Download or read book Information and Complexity in Statistical Modeling written by Jorma Rissanen and published by Springer Science & Business Media. This book was released on 2007-12-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: No statistical model is "true" or "false," "right" or "wrong"; the models just have varying performance, which can be assessed. The main theme in this book is to teach modeling based on the principle that the objective is to extract the information from data that can be learned with suggested classes of probability models. The intuitive and fundamental concepts of complexity, learnable information, and noise are formalized, which provides a firm information theoretic foundation for statistical modeling. Although the prerequisites include only basic probability calculus and statistics, a moderate level of mathematical proficiency would be beneficial.
Download or read book Information And Complexity written by Mark Burgin and published by World Scientific. This book was released on 2016-11-28 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and processes. There are intrinsic relations between information and complexity.The research in information theory, the theory of complexity and their interrelations is very active. The book will expand knowledge on information, complexity and their relations representing the most recent and advanced studies and achievements in this area.The goal of the book is to present the topic from different perspectives — mathematical, informational, philosophical, methodological, etc.
Download or read book Information based Complexity written by Joseph Frederick Traub and published by . This book was released on 1988 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive treatment of information-based complexity, the branch of computational complexity that deals with the intrinsic difficulty of the approximate solution of problems for which the information is partial, noisy, and priced. Such problems arise in many areas including economics, physics, human and robotic vision, scientific and engineering computation, geophysics, decision theory, signal processing and control theory.
Download or read book Complexity and Information written by J. F. Traub and published by Cambridge University Press. This book was released on 1998-12-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.
Download or read book Dynamics Information and Complexity in Quantum Systems written by Fabio Benatti and published by Springer Nature. This book was released on 2023-09-23 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of Dynamics, Information and Complexity in Quantum Systems widens its scope by focussing more on the dynamics of quantum correlations and information in microscopic and mesoscopic systems, and their use for metrological and machine learning purposes. The book is divided into three parts: Part One: Classical Dynamical Systems Addresses classical dynamical systems, classical dynamical entropy, and classical algorithmic complexity. Includes a survey of the theory of simple perceptrons and their storage capacity. Part Two: Quantum Dynamical Systems Focuses on the dynamics of entanglement under dissipative dynamics and its metrological use in finite level quantum systems. Discusses the quantum fluctuation approach to large-scale mesoscopic systems and their emergent dynamics in quantum systems with infinitely many degrees of freedom. Introduces a model of quantum perceptron whose storage capacity is computed and compared with the classical one. Part Three: Quantum Dynamical Entropies and Complexities Devoted to quantum dynamical entropies and algorithmic complexities. This book is meant for advanced students, young and senior researchers working in the fields of quantum statistical mechanics, quantum information, and quantum dynamical systems. It is self-contained, and the only prerequisites needed are a standard knowledge of statistical mechanics, quantum mechanics, and linear operators on Hilbert spaces.
Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Download or read book Complexity Entropy And The Physics Of Information written by Wojciech H. Zurek and published by CRC Press. This book was released on 2018-03-08 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has emerged from a meeting held during the week of May 29 to June 2, 1989, at St. John’s College in Santa Fe under the auspices of the Santa Fe Institute. The (approximately 40) official participants as well as equally numerous “groupies” were enticed to Santa Fe by the above “manifesto.” The book—like the “Complexity, Entropy and the Physics of Information” meeting explores not only the connections between quantum and classical physics, information and its transfer, computation, and their significance for the formulation of physical theories, but it also considers the origins and evolution of the information-processing entities, their complexity, and the manner in which they analyze their perceptions to form models of the Universe. As a result, the contributions can be divided into distinct sections only with some difficulty. Indeed, I regard this degree of overlapping as a measure of the success of the meeting. It signifies consensus about the important questions and on the anticipated answers: they presumably lie somewhere in the “border territory,” where information, physics, complexity, quantum, and computation all meet.
Download or read book Visual Complexity written by Manuel Lima and published by Princeton Architectural Press. This book was released on 2013-09-10 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manuel Lima's smash hit Visual Complexity is now available in paperback. This groundbreaking 2011 book—the first to combine a thorough history of information visualization with a detailed look at today's most innovative applications—clearly illustrates why making meaningful connections inside complex data networks has emerged as one of the biggest challenges in twenty-first-century design. From diagramming networks of friends on Facebook to depicting interactions among proteins in a human cell, Visual Complexity presents one hundred of the most interesting examples of informationvisualization by the field's leading practitioners.
Download or read book Data Complexity in Pattern Recognition written by Mitra Basu and published by Springer Science & Business Media. This book was released on 2006-12-22 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic pattern recognition has uses in science and engineering, social sciences and finance. This book examines data complexity and its role in shaping theory and techniques across many disciplines, probing strengths and deficiencies of current classification techniques, and the algorithms that drive them. The book offers guidance on choosing pattern recognition classification techniques, and helps the reader set expectations for classification performance.
Download or read book Communication Complexity written by Anup Rao and published by Cambridge University Press. This book was released on 2020-02-20 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.
