In this task, you are given a context, a subject, a relation, and many options. Based on the context, from the options select the object entity that has the given relation with the subject. Answer with text (not indexes).

[Q]: Context: A or was a covert agent or mercenary in feudal Japan. The functions of the ninja included espionage, sabotage, infiltration, assassination and guerrilla warfare. Their covert methods of waging irregular warfare were deemed "dishonorable" and "beneath" the samurai-caste, who observed strict rules about honor and combat. The "shinobi" proper, a specially trained group of spies and mercenaries, appeared in the 15th century during the Sengoku period, but antecedents may have existed in the 14th century, and possibly in the 12th century (Heian or early Kamakura era)., Midway Games was an American video game developer and publisher. Its titles included "Mortal Kombat", "Ms. Pac-Man", "Spy Hunter", "Tron", "Rampage", the "Cruis'n" series, "NFL Blitz", and "NBA Jam". Midway also acquired the rights to video games that were originally developed by Williams Electronics and Atari Games, such as "Defender", "Joust", "Robotron 2084", "Gauntlet", and the "Rush" series., Ultimate Mortal Kombat 3 ("UMK3") is a fighting video game in the "Mortal Kombat" series, originally developed and released by Midway Games to arcades in 1995. It is an update of 1995's earlier "Mortal Kombat 3" with an altered gameplay system, additional characters like the returning favorites Kitana and Scorpion who were missing from "Mortal Kombat 3", and some new features., Jean-Claude Camille François Van Varenberg (born 18 October 1960), professionally known as Jean-Claude Van Damme and abbreviated as JCVD, is a Belgian actor, martial artist, screenwriter, film producer, and director best known for his martial arts action films. The most successful of these films include "Bloodsport" (1988), "Kickboxer" (1989), "Lionheart" (1990), "Double Impact" (1991), "Universal Soldier" (1992), "Hard Target" (1993), "Street Fighter" (1994), "Timecop" (1994), "Sudden Death" (1995), "JCVD" (2008) and "The Expendables 2" (2012)., The original console in the series was the first video game console to ship 100 million units, 9 years and 6 months after its initial launch. Its successor, the PlayStation 2, was released in 2000. The PlayStation 2 is the best-selling home console to date, having reached over 155 million units sold as of December 28, 2012. Sony's next console, the PlayStation 3, was released in 2006 and has sold over 80 million consoles worldwide as of November 2013. Sony's latest console, the PlayStation 4, was released in 2013, selling 1 million consoles in its first 24 hours on sale, becoming the fastest selling console in history., A parody (also called a spoof, send-up, take-off, or lampoon) is a work created to imitate, make fun of, or comment on an original workits subject, author, style, or some other targetby means of satiric or ironic imitation. As the literary theorist Linda Hutcheon puts it, "parody  is imitation, not always at the expense of the parodied text." Another critic, Simon Dentith, defines parody as "any cultural practice which provides a relatively polemical allusive imitation of another cultural production or practice."
Parody may be found in art or culture, including literature, music (although "parody" in music has an earlier, somewhat different meaning than for other art forms), animation, gaming, and film., The is an 8-bit handheld video game device with interchangeable cartridges developed and manufactured by Nintendo, which was first released in Japan on , in North America on and in Europe on . It is the first handheld console in the Game Boy line and was created by Satoru Okada and Nintendo Research & Development 1. This same team, led by Gunpei Yokoi at the time, is credited with designing the Game & Watch series as well as several popular games for the Nintendo Entertainment System. Redesigned versions were released in 1996 and 1998 in the form of Game Boy Pocket and Game Boy Light (Japan only), respectively., John Tobias (born August 24, 1969 in Chicago, Illinois) is an American comic book artist, graphic designer, video game designer and writer. Tobias is best known for creating the "Mortal Kombat" series along with Ed Boon., Karate developed on the Ryukyu Islands in what is now Okinawa, Japan. It was brought to the Japanese mainland in the early 20th century during a time of cultural exchanges between the Japanese and the Chinese. It was systematically taught in Japan after the Taish era. In 1922 the Japanese Ministry of Education invited Gichin Funakoshi to Tokyo to give a karate demonstration. In 1924 Keio University established the first university karate club in mainland Japan and by 1932, major Japanese universities had karate clubs. In this era of escalating Japanese militarism, the name was changed from ("Chinese hand" or "Tang hand") to ("empty hand")  both of which are pronounced "karate"  to indicate that the Japanese wished to develop the combat form in Japanese style. After World War II, Okinawa became an important United States military site and karate became popular among servicemen stationed there., Martial arts film is a film genre. A subgenre of the action film, martial arts films contain numerous martial arts fights between characters. They are usually the films' primary appeal and entertainment value, and often are a method of storytelling and character expression and development. Martial arts are frequently featured in training scenes and other sequences in addition to fights. Martial arts films commonly include other types of action, such as hand-to-hand combats, stuntwork, chases, and gunfights., Acclaim Entertainment (stylized as A«laim) was an American video game developer and publisher. It developed, published, marketed and distributed interactive entertainment software for a variety of hardware platforms, including Mega Drive/Genesis, Saturn, Dreamcast, and Game Gear, Nintendo Entertainment System, Super NES, Nintendo 64, GameCube, Game Boy, Game Boy Color, and Game Boy Advance, PlayStation and PlayStation 2, Xbox, personal computer systems and arcade games. They also released video games for the Master System in Europe., Mortal Kombat II (commonly abbreviated as MKII) is a competitive fighting game originally produced by Midway Games for the arcades in . It was later ported to multiple home systems, including the PC, Amiga, Game Boy, Sega Game Gear, Sega Genesis, Sega Saturn, Super Nintendo Entertainment System, and various PlayStation consoles, mostly in licensed versions developed by Probe Entertainment and
Sculptured Software and published by Acclaim Entertainment., Abandoning previous ventures in favor of toys in the 1960s, Nintendo then developed into a video game company in the 1970s, ultimately becoming one of the most influential in the industry and Japan's third most-valuable company with a market value of over $85 billion. From 1992 until 2016, Nintendo was also the majority shareholder of Major League Baseball's Seattle Mariners., The is a 32-bit fifth-generation home video game console that was developed by Sega and released on November 22, 1994 in Japan, May 11, 1995 in North America, and July 8, 1995 in Europe as the successor to the successful Sega Genesis. The Saturn has a dual-CPU architecture and eight processors. Its games are in CD-ROM format, and its game library contains several arcade ports as well as original titles., A fighting game is a video game genre in which the player controls an on-screen character and engages in close combat with an opponent, which can be either an AI or controlled by another player. The fight matches typically consist of several rounds and take place in an arena, while each character has widely differing abilities but each is relatively viable to choose. Players must master techniques such as blocking, counter-attacking, and chaining attacks together into "combos". Since the early 1990s, most fighting games allow the player to execute special attacks by performing specific input combinations. The fighting game genre is related to but distinct from beat 'em ups, which involve large numbers of enemies against the human player., The Super Nintendo Entertainment System (officially abbreviated the Super NES or SNES, and commonly shortened to Super Nintendo) is a 16-bit home video game console developed by Nintendo that was released in 1990 in Japan and South Korea, 1991 in North America, 1992 in Europe and Australasia (Oceania), and 1993 in South America. In Japan, the system is called the , or SFC for short. In South Korea, it is known as the Super Comboy (  "Syupeo Keomboi") and was distributed by Hyundai Electronics. Although each version is essentially the same, several forms of regional lockout prevent the different versions from being compatible with one another. It was released in Brazil on September 2, 1992, by Playtronic., Daniel Pesina ( born March 31 , 1959 in Chicago , Illinois , USA ) is an American martial arts expert and a former employee of Midway . He is the actor who played Johnny Cage and ninjas Sub-Zero , Scorpion , Reptile , Smoke , and Noob Saibot in the video games Mortal Kombat and Mortal Kombat II. His younger brother Carlos , whom he worked with on the first two Mortal Kombat titles , remained with Midway until the company 's closure . Daniel Pesina appeared as one of Shredder 's foot soldiers in the 1991 movie Teenage Mutant Ninja Turtles II : The Secret of the Ooze . In 1994 , Daniel promoted BloodStorm ( a rival fighting game to the Mortal Kombat series ) in an advert , dressed up as Johnny Cage . He had already parted from Midway at this time , so his characters were played by different actors in subsequent installments : the ninja roles were taken over by John Turk in Mortal Kombat 3 and Ultimate Mortal Kombat 3 , while Johnny Cage would be played by Chris Alexander in Mortal Kombat Trilogy . Pesina and his brother Carlos also secretly worked on Tattoo Assassins , another competing game to Mortal Kombat . In the 2003 martial arts movie Book of Swords , which also starred fellow MK actors Zamiar , Ho - Sung Pak and Richard Divizio , he played a hitman whose task was to take out the film 's leading man . Daniel and Carlos also appeared in a videogame - based comedy film entitled Press Start , which was released to DVD on September 25 , 2007 . Daniel 's character is called Sasori , which is Japanese for Scorpion . As of 2004 , Daniel is a teacher at the Chicago Wushuguan School ., The Sega Genesis, known as the in most regions outside North America, is a 16-bit home video game console which was developed and sold by Sega Enterprises, Ltd. The Genesis was Sega's third console and the successor to the Master System. Sega first released the console as the Mega Drive in Japan in 1988, followed by a North American debut under the Genesis moniker in 1989. In 1990, the console was distributed as the Mega Drive by Virgin Mastertronic in Europe, by Ozisoft in Australasia, and by Tec Toy in Brazil. In South Korea, the systems were distributed by Samsung and were known as the Super Gam*Boy, and later the Super Aladdin Boy., Sculptured Software Inc. was a video game developer in the Salt Lake City, Utah metropolitan area. They specialized in porting games to different platforms, especially from arcade games to home console games., Edward John "Ed" Boon (born February 22, 1964) is an American video game programmer and director who had been employed for over 15 years at Midway Games and since 2011 works for Warner Bros. Interactive Entertainment in its subsidiary company NetherRealm Studios. Boon is best known for the widely popular "Mortal Kombat" series, which he created with John Tobias., Noob Saibot is a fictional character from the "Mortal Kombat" fighting game series. He debuted as an unplayable hidden character in "Mortal Kombat II", in which he was a black silhouette of the game's other male ninjas, and made his first selectable appearance in the console versions of "Ultimate Mortal Kombat 3". His name consists of the surnames of "Mortal Kombat" creators Ed Boon and John Tobias spelled backwards. , Johnny Cage is a fictional character from the "Mortal Kombat" fighting game franchise. He debuted as one of the series' original seven characters in the first "Mortal Kombat", and has since become a staple of the series. Created as a parody of martial arts actor and famous karate practitioner Jean-Claude Van Damme, Cage is a cocky and overconfident martial arts film actor who provides the comic relief of the franchise. He became a more layered character in "Mortal Kombat X", which introduced his and Sonya Blade's daughter Cassie Cage., Mortal Kombat is a video game franchise originally developed by Midway Games' Chicago studio in 1992. Following Midway's bankruptcy, the "Mortal Kombat" development team was acquired by Warner Bros. and turned into NetherRealm Studios. Warner Bros. Interactive Entertainment currently owns the rights of the franchise and rebooted it in 2011., General Sonya Blade is a video game character from the "Mortal Kombat" series. Debuting in the original "Mortal Kombat" game from 1992, she was a late addition to the game as developers decided deep into the development cycle that the game needed a female character. In the series canon she is the commanding officer of the United States Special Forces and later of a specialized U.S. government agency. Her goal in most of the games is to pursue and capture Kano, as well as eliminate his criminal syndicate, the Black Dragon. In later games she is joined in this effort by her comrade Jax and her daughter Cassie Cage., Subject: daniel pesina, Relation: occupation, Options: (A) actor (B) architecture (C) artist (D) author (E) canon (F) comic book (G) computer (H) covert agent (I) entertainment (J) game (K) general (L) graphic designer (M) guerrilla (N) hunter (O) literary (P) major (Q) martial artist (R) master (S) mercenary (T) military (U) ministry (V) ninja (W) officer (X) programmer (Y) research (Z) samurai ([) screenwriter (\) shareholder (]) soldier (^) spy (_) video game developer
[A]: martial artist


