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Cooperation is pervasive throughout nature, but its origin remains an open question. For decades, social scientists, business leaders, and economists have struggled with an important question: why is cooperation so ubiquitous among unrelated humans? The answers would have profound effects because anything that promotes cooperation leads to more productive work environments and benefits society at large. Game theory provides an ideal framework for studying social dilemmas, or those situations in which people decide whether to cooperate with others (benefitting the group) or defect by prioritizing their self-interest (benefitting only the individual). The social dilemma is formulated as a mathematical game and then programmed into a computer model. Simulating the game allows researchers to investigate potential theories to explain how cooperation emerges and what promotes its persistence. Over the past 25 years, countless papers on social dilemma games have been published, yet arguably little progress has been made. The problem is the social dilemma game models are unrealistic in the sense they contain artificial constructs that deviate from the way humans act. This book describes the shortcomings in current social dilemma game modeling techniques and provides guidance on designing more effective models. A basic introduction to game theory is provided with an emphasis on the prisoner's dilemma, the most widely studied social dilemma game. Individual chapters are provided detailing the shortcomings of weak selection, spatial games, and the Moran process. Computer model validation is also discussed at length. The recommendations found in this book should help design more realistic social dilemma game models likely to produce a better understanding of human cooperation.

Evolving agents to play games is a promising technology. It can provide entertaining opponents for games like Chess or Checkers, matched to a human opponent as an alternative to the perfect and unbeatable opponents embodied by current artifical intelligences. Evolved agents also permit us to explore the strategy space of mathematical games like Prisoner's Dilemma and Rock-Paper-Scissors. This book summarizes, explores, and extends recent work showing that there are many unsuspected factors that must be controlled in order to create a plausible or useful set of agents for modeling cooperation and conflict, deal making, or other social behaviors. The book also provides a proposal for an agent training protocol that is intended as a step toward being able to train humaniform agents—in other words, agents that plausibly model human behavior.

This book constitutes the refereed proceedings of the 5th International Conference on Mathematical Knowledge Management, MKM 2006, held in Wokingham, UK, August 2006. The book presents 22 revised full papers. Coverage extends to the mathematical knowledge management at the intersection of mathematics, computer science, library science, and scientific publishing. The papers are organized in topical sections on proof representations, proof processing, knowledge extraction, knowledge representation, as well as systems and tools.

This book, which goes far beyond a traditional collection of technical articles, is dedicated to Enric Trillas, a fuzzy systems pioneer but also an internationally renowned researcher in other areas of science, such as mathematics and aerospace, and an outstanding manager of scientific affairs in Spain. Some of the contributions in this book develop technical, state-of-the-art themes obviously related to fuzzy logic, while others resemble popular-science articles that shed light on complex mathematical concepts. There are also chapters that highlight the authors'personal relationships and experiences working with Enric Trillas. While planning this book project, the editors decided to give contributors absolute freedom of thought and expression in preparing their chapters. The result is a colorful and inspiring mixture of styles and topics, which perfectly reflects Enric Trillas's multifaceted contributions to research and his outstanding role in promoting education and technological transfer in the field of soft computing. This Festschrift to Enric Trillas, published on the occasion of his 75th birthday, is not only intended as an exemplary source of information for young scientists dealing with uncertainty, imprecision and accuracy of models, but also as an inspiring guide to the role of scientists in education, politics and communication.

A strong and fluent competency in mathematics is a necessary condition for scientific, technological and economic progress. However, it is widely recognized that problem solving, reasoning, and thinking processes are critical areas in which students'performance lags far behind what should be expected and desired. Mathematics is indeed an important subject, but is also important to be able to use it in extra-mathematical contexts. Thinking strictly in terms of mathematics or thinking in terms of its relations with the real world involve quite different processes and issues. This book includes the revised papers presented at the NATO ARW'Information Technology and Mathematical Problem Solving Research', held in April 1991, in Viana do Castelo, Portugal, which focused on the implications of computerized learning environments and cognitive psychology research for these mathematical activities. In recent years, several committees, professional associations, and distinguished individuals throughout the world have put forward proposals to renew mathematics curricula, all emphasizing the importance of problem solving. In order to be successful, these reforming intentions require a theory-driven research base. But mathematics problem solving may be considered a'chaotic field'in which progress has been quite slow.

