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).

Example Input: Context: Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum., In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found. Conjectures such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (which was a conjecture until proven in 1995) have shaped much of mathematical history as new areas of mathematics are developed in order to prove them., The Riemann zeta function or EulerRiemann zeta function, , is a function of a complex variable "s" that analytically continues the sum of the Dirichlet series , In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . It was proposed by , after whom it is named. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields., A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which proceed by listing the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions., A complex number is a number that can be expressed in the form , where and are real numbers and is the imaginary unit, satisfying the equation . In this expression, is the ' and is the ' of the complex number. If formula_1, then formula_2, In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod when is a prime number., In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation., In mathematics , the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and Generalized Riemann hypothesis . It states that the nontrivial zeros of all automorphic L - functions lie on the critical line 1/2 + it with t a real number variable and i the imaginary unit . The modified grand Riemann hypothesis is the assertion that the nontrivial zeros of all automorphic L - functions lie on the critical line or the real line ., Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework., 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., The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function. One can then ask the same question about the zeros of these "L"-functions, yielding various generalizations of the Riemann hypothesis. Many mathematicians believe these generalizations of the Riemann hypothesis to be true. The only cases of these conjectures which have been proven occur in the function field case (not the number field case)., Subject: grand riemann hypothesis, Relation: instance_of, Options: (A) class (B) complex (C) complex number (D) conjecture (E) definition (F) division (G) equation (H) field (I) function (J) hypothesis (K) magnitude (L) mathematics (M) may (N) number (O) order (P) phrase (Q) plane (R) position (S) prime number (T) quantity (U) relation (V) relationship (W) series (X) space (Y) statement (Z) structure ([) study (\) sum (]) term (^) theorem (_) three (`) time (a) unit of measurement (b) variable
Example Output: conjecture

Example Input: Context: Covent Garden (or ) is a district in London on the eastern fringes of the West End, between St Martin's Lane and Drury Lane. It is associated with the former fruit-and-vegetable market in the central square, now a popular shopping and tourist site, and with the Royal Opera House, which is also known as "Covent Garden". The district is divided by the main thoroughfare of Long Acre, north of which is given over to independent shops centred on Neal's Yard and Seven Dials, while the south contains the central square with its street performers and most of the elegant buildings, theatres and entertainment facilities, including the London Transport Museum and the Theatre Royal, Drury Lane., Edward I. Altman ( born 1941 ) is a Professor of Finance at New York University 's Stern School of Business . He is best known for the development of the Z - Score for predicting bankruptcy which he published in 1968 . Professor Altman is a leading academic on the High - Yield and Distressed Debt markets and is the pioneer in the building of models for credit risk management and bankruptcy prediction . He is the brother of Stuart Altman . Altman teaches `` Bankruptcy and Reorganization '' and `` Credit Risk Management '' in the Risk Management Open Enrollment program for Stern Executive Education , as well as on the TRIUM Global Executive MBA Program , an alliance of NYU Stern , the London School of Economics and HEC School of Management , and for both the Master of Science in Global Finance ( MSGF ) and Master of Science in Risk Management Program for Executives ( MSRM ) . MSGF is jointly offered by NYU Stern and the Hong Kong University of Science and Technology . He also teaches in the school 's MBA programs and has been a Stern faculty member since 1967 . The Z - Score is a multivariate formula for a measurement of the financial health of a company and a powerful diagnostic tool that forecasts the probability of a company entering bankruptcy within a 2 - year period . Studies measuring the effectiveness of the Z - Score have shown that the model has an 80 % -90 % reliability . Altman 's equation did an excellent job at distinguishing bankrupt and non-bankrupt firms . Altman holds a B.A. in Economics , ( CCNY , 1963 ) ; an MBA ( UCLA , 1965 ) ; and a Ph.D. in Finance ( UCLA , 1967 ) . Altman was inducted into the Fixed Income Society 's Hall of Fame in 2001 and was amongst the inaugural inductees into the Turnaround Management 's Hall of Fame in 2008 . He was named one of the `` 100 Most Influential People in Finance '' by the Treasury & Risk Management magazine in 2005 . Co-founder of the International Risk Management Conference , now in its 7th year ., A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking. , The London School of Economics (officially The London School of Economics and Political Science; often referred to as LSE) is a public research university located in London, England and a constituent college of the federal University of London. Founded in 1895 by Fabian Society members Sidney Webb, Beatrice Webb, Graham Wallas and George Bernard Shaw for the betterment of society, LSE joined the University of London in 1900 and established its first degree courses under the auspices of the University in 1901; the LSE has awarded its own degrees since 2008.
