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Mathematical Methods In Modern Complexity Science
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Book Synopsis Mathematical Methods in Modern Complexity Science by : Dimitri Volchenkov
Download or read book Mathematical Methods in Modern Complexity Science written by Dimitri Volchenkov and published by Springer Nature. This book was released on 2022-03-14 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic differential equations, synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems
Book Synopsis Modern Mathematical Methods For Scientists And Engineers: A Street-smart Introduction by : Athanassios Fokas
Download or read book Modern Mathematical Methods For Scientists And Engineers: A Street-smart Introduction written by Athanassios Fokas and published by World Scientific. This book was released on 2022-12-12 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Mathematical Methods for Scientists and Engineers is a modern introduction to basic topics in mathematics at the undergraduate level, with emphasis on explanations and applications to real-life problems. There is also an 'Application' section at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of 'put' and 'call' options in financial markets. The book presents several modern important and computationally efficient topics, including feedforward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods.A unique and novel feature of the book is the introduction of a recently developed method for solving partial differential equations (PDEs), called the unified transform. PDEs are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics to ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge.The unified transform greatly facilitates this task. For example, two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, the unified transform derives in a simple manner a generalization of the d'Alembert solution, valid for general boundary value problems. Moreover, two centuries after Joseph Fourier introduced the classical tool of the Fourier series for solving the heat equation, the unified transform constructs a new solution to this ubiquitous PDE, with important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples.Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering.
Book Synopsis Modern Mathematical Tools and Techniques in Capturing Complexity by : Leandro Pardo
Download or read book Modern Mathematical Tools and Techniques in Capturing Complexity written by Leandro Pardo and published by Springer Science & Business Media. This book was released on 2011-05-26 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately. This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.
Book Synopsis Mathematics in Science and Technology by : A H Siddiqi
Download or read book Mathematics in Science and Technology written by A H Siddiqi and published by World Scientific. This book was released on 2011-06-30 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume presents reviews of research in several important areas of applications of mathematical concepts to science and technology, for example applications of inverse problems and wavelets to real world systems. The book provides a comprehensive overview of current research of several outstanding scholars engaged in diverse fields such as complexity theory, vertex coupling in quantum graphs, mixing of substances by turbulence, network dynamics and architecture, processes with rate — independent hysteresis, numerical analysis of Hamilton Jacobi — Bellman equations, simulations of complex stochastic differential equations, optimal flow control, shape optimal flow control, shape optimization and aircraft designing, mathematics of brain, nanotechnology and DNA structure and mathematical models of environmental problems. The volume also contains contributory talks based on current researches of comparatively young researchers participating in the conference. Contents:Part A Invited Talk:In Appreciation of Dr Zakir Husain Award (M Zuhair Nashed)Kinematical Conservation Laws (KCL): Equations of Evolution of Curves and Surfaces (K R Arun and P Prasad)Systematic Discretization of Input/Output Maps and Control of Partial Differential Equations (J Heiland, V Mehrmann and M Schmidt)Vertex Couplings in Quantum Graphs: Approximations by Scaled Schrödinger Operators (P Exner)Complexity Leads to Randomness in Chaotic Systems (R Lozi)Mathematical Modeling for Unifying Different Branches of Science, Engineering and Technology (N Rudraiah)On Equivalence Transformations and Exact Solutions of a Helmholtz Type Equation (O P Bhutani and L R Chowdhury)Cognitive Radio: State-of-the-Art and Mathematical Challenges (T Nadkar, V Thumar, A Patel, Md Z Ali Khan, U B Desai and S N Merchant)Part B Thematic Reviews:Inverse Problems of Parameter Identification in Partial Differential Equations (B Jadamba, A A Khan