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Mathematics of Information Processing by Michael Anshel Pdf
Features lectures that require a background in the methodologies of discrete mathematics, in particular the elements of algebra, combinatorics and graph theory, discrete probability, logic and the theory of computation. This title covers the two fundamental aspects of the field - database systems and communication networks.
Quantum Information Processing with Finite Resources by Marco Tomamichel Pdf
This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.
This book attempts to lay down some minimal set of coherent and consistent requirements for Advanced Information Processors (AIPs). The idea is advanced that AIPs should reason in an optimal manner by generalizing logic. Logic is generalized through the auspices of probability theory. Probability is presented through the viewpoint of the formal manipulation rules such as Bayes's Theorem and the maximum entropy principle. Information Geometry is an alternative way to think about the mathematical characterization of entropy and the assignment of numerical values to probabilities. The approach emphasizes many solved numerical examples and relies upon the computational ability of Mathematica.
Theory of Neural Information Processing Systems by A.C.C. Coolen,R. Kuehn,P. Sollich Pdf
Theory of Neural Information Processing Systems provides an explicit, coherent, and up-to-date account of the modern theory of neural information processing systems. It has been carefully developed for graduate students from any quantitative discipline, including mathematics, computer science, physics, engineering or biology, and has been thoroughly class-tested by the authors over a period of some 8 years. Exercises are presented throughout the text and notes on historical background and further reading guide the student into the literature. All mathematical details are included and appendices provide further background material, including probability theory, linear algebra and stochastic processes, making this textbook accessible to a wide audience.
Theory of Neural Information Processing Systems by Anthony C. C. Coolen,Reimer Kühn,Peter Sollich Pdf
This interdisciplinary graduate text gives a full, explicit, coherent and up-to-date account of the modern theory of neural information processing systems and is aimed at student with an undergraduate degree in any quantitative discipline (e.g. computer science, physics, engineering, biology, or mathematics). The book covers all the major theoretical developments from the 1940s tot he present day, using a uniform and rigorous style of presentation and of mathematical notation. The text starts with simple model neurons and moves gradually to the latest advances in neural processing. An ideal textbook for postgraduate courses in artificial neural networks, the material has been class-tested. It is fully self contained and includes introductions to the various discipline-specific mathematical tools as well as multiple exercises on each topic.
Cognitive Science and Mathematics Education by Alan H. Schoenfeld Pdf
This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.
Mathematics (Education) in the Information Age by Stacy A. Costa,Marcel Danesi,Dragana Martinovic Pdf
This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique—an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.
Introduction to Quantum Physics and Information Processing by Radhika Vathsan Pdf
An Elementary Guide to the State of the Art in the Quantum Information FieldIntroduction to Quantum Physics and Information Processing guides beginners in understanding the current state of research in the novel, interdisciplinary area of quantum information. Suitable for undergraduate and beginning graduate students in physics, mathematics, or eng
Oscillatory Neural Networks by Margarita G. Kuzmina,Eduard A. Manykin,Evgeny S. Grichuk Pdf
Understanding of the human brain functioning currently represents a challenging problem. In contrast to usual serial computers and complicated hierarchically organized artificial man-made systems, decentralized, parallel and distributed information processing principles are inherent to the brain. Besides adaptation and learning, which play a crucial role in brain functioning, oscillatory neural activity, synchronization and resonance accompany the brain work. Neural-like oscillatory network models, designed by the authors for image processing, allow to elucidate the capabilities of dynamical, synchronization-based types of image processing, presumably exploited by the brain. The oscillatory network models, studied by means of computer modeling and qualitative analysis, are presented and discussed in the book. Some other problems of parallel distributed information processing are also considered, such as a recall process from network memory for large-scale recurrent associative memory neural networks, performance of oscillatory networks of associative memory, dynamical oscillatory network methods of image processing with synchronization-based performance, optical parallel information processing based on the nonlinear optical phenomenon of photon echo, and modeling random electric fields of quasi-monochromatic polarized light beams using systems of superposed stochastic oscillators. This makes the book highly interesting to researchers dealing with various aspects of parallel information processing.
Mathematics and Computation in Imaging Science and Information Processing by Say Song Goh,Amos Ron,Zuowei Shen Pdf
The explosion of data arising from rapid advances in communication, sensing and computational power has concentrated research effort on more advanced techniques for the representation, processing, analysis and interpretation of data sets. In view of these exciting developments, the program OC Mathematics and Computation in Imaging Science and Information ProcessingOCO was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004 to promote and facilitate multidisciplinary research in the area. As part of the program, a series of tutorial lectures were conducted by international experts on a wide variety of topics in mathematical image, signal and information processing. This compiled volume contains survey articles by the tutorial speakers, all specialists in their respective areas. They collectively provide graduate students and researchers new to the field a unique and valuable introduction to a range of important topics at the frontiers of current research. Sample Chapter(s). Foreword (46 KB). Chapter 1: Subdivision on Arbitrary Meshes: Algorithms and Theory (771 KB). Contents: Subdivision on Arbitrary Meshes: Algorithms and Theory (D Zorin); High Order Numerical Methods for Time Dependent Hamilton-Jacobi Equations (C-W Shu); Theory and Computation of Variational Image Deblurring (T F Chan & J Shen); Data Hiding OCo Theory and Algorithms (P Moulin & R Koetter); Image Steganography and Steganalysis: Concepts and Practice (M Kharrazi et al.); The Apriori Algorithm OCo A Tutorial (M Hegland). Readership: Graduate students and researchers in mathematical image, signal and information processing."
Information and Communications Technologies in School Mathematics by David Tinsley,David Carlton Johnson Pdf
The book aims to record the proceedings of an international conference of invited experts and is based on four themes: curriculum; teachers; learners; and human and social issues. The conference is a sequel to two earlier ones held 10 and 20 years ago, and will give an unique insight into developments in secondary schools across the world over three decades.
Pattern Recognition and Information Processing by Sergey V. Ablameyko,Viktor V. Krasnoproshin,Maryna M. Lukashevich Pdf
This book constitutes the refereed proceedings of the 14th International Conference on Pattern Recognition and Information Processing, PRIP 2019, held in Minsk, Belarus, in May 2019. The 25 revised full papers were carefully reviewed and selected from 120 submissions. The papers of this volume are organized in topical sections on pattern recognition and image analysis; information processing and applications.