Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful.

Since the introduction of electrosurgery the techniques of surgery on the nervous system have passed through further improvements (bipolar coagulation, microscope), even if the procedure was not substantially modified. Today, laser represents a new "discipline," as it offers a new way of performing all basic maneuvers (dissection, demolition, hemostasis, vessel sutures). Furthermore, laser offers the possibility of a special maneuver, namely reduction of the volume of a tumoral mass through vaporization. Its application is not restricted to traditional neurosurgery but extends also to stereotactic and vascular neurosurgery. Laser surgery has also influenced the anesthesiologic techniques. At the same time new instrumentation has been introduced: CUSA ultrasonic aspiration, echotomography, and Doppler flowmeter. I have had the chance to utilize these new technologies all at a time and have come to the conclusion that we are facing the dawn of a new methodology which has already shown its validity and lack of inconveniences, and whose object is to increase the precision of neurological surgery. The technological development is still going on, and some improvements are to be foreseen. Laser scalpel is splitting the initial laser surgery into NO TOUCH and TOUCH surgery with laser. As new instrumentarium will be developed, a variable and tunable beam will become available. For example, in a few years Free Electron Laser will further add to the progress in this field."

The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Games and Scales' (Part 1) and 'Suslin Cardinals, Partition Properties, and Homogeneity' (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context. This volume will be an invaluable reference for anyone interested in higher set theory.

Groups of people perform acts that are subject to standards of rationality. A committee may sensibly award fellowships, or may irrationally award them in violation of its own policies. A theory of collective rationality defines collective acts that are evaluable for rationality and formulates principles for their evaluation. This book argues that a group's act is evaluable for rationality if it is the products of acts its members fully control. It also argues that such an act is collectively rational if the acts of the group's members are rational. Efficiency is a goal of collective rationality, but not a requirement, except in cases where conditions are ideal for joint action and agents have rationally prepared for joint action. The people engaged in a game of strategy form a group, and the combination of their acts yields a collective act. If their collective act is rational, it constitutes a solution to their game. A theory of collective rationality yields principles concerning solutions to games. One principle requires that a solution constitute an equilibrium among the incentives of the agents in the game. In a cooperative game some agents are coalitions of individuals, and it may be impossible for all agents to pursue all incentives. Because rationality is attainable, the appropriate equilibrium standard for cooperative games requires that agents pursue only incentives that provide sufficient reasons to act. The book's theory of collective rationality supports an attainable equilibrium-standard for solutions to cooperative games and shows that its realization follows from individuals' rational acts. By extending the theory of rationality to groups, this book reveals the characteristics that make an act evaluable for rationality and the way rationality's evaluation of an act responds to the type of control its agent exercises over the act. The book's theory of collective rationality contributes to philosophical projects such as contractarian ethics and to practical projects such as the design of social institutions.

This book constitutes the refereed proceedings of the 5th International Symposium on Algorithmic Game Theory, SAGT 2012, held in Barcelona, Spain, in October 2012. The 22 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from 65 submissions. The papers present original research at the intersection of Algorithms and Game Theory and address various current topics such as solution concepts in game theory; efficiency of equilibria and price of anarchy; complexity classes in game theory; computational aspects of equilibria; computational aspects of fixed-point theorems; repeated games; evolution and learning in games; convergence of dynamics; coalitions, coordination and collective action; reputation, recommendation and trust systems; graph-theoretic aspects of social networks; network games; cost-sharing algorithms and analysis; computing with incentives; algorithmic mechanism design; computational social choice; decision theory, and pricing; auction algorithms and analysis; economic aspects of distributed computing; internet economics and computational advertising.

This book provides a game theoretic model of interaction among VoIP telecommunications providers regarding their willingness to enter peering agreements with one another. The author shows that the incentive to peer is generally based on savings from otherwise payable long distance fees. At the same time, termination fees can have a countering and dominant effect, resulting in an environment in which VoIP firms decide against peering. Various scenarios of peering and rules for allocation of the savings are considered. The first part covers the relevant aspects of game theory and network theory, trying to give an overview of the concepts required in the subsequent application. The second part of the book introduces first a model of how the savings from peering can be calculated and then turns to the actual formation of peering relationships between VoIP firms. The conditions under which firms are willing to peer are then described, considering the possible influence of a regulatory body.

