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Privacy In Dynamical Systems
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Book Synopsis Privacy in Dynamical Systems by : Farhad Farokhi
Download or read book Privacy in Dynamical Systems written by Farhad Farokhi and published by Springer Nature. This book was released on 2019-11-21 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses privacy in dynamical systems, with applications to smart metering, traffic estimation, and building management. In the first part, the book explores statistical methods for privacy preservation from the areas of differential privacy and information-theoretic privacy (e.g., using privacy metrics motivated by mutual information, relative entropy, and Fisher information) with provable guarantees. In the second part, it investigates the use of homomorphic encryption for the implementation of control laws over encrypted numbers to support the development of fully secure remote estimation and control. Chiefly intended for graduate students and researchers, the book provides an essential overview of the latest developments in privacy-aware design for dynamical systems.
Book Synopsis Numerical Data Fitting in Dynamical Systems by : Klaus Schittkowski
Download or read book Numerical Data Fitting in Dynamical Systems written by Klaus Schittkowski and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real life phenomena in engineering, natural, or medical sciences are often described by a mathematical model with the goal to analyze numerically the behaviour of the system. Advantages of mathematical models are their cheap availability, the possibility of studying extreme situations that cannot be handled by experiments, or of simulating real systems during the design phase before constructing a first prototype. Moreover, they serve to verify decisions, to avoid expensive and time consuming experimental tests, to analyze, understand, and explain the behaviour of systems, or to optimize design and production. As soon as a mathematical model contains differential dependencies from an additional parameter, typically the time, we call it a dynamical model. There are two key questions always arising in a practical environment: 1 Is the mathematical model correct? 2 How can I quantify model parameters that cannot be measured directly? In principle, both questions are easily answered as soon as some experimental data are available. The idea is to compare measured data with predicted model function values and to minimize the differences over the whole parameter space. We have to reject a model if we are unable to find a reasonably accurate fit. To summarize, parameter estimation or data fitting, respectively, is extremely important in all practical situations, where a mathematical model and corresponding experimental data are available to describe the behaviour of a dynamical system.
Book Synopsis Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems by : M. Reza Rahimi Tabar
Download or read book Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems written by M. Reza Rahimi Tabar and published by Springer. This book was released on 2019-07-04 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
Book Synopsis Dynamical Systems by : Shlomo Sternberg
Download or read book Dynamical Systems written by Shlomo Sternberg and published by Courier Corporation. This book was released on 2010-07-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials include PowerPoint slides and MATLAB exercises. 2010 edition.
Book Synopsis Dynamical Systems on Networks by : Mason Porter
Download or read book Dynamical Systems on Networks written by Mason Porter and published by Springer. This book was released on 2016-03-31 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.
Book Synopsis An Introduction to Hybrid Dynamical Systems by : Arjan J. van der Schaft
Download or read book An Introduction to Hybrid Dynamical Systems written by Arjan J. van der Schaft and published by Springer. This book was released on 2007-10-03 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of the interaction between discrete and continuous dynamics. The present volume provides a first attempt in book form to bring together concepts and methods dealing with hybrid systems from various areas, and to look at these from a unified perspective. The authors have chosen a mode of exposition that is largely based on illustrative examples rather than on the abstract theorem-proof format because the systematic study of hybrid systems is still in its infancy. The examples are taken from many different application areas, ranging from power converters to communication protocols and from chaos to mathematical finance. Subjects covered include the following: definition of hybrid systems; description formats; existence and uniqueness of solutions; special subclasses (variable-structure systems, complementarity systems); reachability and verification; stability and stabilizability; control design methods. The book will be of interest to scientists from a wide range of disciplines including: computer science, control theory, dynamical system theory, systems modeling and simulation, and operations research.
Book Synopsis Random Dynamical Systems by : Ludwig Arnold
Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
Book Synopsis Dynamic Systems for Everyone by : Asish Ghosh
Download or read book Dynamic Systems for Everyone written by Asish Ghosh and published by Springer. This book was released on 2015-04-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic systems, as well as in everyday life. Readers from a variety of disciplines will benefit from the understanding of system behaviors and will be able to apply those principles in various contexts. The book includes many examples covering various types of systems. The treatment of the subject is non-mathematical, and the book considers some of the latest concepts in the systems discipline, such as agent-based systems, optimization, and discrete events and procedures.
Book Synopsis Shadowing in Dynamical Systems by : Sergei Yu. Pilyugin
Download or read book Shadowing in Dynamical Systems written by Sergei Yu. Pilyugin and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.
Book Synopsis Discovering Discrete Dynamical Systems by : Aimee Johnson
Download or read book Discovering Discrete Dynamical Systems written by Aimee Johnson and published by American Mathematical Soc.. This book was released on 2017-12-31 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.
Book Synopsis Data-Driven Science and Engineering by : Steven L. Brunton
Download or read book Data-Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Book Synopsis The Dynamical System Generated by the 3n+1 Function by : Günther J. Wirsching
Download or read book The Dynamical System Generated by the 3n+1 Function written by Günther J. Wirsching and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.
Book Synopsis An Introduction to Sequential Dynamical Systems by : Henning Mortveit
Download or read book An Introduction to Sequential Dynamical Systems written by Henning Mortveit and published by Springer Science & Business Media. This book was released on 2007-11-27 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.
Book Synopsis Dynamical Systems by : Pierre N.V. Tu
Download or read book Dynamical Systems written by Pierre N.V. Tu and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic tools of analysis and modelling are increasingly used in Economics and Biology and have become more and more sophisticated in recent years, to the point where the general students without training in Dynamic Systems (DS) would be at a loss. No doubt they are referred to the original sources of mathematical theorems used in the various proofs, but the level of mathematics is generally beyond them. Students are thus left with the burden of somehow understanding advanced mathematics by themselves, with· very little help. It is to these general students, equipped only with a modest background of Calculus and Matrix Algebra that this book is dedicated. It aims at providing them with a fairly comprehensive box of dynamical tools they are expected to have at their disposal. The first three Chapters start with the most elementary notions of first and second order Differential and Difference Equations. For these, no matrix theory and hardly any calculus are needed. Then, before embarking on linear and nonlinear DS, a review of some Linear Algebra in Chapter 4 provides the bulk of matrix theory required for the study of later Chapters. Systems of Linear Differ ential Equations (Ch. 5) and Difference Equations (Ch. 6) then follow to provide students with a good background in linear DS, necessary for the subsequent study of nonlinear systems. Linear Algebra, reviewed in Ch. 4, is used freely in these and subsequent chapters to save space and time.
Book Synopsis Differential Equations, Dynamical Systems, and an Introduction to Chaos by : Morris W. Hirsch
Download or read book Differential Equations, Dynamical Systems, and an Introduction to Chaos written by Morris W. Hirsch and published by Academic Press. This book was released on 2004 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra. The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of.
Download or read book Dynamical Systems written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2005-11-24 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata
Book Synopsis Differential Dynamical Systems, Revised Edition by : James D. Meiss
Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