[Q]: Context: Fujian (pronounced ), formerly romanised as Foken, Fouken, Fukien, and Hokkien, is a province on the southeast coast of mainland China. Fujian is bordered by Zhejiang to the north, Jiangxi to the west, and Guangdong to the south. The name Fujian came from the combination of Fuzhou and Jianzhou (a former name for Jian'ou) two cities in Fujian, during the Tang dynasty. While its population is chiefly of Han origin, it is one of the most culturally and linguistically diverse provinces in China., Anhui is a landlocked province of the People's Republic of China located in the eastern region of the country. Located across the basins of the Yangtze River and the Huai River, it borders Jiangsu to the east, Zhejiang to the southeast, Jiangxi to the south, Hubei to the southwest, Henan to the northwest, and Shandong for a short section in the north. The provincial capital is Hefei., China, officially the People's Republic of China (PRC), is a unitary sovereign state in East Asia. With a population of over 1.381 billion, it is the world's most populous country. The state is governed by the Communist Party of China, and its capital is Beijing. It exercises jurisdiction over 22 provinces, five autonomous regions, four direct-controlled municipalities (Beijing, Tianjin, Shanghai, and Chongqing), and two mostly self-governing special administrative regions (Hong Kong and Macau), and claims sovereignty over Taiwan. The country's major urban areas include Shanghai, Guangzhou, Beijing, Chongqing, Shenzhen, Tianjin and Hong Kong. China is a great power and a major regional power within Asia, and has been characterized as a potential superpower., A county-level municipality, county-level city, or county city is a county-level administrative division of mainland China. County-level cities are usually governed by prefecture-level divisions, but a few are governed directly by province-level divisions., Liuyang is a county-level city the most populous and the easternmost county-level division of Hunan Province, China; it is under the administration of Changsha prefecture-level City. Located on the northeastern margin of Hunan, the city is bordered to the north by Pingjiang County, to the west by Changsha County and Yuhua District, to the south by Shifeng, Hetang Districts of Zhuzhou and Liling City, to the southeast and the east by Yuanzhou District of Yichun, Shangli, Wanzai and Tonggu Counties of Jiangxi. Liuyang City covers with registered population of 1,453,246 and resident population of 1,297,700 (as of 2014). The city has 4 subdistricts, 26 towns and 2 townships under its jurisdiction, the government seat is Guankou Subdistrict ()., The Xiang River, formerly romanized as the Siang Kiang and now also known as the Xiangjiang, is a river in southern China. The river's name and character is used as the Chinese abbreviation for Hunan., Changsha County is a county in Hunan Province, China, it is under the administration of Changsha City. Located in the west of the City proper in Changsha, the county is bordered to the north by Miluo City and Pingjiang County, to the west by Wangcheng, Kaifu and Furong District, to the southwest by Yuhua District, to the southeast and the east by Liuyang City. Changsha County covers , as of 2015 it had a registered population of 743,000 and a permanent resident population of 916,000. The county has 5 subdistricts and 13 towns under its jurisdiction, the county seat is Xingsha Subdistrict ()., Changsha is the capital of Hunan province, south central China. It covers and is bordered by Yueyang and Yiyang to the north, Loudi to the west, Xiangtan and Zhuzhou to the south, Yichun and Pingxiang of Jiangxi province to the east. According to 2010 Census, Changsha had 7,044,118 residents, constituting 10.72% of the province's population., Zhuzhou, formerly Jianning, is a prefecture-level city of Hunan Province, China, a little to the southeast of Changsha and bordering Jiangxi to the east. It is part of the "ChangZhuTan Golden Triangle" (comprising the cities of Changsha, Zhuzhou and Xiangtan). The city has jurisdiction over 5 counties (Yanling, Chaling, Youxian, Liling, Zhuzhou) and four districts (Hetang, Lusong, Shifeng and Tianyuan, a high-tech industrial development zone), and covers an area of ., Hubei is a province of the People's Republic of China, located in the Central China region. The name of the province means "north of the lake", referring to its position north of Dongting Lake. The provincial capital is Wuhan, a major transportation thoroughfare and the political, cultural, and economic hub of Central China., Hunan Province (Hunanese: Shuangfeng, ; Changsha) is a province of the People's Republic of China. It is located in South Central China, south of the middle course of the Yangtze River, and south of Lake Dongting (hence the name "Hunan", which means "south of the lake"). Hunan is sometimes called for short and officially abbreviated as "" (pinyin: Xing), named after the Xiang River which runs through the province., South Central China is a region of the People's Republic of China defined by governmental bureaus that includes the province of Guangdong, Hainan, Henan, Hubei, and Hunan, 
and the Guangxi Zhuang Autonomous Region, however the two provincial-level special administrative regions (SAR) are also often included under South Central China: Hong Kong and Macau. This part is often divided into South China and Central China regions due to difference between civilian customs., The Yangtze River (or ), known in China as the Cháng Jing (literally: "Long River") or the Yángz Jing, is the longest river in Asia and the third-longest in the world. The river is the longest in the world to flow entirely within one country. It drains one-fifth of the land area of the People's Republic of China (PRC) and its river basin is home to one-third of the country's population. The Yangtze is the sixth-largest river by discharge volume in the world., Yi - Liu , sometimes called Yichun dialect ( simplified Chinese :  ; traditional Chinese :  ) after its principal variety , is a dialect of Gan Chinese . It is spoken in Yichun in Jiangxi province and in Liuyang in Hunan , after which it is named , as well as inShanggao , Qingjiang , Xingan , Xinyu City , Fen yi , Pingxiang City , Fengcheng , Wanzai in Jiangxi and in Liling in Hunan ., Jiangxi (Gan: Kongsi) is a province in the People's Republic of China, located in the southeast of the country. Spanning from the banks of the Yangtze river in the north into hillier areas in the south and east, it shares a border with Anhui to the north, Zhejiang to the northeast, Fujian to the east, Guangdong to the south, Hunan to the west, and Hubei to the northwest., Guangdong (Simplified ) is a province on the South China Sea coast of the People's Republic of China. Formerly romanised as Canton or Kwangtung, Guangdong surpassed Henan and Sichuan to become the most populous province in China in January 2005, registering 79.1 million permanent residents and 31 million migrants who lived in the province for at least six months of the year; the total population was 104,303,132 in the 2010 census, accounting for 7.79 percent of Mainland China's population. The provincial capital Guangzhou and economic hub Shenzhen are among the most populous and important cities in China. The population increase since the census has been modest, the province at 2014 end had 107,240,000 people., Pingjiang County is a county in Hunan province, China, it is under the administration of Yueyang City. , Liling is a county-level city and the 12th most populous county-level division in Hunan Province, China; it is under the administration of Zhuzhou prefecture-level City. Located on the middle eastern margin of the province, the city is bordered to the north by Liuyang City, to the west by Lusong District and Zhuzhou County, to the south by You County, to the east by Xiangdong District of Yichun, Shangli County of Jiangxi. Liling City covers with registered population of 978,900 and resident population of 1,060,000 (as of 2015)., Gan is a group of Chinese varieties spoken as the native language by many people in the Jiangxi province of China, as well as significant populations in surrounding regions such as Hunan, Hubei, Anhui, and Fujian. Gan is a member of the Sinitic languages of the Sino-Tibetan language family, and Hakka is the closest Chinese variety to Gan in terms of phonetics., , formerly romanized as Chekiang, is an eastern coastal province of China. Zhejiang is bordered by Jiangsu province and Shanghai municipality to the north, Anhui province to the northwest, Jiangxi province to the west, and Fujian province to the south; to the east is the East China Sea, beyond which lie the Ryukyu Islands of Japan., Hetang District is one of four urban districts of Zhuzhou City, Hunan province, China. Located in the north eastern region of the city proper, the district is bordered to the northeast by Liuyang City, to the southeast, the south and soutuwest by Lusong District, to the west and the northwest by Shifeng District. Hetang District covers , as of 2015, it had a permanent resident population of 311,400. The district has 5 subdistricts and a town under its jurisdiction, the government seat is at Guihua Subdistrict ()., The Sinitic languages, often synonymous with the group of Chinese varieties, are a family of Sino-Tibetan languages. They have frequently been postulated to constitute a primary branch, but this is rejected by an increasing number of researchers. The Bai languages and possible relatives, whose classification is difficult, may also be Sinitic; otherwise Sinitic is equivalent to Chinese, and the term may be used to indicate that the varieties of Chinese are distinct languages rather than dialects of a single language., Subject: yi-liu dialect, Relation: instance_of, Options: (A) 1 (B) abbreviation (C) branch (D) capital (E) census (F) chinese (G) city (H) coast (I) combination (J) communist party (K) country (L) county (M) county seat (N) customs (O) district (P) division (Q) family (R) five (S) government (T) group (U) jurisdiction (V) lake (W) language (X) may (Y) municipality (Z) name ([) people (\) phonetics (]) population (^) prefecture (_) province (`) province of china (a) region (b) republic (c) river (d) sea (e) sovereign state (f) state (g) term (h) two (i) variety (j) volume (k) year
[A]: language


[Q]: 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
[A]:
science