Multifractal Financial Markets explores appropriate models for estimating risk and profiting from market swings, allowing readers to develop enhanced portfolio management skills and strategies. Fractals in finance allow us to understand market instability and persistence. When applied to financial markets, these models produce the requisite amount of data necessary for gauging market risk in order to mitigate loss. This brief delves deep into the multifractal market approach to portfolio management through real-world examples and case studies, providing readers with the tools they need to forecast profound shifts in market activity.

In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter EURO in the problem, the mass of the perturbing body for instance, and for EURO = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for EURO -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an area-preserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods.

Game Theoretic Risk Analysis of Security Threats introduces reliability and risk analysis in the face of threats by intelligent agents. More specifically, game-theoretic models are developed for identifying optimal and/or equilibrium defense and attack strategies in systems of varying degrees of complexity. The book covers applications to networks, including problems in both telecommunications and transportation. However, the book s primary focus is to integrate game theory and reliability methodologies into a set of techniques to predict, detect, diminish, and stop intentional attacks at targets that vary in complexity.

In this book, Bier and Azaiez highlight work by researchers who combine reliability and risk analysis with game theory methods to create a set of functional tools that can be used to offset intentional, intelligent threats (including the threats of terrorism and war). A comprehensive treatment of such problems must consider two aspects: (1) the structure of the system to be protected; and (2) the adaptive nature of the threat). The book provides a set of tools for applying game theory TO reliability problems in the presence of intentional, intelligent threats. These tools will help to address problems of global security and also facilitate more cost-effective defensive investments.

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This volume contains twelve of my game-theoretical papers, published in the period of 1956-80. It complements my Essays on Ethics, Social Behavior, and Scientific Explanation, Reidel, 1976, and my Rational Behavior and Bargaining Equilibrium in Games and Social Situations, Cambridge University Press, 1977. These twelve papers deal with a wide range of game-theoretical problems. But there is a common intellectual thread going though all of them: they are all parts of an attempt to generalize and combine various game-theoretical solution concepts into a unified solution theory yielding one-point solutions for both cooperative and noncooperative games, and covering even such 'non-classical' games as games with incomplete information. SECTION A The first three papers deal with bargaining models. The first one discusses Nash's two-person bargaining solution and shows its equivalence with Zeuthen's bargaining theory. The second considers the rationality postulates underlying the Nash-Zeuthen theory and defends it against Schelling's objections. The third extends the Shapley value to games without transferable utility and proposes a solution concept that is at the same time a generaliza tion of the Shapley value and of the Nash bargaining solution."

Distributed Decision Making and Control is a mathematical treatment of relevant problems in distributed control, decision and multiagent systems, The research reported was prompted by the recent rapid development in large-scale networked and embedded systems and communications. One of the main reasons for the growing complexity in such systems is the dynamics introduced by computation and communication delays. Reliability, predictability, and efficient utilization of processing power and network resources are central issues and the new theory and design methods presented here are needed to analyze and optimize the complex interactions that arise between controllers, plants and networks. The text also helps to meet requirements arising from industrial practice for a more systematic approach to the design of distributed control structures and corresponding information interfaces Theory for coordination of many different control units is closely related to economics and game theory network uses being dictated by congestion-based pricing of a given pathway. The text extends existing methods which represent pricing mechanisms as Lagrange multipliers to distributed optimization in a dynamic setting. In Distributed Decision Making and Control, the main theme is distributed decision making and control with contributions to a general theory and methodology for control of complex engineering systems in engineering, economics and logistics. This includes scalable methods and tools for modeling, analysis and control synthesis, as well as reliable implementations using networked embedded systems. Academic researchers and graduate students in control science, system theory, and mathematical economics and logistics will find mcu to interest them in this collection, first presented orally by the contributors during a sequence of workshops organized in Spring 2010 by the Lund Center for Control of Complex Engineering Systems, a Linnaeus Center at Lund University, Sweden.>

