Download or read book Discrete Mathematics of Neural Networks written by Martin Anthony and published by SIAM. This book was released on 2001-01-01 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks. Neural networks have emerged as a key technology in many fields of application, and an understanding of the theories concerning what such systems can and cannot do is essential. Some classical results are presented with accessible proofs, together with some more recent perspectives, such as those obtained by considering decision lists. In addition, probabilistic models of neural network learning are discussed. Graph theory, some partially ordered set theory, computational complexity, and discrete probability are among the mathematical topics involved. Pointers to further reading and an extensive bibliography make this book a good starting point for research in discrete mathematics and neural networks.

Download or read book Mathematics of Neural Networks written by Stephen W. Ellacott and published by Springer Science & Business Media. This book was released on 1997-05-31 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of research papers comprises the proceedings of the first International Conference on Mathematics of Neural Networks and Applications (MANNA), which was held at Lady Margaret Hall, Oxford from July 3rd to 7th, 1995 and attended by 116 people. The meeting was strongly supported and, in addition to a stimulating academic programme, it featured a delightful venue, excellent food and accommo dation, a full social programme and fine weather - all of which made for a very enjoyable week. This was the first meeting with this title and it was run under the auspices of the Universities of Huddersfield and Brighton, with sponsorship from the US Air Force (European Office of Aerospace Research and Development) and the London Math ematical Society. This enabled a very interesting and wide-ranging conference pro gramme to be offered. We sincerely thank all these organisations, USAF-EOARD, LMS, and Universities of Huddersfield and Brighton for their invaluable support. The conference organisers were John Mason (Huddersfield) and Steve Ellacott (Brighton), supported by a programme committee consisting of Nigel Allinson (UMIST), Norman Biggs (London School of Economics), Chris Bishop (Aston), David Lowe (Aston), Patrick Parks (Oxford), John Taylor (King's College, Lon don) and Kevin Warwick (Reading). The local organiser from Huddersfield was Ros Hawkins, who took responsibility for much of the administration with great efficiency and energy. The Lady Margaret Hall organisation was led by their bursar, Jeanette Griffiths, who ensured that the week was very smoothly run.

Download or read book Practical Discrete Mathematics written by Ryan T. White and published by Packt Publishing Ltd. This book was released on 2021-02-22 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data science Key FeaturesApply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook Description Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning. What you will learnUnderstand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is for This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.

Download or read book Neural and Automata Networks written by E. Goles and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Et moi ..., si j'avait Sll comment en revenir. One sennce mathematics has rendered the human race. It has put common sense back je n'y serais point alle.' Jules Verne whe", it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be smse'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'!ltre of this series

Download or read book Discrete Neural Computation written by Kai-Yeung Siu and published by Prentice Hall. This book was released on 1995 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the three leading authorities in the field, this book brings together -- in one volume -- the recent developments in discrete neural computation, with a focus on neural networks with discrete inputs and outputs. It integrates a variety of important ideas and analytical techniques, and establishes a theoretical foundation for discrete neural computation. Discusses the basic models for discrete neural computation and the fundamental concepts in computational complexity; establishes efficient designs of threshold circuits for computing various functions; develops techniques for analyzing the computational power of neural models. A reference/text for computer scientists and researchers involved with neural computation and related disciplines.

Download or read book Applications of Discrete Mathematics for Understanding Dynamics of Synapses and Networks in Neuroscience written by Caitlyn M. Parmelee and published by . This book was released on 2016 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling has broad applications in neuroscience whether we are modeling the dynamics of a single synapse or the dynamics of an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better understand how visual information is processed. In Part II, we explore a simple model of neural networks with the goal of discovering how network structure shapes the behavior of the network.

Download or read book Turing s Connectionism written by Christof Teuscher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Christof Teuscher revives, analyzes, and simulates Turing's ideas, applying them to different types of problems, and building and training Turing's machines using evolutionary algorithms. In a little known paper entitled 'Intelligent Machinery' Turing investigated connectionist networks, but his work was dismissed as a 'schoolboy essay'and it was left unpublished until 1968, 14 years after his death. This is not a book about today's (classical) neural networks, but about the neuron network-like structures proposed by Turing. One of its novel features is that it actually goes beyond Turing's ideas by proposing new machines. The book also contains a Foreward by B. Jack Copeland and D. Proudfoot.

Download or read book Discrete Mathematics and Its Applications written by M. Sethumadhavan and published by Alpha Science Int'l Ltd.. This book was released on 2006 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Mathematics and its Applications provides an in-depth review of recent applications in the area and points to the directions of research. It deals with a wide range of topics like Cryptology Graph Theory Fuzzy Topology Computer Science Mathematical Biology A resource for researchers to keep track of the latest developments in these topics. Of interest to graph theorists, computer scientists, cryptographers, security specialists.

Download or read book Neural Networks Theory written by Alexander I. Galushkin and published by Springer Science & Business Media. This book was released on 2007-10-29 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by a leader in neural network theory in Russia, uses mathematical methods in combination with complexity theory, nonlinear dynamics and optimization. It details more than 40 years of Soviet and Russian neural network research and presents a systematized methodology of neural networks synthesis. The theory is expansive: covering not just traditional topics such as network architecture but also neural continua in function spaces as well.

Download or read book Mathematical Perspectives on Neural Networks written by Paul Smolensky and published by Psychology Press. This book was released on 2013-05-13 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.

Download or read book Stability Analysis of Neural Networks written by Grienggrai Rajchakit and published by Springer Nature. This book was released on 2021-12-05 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent research on the stability of various neural networks with constrained signals. It investigates stability problems for delayed dynamical systems where the main purpose of the research is to reduce the conservativeness of the stability criteria. The book mainly focuses on the qualitative stability analysis of continuous-time as well as discrete-time neural networks with delays by presenting the theoretical development and real-life applications in these research areas. The discussed stability concept is in the sense of Lyapunov, and, naturally, the proof method is based on the Lyapunov stability theory. The present book will serve as a guide to enable the reader in pursuing the study of further topics in greater depth and is a valuable reference for young researcher and scientists.

Download or read book Discrete Time Recurrent Neural Control written by Edgar N. Sanchez and published by CRC Press. This book was released on 2018-09-03 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents recent advances in the theory of neural control for discrete-time nonlinear systems with multiple inputs and multiple outputs. The simulation results that appear in each chapter include rigorous mathematical analyses, based on the Lyapunov approach, to establish its properties. The book contains two sections: the first focuses on the analyses of control techniques; the second is dedicated to illustrating results of real-time applications. It also provides solutions for the output trajectory tracking problem of unknown nonlinear systems based on sliding modes and inverse optimal control scheme. "This book on Discrete-time Recurrent Neural Control is unique in the literature, with new knowledge and information about the new technique of recurrent neural control especially for discrete-time systems. The book is well organized and clearly presented. It will be welcome by a wide range of researchers in science and engineering, especially graduate students and junior researchers who want to learn the new notion of recurrent neural control. I believe it will have a good market. It is an excellent book after all." — Guanrong Chen, City University of Hong Kong "This book includes very relevant topics, about neural control. In these days, Artificial Neural Networks have been recovering their relevance and well-stablished importance, this due to its great capacity to process big amounts of data. Artificial Neural Networks development always is related to technological advancements; therefore, it is not a surprise that now we are being witnesses of this new era in Artificial Neural Networks, however most of the developments in this research area only focuses on applicability of the proposed schemes. However, Edgar N. Sanchez author of this book does not lose focus and include both important applications as well as a deep theoretical analysis of Artificial Neural Networks to control discrete-time nonlinear systems. It is important to remark that first, the considered Artificial Neural Networks are development in discrete-time this simplify its implementation in real-time; secondly, the proposed applications ranging from modelling of unknown discrete-time on linear systems to control electrical machines with an emphasize to renewable energy systems. However, its applications are not limited to these kind of systems, due to their theoretical foundation it can be applicable to a large class of nonlinear systems. All of these is supported by the solid research done by the author." — Alma Y. Alanis, University of Guadalajara, Mexico "This book discusses in detail; how neural networks can be used for optimal as well as robust control design. Design of neural network controllers for real time applications such as induction motors, boost converters, inverted pendulum and doubly fed induction generators has also been carried out which gives the book an edge over other similar titles. This book will be an asset for the novice to the experienced ones." — Rajesh Joseph Abraham, Indian Institute of Space Science & Technology, Thiruvananthapuram, India

Download or read book An Introduction to Neural Networks written by Kevin Gurney and published by CRC Press. This book was released on 2018-10-08 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though mathematical ideas underpin the study of neural networks, the author presents the fundamentals without the full mathematical apparatus. All aspects of the field are tackled, including artificial neurons as models of their real counterparts; the geometry of network action in pattern space; gradient descent methods, including back-propagation; associative memory and Hopfield nets; and self-organization and feature maps. The traditionally difficult topic of adaptive resonance theory is clarified within a hierarchical description of its operation. The book also includes several real-world examples to provide a concrete focus. This should enhance its appeal to those involved in the design, construction and management of networks in commercial environments and who wish to improve their understanding of network simulator packages. As a comprehensive and highly accessible introduction to one of the most important topics in cognitive and computer science, this volume should interest a wide range of readers, both students and professionals, in cognitive science, psychology, computer science and electrical engineering.

Download or read book Discrete Mathematics with Applications written by Thomas Koshy and published by Elsevier. This book was released on 2004-01-19 with total page 1079 pages. Available in PDF, EPUB and Kindle. Book excerpt: This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects* Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises* Features interesting anecdotes and biographies of 60 mathematicians and computer scientists* Instructor's Manual available for adopters* Student Solutions Manual available separately for purchase (ISBN: 0124211828)

Download or read book Neural Network Fundamentals with Graphs Algorithms and Applications written by Nirmal K. Bose and published by McGraw-Hill Companies. This book was released on 1996 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematics for Machine Learning written by Marc Peter Deisenroth and published by Cambridge University Press. This book was released on 2020-04-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.