LSE is located in Westminster, central London, near the boundary between Covent Garden and Holborn. The area is historically known as Clare Market. It has students and 3,300 staff, just under half of whom come from outside the UK. It had a total income of £340.7 million in 2015/16, of which £30.3 million was from research grants.<ref name="LSE Financial Statement 15/16"></ref> 155 nationalities are represented amongst LSE's student body and the school has the highest percentage of international students (70%) of all British universities. Despite its name, the school is organised into 25 academic departments and institutes which conduct teaching and research across a range of legal studies and social sciences.
The School is generally recognised as one of the most prestigious universities in the world and as one of the world's leading social science universities, ranked among the top 10 universities nationally by two of the three UK tables and in the top 100 internationally by three of the four major global rankings. In the 2014 Research Excellence Framework, the School had the highest proportion of world-leading research among research submitted of any British non-specialist university. LSE is usually considered part of the golden triangle of highly research-intensive universities in southeast England. It is a member of academic organisations such as the Association of Commonwealth Universities, the European University Association and the Russell Group.
The LSE has produced many notable alumni in the fields of law, history, economics, philosophy, business, literature, media and politics. Alumni and staff include 52 past or present heads of state or government and 20 members of the current British House of Commons. To 2016, 27% (or 13 out of 48) of all the Nobel Prizes in Economics have been awarded or jointly awarded to LSE alumni, current staff or former staff, making up 17% (13 out of 78) of all laureates. LSE alumni and staff have also won 3 Nobel Peace Prizes, and 2 Nobel Prizes in Literature. Out of all European universities, LSE has educated the most billionaires according to a 2014 global census of dollar billionaires. LSE graduates earn higher incomes on average than those of any other British university., The University of London is a collegiate research university located in London, England, consisting of 18 constituent colleges, nine research institutes and a number of central bodies., The Russell Group is a self-selected association of twenty-four public research universities in the United Kingdom. The group is headquartered in London and was established in 1994 to represent its members' interests, principally to government and parliament; nineteen smaller British research universities formed the 1994 Group in response, which has since dissolved. In 2010, Russell Group members received approximately two-thirds of all university research grant and contract income in the United Kingdom. The group is widely perceived as representing the best universities in the country., The Research Excellence Framework is the successor to the Research Assessment Exercise. It is an Impact evaluation; assessing the research of British higher education institutions. It was used in 2014 to assess UK research during the period 20082013., Finance is a field that deals with the study of investments. It includes the dynamics of assets and liabilities over time under conditions of different degrees of uncertainty and risk. Finance can also be defined as the science of money management. Finance aims to price assets based on their risk level and their expected rate of return. Finance can be broken into three different sub-categories: public finance, corporate finance and personal finance., The European University Association (EUA) represents and supports more than 850 institutions of higher education in 47 countries, providing them with a forum for cooperation and exchange of information on higher education and research policies. Members of the Association are European universities involved in teaching and research, national associations of rectors and other organisations active in higher education and research., In finance, return is a profit on an investment. It comprises any change in value and interest or dividends or other such cash flows which the investor receives from the investment. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return., The Hong Kong University of Science and Technology (HKUST) is a public research university in Clear Water Bay Peninsula, Hong Kong. Established in 1991, it is the territory's youngest higher learning institution with no precursory existence., In financial accounting, an asset is an economic resource. Anything tangible or intangible that can be owned or controlled to produce value and that is held to have positive economic value is considered an asset. Simply stated, assets represent value of ownership that can be converted into cash (although cash itself is also considered an asset)., George Bernard Shaw (26 July 1856  2 November 1950), known at his insistence simply as Bernard Shaw, was an Irish playwright, critic, and polemicist whose influence on Western theatre, culture, and politics extended from the 1880s to his death and beyond. He wrote more