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On Coordination in Non-Cooperative Game Theory: Explaining How and Why an Equilibrium Occurs and Prevails (Springer Studies in the History of Economic Thought)
by Lauren LarrouyBy offering a critical assessment of the evolution of standard game theory, this book argues for a shift in the ontology and methodology of game theory for appraising games, one based on understanding the players’ strategic reasoning process. Analyzing the history of economic thought, the book highlights the methodological issues faced by standard game theory in its treatment of strategic reasoning and the consequence it has on the status of players’ beliefs. It also highlights how the two original contributions of T. C. Schelling and M. Bacharach can be applied to these issues. Furthermore, the book assesses the intersubjective dimension in games by applying the cognitive sciences and by integrating simulation theory into game theory. Consequently, this book offers an interdisciplinary approach for reassessing the nature of the intersubjectivity involved in strategic reasoning. It shows that the analysis of games should involve the study and identification of the reasoning process that leads the players to a specific outcome, i.e., to a specific solution. A game should not be understood (as is done in standard game theory) as a mathematical representation of an individual choice at equilibrium. This requires investigating the players’ capacity for coordination. Understanding the process of coordination allows us to understand strategic reasoning and ultimately to provide new answers to the indeterminacy problem, one of the central hurdles in game theory, and one that underscores its normative difficulties.
On Exciton–Vibration and Exciton–Photon Interactions in Organic Semiconductors (Springer Theses)
by Antonios M. AlvertisWhat are the physical mechanisms that underlie the efficient generation and transfer of energy at the nanoscale? Nature seems to know the answer to this question, having optimised the process of photosynthesis in plants over millions of years of evolution. It is conceivable that humans could mimic this process using synthetic materials, and organic semiconductors have attracted a lot of attention in this respect. Once an organic semiconductor absorbs light, bound pairs of electrons with positively charged holes, termed `excitons’, are formed. Excitons behave as fundamental energy carriers, hence understanding the physics behind their efficient generation and transfer is critical to realising the potential of organic semiconductors for light-harvesting and other applications, such as LEDs and transistors. However, this problem is extremely challenging since excitons can interact very strongly with photons. Moreover, simultaneously with the exciton motion, organic molecules can vibrate in hundreds of possible ways, having a very strong effect on energy transfer. The description of these complex phenomena is often beyond the reach of standard quantum mechanical methods which rely on the assumption of weak interactions between excitons, photons and vibrations. In this thesis, Antonios Alvertis addresses this problem through the development and application of a variety of different theoretical methods to the description of these strong interactions, providing pedagogical explanations of the underlying physics. A comprehensive introduction to organic semiconductors is followed by a review of the background theory that is employed to approach the relevant research questions, and the theoretical results are presented in close connection with experiment, yielding valuable insights for experimentalists and theoreticians alike.
On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Dover Books on Mathematics)
by Kurt GödelIn 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
On Functions and Functional Equations
by J. SmitalOn Functions and Functional Equations introduces the main topics in iteration theory and the theory of functional equations with emphasis on applications in the fields of mathematics, physics, biology, chemistry, and electronics and mechanical engineering. The book contains many classical results as well as important, more recent results. It also includes numerous exercise and some problems that have yet to be resolved. The book is accessible to readers having a secondary level mathematical education.
On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions
by Markus Q. HuberQuarks are the main constituents of protons and neutrons and hence are important building blocks of all the matter that surrounds us. However, quarks have the intriguing property that they never appear as isolated single particles but only in bound states. This phenomenon is called confinement and has been a central research topic of elementary particle physics for the last few decades. In order to find the mechanism that forbids the existence of free quarks many approaches and ideas are being followed, but by now it has become clear that they are not mutually exclusive but illuminate the problem from different perspectives. Two such confinement scenarios are investigated in this thesis: Firstly, the importance of Abelian field components for the low-energy regime is corroborated, thus supporting the dual superconductor picture of confinement and secondly, the influence of the Gribov horizon on non-perturbative solutions is studied.
On Graph Approaches to Contextuality and their Role in Quantum Theory (SpringerBriefs in Mathematics)
by Barbara Amaral Marcelo Terra CunhaThis book explores two of the most striking features of quantum theory – contextuality and nonlocality – using a formulation based on graph theory. Quantum theory provides a set of rules to predict probabilities of different outcomes in different experimental settings, and both contextuality and nonlocality play a fundamental role in interpreting the outcomes. In this work, the authors highlight how the graph approach can lead to a better understanding of this theory and its applications. After presenting basic definitions and explaining the non-contextuality hypothesis, the book describes contextuality scenarios using compatibility hypergraphs. It then introduces the exclusivity graph approach, which relates a number of important graph-theoretical concepts to contextuality. It also presents open problems such as the so-called Exclusivity Principle, as well as a selection of important topics, like sheaf-theoretical approach, hypergraph approach, and alternative proofs of contextuality.
On Hilbert-Type and Hardy-Type Integral Inequalities and Applications (SpringerBriefs in Mathematics)
by Bicheng Yang Michael Th. RassiasThis book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications. Theories, methods, and techniques of real analysis and functional analysis are applied to equivalent formulations of Hilbert-type inequalities, Hardy-type integral inequalities as well as their parameterized reverses. Special cases of these integral inequalities across an entire plane are considered and explained. Operator expressions with the norm and some particular analytic inequalities are detailed through several lemmas and theorems to provide an extensive account of inequalities and operators.
On Hilbert's Sixth Problem (Synthese Library #441)
by Newton C. da Costa Francisco Antonio DoriaThis book explores the premise that a physical theory is an interpretation of the analytico–canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico–canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism.The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler–Lagrange equations. The theory of Suppes predicates as the main tool in the axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences.This volume looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set–theoretically generic spacetimes.
On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory
by Susanne Saminger-Platz Radko MesiarThe book is a collection of contributionsby leading experts, developed around traditional themes discussed at the annualLinz Seminars on Fuzzy Set Theory. The different chapters have been written byformer PhD students, colleagues, co-authors and friends of Peter Klement, aleading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement'sresearch activities, concerning copulas, measures and integrals, as well asaggregation problems. Some of the chapters reflect personal views andcontroversial aspects of traditional topics, while others deal with deepmathematical theories, such as the algebraic and logical foundations of fuzzyset theory and fuzzy logic. Originally thought as an homage to Peter Klement,the book also represents an advanced reference guide to the mathematicaltheories related to fuzzy logic and fuzzy set theory with the potential tostimulate important discussions on new research directions in the field.
On Normalized Integral Table Algebras (Fusion Rings)
by Arisha Haj Ihia Hussam Mikhail Muzychuk Zvi Arad Effi Cohen Guiyun Chen Xu BangtengThe theory of table algebras was introduced in 1991 by Z. Arad and H. Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras. This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C). This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras.
On-Orbit Operations Optimization
by Leping Yang Yanwei Zhu Xianhai Ren Yuanwen ZhangOn-orbit operations optimization among multiple cooperative or noncooperative spacecraft, which is often challenged by tight constraints and shifting parameters, has grown to be a hot issue in recent years. The authors of this book summarize related optimization problems into four planning categories: spacecraft multi-mission planning, far-range orbital maneuver planning, proximity relative motion planning and multi-spacecraft coordinated planning. The authors then formulate models, introduce optimization methods, and investigate simulation cases that address problems in these four categories. This text will serve as a quick reference for engineers, graduate students, postgraduates in the fields of optimization research and on-orbit operation mission planning.
On Privilege (Little Books On Big Themes Ser.)
by Julian BurnsideRenowned barrister, ethicist and human rights advocate Julian Burnside QC's grandparents lived in a world of handsome cars, elegant tennis parties and coiffed women. As a five-year-old, he saw privilege before he heard the word or learned its meaning. In this powerful broadside that takes in politicians and infamous legal cases, Julian Burnside explores the concept of privilege and the people who have it.
On Quaternions and Octonions
by John H. Conway Derek A. SmithThis book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f
On Raising a Digital Human: A Personal Evolution (Synthesis Lectures on Computer Science)
by Norman I. BadlerThis book tells the story of building digital virtual human models in the context of the background, choices, and occurrences that shaped the author's own involvement and personal evolution. Such digital models found motivating applications in engineering, anthropology, medical, and group simulation problems, and numerous connections to other disciplines informed and enriched their design, development, and deployment. This personal perspective on developments in the field is enhanced by extensive citations that provide pointers into relevant literature, recognize the contributions of co-authors and collaborators, and give external evidence for claims. Both academic and corporate interest in virtual beings has exploded in recent years, and while this book does not survey the current state of the art it is an essential window into how the field arrived where it is today. The technical discussions throughout the book are deliberately accessible with extensive references to the literature for further reading. This book will be of interest to readers who want to understand the history of virtual human beings, how they evolved, and especially how they must address numerous human characteristics to achieve any sense of "human-ness."
On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises (Dover Books on Mathematics)
by Felix KleinA consideration of the investigations in the first part of Riemann's Theory of Abelian Functions, this volume introduces Riemann's approach to multiple-value functions and the geometrical representation of these functions by what later became known as Riemann surfaces. It further concentrates on the kinds of functions that can be defined on these surfaces, confining the treatment to rational functions and their integrals, and then demonstrates how Riemann's mathematical ideas about Abelian integrals can be arrived at by thinking in terms of the flow of electric current on surfaces. Deeply significant in the area of complex functions, this work constitutes one of the best introductions to the origins of topological problems. Unabridged republication of the classic 1893 edition. 43 figures. Glossary.
On Riemann's Theory of Algebraic Functions and Their Integrals: A Supplement to the Usual Treatises (Dover Books on Mathematics)
by Felix KleinA great researcher, writer, and teacher in an era of tremendous mathematical ferment, Felix Klein (1849–1925) occupies a prominent place in the history of mathematics. His many talents included an ability to express complicated mathematical ideas directly and comprehensively, and this book, a consideration of the investigations in the first part of Riemann's Theory of Abelian Functions, is a prime example of his expository powers.
On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics (The\mit Press Ser.)
by Agustin RayoAn introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory.This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof.The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.
On the Class Number of Abelian Number Fields: Extended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi
by Helmut HasseWith this translation, the classic monograph Über die Klassenzahl abelscher Zahlkörper by Helmut Hasse is now available in English for the first time.The book addresses three main topics: class number formulas for abelian number fields; expressions of the class number of real abelian number fields by the index of the subgroup generated by cyclotomic units; and the Hasse unit index of imaginary abelian number fields, the integrality of the relative class number formula, and the class number parity. Additionally, the book includes reprints of works by Ken-ichi Yoshino and Mikihito Hirabayashi, which extend the tables of Hasse unit indices and the relative class numbers to imaginary abelian number fields with conductor up to 100. The text provides systematic and practical methods for deriving class number formulas, determining the unit index and calculating the class number of abelian number fields. A wealth of illustrative examples, together with corrections and remarks on the original work, make this translation a valuable resource for today’s students of and researchers in number theory.
On the Edge: The Art of Risking Everything
by Nate SilverIn the bestselling The Signal and the Noise, Nate Silver showed how forecasting would define the age of Big Data. Now, in this timely and riveting new book, Silver investigates “the River,” the community of like-minded people whose mastery of risk allows them to shape—and dominate—so much of modern life. <P><P> These professional risk-takers—poker players and hedge fund managers, crypto true believers and blue-chip art collectors—can teach us much about navigating the uncertainty of the twenty-first century. By immersing himself in the worlds of Doyle Brunson, Peter Thiel, Sam Bankman-Fried, Sam Altman, and many others, Silver offers insight into a range of issues that affect us all, from the frontiers of finance to the future of AI. <P><P> Most of us don’t have traits commonly found in the River: high tolerance for risk, appreciation of uncertainty, affinity for numbers—paired with an instinctive distrust of conventional wisdom and a competitive drive so intense it can border on irrational. For those in the River, complexity is baked in, and the work is how to navigate it. People in the River have increasing amounts of wealth and power in our society, and understanding their mindset—and the flaws in their thinking— is key to understanding what drives technology and the global economy today. <P><P> Taking us behind the scenes from casinos to venture capital firms, and from the FTX inner sanctum to meetings of the effective altruism movement, On the Edge is a deeply reported, all-access journey into a hidden world of power brokers and risk-takers. <p> <b>New York Times Bestseller</b>
On the Edge of Infinity: Encounters with the Beauty of the Universe
by Stefan KleinFrom the award-winning, bestselling German science author Stefan Klein An original way into the most thought-provoking scientific theories and ideas, On The Edge of Infinity is the perfect read for those curious about the workings of the universe.*How can a hurricane can reveal the world's unpredictability?How can a greying beard might demonstrate the irreversibility of time?How do the exploits of burglars in New York and London demonstrate how everything can be in two places at once?Employing stories about simple everyday items or occurrences as analogies to illuminate counterintuitive realities behind the visible world, On The Edge of Infinity reveals the astonishing beauty of the universe. This book transforms a simple everyday thing such as a rose blossom, or a day of stormy weather, into a key to understanding the most complex ideas and theories in 21st century physics. Stefan Klein unpicks the complexities and intricacies of physics, from the answered questions to the dark corners of what we have yet to discover, making this an accessible read to those with no previous knowledge of the subject.
On the Emergence of Time and Space in Closed Quantum Systems (Springer Theses)
by Tommaso FavalliTime, space and entanglement are the main characters in this book. Their nature is still a great mystery in physics and we study here the possibility that these three phenomena are closely connected, showing how entanglement can be at the basis of the emergence of time and space within closed quantum systems. We revisit and extend the Page and Wootters theory that was originally introduced in order to describe the emergence of time through entanglement between subsystems in a globally static, quantum Universe. In the book, after providing a complete review of the salient aspects of the theory, we establish a connection with recent research on the foundations of statistical mechanics and we provide a new understanding of the thermalization process. Furthermore, we generalize the framework in order describe the spatial degree of freedom and we provide a model of 3+1 dimensional, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe. Finally, via the Page and Wootters theory, the evolution of quantum clocks within a gravitational field is treated and a time dilation effect is obtained in agreement with the Schwarzschild solution.
On the Epistemology of Data Science: Conceptual Tools for a New Inductivism (Philosophical Studies Series #148)
by Wolfgang PietschThis book addresses controversies concerning the epistemological foundations of data science: Is it a genuine science? Or is data science merely some inferior practice that can at best contribute to the scientific enterprise, but cannot stand on its own? The author proposes a coherent conceptual framework with which these questions can be rigorously addressed. Readers will discover a defense of inductivism and consideration of the arguments against it: an epistemology of data science more or less by definition has to be inductivist, given that data science starts with the data. As an alternative to enumerative approaches, the author endorses Federica Russo’s recent call for a variational rationale in inductive methodology. Chapters then address some of the key concepts of an inductivist methodology including causation, probability and analogy, before outlining an inductivist framework. The inductivist framework is shown to be adequate and useful for an analysis of the epistemological foundations of data science. The author points out that many aspects of the variational rationale are present in algorithms commonly used in data science. Introductions to algorithms and brief case studies of successful data science such as machine translation are included. Data science is located with reference to several crucial distinctions regarding different kinds of scientific practices, including between exploratory and theory-driven experimentation, and between phenomenological and theoretical science. Computer scientists, philosophers and data scientists of various disciplines will find this philosophical perspective and conceptual framework of great interest, especially as a starting point for further in-depth analysis of algorithms used in data science.
On the Estimation of Multiple Random Integrals and U-Statistics
by Péter MajorThis work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because the linearized version is simpler. But in order to apply such a method we have to show that the linearization causes a negligible error. The estimation of this error leads to some important large deviation type problems, and the main subject of this work is their investigation. We provide sharp estimates of the tail distribution of multiple integrals with respect to a normalized empirical measure and so-called degenerate U-statistics and also of the supremum of appropriate classes of such quantities. The proofs apply a number of useful techniques of modern probability that enable us to investigate the non-linear functionals of independent random variables. This lecture note yields insights into these methods, and may also be useful for those who only want some new tools to help them prove limit theorems when standard methods are not a viable option.
On the Fractal Language of Medicine (Fractional Order Thinking in Exploring the Frontiers of STEM)
by Bruce J. West W. Alan MutchOn the Fractal Language of Medicine bridges a very clear gap among the knowledge gained over the last 20 years in the physical and life sciences on network theory, organ synchronicity and communication, the understanding of fractal signatures in health and disease and the importance of fractional calculus in integrating these concepts.The authors opine that the field of medicine has not appreciated this hard-won knowledge and has suffered greatly as a result. This book addresses this perceived deficiency by introducing medical researchers, clinicians, residents, first-year medical students and members of allied fields to the work of the so-called hard sciences. It seeks to facilitate effective communication between empiricists and theorists by making interdisciplinary efforts to explain complex mathematical concepts to physicians and, equally important, to elucidate complex medical concepts to physicists or mathematicians.This book will be of great interest to medical students, professionals and academics, as well as students and researchers of applied mathematics, especially those interested in fractional calculus and fractals.