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Angel Problem
The angel problem is a question in combinatorial game theory proposed by John Horton Conway. The game is commonly referred to as the angels and devils game.John H. Conway, The angel problem', in: Richard Nowakowski (editor) ''Games of No Chance'', volume 29 of MSRI Publications, pages 3–12, 1996. The game is played by two players called the angel and the devil. It is played on an infinite chessboard (or equivalently the points of a 2D lattice). The angel has a power ''k'' (a natural number 1 or higher), specified before the game starts. The board starts empty with the angel in one square. On each turn, the angel jumps to a different empty square which could be reached by at most ''k'' moves of a chess king, i.e. the distance from the starting square is at most ''k'' in the infinity norm. The devil, on its turn, may add a block on any single square not containing the angel. The angel may leap over blocked squares, but cannot land on them. The devil wins if the angel is u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brian H
Brian (sometimes spelled Bryan in English) is a male given name of Irish and Breton origin, as well as a surname of Occitan origin. It is common in the English-speaking world. It is possible that the name is derived from an Old Celtic word meaning "high" or "noble". For example, the element ''bre'' means "hill"; which could be transferred to mean "eminence" or "exalted one". The name is quite popular in Ireland, on account of Brian Boru, a 10th-century High King of Ireland. The name was also quite popular in East Anglia during the Middle Ages. This is because the name was introduced to England by Bretons following the Norman Conquest. Bretons also settled in Ireland along with the Normans in the 12th century, and 'their' name was mingled with the 'Irish' version. Also, in the north-west of England, the 'Irish' name was introduced by Scandinavian settlers from Ireland. Within the Gaelic-speaking areas of Scotland, the name was at first only used by professional families of Iris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace's Demon
In the history of science, Laplace's demon was a notable published articulation of causal determinism on a scientific basis by Pierre-Simon Laplace in 1814. According to determinism, if someone (the demon) knows the precise location and momentum of every particle in the universe, their past and future values for any given time are entailed; they can be calculated from the laws of classical mechanics. English translation This intellect is often referred to as ''Laplace's demon'' (and sometimes ''Laplace's Superman'', after Hans Reichenbach). Laplace himself did not use the word "demon", which was a later embellishment. As translated into English above, he simply referred to: ''"Une intelligence ... Rien ne serait incertain pour elle, et l'avenir, comme le passé, serait présent à ses yeux."'' This idea seems to have been widespread around the time that Laplace first expressed it in 1773, particularly in France. Variations can be found in Maupertuis (1756), Nicolas de Condo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell's Demon
Maxwell's demon is a thought experiment that appears to disprove the second law of thermodynamics. It was proposed by the physicist James Clerk Maxwell in 1867. In his first letter, Maxwell referred to the entity as a "finite being" or a "being who can play a game of skill with the molecules". Lord Kelvin would later call it a "''demon''". In the thought experiment, a demon controls a door between two chambers containing gas. As individual gas molecules (or atoms) approach the door, the demon quickly opens and closes the door to allow only fast-moving molecules to pass through in one direction, and only slow-moving molecules to pass through in the other. Because the kinetic temperature of a gas depends on the velocities of its constituent molecules, the demon's actions cause one chamber to warm up and the other to cool down. This would decrease the total entropy of the system, seemingly without applying any work, thereby violating the second law of thermodynamics. The concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pursuit–evasion
Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically. In 1976, Torrence Parsons introduced a formulation whereby movement is constrained by a graph. The geometric formulation is sometimes called continuous pursuit–evasion, and the graph formulation discrete pursuit–evasion (also called graph searching). Current research is typically limited to one of these two formulations. Discrete formulation In the discrete formulation of the pursuit–evasion problem, the environment is modeled as a graph. Problem definition There are innumerable possible variants of pursuit–evasion, though they tend to share many elements. A typical, basic example is as follows (cops and robber games): Pursuers and evaders occupy nodes of a gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homicidal Chauffeur Problem