than sixty plays, including major works such as "Man and Superman" (1903), "Pygmalion" (1913), and "Saint Joan" (1923). With a range incorporating both contemporary satire and historical allegory, Shaw became the leading dramatist of his generation, and in 1925 was awarded the Nobel Prize in Literature., Central London is the innermost part of London, England. There is no official definition of its area but its characteristics are understood to include a high density built environment, high land values, an elevated daytime population and a concentration of regionally, nationally and internationally significant organisations and facilities. Over time a number of definitions have been used to define the scope of central London for statistics, urban planning and local government. , Martha Beatrice Webb, Baroness Passfield, (née Potter; 22 January 1858  30 April 1943), was an English sociologist, economist, socialist, labour historian and social reformer. It was Webb who coined the term "collective bargaining". She was among the founders of the London School of Economics and played a crucial role in forming the Fabian Society., Graham Wallas (31 May 1858  9 August 1932) was an English socialist, social psychologist, educationalist, a leader of the Fabian Society and a co-founder of the London School of Economics., The Fabian Society is a British socialist organisation whose purpose is to advance the principles of democratic socialism via gradualist and reformist effort in democracies, rather than by revolutionary overthrow. As one of the founding organisations of the Labour Representation Committee in 1900, and as an important influence upon the Labour Party which grew from it, the Fabian Society has had a powerful influence on British politics. Later members of the Fabian Society included Jawaharlal Nehru and other leaders of new nations created out of the former British Empire, who used Fabian principles to create socialist democracies in India, Pakistan, Nigeria and elsewhere as Britain decolonised after World War II., Subject: edward altman, Relation: occupation, Options: (A) academic (B) accounting (C) critic (D) economist (E) entertainment (F) faculty (G) founder (H) investor (I) leader (J) official (K) opera (L) playwright (M) potter (N) psychologist (O) research (P) revolutionary (Q) science (R) social psychologist (S) socialist (T) sociologist (U) student (V) united kingdom
Example Output: economist

Example Input: Context: Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion., Johann Peter Gustav Lejeune Dirichlet (or ; 13 February 1805  5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function., (X_i) = n p_i (1-p_i)</math><br>formula_1|
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for rolling a "k" sided dice "n" times. For "n" independent trials each of which leads to a success for exactly one of "k" categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories., Mathematical analysis is the branch of mathematics dealing with limits
and related theories, such as differentiation, integration, measure, infinite series, and analytic functions., George Alfred Barnard (23 September 1915  9 August 2002) was a British statistician known particularly for his work on the foundations of statistics and on quality control., In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet "L"-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem).
Branches of analytic number theory.
Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique., Robert O. Schlaifer (13 September 1914  24 July 1994) was a pioneer of Bayesian decision theory. At the time of his death he was William Ziegler Professor of Business Administration Emeritus of the Harvard Business School. In 1961 he was elected as a Fellow of the American Statistical Association., Thomas Bayes (c. 1701 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for having formulated a specific case of the theorem that bears his name: Bayes' theorem. Bayes never published what would eventually become his most famous accomplishment; his notes were edited and published after his death by Richard Price., </math> In probability theory and statistics, the binomial distribution with parameters "n" and "p" is the discrete probability distribution of the number of successes in a sequence of "n" independent yes/no experiments, each of which yields success with probability "p". A success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when "n" = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance., Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers)., Debt, AIDS, Trade, Africa (DATA) was a multinational non-government organization founded in January 2002 in London by U2's Bono along with Bobby Shriver and activists from the Jubilee 2000 Drop the Debt campaign., In Bayesian probability theory, if the posterior distributions "p"(|"x") are in the same family as the prior probability distribution "p"(), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function. For example, the Gaussian family is conjugate to itself (or "self-conjugate") with respect to a Gaussian likelihood function: if the likelihood function is Gaussian, choosing a Gaussian prior over the mean will ensure that the posterior distribution is also Gaussian. This means that the Gaussian distribution is a conjugate prior for the likelihood that is also Gaussian. The concept, as well as the term "conjugate prior", were introduced by Howard Raiffa and Robert Schlaifer in their work on Bayesian decision theory. A similar concept had been discovered independently by George Alfred Barnard., Bayesian statistics, named for Thomas Bayes (17011761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of "degrees of belief" known as Bayesian probabilities. Such an interpretation is only one of a number of interpretations of probability and there are other statistical techniques that are not based on 'degrees of belief'. One of the key ideas of Bayesian statistics is that "probability is orderly opinion, and that inference from data is nothing other than the revision of such opinion in the light of relevant new information.", In probability theory and statistics, a probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probability of occurrence of different possible outcomes in an experiment. For instance, if the random variable X is used to denote the outcome of a coin toss ('the experiment'), then the probability distribution of X would take the value 0.5 for formula_1, and 0.5 for formula_2. , An "a priori" probability is a probability that is derived purely by deductive reasoning. One way of deriving "a priori" probabilities is the principle of indifference, which has the character of saying that, if there are "N" mutually exclusive and exhaustive events and if they are equally likely, then the probability of a given event occurring is 1/"N". Similarly the probability of one of a given collection of "K" events is "K"/"N"., ([x=i]) = p_i (1-p_i)</math><br>formula_1|, Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384322 B.C.), though "analysis" as a formal concept is a relatively recent development., In mathematics, a Fourier series is a way to represent a (wave-like) function as the sum of simple sine waves. More formally, it decomposes any periodic function or periodic signal into the sum of a (possibly infinite) set of simple oscillating functions, namely sines and cosines (or, equivalently, complex exponentials). The discrete-time Fourier transform is a periodic function, often defined in terms of a Fourier series. The Z-transform, another example of application, reduces to a Fourier series for the important case |z|=1. Fourier series are also central to the original proof of the NyquistShannon sampling theorem. The study of Fourier series is a branch of Fourier analysis., In probability and statistics , the Dirichlet distribution ( after Peter Gustav Lejeune Dirichlet ) , often denoted \ operatorname ( Dir ) ( \ boldsymbol \ alpha ) , is a family of continuous multivariate probability distributions parameterized by a vector \ boldsymbol \ alpha of positive reals . It is the multivariate generalization of the beta distribution . Dirichlet distributions are very often used as prior distributions in Bayesian statistics , and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution . The infinite - dimensional generalization of the Dirichlet distribution is the Dirichlet process ., Howard Raiffa (January 24, 1924  July 8, 2016) was an American academic who was the Frank P. Ramsey Professor (Emeritus) of Managerial Economics, a joint chair held by the Business School and the Kennedy School of Government at Harvard University. He was an influential Bayesian decision theorist and pioneer in the field of decision analysis, with works in statistical decision theory, game theory, behavioral decision theory, risk analysis, and negotiation analysis. He helped found and was the first director of the International Institute for Applied Systems Analysis. , 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., In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized by two positive shape parameters, denoted by "" and "", that appear as exponents of the random variable and control the shape of the distribution., Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, assigned probabilities represent states of knowledge or belief., In probability theory and statistics, a shape parameter is a kind of numerical parameter of a parametric family of probability distributions., A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems., Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is unbiased, the two outcomes ("head" and "tail") are both equally probable; the probability of "head" equals the probability of "tail". Since no other outcomes are possible, the probability is 1/2 (or 50%), of either "head" or "tail". In other words, the probability of "head" is 1 out of 2 outcomes and the probability of "tail" is also 1 out of 2 outcomes, expressed as 0.5 when converted to decimal, with the above-mentioned quantification system. This type of probability is also called a priori probability., Subject: dirichlet distribution, Relation: named_after, Options: (A) 1 (B) 2 (C) 5 (D) 7 (E) 8 (F) 9 (G) africa (H) aristotle (I) c (J) concept (K) death (L) english (M) family (N) johann peter gustav lejeune dirichlet (O) london (P) mathematics (Q) p (R) peter (S) robert (T) technique (U) thomas bayes (V) wave
Example Output:
johann peter gustav lejeune dirichlet