and M Sama)Finite Element Methods for HJB Equations (M Boulbrachene)Dynamics and Control of Underactuated Space Systems (K D Kumar and Godard)Some New Classes of Inverse Coefficient Problems in Engineering Mechanics and Computational Material Science Based on Boundary Measured Data (A Hasanov)Some Recent Developments on Mathematical Aspect of Wavelets (P Manchanda and Meenakshi)Relevance of Wavelets and Inverse Problems to Brain (A H Siddiqi, H K Sevindir, Z Aslan and C Yazici)Wavelets and Inverse Problems (K Goyal and M Mehra)Optimization Models for a Class of Structured Stochastic Games (S K Neogy, S Sinha, A K Das and A Gupta)Part C Contributory Talks:Predator-Prey Relations for Mammals where Prey Suppress Breeding (Q J Khan and M Al-Lawatia)SEI Model with Varying Transmission and Mortality Rates (G Rost)Trajectories and Stability Regions of the Lagrangian Points in the Generalized Chermnykh-Like Problem (B S Kushvah)MHD Flow Past an Infinite Plate Under the Effect of Gravity Modulation (S Wasu and S C Rajvanshi) Readership: Researchers in mathematical modeling, numerical analysis and computational mathematics. Keywords:Complexity Theory;Vertex Coupling in Quantum Graphs;Hamilton-JacobiâBellman Equation;Prey and Predator Model;Inverse Problems and Wavelets;Dynamics and Control of Under Actuated Space Systems
Book Synopsis Modern Mathematical Methods In Technology by : S. Fenyo
Download or read book Modern Mathematical Methods In Technology written by S. Fenyo and published by Elsevier. This book was released on 2012-12-02 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern Mathematical Methods in Technology deals with applied mathematics and its finite methods. The book explains the linear algebra, optimization theory, and elements of the theory of graphs. This book explains the matrix theory and analysis, as well as the applications of matrix calculus. It discusses the linear mappings, basic matrix operations, hypermatrices, vector systems, and other algebraic concepts. In addition, it presents the sequences, series, continuity, differentiation, and integration of matrices, as well as the analytical matrix functions. The book discusses linear optimization, linear programming problems, and their solution. It also describes transportation problems and their solution by Hungarian method, as well as convex optimization and the Kuhn-Tucker theorem. The book discusses graphs including sub-, complete, and complementary graphs. It also presents the Boolean algebra and Ford-Fulkerson theorem. This book is invaluable to Math practitioners and non-practitioners.
Book Synopsis Algorithms and Complexity in Mathematics, Epistemology, and Science by : Nicolas Fillion
Download or read book Algorithms and Complexity in Mathematics, Epistemology, and Science written by Nicolas Fillion and published by Springer. This book was released on 2019-02-07 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.
Book Synopsis Theory of Computational Complexity by : Ding-Zhu Du
Download or read book Theory of Computational Complexity written by Ding-Zhu Du and published by John Wiley & Sons. This book was released on 2014-06-30 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition "... complete, up-to-date coverage of computational complexity theory...the book promises to become the standard reference on computational complexity." —Zentralblatt MATH A thorough revision based on advances in the field of computational complexity and readers’ feedback, the Second Edition of Theory of Computational Complexity presents updates to the principles and applications essential to understanding modern computational complexity theory. The new edition continues to serve as a comprehensive resource on the use of software and computational approaches for solving algorithmic problems and the related difficulties that can be encountered. Maintaining extensive and detailed coverage, Theory of Computational Complexity, Second Edition, examines the theory and methods behind complexity theory, such as computational models, decision tree complexity, circuit complexity, and probabilistic complexity. The Second Edition also features recent developments on areas such as NP-completeness theory, as well as: A new combinatorial proof of the PCP theorem based on the notion of expander graphs, a research area in the field of computer science Additional exercises at varying levels of difficulty to further test comprehension of the presented material End-of-chapter literature reviews that summarize each topic and offer additional sources for further study Theory of Computational Complexity, Second Edition, is an excellent textbook for courses on computational theory and complexity at the graduate level. The book is also a useful reference for practitioners in the fields of computer science, engineering, and mathematics who utilize state-of-the-art software and computational methods to conduct research.
Book Synopsis Handbook of Computability and Complexity in Analysis by : Vasco Brattka
Download or read book Handbook of Computability and Complexity in Analysis written by Vasco Brattka and published by Springer Nature. This book was released on 2021-06-04 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computable analysis is the modern theory of computability and complexity in analysis that arose out of Turing's seminal work in the 1930s. This was motivated by questions such as: which real numbers and real number functions are computable, and which mathematical tasks in analysis can be solved by algorithmic means? Nowadays this theory has many different facets that embrace topics from computability theory, algorithmic randomness, computational complexity, dynamical systems, fractals, and analog computers, up to logic, descriptive set theory, constructivism, and reverse mathematics. In recent decades computable analysis has invaded many branches of analysis, and researchers have studied computability and complexity questions arising from real and complex analysis, functional analysis, and the theory of differential equations, up to (geometric) measure theory and topology. This handbook represents the first coherent cross-section through most active research topics on the more theoretical side of the field. It contains 11 chapters grouped into parts on computability in analysis; complexity, dynamics, and randomness; and constructivity, logic, and descriptive complexity. All chapters are written by leading experts working at the cutting edge of the respective topic. Researchers and graduate students in the areas of theoretical computer science and mathematical logic will find systematic introductions into many branches of computable analysis, and a wealth of information and references that will help them to navigate the modern research literature in this field.
Book Synopsis Approaches to Geo-mathematical Modelling by : Alan G. Wilson
Download or read book Approaches to Geo-mathematical Modelling written by Alan G. Wilson and published by John Wiley & Sons. This book was released on 2016-09-26 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geo-mathematical modelling: models from complexity science Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London Mathematical and computer models for a complexity science tool kit Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often partial, of these entities, and in many cases this understanding is represented in theories and associated mathematical models. In this book, the main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid together with examples at finer scales. This provides an effective toolkit that can not only be applied to global systems, but more widely in the modelling of complex systems. All complex systems involve nonlinearities involving path dependence and the possibility of phase changes and this makes the mathematical aspects particularly interesting. It is through these mechanisms that new structures can be seen to ‘emerge’, and hence the current notion of ‘emergent behaviour’. The range of models demonstrated include account-based models and biproportional fitting, structural dynamics, space-time statistical analysis, real-time response models, Lotka-Volterra models representing ‘war’, agent-based models, epidemiology and reaction-diffusion approaches, game theory, network models and finally, integrated models. Geo-mathematical modelling: Presents mathematical models with spatial dimensions. Provides representations of path dependence and phase changes. Illustrates complexity science using models of trade, migration, security and development aid. Demonstrates how generic models from the complexity science tool kit can each be applied in a variety of situations This book is for practitioners and researchers in applied mathematics, geography, economics, and interdisciplinary fields such as regional science and complexity science. It can also be used as the basis of a modelling course for postgraduate students.
Book Synopsis Computational Complexity and Statistical Physics by : Allon Percus
Download or read book Computational Complexity and Statistical Physics written by Allon Percus and published by OUP USA. This book was released on 2006-02-23 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science and physics have been closely linked since the birth of modern computing. In recent years, an interdisciplinary area has blossomed at the junction of these fields, connecting insights from statistical physics with basic computational challenges. Researchers have successfully applied techniques from the study of phase transitions to analyze NP-complete problems such as satisfiability and graph coloring. This is leading to a new understanding of the structure of these problems, and of how algorithms perform on them. Computational Complexity and Statistical Physics will serve as a standard reference and pedagogical aid to statistical physics methods in computer science, with a particular focus on phase transitions in combinatorial problems. Addressed to a broad range of readers, the book includes substantial background material along with current research by leading computer scientists, mathematicians, and physicists. It will prepare students and researchers from all of these fields to contribute to this exciting area.
Book Synopsis Thinking in Complexity by : Klaus Mainzer
Download or read book Thinking in Complexity written by Klaus Mainzer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition also treats smart materials and artificial life. A new chapter on information and computational dynamics takes up many recent discussions in the community.
Author :Demosthenis I. Bardzokas Publisher :Springer Science & Business Media ISBN 13 :3540710310 Total Pages :539 pages Book Rating :4.5/5 (47 download)
Book Synopsis Mathematical Methods in Electro-Magneto-Elasticity by : Demosthenis I. Bardzokas
Download or read book Mathematical Methods in Electro-Magneto-Elasticity written by Demosthenis I. Bardzokas and published by Springer Science & Business Media. This book was released on 2007-05-19 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanics of Coupled Fields is a discipline at the edge of modern research connecting Continuum Mechanics with Solid State Physics. This book fills many gaps in the theoretical literature which arise due to the complexity of the problem. A vast number of problems are considered so that the reader can get a clear quantitative and qualitative understanding of the phenomena taking place.
Book Synopsis Thinking in Complexity by : Klaus Mainzer
Download or read book Thinking in Complexity written by Klaus Mainzer and published by Springer Science & Business Media. This book was released on 2007-09-10 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition also treats smart materials and artificial life. A new chapter on information and computational dynamics takes up many recent discussions in the community.
Book Synopsis Complexity Of Groundwater Systems by : Teng Ma
Download or read book Complexity Of Groundwater Systems written by Teng Ma and published by World Scientific. This book was released on 2023-05-19 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive compendium overviews the complexity and uncertainty of groundwater systems, including groundwater boundaries, runoff, media, dynamic and chemical field, and stress and thermal field. The research methods and study examples were also introduced in great detail.The unique reference text is a valuable resource for researchers, academics, professionals, undergraduate and graduate students devoted to groundwater system study and complexity science.
Book Synopsis Managing Complexity: A Systems Approach by : The Open University
Download or read book Managing Complexity: A Systems Approach written by The Open University and published by The Open University. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This 20-hour free course showed how, by taking a systems approach to complex situations, it can become a lot easier to arrive at management decisions.
Book Synopsis Computability and Complexity Theory by : Steven Homer
Download or read book Computability and Complexity Theory written by Steven Homer and published by Springer Science & Business Media. This book was released on 2001 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces materials that are the core knowledge in the theory of computation. The book is self-contained, with a preliminary chapter describing key mathematical concepts and notations and subsequent chapters moving from the qualitative aspects of classical computability theory to the quantitative aspects of complexity theory. Dedicated chapters on undecidability, NP-completeness, and relative computability round off the work, which focuses on the limitations of computability and the distinctions between feasible and intractable.Topics and features:*Concise, focused materials cover the most fundamental concepts and results in the field of modern complexity theory, including the theory of NP-completeness, NP-hardness, the polynomial hierarchy, and complete problems for other complexity classes*Contains information that otherwise exists only in research literature and presents it in a unified, simplified manner; for example, about complements of complexity classes, search problems, and intermediate problems in NP*Provides key mathematical background information, including sections on logic and number theory and algebra*Supported by numerous exercises and supplementary problems for reinforcement and self-study purposes With its accessibility and well-devised organization, this text/reference is an excellent resource and guide for those looking to develop a solid grounding in the theory of computing. Beginning graduates, advanced undergraduates, and professionals involved in theoretical computer science, complexity theory, and computability will find the book an essential and practical learning tool.
Book Synopsis Numerical Methods in Scientific Computing by : Germund Dahlquist
Download or read book Numerical Methods in Scientific Computing written by Germund Dahlquist and published by SIAM. This book was released on 2008-01-01 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book from the authors of the classic book Numerical methods addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines traditional and well-developed topics with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLAB multiple precision package; and a guide to literature, algorithms, and software in numerical analysis. Review questions, problems, and computer exercises are also included. For use in an introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.