Climate change is one of the major environmental concern of many countries in the world. Negotiations to control potential climate changes have been taking place, from Rio to Kyoto, for the last five years. There is a widespread consciousness that the risk of incurring in relevant economic and environmental losses due to climate change is high. Scientific analyses have become more and more precise on the likely impacts of climate change. According to the Second Assessment Report of the Intergovernmental Panel on Climate Change, current trends in greenhouse gases (GHGs) emissions may indeed cause the average global temperature to increase by 1-3. 5 DegreesC over the next 100 years. As a result, sea levels are expected to rise by 15 to 95 em and climate zones to shift towards the poles by 150 to 550 km in mid latitudes. In order to mitigate the adverse effects of climate change, the IPCC report concludes that a stabilization of atmospheric concentration of carbon dioxide - one of the major GHGs - at 550 parts per million by volume (ppmv) is recommended. This would imply a reduction of global emissions of about 50 per cent with respect to current levels. In this context, countries are negotiating to achieve a world-wide agreement on GHGs emissions control in order to stabilize climate changes. Despite the agreement on targets achieved in Kyoto, many issues still remain unresolved.

The theory of social choice deals with both the processes and results of col lective decision making. In this book, we explore some issues in the theory of social choice and mechanism design. We examine the premises of this theory, the axiomatic approach, and the mechanism design approach. The main questions are what is collective interest, how is it related to individuals' interests, how should one design social interactions, laws, and in stitutions? These questions are not new. Philosophers, social scientists have indeed pondered upon them for years. And, in fact, the organizational struc tures of many social institutions -courts, parliaments, committees and reg ulatory boards -often lack a sound theoretical base. This is not surprising, as it is, indeed, difficult to provide for a comprehensive formalization of the activities of such organizations. Nevertheless, there has been a definite trend towards providing clear and unambiguous rules for collective decision mak ing. These very rules constitute the body of social choice theory and its main object. The basic problem of social choice We explain here more precisely what a problem of social choice is, what approaches might be used to tackle it, and what kind of solutions it leads to. We introduce a few basic notions in preliminarily fashion and, in doing so, we stress both motivations and explanations."

The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before. Here, several topics of current and growing interest are systematically presented, such as fixed point theory, best approximation, the KKM-map principle, and results related to optimization theory, variational inequalities and complementarity problems. Illustrations of suitable applications are given, the links between results in various fields of research are highlighted, and an up-to-date bibliography is included to assist readers in further studies. Audience: This book will be of interest to graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations and expansions, convex sets and related geometric topics and game theory.

Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc. Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory. In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.

In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented.
Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

The use of the internet for commerce has spawned a variety of auctions, marketplaces, and exchanges for trading everything from bandwidth to books. Mechanisms for bidding agents, dynamic pricing, and combinatorial bids are being implemented in support of internet-based auctions, giving rise to new versions of optimization and resource allocation models. This volume, a collection of papers from an IMA "Hot Topics" workshop in internet auctions, includes descriptions of real and proposed auctions, complete with mathematical model formulations, theoretical results, solution approaches, and computational studies.
This volume also provides a mathematical programming perspective on open questions in auction theory, and provides a glimpse of the growing area of dynamic pricing.

In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http: //www.genconv.org) consists of more than 300 researchers coming from 36 countries

This book tries to sort out the different meanings of uncertainty and to discover their foundations. It shows that uncertainty can be represented using various tools and mental guidelines. Coverage also examines alternative ways to deal with risk and risk attitude concepts. Behavior under uncertainty emerges from this book as something to base more on inquiry and reflection rather than on mere intuition.