Download or read book Visualizing Complexity written by Darjan Hil and published by Birkhäuser. This book was released on 2022-05-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can you turn dry statistics into attractive and informative graphs? How can you present complex data sets in an easily understandable way? How can you create narrative diagrams from unstructured data? This handbook of information design answers these questions. Nicole Lachenmeier and Darjan Hil condense their extensive professional experience into an illustrated guide that offers a modular design system comprised of 80 elements. Their systematic design methodology makes it possible for anyone to visualize complex data attractively and using different perspectives. At the intersection of design, journalism, communication and data science, Visualizing Complexity opens up new ways of working with abstract data and invites readers to try their hands at information design.
Download or read book Computational Complexity written by Sanjeev Arora and published by Cambridge University Press. This book was released on 2009-04-20 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.
Download or read book Data Science written by Ivo D. Dinov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-12-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of new information is constantly increasing, faster than our ability to fully interpret and utilize it to improve human experiences. Addressing this asymmetry requires novel and revolutionary scientific methods and effective human and artificial intelligence interfaces. By lifting the concept of time from a positive real number to a 2D complex time (kime), this book uncovers a connection between artificial intelligence (AI), data science, and quantum mechanics. It proposes a new mathematical foundation for data science based on raising the 4D spacetime to a higher dimension where longitudinal data (e.g., time-series) are represented as manifolds (e.g., kime-surfaces). This new framework enables the development of innovative data science analytical methods for model-based and model-free scientific inference, derived computed phenotyping, and statistical forecasting. The book provides a transdisciplinary bridge and a pragmatic mechanism to translate quantum mechanical principles, such as particles and wavefunctions, into data science concepts, such as datum and inference-functions. It includes many open mathematical problems that still need to be solved, technological challenges that need to be tackled, and computational statistics algorithms that have to be fully developed and validated. Spacekime analytics provide mechanisms to effectively handle, process, and interpret large, heterogeneous, and continuously-tracked digital information from multiple sources. The authors propose computational methods, probability model-based techniques, and analytical strategies to estimate, approximate, or simulate the complex time phases (kime directions). This allows transforming time-varying data, such as time-series observations, into higher-dimensional manifolds representing complex-valued and kime-indexed surfaces (kime-surfaces). The book includes many illustrations of model-based and model-free spacekime analytic techniques applied to economic forecasting, identification of functional brain activation, and high-dimensional cohort phenotyping. Specific case-study examples include unsupervised clustering using the Michigan Consumer Sentiment Index (MCSI), model-based inference using functional magnetic resonance imaging (fMRI) data, and model-free inference using the UK Biobank data archive. The material includes mathematical, inferential, computational, and philosophical topics such as Heisenberg uncertainty principle and alternative approaches to large sample theory, where a few spacetime observations can be amplified by a series of derived, estimated, or simulated kime-phases. The authors extend Newton-Leibniz calculus of integration and differentiation to the spacekime manifold and discuss possible solutions to some of the "problems of time". The coverage also includes 5D spacekime formulations of classical 4D spacetime mathematical equations describing natural laws of physics, as well as, statistical articulation of spacekime analytics in a Bayesian inference framework. The steady increase of the volume and complexity of observed and recorded digital information drives the urgent need to develop novel data analytical strategies. Spacekime analytics represents one new data-analytic approach, which provides a mechanism to understand compound phenomena that are observed as multiplex longitudinal processes and computationally tracked by proxy measures. This book may be of interest to academic scholars, graduate students, postdoctoral fellows, artificial intelligence and machine learning engineers, biostatisticians, econometricians, and data analysts. Some of the material may also resonate with philosophers, futurists, astrophysicists, space industry technicians, biomedical researchers, health practitioners, and the general public.
Download or read book Descriptive Complexity written by Neil Immerman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: By virtue of the close relationship between logic and relational databases, it turns out that complexity has important applications to databases such as analyzing the parallel time needed to compute a query, and the analysis of nondeterministic classes. This book is a relatively self-contained introduction to the subject, which includes the necessary background material, as well as numerous examples and exercises.
Download or read book Algorithmic Randomness and Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2010-10-29 with total page 883 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.
Download or read book Structural Information and Communication Complexity written by Tomasz Jurdziński and published by Springer Nature. This book was released on 2021-06-19 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed conference proceedings of the 28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021, held in Wrocław, Poland, in June 2021. Due to COVID-19, the conference will be held online. The 20 full papers presented in this book were carefully reviewed and selected from 48 submissions. The papers are solicited from all areas of study of local structural knowledge and global communication and computational complexities. Among the typical areas are distributed computing, communication networks, game theory, parallel computing, social networks, mobile computing
Download or read book Complexity Theory and Cryptology written by Jörg Rothe and published by Springer Science & Business Media. This book was released on 2005-07-22 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern cryptology increasingly employs mathematically rigorous concepts and methods from complexity theory. Conversely, current research topics in complexity theory are often motivated by questions and problems from cryptology. This book takes account of this situation, and therefore its subject is what may be dubbed "cryptocomplexity'', a kind of symbiosis of these two areas. This book is written for undergraduate and graduate students of computer science, mathematics, and engineering, and can be used for courses on complexity theory and cryptology, preferably by stressing their interrelation. Moreover, it may serve as a valuable source for researchers, teachers, and practitioners working in these fields. Starting from scratch, it works its way to the frontiers of current research in these fields and provides a detailed overview of their history and their current research topics and challenges.
