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Rendezvous Problem
The rendezvous dilemma is a logical dilemma, typically formulated in this way: :Two people have a date in a park they have never been to before. Arriving separately in the park, they are both surprised to discover that it is a huge area and consequently they cannot find one another. In this situation each person has to choose between waiting in a fixed place in the hope that the other will find them, or else starting to look for the other in the hope that ''they'' have chosen to wait somewhere. If they both choose to wait, they will never meet. If they both choose to walk there are chances that they meet and chances that they do not. If one chooses to wait and the other chooses to walk, then there is a theoretical certainty that they will meet eventually; in practice, though, it may take too long for it to be guaranteed. The question posed, then, is: what strategies should they choose to maximize their probability of meeting? Examples of this class of problems are known as rendezv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Steve Alpern
Professor Steve Alpern is a professor of Operational Research at the University of Warwick, where he recently moved after working for many years at the London School of Economics. His early work was mainly in the area of dynamical systems and ergodic theory, but his more recent research has been concentrated in the fields of search games and rendezvous. He informally introduced the rendezvous problem as early as 1976.Steve Alpern (1976). ''Hide and Seek Games''. Seminar, Institut fur Hohere Studien, Wien, 26 July His collaborators include Shmuel Gal, Vic Baston and Robbert Fokkink. External links Author profilein the database zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure mathematics, pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Informa ... References Academics of the University of Warwick Game theorists Living people Courant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Richard Weber (mathematician)
Richard Robert Weber (born 25 February 1953) is a mathematician working in operational research. He is Emeritus Churchill Professor of Mathematics for Operational Research in the Statistical Laboratory, University of Cambridge. Weber was educated at Walnut Hills High School, Solihull School and Downing College, Cambridge. He graduated in 1974, and completed his PhD in 1980 under the supervision of Peter Nash. He has been on the faculty of the University of Cambridge since 1978, and a fellow of Queens' College since 1977 where he has been Vice President from 1996–2007 and again from 2018–2020. He was appointed Churchill Professor in 1994, and he became Emeritus Churchill Professor on retirement in 2017. He was Director of the Statistical Laboratory from 1999 to 2009, and is a trustee of the Rollo Davidson Trust. He works on the mathematics of large complex systems subject to uncertainty. He has made contributions to stochastic scheduling, Markov decision pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Synchronization
Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are said to be synchronous or ''in sync''—and those that are not are '' asynchronous''. Today, time synchronization can occur between systems around the world through satellite navigation signals and other time and frequency transfer techniques. Navigation and railways Time-keeping and synchronization of clocks is a critical problem in long-distance ocean navigation. Before radio navigation and satellite-based navigation, navigators required accurate time in conjunction with astronomical observations to determine how far east or west their vessel traveled. The invention of an accurate marine chronometer revolutionized marine navigation. By the end of the 19th century, important ports provided time signals in the form of a signal gun, flag, or dropping ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Operating System
An operating system (OS) is system software that manages computer hardware, software resources, and provides common daemon (computing), services for computer programs. Time-sharing operating systems scheduler (computing), schedule tasks for efficient use of the system and may also include accounting software for cost allocation of Scheduling (computing), processor time, mass storage, printing, and other resources. For hardware functions such as input and output and memory allocation, the operating system acts as an intermediary between programs and the computer hardware, although the application code is usually executed directly by the hardware and frequently makes system calls to an OS function or is interrupted by it. Operating systems are found on many devices that contain a computer from cellular phones and video game consoles to web servers and supercomputers. The dominant general-purpose personal computer operating system is Microsoft Windows with a market share of aroun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Operations Research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Search And Rescue
Search and rescue (SAR) is the search for and provision of aid to people who are in distress or imminent danger. The general field of search and rescue includes many specialty sub-fields, typically determined by the type of terrain the search is conducted over. These include mountain rescue; ground search and rescue, including the use of search and rescue dogs; urban search and rescue in cities; combat search and rescue on the battlefield and air-sea rescue over water. International Search and Rescue Advisory Group (INSARAG) is a UN organization that promotes the exchange of information between national urban search and rescue organizations. The duty to render assistance is covered by Article 98 of the UNCLOS. Definitions There are many different definitions of search and rescue, depending on the agency involved and country in question. *Canadian Forces: "Search and Rescue comprises the search for, and provision of aid to, persons, ships or other craft which are, or are fear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Determinism
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. The opposite of determinism is some kind of indeterminism (otherwise called nondeterminism) or randomness. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible.For example, see Determinism is often used to mean ''causal determinism'', which in physics is known as cause-and-effect. This is the concept that events within a given paradigm are bound by causality in such a way that any state of an object or event is completely determined by its prior states. This meaning can be distinguished from other varieties of determinism mentioned below. Debates about determinism often concern the scope of determined systems; some maintain that the entire universe is a single determi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Symmetry Breaking
In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or " noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. The phenomenon is part of most theories of everything. Symmetry breaking is thought to play a major role in pattern formation. In his 1972 ''Science'' paper titled "More is different" Nobel laureate P.W. Anderson used the idea of symmetry breaking to show that even if reductionism is true, its converse, constructionism, which is the idea that scientists can easily predict complex phenomena given theories describing their components, is not. Symmetry breaking can be distinguished into two typ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Coordination Game
A coordination game is a type of simultaneous game found in game theory. It describes the situation where a player will earn a higher payoff when they select the same course of action as another player. The game is not one of pure conflict, which results in multiple pure strategy Nash equilibrium, Nash equilibria in which players choose matching strategies. Figure 1 shows a 2-player example. Both (Up, Left) and (Down, Right) are Nash equilibria. If the players expect (Up, Left) to be played, then player 1 thinks their payoff would fall from 2 to 1 if they deviated to Down, and player 2 thinks their payoff would fall from 4 to 3 if they chose Right. If the players expect (Down, Right), player 1 thinks their payoff would fall from 2 to 1 if they deviated to Up, and player 2 thinks their payoff would fall from 4 to 3 if they chose Left. A player's optimal move depends on what they expect the other player to do, and they both do better if they coordinate than if they played an off-eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Dining Philosophers Problem
In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them. It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals. Soon after, Tony Hoare gave the problem its present form. Problem statement Five philosophers dine together at the same table. Each philosopher has their own place at the table. There is a fork between each plate. The dish served is a kind of spaghetti which has to be eaten with two forks. Each philosopher can only alternately think and eat. Moreover, a philosopher can only eat their spaghetti when they have both a left and right fork. Thus two forks will only be available when their two nearest neighbors are thinking, not eating. After an individual philosopher finishes eating, they will put down both forks. The problem is how ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Probabilistic Algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables. One has to distinguish between algorithms that use the random input so that they always terminate with the correct answer, but where the expected running time is finite (Las Vegas algorithms, for example Quicksort), and algorithms which have a chance of producing an incorrect result (Monte Carlo algorithms, for example the Monte Carlo algorithm for the MFAS problem) or fail to produce a result either by signaling a failure or failing to terminate. In some cases, probabilistic algorithms are the only practical means of solving a problem. In common practice, randomized algor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Search Games
A search game is a two-person zero-sum game which takes place in a set called the search space. The searcher can choose any continuous trajectory subject to a maximal velocity constraint. It is always assumed that neither the searcher nor the hider has any knowledge about the movement of the other player until their distance apart is less than or equal to the discovery radius and at this very moment capture occurs. As mathematical models, search games can be applied to areas such as hide-and-seek games that children play or representations of some tactical military situations. The area of search games was introduced in the last chapter of Rufus Isaacs' classic book "Differential Games" and has been developed further by Shmuel GalS. Gal, ''Search Games'', Academic Press, New York (1980)S. Alpern and S. Gal, The Theory of Search Games and Rendezvous', Springer (2003). and Steve Alpern. The princess and monster game deals with a moving target. Strategy A natural strategy to search f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |