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Analysis and Control of Polynomial Dynamic Models with Biological Applications

Analysis and Control of Polynomial Dynamic Models with Biological Applications
Author: Gabor Szederkenyi
Publisher: Academic Press
Total Pages: 186
Release: 2018-03-30
Genre: Mathematics
ISBN: 0128154969

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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


Dynamic Models and Control of Biological Systems

Dynamic Models and Control of Biological Systems
Author: Vadrevu Sree Hari Rao
Publisher: Springer
Total Pages: 0
Release: 2014-11-29
Genre: Science
ISBN: 9781489984982

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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.


Dynamical Models in Biology

Dynamical Models in Biology
Author: Miklós Farkas
Publisher: Academic Press
Total Pages: 199
Release: 2001-06-15
Genre: Mathematics
ISBN: 0080530605

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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


Computational and Mathematical Models in Biology

Computational and Mathematical Models in Biology
Author: Carla M.A. Pinto
Publisher: Springer Nature
Total Pages: 331
Release: 2024-01-09
Genre: Mathematics
ISBN: 3031426894

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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


Analysis and Synthesis of Polynomial Discrete-Time Systems

Analysis and Synthesis of Polynomial Discrete-Time Systems
Author: Mohd Shakir Md Saat
Publisher: Butterworth-Heinemann
Total Pages: 202
Release: 2017-07-10
Genre: Science
ISBN: 0081019025

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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


Optimal Control Applied to Biological Models

Optimal Control Applied to Biological Models
Author: Suzanne Lenhart
Publisher: CRC Press
Total Pages: 272
Release: 2007-05-07
Genre: Mathematics
ISBN: 1584886404

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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.


Automated Reasoning for Systems Biology and Medicine

Automated Reasoning for Systems Biology and Medicine
Author: Pietro Liò
Publisher: Springer
Total Pages: 474
Release: 2019-06-11
Genre: Computers
ISBN: 303017297X

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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


Information Computing and Applications

Information Computing and Applications
Author: Chunfeng Liu
Publisher: Springer
Total Pages: 880
Release: 2012-09-07
Genre: Computers
ISBN: 3642340385

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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.


Applications of Polynomial Systems

Applications of Polynomial Systems
Author: David A. Cox
Publisher: American Mathematical Soc.
Total Pages: 250
Release: 2020-03-02
Genre: Education
ISBN: 1470451379

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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.