Information And Complexity

Information And Complexity
Author: Mark Burgin
Publisher: World Scientific
Total Pages: 410
Release: 2016-11-28
Genre: Computers
ISBN: 9813109041

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.

Information and Complexity in Statistical Modeling

Information and Complexity in Statistical Modeling
Author: Jorma Rissanen
Publisher: Springer Science & Business Media
Total Pages: 145
Release: 2007-12-15
Genre: Mathematics
ISBN: 0387688129

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.

An Introduction to Kolmogorov Complexity and Its Applications

An Introduction to Kolmogorov Complexity and Its Applications
Author: Ming Li
Publisher: Springer Science & Business Media
Total Pages: 655
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475726066

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).

Data Science

Data Science
Author: Ivo D. Dinov
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 489
Release: 2021-12-06
Genre: Computers
ISBN: 3110697823

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.

Computational Complexity

Computational Complexity
Author: Sanjeev Arora
Publisher: Cambridge University Press
Total Pages: 609
Release: 2009-04-20
Genre: Computers
ISBN: 0521424267

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Complexity and Real Computation

Complexity and Real Computation
Author: Lenore Blum
Publisher: Springer Science & Business Media
Total Pages: 456
Release: 2012-12-06
Genre: Computers
ISBN: 1461207010

The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.

Visualizing Complexity

Visualizing Complexity
Author: Darjan Hil
Publisher: Birkhäuser
Total Pages: 232
Release: 2022-05-09
Genre: Architecture
ISBN: 3035625069

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.

Stochastic Complexity In Statistical Inquiry

Stochastic Complexity In Statistical Inquiry
Author: Jorma Rissanen
Publisher: World Scientific
Total Pages: 191
Release: 1998-10-07
Genre: Technology & Engineering
ISBN: 9814507407

This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of 'true' data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression.

Algorithmic Randomness and Complexity

Algorithmic Randomness and Complexity
Author: Rodney G. Downey
Publisher: Springer Science & Business Media
Total Pages: 883
Release: 2010-10-29
Genre: Computers
ISBN: 0387684417

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.

Data Complexity in Pattern Recognition

Data Complexity in Pattern Recognition
Author: Mitra Basu
Publisher: Springer Science & Business Media
Total Pages: 309
Release: 2006-12-22
Genre: Computers
ISBN: 1846281725

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.