This volume contains a selection consisting of the best papers presented at the FUR XII conference, held at LUISS in Roma, Italy, in June 2006, organized by John Hey and Daniela Di Cagno. The objectives of the FUR (Foundations of Utility and Risk theory) conferences have always been to bring together leading academics from Economics, Psychology, Statistics, Operations Research, Finance, Applied Mat- matics, and other disciplines, to address the issues of decision-making from a g- uinely multi-disciplinary point of view. This twelfth conference in the series was no exception. The early FUR conferences - like FUR I (organized by Maurice Allais and Ole Hagen) and FUR III (organized by Bertrand Munier) - initiated the move away from the excessively rigid and descriptively-inadequate modelling of beh- iour under risk and uncertainty that was in vogue in conventional economics at that time. More than twenty years later, things have changed fundamentally, and now - novations arising from the FUR conferences, and manifesting themselves in the new behavioural economics, are readily accepted by the profession. Working with new models of ambiguity, and bounded rationality, for example, behavioural decision making is no longer considered a sign of mere non-standard intellectual diversi?- tion. FUR XII was organised with this new spirit. In the sense that the behavioural concerns initiated by the ?rst FUR conferences are now part of conventional e- nomics, and the design and organisation of FUR XII re?ects this integration, FUR XII represents a key turning point in the FUR conference series.

Reprinted by popular demand, this monograph presents a comprehensive study of positive operators between Riesz spaces and Banach lattices. Since publication of this book in 1985, the subject of positive operators and Riesz spaces has found practical applications in disciplines including social sciences and engineering. This book examines positive operators in the setting of Riesz spaces and Banach lattices, from both the algebraic and topological points of view.

The book compiles research on Condorcet's Paradox over some two centuries. It begins with a historical overview of the discovery of Condorcet's Paradox in the 18th Century, reviews numerous studies conducted to find actual occurrences of the paradox, and compiles research that has been done to develop mathematical representations for the probability that the paradox will be observed. Combines all approaches that have been used to study this very interesting phenomenon.

Efficiency and Equity of Climate Change Policy is a comprehensive assessment of the economic effects of climate change policy, addressing the issues with a quantitative modelling approach. The book thus goes beyond the usual statements on the efficiency of economic instruments to identify the way gains and losses are distributed; who gains and who loses. Both the costs and benefits of climate change policies are analyzed. Most papers also provide useful information on the economic features of the Kyoto Protocol, its possible extensions, and the effect of different implementation strategies (such as the debate on emissions trading ceilings). Readership: Scientists and policy makers, students and specialists in climate related industries, members of NGOs, and policy advisors.

Social computing concerns the study of social behavior and context based on computational systems. Behavioral modeling reproduces the social behavior, and allows for experimenting with and deep understanding of behavior, patterns, and potential outcomes. The pervasive use of computer and Internet technologies provides an unprecedented environment where people can share opinions and experiences, offer suggestions and advice, debate, and even conduct experiments. Social computing facilitates behavioral modeling in model building, analysis, pattern mining, anticipation, and prediction. The proceedings from this interdisciplinary workshop provide a platform for researchers, practitioners, and graduate students from sociology, behavioral and computer science, psychology, cultural study, information systems, and operations research to share results and develop new concepts and methodologies aimed at advancing and deepening our understanding of social and behavioral computing to aid critical decision making.

Linear programming attracted the interest of mathematicians during and after World War II when the first computers were constructed and methods for solving large linear programming problems were sought in connection with specific practical problems for example, providing logistical support for the U.S. Armed Forces or modeling national economies. Early attempts to apply linear programming methods to solve practical problems failed to satisfy expectations. There were various reasons for the failure. One of them, which is the central topic of this book, was the inexactness of the data used to create the models. This phenomenon, inherent in most pratical problems, has been dealt with in several ways. At first, linear programming models used "average" values of inherently vague coefficients, but the optimal solutions of these models were not always optimal for the original problem itself. Later researchers developed the stochastic linear programming approach, but this too has its limitations. Recently, interest has been given to linear programming problems with data given as intervals, convex sets and/or fuzzy sets. The individual results of these studies have been promising, but the literature has not presented a unified theory. Linear Optimization Problems with Inexact Data attempts to present a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework."