About this textbook
* Applications covered: optimization, finance, statistical mechanics, birth and death processes, and gambling systems
* Hands-on approach is used via realistic problems demonstrated with examples and numerical simulations
* A wealth of completely solved example problems provide the reader with a sourcebook to follow toward the solution of their own computational problems
* Each chapter ends with a large collection of homework problems illustrating and directing the material
Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems.
Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material.
This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics. The problem-oriented approach makes it ideal for an applied course in basic probability and for a more specialized course in Monte Carlo methods. Topics include probability distributions, counting combinatorial objects, simulated annealing, genetic algorithms, option pricing, gamblers ruin, statistical mechanics, sampling, and random number generation.
Written for:
Undergraduate students in engineering and the sciences, and mathematics; ideal for an applied course in basic probability, as well as a more specialized course in Monte Carlo methods
Keywords:
* Matlab
* algorithims
* histogramming
* markov chain
* probability
* random number generator
* stochastic processes

Uses the "modified Moore method" approach in which examples and proof opportunities are worked into the text in order to encourage students to develop some of the content through their own examples and arguments while they are reading the text
Concentrates on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them
The material progresses at a gentle and inviting pace
Ample examples and exercises are included
This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment allows the use of the "modified Moore method" approach by working examples and proof opportunities into the text in order to encourage students to develop some of the content through their own experiments and arguments while reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them. In particular, the author uses the Simplex Algorithm to motivate these concepts. The text progresses at a gentle and inviting pace. The presentation is driven by numerous examples and illustrations. Ample exercises are provided at the end of each chapter for mastering the material. Opportunities for integrating Maple (or similar) software are included in the book. The author’s own WebSim software can be freely downloaded from his website for pedagogical use.
The teacher's version of the text contains solutions embedded within the text, rather than in an appendix. It also has extra material and suggestions for the teacher’s benefit. Junior/senior level undergraduate students will benefit from the book, as will beginning graduate students. Future secondary school mathematics teachers will also find this book useful.
Arizona State University Professor Glenn H. Hurlbert has published nearly 50 articles in graph theory, combinatorics, and optimization, and has been the recipient of numerous teaching and mentoring awards from ASU, the ASU Parents Association, the School of Mathematical and Statistical Sciences, and the Mathematical Association of America.
Content Level » Graduate
Keywords » Convex Geometry - Convexity - Duality - Linear Programming - Networks - Simplex Algorithm - integer optimization - linear optimization - matrix games - modified Moore method

This book is intended to introduce coding theory and information theory to undergraduate students of mathematics and computer science. It begins with a review of probablity theory as applied to finite sample spaces and a general introduction to the nature and types of codes. The two subsequent chapters discuss information theory: efficiency of codes, the entropy of information sources, and Shannon's Noiseless Coding Theorem. The remaining three chapters deal with coding theory: communication channels, decoding in the presence of errors, the general theory of linear codes, and such specific codes as Hamming codes, the simplex codes, and many others.

Scientists' understanding of two central problems in neuroscience, psychology, and philosophy has been greatly influenced by the work of David Hubel and Torsten Wiesel: (1) What is it to see? This relates to the machinery that underlies visual perception. (2) How do we acquire the brain's mechanisms for vision? This is the nature-nurture question as to whether the nerve connections responsible for vision are innate or whether they develop through experience in the early life of an animal or human. This is a book about the collaboration between Hubel and Wiesel, which began in 1958, lasted until about 1982, and led to a Nobel Prize in 1981. It opens with short autobiographies of both men, describes the state of the field when they started, and tells about the beginnings of their collaboration. It emphasizes the importance of various mentors in their lives, especially Stephen W. Kuffler, who opened up the field by studying the cat retina in 1950, and founded the department of neurobiology at Harvard Medical School, where most of their work was done. The main part of the book consists of Hubel and Wiesel's most important publications. Each reprinted paper is preceded by a foreword that tells how they went about the research, what the difficulties and the pleasures were, and whether they felt a paper was important and why. Each is also followed by an afterword describing how the paper was received and what developments have occurred since its publication. The reader learns things that are often absent from typical scientific publications, including whether the work was difficult, fun, personally rewarding, exhilarating, or just plain tedious. The book ends with a summing-up of the authors' view of the present state of the field. This is much more than a collection of reprinted papers. Above all it tells the story of an unusual scientific collaboration that was hugely enjoyable and served to transform an entire branch of neurobiology. It will appeal to neuroscientists, vision scientists, biologists, psychologists, physicists, historians of science, and to their students and trainees, at all levels from high school on, as well as anyone else who is interested in the scientific process.

In The Birth of the Mind , award-winning cognitive scientist Gary Marcus irrevocably alters the nature vs. nurture debate by linking the findings of the Human Genome Project to the development of the brain. Scientists have long struggled to understand how a tiny number of genes could contain the instructions for building the human brain, arguably the most complex device in the known universe. Synthesizing up-to-the-minute research with his own original findings on child development, Marcus is the first to resolve this apparent contradiction. Vibrantly written and completely accessible to the lay reader, The Birth of the Mind will forever change the way we think about our origins and ourselves.

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

This book presents a coherent approach to the fast moving field of machine vision, using a consistent notation based on a detailed understanding of the image formation process. It covers even the most recent research and will provide a useful and current reference for professionals working in the fields of machine vision, image processing, and pattern recognition.An outgrowth of the author's course at MIT, Robot Vision presents a solid framework for understanding existing work and planning future research. Its coverage includes a great deal of material that important to engineers applying machine vision methods in the real world. The chapters on binary image processing, for example, help explain and suggest how to improve the many commercial devices now available. And the material on photometric stereo and the extended Gaussian image points the way to what may be the next thrust in commercialization of the results in this area. The many exercises complement and extend the material in the text, and an extensive bibliography will serve as a useful guide to current research.Contents: Image Formation and Image Sensing. Binary Images: Geometrical Properties; Topological Properties. Regions and Image Segmentation. Image Processing: Continuous Images; Discrete Images. Edges and Edge Finding. Lightness and Color. Reflectance Map: Photometric Stereo Reflectance Map; Shape from Shading. Motion Field and Optical Flow. Photogrammetry and Stereo. Pattern Classification. Polyhedral Objects. Extended Gaussian Images. Passive Navigation and Structure from Motion. Picking Parts out of a Bin.Berthold Klaus Paul Horn is Associate Professor, Department of Electrical Engineering and Computer Science, MIT. Robot Vision is included in the MIT Electrical Engineering and Computer Science Series.

Are we “noble in reason”? Perfect, in God’s image? Far from it, says New York University psychologist Gary Marcus. In this lucid and revealing book, Marcus argues that the mind is not an elegantly designed organ but rather a “kluge,” a clumsy, cobbled-together contraption. He unveils a fundamentally new way of looking at the human mind -- think duct tape, not supercomputer -- that sheds light on some of the most mysterious aspects of human nature.
Taking us on a tour of the fundamental areas of human experience -- memory, belief, decision-making, language, and happiness -- Marcus reveals the myriad ways our minds fall short. He examines why people often vote against their own interests, why money can’t buy happiness, why leaders often stick to bad decisions, and why a sentence like “people people left left” ties us in knots even though it’s only four words long.
Marcus also offers surprisingly effective ways to outwit our inner kluge, for the betterment of ourselves and society. Throughout, he shows how only evolution -- haphazard and undirected -- could have produced the minds we humans have, while making a brilliant case for the power and usefulness of imperfection.

Psychology is now ready for unified theories of cognition--so says Allen Newell, a leading investigator in computer science and cognitive psychology. Not everyone will agree on a single set of mechanisms that will explain the full range of human cognition, but such theories are within reach and we should strive to articulate them. In this book, Newell makes the case for unified theories by setting forth a candidate. After reviewing the foundational concepts of cognitive science--knowledge, representation, computation, symbols, architecture, intelligence, and search--Newell introduces Soar, an architecture for general cognition. A pioneer system in artificial intelligence, Soar is the first problem solver to create its own subgoals and learn continuously from its own experience. Newell shows how Soar's ability to operate within the real-time constraints of intelligent behavior, such as immediate-response and item-recognition tasks, illustrates important characteristics of the human cognitive structure. Throughout, Soar remains an exemplar: we know only enough to work toward a fully developed theory of cognition, but Soar's success so far establishes the viability of the enterprise. Given its integrative approach, Unified Theories of Cognition will be of tremendous interest to researchers in a variety of fields, including cognitive science, artificial intelligence, psychology, and computer science. This exploration of the nature of mind, one of the great problems of philosophy, should also transcend disciplines and attract a large scientific audience.

The six contributions in Connectionist Symbol Processing address the current tension within the artificial intelligence community between advocates of powerful symbolic representations that lack efficient learning procedures and advocates of relatively simple learning procedures that lack the ability to represent complex structures effectively. The authors seek to extend the representational power of connectionist networks without abandoning the automatic learning that makes these networks interesting.Aware of the huge gap that needs to be bridged, the authors intend their contributions to be viewed as exploratory steps in the direction of greater representational power for neural networks. If successful, this research could make it possible to combine robust general purpose learning procedures and inherent representations of artificial intelligence -- a synthesis that could lead to new insights into both representation and learning.

Recent work in cognitive science, much of it placed in opposition to a computational view of the mind, has argued that the concept of representation and theories based on that concept are not sufficient to explain the details of cognitive processing. These attacks on representation have focused on the importance of context sensitivity in cognitive processing, on the range of individual differences in performance, and on the relationship between minds and the bodies and environments in which they exist. In each case, models based on traditional assumptions about representation have been assumed to be too rigid to account for the effects of these factors on cognitive processing. In place of a representational view of mind, other formalisms and methodologies, such as nonlinear differential equations (or dynamical systems) and situated robotics, have been proposed as better explanatory tools for understanding cognition. This book is based on the notion that, while new tools and approaches for understanding cognition are valuable, representational approaches do not need to be abandoned in the course of constructing new models and explanations. Rather, models that incorporate representation are quite compatible with the kinds of complex situations being modeled with the new methods. This volume illustrates the power of this explicitly representational approach--labeled "cognitive dynamics"--in original essays by prominent researchers in cognitive science. Each chapter explores some aspect of the dynamics of cognitive processing while still retaining representations as the centerpiece of the explanations of the key phenomena. These chapters serve as an existence proof that representation is not incompatible with the dynamics of cognitive processing. The book is divided into sections on foundational issues about the use of representation in cognitive science, the dynamics of low level cognitive processes (such as visual and auditory perception and simple lexical priming), and the dynamics of higher cognitive processes (including categorization, analogy, and decision making).