{{Short description, Mathematical pursuit problem In game theory, the homicidal chauffeur problem is a mathematical pursuit problem which pits a hypothetical runner, who can only move slowly, but is highly maneuverable, against the driver of a motor vehicle, which is much faster but far less maneuverable, who is attempting to run him down. Both runner and driver are assumed to never tire. The question to be solved is: under what circumstances, and with what strategy, can the driver of the car guarantee that he can always catch the pedestrian, or the pedestrian guarantee that he can indefinitely elude the car? The problem is often used as an unclassified proxy for missile defense and other military targeting, allowing scientists to publish on it without security implications. The problem was proposed by Rufus Isaacs in a 1951 report for the RAND Corporation, and in the book ''Differential Games''.R. Isaacs, ''Differential Games: A Mathematical Theory with Applications to Warfare a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Kutz
Martin may refer to: Places Antarctica * Martin Peninsula, Marie Byrd Land * Port Martin, Adelie Land * Point Martin, South Orkney Islands Europe * Martin, Croatia, a village * Martin, Slovakia, a city * MartÃn del RÃo, Aragón, Spain * MartÃn River, a tributary of the Ebro river in Spain * Martin (Val Poschiavo), Switzerland England * Martin, Hampshire * Martin, Kent * Martin, East Lindsey, Lincolnshire, a hamlet and former parish * Martin, North Kesteven, Lincolnshire, a village and parish * Martin Hussingtree, Worcestershire * Martin Mere, a lake in Lancashire ** WWT Martin Mere, a wetland nature reserve that includes the lake and surrounding areas North America Canada * Rural Municipality of Martin No. 122, Saskatchewan, Canada * Martin Islands, Nunavut, Canada United States * Martin, Florida * Martin, Georgia * Martin, Indiana * Martin, Kentucky * Martin, Louisiana * Martin, Michigan * Martin, Nebraska * Martin, North Dakota * Martin, Ohio * Martin, South Carolina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Béla Bollobás
Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul Erdős from the age of 14. Early life and education As a student, he took part in the first three International Mathematical Olympiads, winning two gold medals. Paul Erdős invited Bollobás to lunch after hearing about his victories, and they kept in touch afterward. Bollobás's first publication was a joint publication with ErdősBollobás, Béla; Erdös, Paul, Über graphentheoretische Extremalprobleme (Extremal problems in graph theory), Mat. Lapok 13, 143-152 (1962) on extremal problems in graph theory, written when he was in high school in 1962. With Erdős's recommendation to Harold Davenport and a long struggle for permission from the Hungarian authorities, Bollobás was able to spend an undergraduate year in Cambridge, England. Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imre Leader
Imre Bennett Leader (born 30 October 1963) is a British mathematician, a professor in DPMMS at the University of Cambridge working in the field of combinatorics. He is also known as an Othello player. Life He is the son of the physicist Elliot Leader and his first wife Ninon Neményi (his mother was previously married to the poet Endre Kövesi); Darian Leader is his brother. Imre Lakatos was a family friend and his godfather. Leader was educated at St Paul's School in London, from 1976 to 1980. He won a silver medal on the British team at the 1981 International Mathematical Olympiad (IMO) for pre-undergraduates. He later acted as the official leader of the British IMO team, taking over from Adam McBride in 1999, to 2001. He was the IMO's Chief Coordinator and Problems Group Chairman in 2002. Leader went on to Trinity College, Cambridge, where he graduated B.A. in 1984, M.A. in 1989, and Ph.D. in 1989. His Ph.D. was in mathematics was for work on combinatorics, supervised by Bà ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics, Probability And Computing
''Combinatorics, Probability and Computing'' is a peer-reviewed scientific journal in mathematics published by Cambridge University Press. Its editor-in-chief is Béla Bollobás ( DPMMS and University of Memphis). History The journal was established by Bollobás in 1992. Fields Medalist Timothy Gowers calls it "a personal favourite" among combinatorics journals and writes that it "maintains a high standard". Content The journal covers combinatorics, probability theory, and theoretical computer science. Currently, it publishes six issues annually. As with other journals from the same publisher, it follows a hybrid green/gold open access policy, in which authors may either place copies of their papers in an institutional repository after a six-month embargo period, or pay an open access charge to make their papers free to read on the journal's website. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Gacs
Péter Gács (Hungarian pronunciation: pe:ter 'ga:tʃ born May 9, 1947), professionally also known as Peter Gacs, is a Hungarian-American mathematician and computer scientist, professor, and an external member of the Hungarian Academy of Sciences. He is well known for his work in reliable computation, randomness in computing, algorithmic complexity, algorithmic probability, and information theory. Career Peter Gacs attended high school in his hometown, then obtained a diploma (M.S.) at Loránd Eötvös University in Budapest in 1970. Gacs started his career as a researcher at the Applied Mathematics Institute of the Hungarian Academy of Science. He obtained his doctoral degree from the Goethe University Frankfurt in 1978. Throughout his studies he had the opportunity to visit Moscow State University and work with Andrey Kolmogorov and his student Leonid A Levin. Through 1979 he was a visiting research associate at Stanford University. He was an assistant professor at Univ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |