpoint; The History and Concept of Mathematical Proof; Geometry in The 20th Century; Bourbaki: An Epiphenomenon in The History of Mathematics This volume is aimed at the following five major target audiences: University and College Students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers, NGOs and GOs. |
| dynamic models in biology ellner: Dynamical Models in Biology Miklós Farkas, 2001-06-15 Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation. Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists. Key Topics Include: - Chaotic dynamics of populations - The spread of sexually transmitted diseases - Problems of the origin of life - Models of immunology - Formation of animal hide patterns - The intuitive meaning of mathematical formulae explained with many figures - Applying new mathematical results in modeling biological phenomena Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education. - A 'down-to-earth' introduction to the growing field of modern mathematical biology - Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra |
| dynamic models in biology ellner: Advances in Behavioral Based Safety N. A. Siddiqui, Faisal Khan, S. M. Tauseef, Waddah S. Ghanem, Vikram Garaniya, 2022-06-15 This book presents the proceedings of the International Conference on Health, Safety, Fire, Environment, and Allied Sciences 2020. It highlights latest developments in the field of science and technology aimed at improving health and safety in the workplace. The volume comprises content from leading scientists, engineers, and policy makers discussing issues relating to industrial safety, fire hazards and their management in industry, forests and other settings. Also dealt with are issues of occupational health in engineering, process and agricultural industry and protection against incidents of arson and terror attacks. The contents of this volume will be of interest to researchers, practitioners, and policy makers alike. |
| dynamic models in biology ellner: Feedback Systems Karl Johan Åström, Richard Murray, 2021-02-02 The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory |
| dynamic models in biology ellner: Nonlinear Physics of Ecosystems Ehud Meron, 2015-04-15 Nonlinear Physics of Ecosystems introduces the concepts and tools of pattern formation theory and demonstrates their utility in ecological research using problems from spatial ecology. Written in language understandable to both physicists and ecologists in most parts, the book reveals the mechanisms of pattern formation and pattern dynamics. It als |
| dynamic models in biology ellner: Computer Methods, Part C , 2010-12-24 The combination of faster, more advanced computers and more quantitatively oriented biomedical researchers has recently yielded new and more precise methods for the analysis of biomedical data. These better analyses have enhanced the conclusions that can be drawn from biomedical data, and they have changed the way that experiments are designed and performed. This volume, along with the 2 previous Computer Methods volumes for the Methods in Enzymology serial, aims to inform biomedical researchers about recent applications of modern data analysis and simulation methods as applied to biomedical research. - Presents step-by-step computer methods and discusses the techniques in detail to enable their implementation in solving a wide range of problems - Informs biomedical researchers of the modern data analysis methods that have developed alongside computer hardware - Presents methods at the nuts and bolts level to identify and resolve a problem and analyze what the results mean |
| dynamic models in biology ellner: Dynamic Data Analysis James Ramsay, Giles Hooker, 2017-06-27 This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap. |
| dynamic models in biology ellner: The Nature of Mathematical Modeling Neil Gershenfeld, 2011-06-23 This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications. |
| dynamic models in biology ellner: Fundamentals of Neuromechanics Francisco J. Valero-Cuevas, 2015-09-07 This book provides a conceptual and computational framework to study how the nervous system exploits the anatomical properties of limbs to produce mechanical function. The study of the neural control of limbs has historically emphasized the use of optimization to find solutions to the muscle redundancy problem. That is, how does the nervous system select a specific muscle coordination pattern when the many muscles of a limb allow for multiple solutions? I revisit this problem from the emerging perspective of neuromechanics that emphasizes finding and implementing families of feasible solutions, instead of a single and unique optimal solution. Those families of feasible solutions emerge naturally from the interactions among the feasible neural commands, anatomy of the limb, and constraints of the task. Such alternative perspective to the neural control of limb function is not only biologically plausible, but sheds light on the most central tenets and debates in the fields of neural control, robotics, rehabilitation, and brain-body co-evolutionary adaptations. This perspective developed from courses I taught to engineers and life scientists at Cornell University and the University of Southern California, and is made possible by combining fundamental concepts from mechanics, anatomy, mathematics, robotics and neuroscience with advances in the field of computational geometry. Fundamentals of Neuromechanics is intended for neuroscientists, roboticists, engineers, physicians, evolutionary biologists, athletes, and physical and occupational therapists seeking to advance their understanding of neuromechanics. Therefore, the tone is decidedly pedagogical, engaging, integrative, and practical to make it accessible to people coming from a broad spectrum of disciplines. I attempt to tread the line between making the mathematical exposition accessible to life scientists, and convey the wonder and complexity of neuroscience to engineers and computational scientists. While no one approach can hope to definitively resolve the important questions in these related fields, I hope to provide you with the fundamental background and tools to allow you to contribute to the emerging field of neuromechanics. |
| dynamic models in biology ellner: Encyclopedia of Evolutionary Biology , 2016-04-14 Encyclopedia of Evolutionary Biology, Four Volume Set is the definitive go-to reference in the field of evolutionary biology. It provides a fully comprehensive review of the field in an easy to search structure. Under the collective leadership of fifteen distinguished section editors, it is comprised of articles written by leading experts in the field, providing a full review of the current status of each topic. The articles are up-to-date and fully illustrated with in-text references that allow readers to easily access primary literature. While all entries are authoritative and valuable to those with advanced understanding of evolutionary biology, they are also intended to be accessible to both advanced undergraduate and graduate students. Broad topics include the history of evolutionary biology, population genetics, quantitative genetics; speciation, life history evolution, evolution of sex and mating systems, evolutionary biogeography, evolutionary developmental biology, molecular and genome evolution, coevolution, phylogenetic methods, microbial evolution, diversification of plants and fungi, diversification of animals, and applied evolution. Presents fully comprehensive content, allowing easy access to fundamental information and links to primary research Contains concise articles by leading experts in the field that ensures current coverage of each topic Provides ancillary learning tools like tables, illustrations, and multimedia features to assist with the comprehension process |
| dynamic models in biology ellner: Theory-based Ecology Liz Pásztor, Zoltán Botta-Dukát, Gabriella Magyar, Tamás Czárán, Géza Meszéna, 2016 The first text to adopt a Darwinian approach to develop a universal, coherent and robust theory of ecology and provide a unified treatment of ecology and evolution. |
| dynamic models in biology ellner: Complex and Adaptive Dynamical Systems Claudius Gros, 2015-04-01 This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard mathematical tools for an advanced undergraduate course in the natural sciences or engineering. Each chapter includes exercises and suggestions for further reading, and the solutions to all exercises are provided in the last chapter. From the reviews of previous editions: This is a very interesting introductory book written for a broad audience of graduate students in natural sciences and engineering. It can be equally well used both for teac hing and self-education. Very well structured and every topic is illustrated with simple and motivating examples. This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) Claudius Gros’ Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature. A particular strength of the book is its emphasis on analytical techniques for studying complex systems. (David P. Feldman, Physics Today, July, 2009). |
| dynamic models in biology ellner: Mathematical Reviews , 2006 |
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DYNAMIC Definition & Meaning - Merriam-Webster
The meaning of DYNAMIC is marked by usually continuous and productive activity or change. How to use dynamic in a sentence.
DYNAMIC | English meaning - Cambridge Dictionary
DYNAMIC definition: 1. having a lot of ideas and enthusiasm: 2. continuously changing or developing: 3. relating to…. Learn more.
DYNAMIC Definition & Meaning | Dictionary.com
Dynamic definition: pertaining to or characterized by energy or effective action; vigorously active or forceful; energetic.. See examples of DYNAMIC used in a sentence.
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The dynamic of a system or process is the force that causes it to change or progress. The dynamic of the market demands constant change and adjustment. Politics has its own dynamic.
Dynamic - definition of dynamic by The Free Dictionary
dynamic - characterized by action or forcefulness or force of personality; "a dynamic market"; "a dynamic speaker"; "the dynamic president of the firm"
What does dynamic mean? - Definitions.net
Dynamic is a term often used to refer to something that is constantly changing or evolving. It may also refer to an interaction or system characterized by constant change, activity, or progress. In …
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