Task: Question Answering
Input (English): Context: In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero-sum game if all participants value each unit of cake equally (see marginal utility). , The von Neumann architecture, which is also known as the von Neumann model and Princeton architecture, is a computer architecture based on that described in 1945 by the mathematician and physicist John von Neumann and others in the "First Draft of a Report on the EDVAC". This describes a design architecture for an electronic digital computer with parts consisting of a processing unit containing an arithmetic logic unit and processor registers; a control unit containing an instruction register and program counter; a memory to store both data and instructions; external mass storage; and input and output mechanisms. The meaning has evolved to be any stored-program computer in which an instruction fetch and a data operation cannot occur at the same time because they share a common bus. This is referred to as the von Neumann bottleneck and often limits the performance of the system., Physics (from , from "phúsis" "nature") is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental scientific disciplines, the main goal of physics is to understand how the universe behaves., Computing is any goal-oriented activity requiring, benefiting from, or creating a mathematical sequence of steps known as an algorithm  e.g. through computers. Computing includes designing, developing and building hardware and software systems; processing, structuring, and managing various kinds of information; doing scientific research on and with computers; making computer systems behave intelligently; and creating and using communications and entertainment media. The field of computing includes computer engineering, software engineering, computer science, information systems, and information technology., Computer science is the study of the theory, experimentation, and engineering that form the basis for the design and use of computers. It is the scientific and practical approach to computation and its applications and the systematic study of the feasibility, structure, expression, and mechanization of the methodical procedures (or algorithms) that underlie the acquisition, representation, processing, storage, communication of, and access to information. An alternate, more succinct definition of computer science is the study of automating algorithmic processes that scale. A computer scientist specializes in the theory of computation and the design of computational systems., In mathematics, topology (from the Greek , "place", and , "study") is concerned with the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into what is known as a topological space. Important topological properties include connectedness and compactness., Oskar Morgenstern (January 24, 1902  July 26, 1977) was a German-born economist. In collaboration with mathematician John von Neumann, he founded the mathematical field of game theory and its application to economics (see von NeumannMorgenstern utility theorem)., The Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large., Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers." Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science and biology. Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers., A society is a group of people involved in persistent social interaction, or a large social grouping sharing the same geographical or social territory, typically subject to the same political authority and dominant cultural expectations. Societies are characterized by patterns of relationships (social relations) between individuals who share a distinctive culture and institutions; a given society may be described as the sum total of such relationships among its constituent members. In the social sciences, a larger society often evinces stratification or dominance patterns in subgroups., A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (such as computer science, artificial intelligence), as well as in the social sciences (such as economics, psychology, sociology, political science). Physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour., Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator "S", which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space "H" describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic., Princeton University is a private Ivy League research university in Princeton, New Jersey, United States., A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br>
It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox., Theory of Games and Economic Behavior , published in 1944 by Princeton University Press , is a book by mathematician John von Neumann and economist Oskar Morgenstern which is considered the groundbreaking text that created the interdisciplinary research field of game theory . In the introduction of its 60th anniversary commemorative edition from the Princeton University Press , the book is described as `` the classic work upon which modern - day game theory is based . '' The book is based on earlier research by Neumann , published in 1928 under the German title `` Zur Theorie der Gesellschaftsspiele '' ( `` On the Theory of Parlor Games '' ) . The derivation of expected utility from its axioms appeared in an appendix to the Second Edition ( 1947 ) . Von Neumann and Morgenstern used objective probabilities , supposing that all the agents had the same probability distribution , as a convenience . However , Neumann and Morgenstern mentioned that a theory of subjective probability could be provided , and this task was completed by Jimmie Savage in 1954 and Johann Pfanzagl in 1967 . Savage extended von Neumann and Morgenstern 's axioms of rational preferences to endogenize probability and make it subjective . He then used Bayes Theorem to update these subject probabilities in light of new information , thus linking rational choice and inference ., Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics)., Economics (, ) is a social science concerned with the factors that determine the production, distribution, and consumption of goods and services. The term "economics" comes from the Ancient Greek from (', pronounced "eekos", "house") and (', "custom" or "law"), hence "rules of the house (hold for good management)". 'Political economy' was the earlier name for the subject, but economists in the late 19th century suggested "economics" as a shorter term for "economic science" to establish itself as a separate discipline outside of political science and other social sciences., John von Neumann (; December 28, 1903  February 8, 1957) was a Hungarian-American mathematician, physicist, inventor, computer scientist, and polymath. He made major contributions to a number of fields, including mathematics (foundations of mathematics, functional analysis, ergodic theory, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics., Political science is a social science which deals with systems of government, and the analysis of political activities, political thoughts and political behaviour. It deals extensively with the theory and practice of politics which is commonly thought of as determining of the distribution of power and resources. Political scientists "see themselves engaged in revealing the relationships underlying political events and conditions, and from these revelations they attempt to construct general principles about the way the world of politics works." , Psychology is the study of behavior and mind, embracing all aspects of conscious and unconscious experience as well as thought. It is an academic discipline and a social science which seeks to understand individuals and groups by establishing general principles and researching specific cases. In this field, a professional or researcher is called a psychologist and can be classified as a social, behavioral, or cognitive scientist. Psychologists attempt to understand the role of mental functions in individual and social behavior, while also exploring the physiological and biological processes that underlie cognitive functions and behaviors.
Psychologists explore behavior and mental processes, including perception, cognition, attention, emotion (affect), intelligence, phenomenology, motivation (conation), brain functioning, and personality. This extends to interaction between people, such as interpersonal relationships, including psychological resilience, family resilience, and other areas. Psychologists of diverse orientations also consider the unconscious mind. Psychologists employ empirical methods to infer causal and correlational relationships between psychosocial variables. In addition, or in opposition, to employing empirical and deductive methods, someespecially clinical and counseling psychologistsat times rely upon symbolic interpretation and other inductive techniques. Psychology has been described as a "hub science", with psychological findings linking to research and perspectives from the social sciences, natural sciences, medicine, humanities, and philosophy.
While psychological knowledge is often applied to the assessment and treatment of mental health problems, it is also directed towards understanding and solving problems in several spheres of human activity. By many accounts psychology ultimately aims to benefit society. The majority of psychologists are involved in some kind of therapeutic role, practicing in clinical, counseling, or school settings. Many do scientific research on a wide range of topics related to mental processes and behavior, and typically work in university psychology departments or teach in other academic settings (e.g., medical schools, hospitals). Some are employed in industrial and organizational settings, or in other areas such as human development and aging, sports, health, and the media, as well as in forensic investigation and other aspects of law., A physicist is a scientist who has specialized knowledge in the field of physics, the exploration of the interactions of matter and energy across the physical universe., Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer., Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague.
Foundations of mathematics can be conceived as the study of the basic mathematical concepts (number, geometrical figure, set, function, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges., A computer scientist is a scientist who has acquired the knowledge of computer science, the study of the theoretical foundations of information and computation and their application., Quantum mechanics (QM; also known as quantum physics or quantum theory), including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large (macroscopic) scales. Quantum mechanics differs from classical physics in that energy, momentum and other quantities are often restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to the precision with which quantities can be known (Uncertainty principle). , Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments., Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations., Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, evolution, distribution, identification and taxonomy. Modern biology is a vast and eclectic field, composed of many branches and subdisciplines. However, despite the broad scope of biology, there are certain general and unifying concepts within it that govern all study and research, consolidating it into single, coherent field. In general, biology recognizes the cell as the basic unit of life, genes as the basic unit of heredity, and evolution as the engine that propels the synthesis and creation of new species. It is also understood today that all the organisms survive by consuming and transforming energy and by regulating their internal environment to maintain a stable and vital condition known as homeostasis., Ergodic theory (Ancient Greek: "ergon" work, "hodos" way) is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics., Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics., A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems., An economist is a practitioner in the social science discipline of economics., Subject: theory of games and economic behavior, Relation: genre, Options: (A) abstract (B) academia (C) biology (D) country (E) design (F) economics (G) entertainment (H) game (I) geometry (J) information (K) instruction (L) intelligence (M) law (N) logic (O) mass (P) mathematics (Q) nature (R) paradox (S) philosophy (T) physics (U) political science (V) psychology (W) representation (X) research (Y) science (Z) society ([) space (\) statistics (]) study (^) universe (_) various
Output (English): science