TASK DEFINITION: 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).
PROBLEM: Context: W5 is a Canadian news magazine television series produced by CTV News . The program is broadcast Saturday nights at 7 p.m. on CTV , with repeat broadcasts at later times on CTV as well as co-owned channels CTV Two , and Investigation Discovery . The program is also simulcast on CFRB in Toronto . The title refers to the Five Ws of journalism : Who , What , Where , When and Why ? It is the longest - running newsmagazine / documentary program in North America and the most - watched program of its type in Canada ., Bell Canada (commonly referred to as Bell) is a Canadian telecommunications and media company headquartered in Montreal, Quebec. Its subsidiaries include Bell Aliant, Northwestel, Télébec, Dryden Municipal Telephone Service and NorthernTel, it is the incumbent local exchange carrier for telephone and DSL Internet services in most of Canada east of Manitoba and in the northern territories, and a major competitive local exchange carrier for enterprise customers in the western provinces. Its subsidiary Bell Mobility (including Virgin Mobile Canada) is one of Canada's "big three" mobile telecommunications providers, while Bell TV provides direct-to-home satellite TV service. Bell Canada's principal competitors are Rogers Communications Canada in Ontario and Vidéotron General Partnership and Telus in Quebec. The company serves over 13 million phone lines and is headquartered at the Campus Bell complex in Montreal., British Columbia (BC) is the westernmost province of Canada, with a population of more than four million people located between the Pacific Ocean and the Rocky Mountains. 
British Columbia is also a component of the Pacific Northwest and the Cascadia bioregion, along with the U.S. states of Idaho, Oregon, Washington and Alaska., Canada (French: ) is a country in the northern half of North America. Its ten provinces and three territories extend from the Atlantic to the Pacific and northward into the Arctic Ocean, covering , making it the world's second-largest country by total area and the fourth-largest country by land area. Canada's border with the United States is the world's longest land border. The majority of the country has a cold or severely cold winter climate, but southerly areas are warm in summer. Canada is sparsely populated, the majority of its land territory being dominated by forest and tundra and the Rocky Mountains. About four-fifths of the country's population of 36 million people is urbanized and live near the southern border. Its capital is Ottawa, its largest city is Toronto; other major urban areas include Montreal, Vancouver, Calgary, Edmonton, Quebec City, Winnipeg and Hamilton., Ontario, one of the 13 provinces and territories of Canada, is located in east-central Canada. It is Canada's most populous province by a large margin, accounting for nearly 40 percent of all Canadians, and is the second-largest province in total area. Ontario is fourth-largest in total area when the territories of the Northwest Territories and Nunavut are included. It is home to the nation's capital city, Ottawa, and the nation's most populous city, Toronto., Toronto is the most populous city in Canada, the provincial capital of Ontario, and the centre of the Greater Toronto Area, the most populous metropolitan area in Canada. Growing in population, the 2011 census recorded a population of 2,615,060. As of 2015, the population is now estimated at 2,826,498, making Toronto the fourth-largest city in North America based on the population within its city limits. Toronto trails only Mexico City, New York City, and Los Angeles by this measure, while it is the fifth-largest (behind also Chicago) if ranked by the size of its metropolitan area . An established global city, Toronto is an international centre of business, finance, arts, and culture, and widely recognized as one of the most multicultural and cosmopolitan cities in the world., CTV is an English-language broadcast television network in Canada launched in 1961. Since 2000 it is owned by the Bell Media division of BCE, Inc. It is Canada's largest privately or commercially owned network, and has consistently been placed as Canada's top-rated network in total viewers and in key demographics since 2002, after several years trailing the rival Global Television Network in key markets., 299 Queen Street West, also known as Bell Media Queen Street, is the headquarters of the television/radio broadcast hub of Bell Canada's media unit, Bell Media located at the intersection of Queen Street West and John Street in Downtown Toronto, Ontario, Canada. The building previously served as the headquarters of CTVglobemedia until Bell Canada acquired CTV again in 2011 as well as CHUM Television, a division of CHUM Limited, until CTV acquired CHUM in 2007, and was once known as the CHUM-City Building. It is now head offices and downtown Toronto studios for Bell Media., Simulcast, a portmanteau of simultaneous broadcast, is the broadcasting of programs or events across more than one medium, or more than one service on the same medium, at exactly the same time. For example, Absolute Radio is simulcast on both AM and on satellite radio, and the BBC's Prom concerts were formerly simulcast on both BBC Radio 3 and BBC Television. Another application is the transmission of the original-language soundtrack of movies or TV series over local or Internet radio, with the television broadcast having been dubbed into a local language., Atlantic Canada is the region of Canada comprising the four provinces located on the Atlantic coast, excluding Quebec: the three Maritime provinces  New Brunswick, Prince Edward Island, and Nova Scotia  and the easternmost province of Newfoundland and Labrador. The population of the four Atlantic provinces in 2011 was about 2,300,000 on half a million km., English is a West Germanic language that was first spoken in early medieval England and is now a global "lingua franca". Named after the Angles, one of the Germanic tribes that migrated to England, it ultimately derives its name from the Anglia (Angeln) peninsula in the Baltic Sea. It is most closely related to the Frisian languages, although its vocabulary has been significantly influenced by other Germanic languages in the early medieval period, and later by Romance languages, particularly French. English is either the official language or one of the official languages in almost 60 sovereign states. It is the most commonly spoken language in the United Kingdom, the United States, Canada, Australia, Ireland, and New Zealand, and is widely spoken in some areas of the Caribbean, Africa, and South Asia. It is the third most common native language in the world, after Mandarin and Spanish. It is the most widely learned second language and an official language of the United Nations, of the European Union, and of many other world and regional international organisations. It is the most widely spoken Germanic language, accounting for at least 70% of speakers of this Indo-European branch., CTV Two (also known as "CTV 2") is a Canadian English language television system that is owned by the Bell Media subsidiary of Bell Canada. The system consists of four over-the-air owned-and-operated television stations (O&Os) in Ontario and three in British Columbia, and two regional cable-only channels, one in Atlantic Canada and the other being the provincial cable-only educational channel in Alberta., CTV News is the news division of the CTV Television Network in Canada. The name "CTV News" is also applied as the title of local and regional newscasts on the network's owned-and-operated stations (O&Os), which are closely tied to the national news division. Local newscasts on CTV Two are also branded as "CTV News", although in most cases they are managed separately from the newscasts on the main CTV network., Mississauga is the sixth most populous city in Canada. Situated in Southern Ontario, it lies on the shores of Lake Ontario. It is located in the Regional Municipality of Peel in the central part of the Greater Toronto Area, to the west of Toronto. The city has a population of 713,443 as of the Canada 2011 Census, and is Canada's sixth-most populous municipality., CFRB, branded as In-Depth Radio Newstalk 1010, is an AM radio clear-channel station in Toronto, Ontario, Canada, broadcasting a news/talk format on 1010 kHz, with a shortwave radio simulcast on CFRX on 6.07 MHz on the 49m band. CFRB's studios are located in the Entertainment District at 250 Richmond Street West, a building which is adjacent to 299 Queen Street West, while its 4-tower transmitter array is located in the Clarkson neighbourhood of Mississauga., Subject: w5 , Relation: original_network, Options: (A) bbc (B) bbc television (C) city (D) ctv television network (E) four (F) global television network (G) one (H) ten

SOLUTION: ctv television network

PROBLEM: Context: Screenwriting, also called scriptwriting, is the art and craft of writing scripts for mass media such as feature films, television productions or video games. It is frequently a freelance profession., Nithiwat Tharathorn is a Thai film director. He made his directorial debut alongside five other directors on the 2003 childhood romantic comedy "Fan Chan" (2003) and his solo debut with the romantic comedy "Seasons Change" in 2006. and now, he have romantic drama film "Teacher's Diary" in 2014, The mass media is a diversified collection of media technologies that reach a large audience via mass communication. The technologies through which this communication takes place include a variety of outlets., A writer is a person who uses written words in various styles and techniques to communicate their ideas. Writers produce various forms of literary art and creative writing such as novels, short stories, poetry, plays, screenplays, and essays as well as various reports and news articles that may be of interest to the public. Writers' texts are published across a range of media. Skilled writers who are able to use language to express ideas well often contribute significantly to the cultural content of a society. The word is also used elsewhere in the arts  such as songwriter  but as a standalone term, "writer" normally refers to the creation of written language. Some writers work from an oral tradition., A screenplay writer, screenwriter for short, scriptwriter or scenarist is a writer who practices the craft of screenwriting, writing screenplays on which mass media such as films, television programs, comics or video games are based., Thailand (or  ), officially the Kingdom of Thailand, formerly known as Siam, is a country at the centre of the Indochinese peninsula in Southeast Asia. With a total area of approximately , Thailand is the world's 51st-largest country. It is the 20th-most-populous country in the world, with around 66 million people. The capital and largest city is Bangkok., A screenplay or script is a written work by screenwriters for a film, video game, or television program. These screenplays can be original works or adaptations from existing pieces of writing. In them, the movement, actions, expression, and dialogues of the characters are also narrated. A screenplay written for television is also known as a teleplay., Southeast Asia or Southeastern Asia is a subregion of Asia, consisting of the countries that are geographically south of China, east of India, west of New Guinea and north of Australia. The region lies near the intersection of geological plates, with heavy seismic and volcanic activity. Southeast Asia consists of two geographic regions:, A film, also called a movie, motion picture, theatrical film or photoplay, is a series of still images which, when shown on a screen, creates the illusion of moving images due to the phi phenomenon. This optical illusion causes the audience to perceive continuous motion between separate objects viewed rapidly in succession. The process of filmmaking is both an art and an industry. A film is created by photographing actual scenes with a motion picture camera; by photographing drawings or miniature models using traditional animation techniques; by means of CGI and computer animation; or by a combination of some or all of these techniques and other visual effects., Bangkok is the capital and most populous city of Thailand. It is known in Thai as "Krung Thep Maha Nakhon" (pronounced ) or simply . The city occupies in the Chao Phraya River delta in Central Thailand, and has a population of over 8 million, or 12.6 percent of the country's population. Over 14 million people (22.2 percent) live within the surrounding Bangkok Metropolitan Region, making Bangkok an extreme primate city, significantly dwarfing Thailand's other urban centres in terms of importance. There are 581 high-rise buildings in the city, ranking number 5 in the world., Fan Chan ( Thai :  , English : My Girl ) is a 2003 Thai romantic film offering a nostalgic look back at the childhood friendship of a boy and girl growing up in a small town in Thailand in the 1980s . It was the debut film by six young screenwriter - directors , Vitcha Gojiew , Songyos Sugmakanan , Nithiwat Tharathorn , Witthaya Thongyooyong , Anusorn Trisirikasem and Komgrit Triwimol . With a soundtrack that featured Thai pop music of the era , Fan Chan was the top domestic film at the Thailand box office in 2003 , earning 140 million baht ., A film director is a person who directs the making of a film. Generally, a film director controls a film's artistic and dramatic aspects, and visualizes the script while guiding the technical crew and actors in the fulfillment of that vision. The director has a key role in choosing the cast members, production design, and the creative aspects of filmmaking. Under European Union law, the director is viewed as the author of the film., The history of comics has followed different paths in different cultures. Scholars have posited a pre-history as far back as the Lascaux cave paintings. By the mid-20th century, comics flourished particularly in the United States, western Europe (especially in France and Belgium), and Japan. The history of European comics is often traced to Rodolphe Töpffer's cartoon strips of the 1830s, and became popular following the success in the 1930s of strips and books such as "The Adventures of Tintin". American comics emerged as a mass medium in the early 20th century with the advent of newspaper comic strips; magazine-style comic books followed in the 1930s, in which the superhero genre became prominent after Superman appeared in 1938. Histories of Japanese comics and cartooning ("") propose origins as early as the 12th century. Modern comic strips emerged in Japan in the early 20th century, and the output of comics magazines and books rapidly expanded in the post-World War II era with the popularity of cartoonists such as Osamu Tezuka. had a lowbrow reputation for much of its history, but towards the end of the 20th century began to find greater acceptance with the public and in academia., A television program is a segment of content intended for broadcast on over-the-air, cable television, or Internet television, other than a commercial, trailer, or any other segment of content not serving as attraction for viewership. It may be a single production, or more commonly, a series of related productions (also called a television series or a television show)., Subject: fan chan, Relation: genre, Options: (A) academia (B) art (C) cartoon (D) comedy (E) comic (F) computer animation (G) country (H) design (I) dramatic (J) genre (K) history (L) india (M) japanese (N) mass (O) miniature (P) music (Q) news (R) optical illusion (S) poetry (T) pop (U) romantic (V) romantic comedy (W) screenplay (X) society (Y) superhero (Z) television ([) thai pop music (\) urban (]) variety (^) various (_) video (`) western

SOLUTION: romantic comedy

PROBLEM: Context: In mathematics, a real number is a value that represents a quantity along a line. The adjective "real" in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials., In planar geometry, an angle is the figure formed by two rays, called the "sides" of the angle, sharing a common endpoint, called the "vertex" of the angle.
Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles., Thierry Aubin ( 6 May 1942 -- 21 March 2009 ) was a French mathematician who worked at the Centre de Mathématiques de Jussieu , and was a leading expert on Riemannian geometry and non-linear partial differential equations . His fundamental contributions to the theory of the Yamabe equation led , in conjunction with results of Trudinger and Schoen , to a proof of the Yamabe Conjecture : every compact Riemannian manifold can be conformally rescaled to produce a manifold of constant scalar curvature . Along with Yau , he also showed that Kähler manifolds with negative first Chern classes always admit Kähler -- Einstein metrics , a result closely related to the Calabi conjecture . The latter result provides the largest class of known examples of compact Einstein manifolds . Aubin was a visiting scholar at the Institute for Advanced Study in 1979 . He was elected to the Académie des sciences in 2003 ., In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term "Euclidean" distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalize to higher dimensions., Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces., In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object such as a surface deviates from being a "flat" plane, or a curve from being "straight" as in the case of a line, but this is defined in different ways depending on the context. There is a key distinction between "extrinsic curvature", which is defined for objects embedded in another space (usually a Euclidean space)  in a way that relates to the radius of curvature of circles that touch the object  and "intrinsic curvature", which is defined in terms of the lengths of curves within a Riemannian manifold. , In Riemannian geometry, the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the intrinsic geometry of the manifold near that point. Specifically, the scalar curvature represents the amount by which the volume of a small geodesic ball in a Riemannian manifold deviates from that of the standard ball in Euclidean space. In two dimensions, the scalar curvature is twice the Gaussian curvature, and completely characterizes the curvature of a surface. In more than two dimensions, however, the curvature of Riemannian manifolds involves more than one functionally independent quantity., Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. , The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The Fields Medal is sometimes viewed as the highest honor a mathematician can receive. The Fields Medal and the Abel Prize have often been described as the mathematician's "Nobel Prize". The Fields Medal differs from the Abel in view of the age restriction mentioned above., In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions have found applications everywhere in differential geometry., Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a "Riemannian metric", i.e. with an inner product on the tangent space at each point that varies smoothly from point to point. This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions., In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in C, such that the transition maps are holomorphic., In mathematics, the Calabi conjecture was a conjecture about the existence of certain "nice" Riemannian metrics on certain complex manifolds, made by and proved by . Yau received the Fields Medal in 1982 in part for this proof., In differential geometry, the Gaussian curvature or Gauss curvature "" of a surface at a point is the product of the principal curvatures, "" and "", at the given point:
For example, a sphere of radius "r" has Gaussian curvature "1/r" everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus., In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other., In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space ("M","g") is a real smooth manifold "M" equipped with an inner product formula_1 on the tangent space formula_2 at each point formula_3 that varies smoothly from point to point in the sense that if "X" and "Y" are vector fields on "M", then formula_4 is a smooth function. The family formula_1 of inner products is called a Riemannian metric (tensor). These terms are named after the German mathematician Bernhard Riemann. The study of Riemannian manifolds constitutes the subject called Riemannian geometry., In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles., Subject: thierry aubin, Relation: field_of_work, Options: (A) algebra (B) differential geometry (C) gas (D) geometry (E) mathematician (F) mathematics

SOLUTION:
differential geometry