Download or read book Analysis and Control of Polynomial Dynamic Models with Biological Applications written by Gabor Szederkenyi and published by Academic Press. This book was released on 2018-03-30 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological sciences (in particular, dynamic analysis and controller design of QP and polynomial systems arising from predator-prey and biochemical models). The book puts a significant emphasis on applications, focusing on quasi-polynomial (QP, or generalized Lotka-Volterra) and kinetic systems (also called biochemical reaction networks or simply CRNs) since they are universal descriptors for smooth nonlinear systems and can represent all important dynamical phenomena that are present in biological (and also in general) dynamical systems. Describes and illustrates the relationship between the dynamical, algebraic and structural features of the quasi-polynomial (QP) and kinetic models Shows the applicability of kinetic and QP representation in biological modeling and control through examples and case studies Emphasizes the importance and applicability of quantitative models in understanding and influencing natural phenomena

Download or read book Dynamical Models in Biology written by Miklós Farkas and published by Academic Press. This book was released on 2001-06-15 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Optimal Control Applied to Biological Models written by Suzanne Lenhart and published by CRC Press. This book was released on 2007-05-07 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: From economics and business to the biological sciences to physics and engineering, professionals successfully use the powerful mathematical tool of optimal control to make management and strategy decisions. Optimal Control Applied to Biological Models thoroughly develops the mathematical aspects of optimal control theory and provides insight into the application of this theory to biological models. Focusing on mathematical concepts, the book first examines the most basic problem for continuous time ordinary differential equations (ODEs) before discussing more complicated problems, such as variations of the initial conditions, imposed bounds on the control, multiple states and controls, linear dependence on the control, and free terminal time. In addition, the authors introduce the optimal control of discrete systems and of partial differential equations (PDEs). Featuring a user-friendly interface, the book contains fourteen interactive sections of various applications, including immunology and epidemic disease models, management decisions in harvesting, and resource allocation models. It also develops the underlying numerical methods of the applications and includes the MATLAB® codes on which the applications are based. Requiring only basic knowledge of multivariable calculus, simple ODEs, and mathematical models, this text shows how to adjust controls in biological systems in order to achieve proper outcomes.

Download or read book Dynamic Models and Control of Biological Systems written by Vadrevu Sree Hari Rao and published by Springer. This book was released on 2014-11-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Biology has grown at an astonishing rate and has established itself as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biological sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems which arise in the biological sciences and gives some indication of the wide spectrum of questions that modeling can address.

Download or read book Analysis and Synthesis of Polynomial Discrete Time Systems written by Mohd Shakir Md Saat and published by Butterworth-Heinemann. This book was released on 2017-07-10 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis and Synthesis of Polynomial Discrete-time Systems: An SOS Approach addresses the analysis and design of polynomial discrete-time control systems. The book deals with the application of Sum of Squares techniques in solving specific control and filtering problems that can be useful to solve advanced control problems, both on the theoretical side and on the practical side. Two types of controllers, state feedback controller and output feedback controller, along with topics surrounding the nonlinear filter and the H-infinity performance criteria are explored. The book also proposes a solution to global stabilization of discrete-time systems. Presents recent developments of the Sum of Squares approach in control of Polynomial Discrete-time Systems Includes numerical and practical examples to illustrate how design methodologies can be applied Provides a methodology for robust output controller design with an H-infinity performance index for polynomial discrete-time systems Offers tools for the analysis and design of control processes where the process can be represented in polynomial form Uses the Sum of Squares method for solving controller and filter design problems Provides MATLAB® code and simulation files of all illustrated example

Download or read book Computational and Mathematical Models in Biology written by Carla M.A. Pinto and published by Springer Nature. This book was released on 2024-01-09 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the most valuable and updated research on computational and mathematical models in biological systems from influential researchers around the world and contributes to the development of future research guidelines in this topic. Topics include (but are not limited to): modeling infectious and dynamic diseases; regulation of cell function; biological pattern formation; biological networks; tumor growth and angiogenesis; complex biological systems; Monte Carlo methods; Control theory, optimization and their applications

Download or read book Applications of Polynomial Systems written by David A. Cox and published by American Mathematical Soc.. This book was released on 2020-03-02 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bézier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century. The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.

Download or read book Application of Global Polynomial Models in the Identification Analysis and Control of Nonlinear Dynamics and Chaos written by Luis Antonio Aguirre and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Modeling Biological Cellular Control Systems written by Weijiu Liu and published by Springer. This book was released on 2014-03-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook contains the essential knowledge in modeling, simulation, analysis, and applications in dealing with biological cellular control systems. In particular, the book shows how to use the law of mass balance and the law of mass action to derive an enzyme kinetic model - the Michaelis-Menten function or the Hill function, how to use a current-voltage relation, Nernst potential equilibrium equation, and Hodgkin and Huxley's models to model an ionic channel or pump, and how to use the law of mass balance to integrate these enzyme or channel models into a complete feedback control system. The book also illustrates how to use data to estimate parameters in a model, how to use MATLAB to solve a model numerically, how to do computer simulations, and how to provide model predictions. Furthermore, the book demonstrates how to conduct a stability and sensitivity analysis on a model.

Download or read book Numerical Methods for Optimal Control Problems with Biological Applications written by Giulia Fabrini and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is divided in two parts: in the first part we focus on numerical methods for optimal control problems, in particular on the Dynamic Programming Principle and on Model Predictive Control (MPC), in the second part we present some applications of the control techniques in biology. In the first part of the thesis, we consider the approximation of an optimal control problem with an infinite horizon, which combines a first step based on MPC, to obtain a fast but rough approximation of the optimal trajectory and a second step where we solve the Bellman equation in a neighborhood of the reference trajectory. In this way, we can reduce the size of the domain in which the Bellman equation can be solved and so the computational complexity is reduced as well. The second topic of this thesis is the control of the Level Set methods: we consider an optimal control, in which the dynamics is given by the propagation of a one dimensional graph, which is controlled by the normal velocity. A final state is fixed and the aim is to reach the trajectory chosen as a target minimizing an appropriate cost functional. To apply the Dynamic Programming approach we firstly reduce the size of the system using the Proper Orthogonal Decomposition. The second part of the thesis is devoted to the application of control methods in biology. We present a model described by a partial differential equation that models the evolution of a population of tumor cells. We analyze the mathematical and biological features of the model. Then we formulate an optimal control problem for this model and we solve it numerically.

Download or read book Dynamic Systems Models written by Josif A. Boguslavskiy and published by Springer. This book was released on 2018-04-19 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included. Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution.

Download or read book Emerging Applications of Algebraic Geometry written by Mihai Putinar and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.

Download or read book Automated Reasoning for Systems Biology and Medicine written by Pietro Liò and published by Springer. This book was released on 2019-06-11 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents outstanding contributions in an exciting, new and multidisciplinary research area: the application of formal, automated reasoning techniques to analyse complex models in systems biology and systems medicine. Automated reasoning is a field of computer science devoted to the development of algorithms that yield trustworthy answers, providing a basis of sound logical reasoning. For example, in the semiconductor industry formal verification is instrumental to ensuring that chip designs are free of defects (or “bugs”). Over the past 15 years, systems biology and systems medicine have been introduced in an attempt to understand the enormous complexity of life from a computational point of view. This has generated a wealth of new knowledge in the form of computational models, whose staggering complexity makes manual analysis methods infeasible. Sound, trusted, and automated means of analysing the models are thus required in order to be able to trust their conclusions. Above all, this is crucial to engineering safe biomedical devices and to reducing our reliance on wet-lab experiments and clinical trials, which will in turn produce lower economic and societal costs. Some examples of the questions addressed here include: Can we automatically adjust medications for patients with multiple chronic conditions? Can we verify that an artificial pancreas system delivers insulin in a way that ensures Type 1 diabetic patients never suffer from hyperglycaemia or hypoglycaemia? And lastly, can we predict what kind of mutations a cancer cell is likely to undergo? This book brings together leading researchers from a number of highly interdisciplinary areas, including: · Parameter inference from time series · Model selection · Network structure identification · Machine learning · Systems medicine · Hypothesis generation from experimental data · Systems biology, systems medicine, and digital pathology · Verification of biomedical devices “This book presents a comprehensive spectrum of model-focused analysis techniques for biological systems ...an essential resource for tracking the developments of a fast moving field that promises to revolutionize biology and medicine by the automated analysis of models and data.”Prof Luca Cardelli FRS, University of Oxford

Download or read book Information Computing and Applications written by Chunfeng Liu and published by Springer. This book was released on 2012-09-07 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set of CCIS 307 and CCIS 308 constitutes the refereed proceedings of the Third International Conference on Information Computing and Applications, ICICA 2012, held in Chengde, China, in September 2012. The 330 revised full papers presented in both volumes were carefully reviewed and selected from 1089 submissions. The papers are organized in topical sections on internet computing and applications; multimedia networking and computing; intelligent computing and applications; computational statistics and applications; knowledge management and applications; communication technology and applications; information management system; control engineering and applications; business intelligence and applications; cloud and evolutionary computing; computational genomics and proteomics; engineering management and applications.

Download or read book Stochastic Game Strategies and their Applications written by Bor-Sen Chen and published by CRC Press. This book was released on 2019-07-31 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Game theory involves multi-person decision making and differential dynamic game theory has been widely applied to n-person decision making problems, which are stimulated by a vast number of applications. This book addresses the gap to discuss general stochastic n-person noncooperative and cooperative game theory with wide applications to control systems, signal processing systems, communication systems, managements, financial systems, and biological systems. H∞ game strategy, n-person cooperative and noncooperative game strategy are discussed for linear and nonlinear stochastic systems along with some computational algorithms developed to efficiently solve these game strategies.

Download or read book Advanced Models of Neural Networks written by Gerasimos G. Rigatos and published by Springer. This book was released on 2014-08-27 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete study on neural structures exhibiting nonlinear and stochastic dynamics, elaborating on neural dynamics by introducing advanced models of neural networks. It overviews the main findings in the modelling of neural dynamics in terms of electrical circuits and examines their stability properties with the use of dynamical systems theory. It is suitable for researchers and postgraduate students engaged with neural networks and dynamical systems theory.

Download or read book Identifiability and Regression Analysis of Biological Systems Models written by Paola Lecca and published by Springer Nature. This book was released on 2020-03-05 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated book presents the objectives of, and the latest techniques for, the identifiability analysis and standard and robust regression analysis of complex dynamical models. The book first provides a definition of complexity in dynamic systems by introducing readers to the concepts of system size, density of interactions, stiff dynamics, and hybrid nature of determination. In turn, it presents the mathematical foundations of and algorithmic procedures for model structural and practical identifiability analysis, multilinear and non-linear regression analysis, and best predictor selection. Although the main fields of application discussed in the book are biochemistry and systems biology, the methodologies described can also be employed in other disciplines such as physics and the environmental sciences. Readers will learn how to deal with problems such as determining the identifiability conditions, searching for an identifiable model, and conducting their own regression analysis and diagnostics without supervision. Featuring a wealth of real-world examples, exercises, and codes in R, the book addresses the needs of doctoral students and researchers in bioinformatics, bioengineering, systems biology, biophysics, biochemistry, the environmental sciences and experimental physics. Readers should be familiar with the fundamentals of probability and statistics (as provided in first-year university courses) and a basic grasp of R.