The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe­ matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g., does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g., what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus'activity, to whom this volume is dedicated. They range from real analysis to DNA com­ puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical'open problems'. They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.

The book discusses a broad overview of traditional machine learning methods and state-of-the-art deep learning practices for hardware security applications, in particular the techniques of launching potent'modeling attacks'on Physically Unclonable Function (PUF) circuits, which are promising hardware security primitives. The volume is self-contained and includes a comprehensive background on PUF circuits, and the necessary mathematical foundation of traditional and advanced machine learning techniques such as support vector machines, logistic regression, neural networks, and deep learning. This book can be used as a self-learning resource for researchers and practitioners of hardware security, and will also be suitable for graduate-level courses on hardware security and application of machine learning in hardware security. A stand-out feature of the book is the availability of reference software code and datasets to replicate the experiments described in the book.

Games, whether educational or recreational, are meant to be fun. How do we ensure that the game delivers its intent? The answer to this question is playtesting. However, a haphazard playtest process cannot discover play experience from various dimensions. Players'perceptions, affordances, age, gender, culture, and many more human factors influence play experience. A playtest requires an intensive experimental process and scientific protocols to ensure that the outcomes seen are reliable for the designer. Playtesting and players'affordances are the focus of this book. This book is not just about the playtest procedures but also demonstrates how they lead to the conclusions obtained when considering data sets. The playtest process or playtest stories differ according to the hypothesis under investigation. We cover examples of playtesting to identify the impact of human factors, such as age and gender, to examine a player's preferences for game objects'design and colors. The book details topics to reflect on possible emotional outcomes of the player at the early stages of game design as well as the methodology for presenting questions to players in such a way as to elicit authentic feedback. This book is intended mainly for game designers, researchers, and developers. However, it provides a general understanding of affordances and human factors that can be informative for readers working in any domain.

Research on general video game playing aims at designing agents or content generators that can perform well in multiple video games, possibly without knowing the game in advance and with little to no specific domain knowledge. The general video game AI framework and competition propose a challenge in which researchers can test their favorite AI methods with a potentially infinite number of games created using the Video Game Description Language. The open-source framework has been used since 2014 for running a challenge. Competitors around the globe submit their best approaches that aim to generalize well across games. Additionally, the framework has been used in AI modules by many higher-education institutions as assignments, or as proposed projects for final year (undergraduate and Master's) students and Ph.D. candidates. The present book, written by the developers and organizers of the framework, presents the most interesting highlights of the research performed by the authors duringthese years in this domain. It showcases work on methods to play the games, generators of content, and video game optimization. It also outlines potential further work in an area that offers multiple research directions for the future.

Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu­ man thinking wherever logical or mathematical reasoning about cer­ tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order­ preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the'hierarchies'in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an'adjoint situation'is that information about objects and relationships in one of the two worlds may be used to gain new information about the other world, and vice versa. In classical Galois theory, for instance, properties of permutation groups are used to study field extensions. Or, in algebraic geometry, a good knowledge of polynomial rings gives insight into the structure of curves, surfaces and other algebraic vari­ eties, and conversely. Moreover, restriction to the'Galois-closed'or'Galois-open'objects (the fixed points of the composite maps) leads to a precise'duality between two maximal subworlds'.

Most would agree that the acquisition of problem-solving ability is a primary goal of education. The emergence of the new information technologiesin the last ten years has raised high expectations with respect to the possibilities of the computer as an instructional tool for enhancing students'problem-solving skills. This volume is the first to assemble, review, and discuss the theoretical, methodological, and developmental knowledge relating to this topical issue in a multidisciplinary confrontation of highly recommended experts in cognitive science, computer science, educational technology, and instructional psychology. Contributors describe the most recent results and the most advanced methodological approaches relating to the application of the computer for encouraging knowledge construction, stimulating higher-order thinking and problem solving, and creating powerfullearning environments for pursuing those objectives. The computer applications relate to a variety of content domains and age levels.

These essays have been written to honor W. W. Bledsoe, a scientist who has contributed to such diverse fields as mathematics, systems analysis, pattern recognition, biology, artificial intelligence, and automated reasoning. The first essay provides a sketch of his life, emphasizing his scientific contributions. The diversity of the fields to which Bledsoe has contributed is reflected in the range of the other essays, which are original scientific contributions by some of his many friends and colleagues. Bledsoe is a founding father of the field of automated reasoning, and a majority of the essays are on that topic. These essays are collected together here not only to acknowledge Bledsoe's manifold and substantial scientific contributions but also to express our appreciation for the great care and energy that he has devoted to nurturing many of the scientists working in those scientific fields he has helped found. Robert S. Boyer Austin February, 1991 ix Acknow ledgements Thanks to Larry Wos, editor of the Journal of Automated Reasoning, and Derek Middleton and Martin Scrivener, Kluwer Academic editors, for sup­ porting the idea of initiating this collection of essays. Thanks to A. Michael Ballantyne and Michael Spivak, for help with lffi.TWC, especially in identifying many formatting problems and providing fixes.

The doctrine of computer life is not congenial to many people. Often they have not thought in any depth about the idea, and it necessarily disturbs their psychological and intellectual frame of reference: it forces a reappraisal of what it is to be alive, what it is to be human, and whether there are profound, yet un­ expected, implications in the development of modern com­ puters. There is abundant evidence to suggest that we are wit­ nessing the emergence of a vast new family of life-forms on earth, organisms that are not based on the familiar metabolic chemistries yet whose manifest'life credentials'are accumulating year by year. It is a mistake to regard biology as a closed science, with arbitrarily limited categories; and we should agree with Jacob (1974) who observed that'Contrary to what is imagined, biology is not a unified science'. Biology is essentially concerned with living things, and we should be reluctant to assume that at anyone time our concept and understanding of life are complete and incapable of further refinement. And it seems clear that much of the continuing refinement of biological categories will be stimulated by advances in systems theory, and in particular by those advances that relate to the rapidly expanding world of computing and robotics. We should also remember what Pant in (1968) said in a different context:'the biological sciences are unrestricted... and their investigator must be prepared to follow their problems into any other science whatsoever.

In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on'the big picture'- automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.

The second, revised edition of this book was suggested by the impressive sales of the first edition. Fortunately this enabled us to incorporate new important results that had just been obtained. The ASSOM (Adaptive-Subspace SOM) is a new architecture in which invariant-feature detectors emerge in an unsupervised learning process. Its basic principle was already introduced in the first edition, but the motiva­ tion and theoretical discussion in the second edition is more thorough and consequent. New material has been added to Sect. 5.9 and this section has been rewritten totally. Correspondingly, Sect. 1.4, which deals with adaptive­ subspace classifiers in general and constitutes the prerequisite for the ASSOM principle, has also been extended and rewritten totally. Another new SOM development is the WEBSOM, a two-layer architecture intended for the organization of very large collections of full-text documents such as those found in the Internet and World Wide Web. This architecture was published after the first edition came out. The idea and results seemed to be so important that the new Sect. 7.8 has now been added to the second edition. Another addition that contains new results is Sect. 3.15, which describes the acceleration in the computing of very large SOMs. It was also felt that Chap. 7, which deals with 80M applications, had to be extended.

Agents act on the basis of their beliefs and these beliefs change as they interact with other agents. In this book the authors propose and explain general logical tools for handling change. These tools include preferential reasoning, theory revision, and reasoning in inheritance systems, and the authors use these tools to examine nonmonotonic logic, deontic logic, counterfactuals, modal logic, intuitionistic logic, and temporal logic. This book will be of benefit to researchers engaged with artificial intelligence, and in particular agents, multiagent systems and nonmonotonic logic.

This book analyzes the existence of equilibria in economies having a measured space of agents and a continuum of agents and commodities. Excessive homogeneity with respect to agent productivity leads to instability and non-uniqueness of a given stationary state and the indeterminacy of the corresponding stationary state equilibrium. Sufficient heterogeneity leads to global saddle-path stability, uniqueness of a given stationary state and the global uniqueness of the corresponding equilibrium. The variety and variance of agent capabilities is reflected in such constructions as culture, social relations, ideology, politics, and preferences that change continuously with historical development. Information variety is an efficacious companion of systemic variety, and can support the performance of an economy, and can be an economically efficient cradle for adaptation to environmental and individual change and systemic evolution.