|
Mabinogion Sheep Problem
In probability theory, the Mabinogion sheep problem or Mabinogian urn is a problem in stochastic control introduced by , who named it after a herd of magic sheep in the Welsh collection of tales, the ''Mabinogion The ''Mabinogion'' () are the earliest Welsh prose stories, and belong to the Matter of Britain. The stories were compiled in Middle Welsh in the 12th–13th centuries from earlier oral traditions. There are two main source manuscripts, create ...''. Statement At time ''t'' = 0 there is a herd of sheep each of which is black or white. At each time ''t'' = 1, 2, ... a sheep is selected at random, and a sheep of the opposite color (if one exists) is changed to be the same color as the selected sheep. At any time one may remove as many sheep (of either color) as one wishes from the flock. The problem is to do this in such a way as to maximize the expected final number of black sheep. The optimal solution at each step is to remove just enou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Control
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise. The context may be either discrete time or continuous time. Certainty equivalence An extremely well-studied formulation in stochastic control is that of linear quadratic Gaussian control. Here the model is linear, the objective function is the expected value of a quadratic form, and the disturbances are purely additive. A basic result for discrete-time centralized systems with only additive uncertainty is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mabinogion
The ''Mabinogion'' () are the earliest Welsh prose stories, and belong to the Matter of Britain. The stories were compiled in Middle Welsh in the 12th–13th centuries from earlier oral traditions. There are two main source manuscripts, created c. 1350–1410, as well as a few earlier fragments. The title covers a collection of eleven prose stories of widely different types, offering drama, philosophy, romance, tragedy, fantasy and humour, and created by various narrators over time. There is a classic hero quest, "Culhwch and Olwen"; a historic legend in " Lludd and Llefelys," complete with glimpses of a far off age; and other tales portray a very different King Arthur from the later popular versions. The highly sophisticated complexity of the Four Branches of the Mabinogi defies categorisation. The stories are so diverse that it has been argued that they are not even a true collection. Scholars from the 18th century to the 1970s predominantly viewed the tales as fragmentary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peredur Son Of Efrawg
''Peredur son of Efrawg'' is one of the Three Welsh Romances associated with the ''Mabinogion''. It tells a story roughly analogous to Chrétien de Troyes' unfinished romance ''Perceval, the Story of the Grail'', but it contains many striking differences from that work, most notably the absence of the French poem's central object, the grail. Synopsis The central character of the tale is Peredur, son of Efrawg (''York''). As in Chrétien's ''Percival'', the hero's father dies when he is young, and his mother takes him into the woods and raises him in isolation. Eventually, he meets a group of knights and determines to become like them, so he travels to the court of King Arthur. There he is ridiculed by Cei and sets out on further adventures, promising to avenge Cei's insults to himself and those who defended him. While travelling, he meets two of his uncles. The first (playing the role of ''Percivals Gornemant) educates him in arms and warns him not to ask the significance o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lady Charlotte Guest
Lady Charlotte Elizabeth Guest (née Bertie; 19 May 1812 – 15 January 1895), later Lady Charlotte Schreiber, was an English aristocrat who is best known as the first publisher in modern print format of the '' Mabinogion'', the earliest prose literature of Britain. Guest established the ''Mabinogion'' as a source literary text of Europe, claiming this recognition among literati in the context of contemporary passions for the chivalric romance of King Arthur and the Gothic movement. The name Guest used for the book was derived from a mediaeval copyist's error, already established in the 18th century by William Owen Pughe and the London Welsh societies. As an accomplished linguist, and the wife of a foremost Welsh ironmaster John Josiah Guest, she became a leading figure in the study of literature and the wider Welsh Renaissance of the 19th century. With her second husband, Charles Schreiber, she became a well known Victorian collector of porcelain; their collection is held in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martingale (probability Theory)
In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence is equal to the present value, regardless of all prior values. History Originally, ''martingale'' referred to a class of betting strategies that was popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins their stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double their bet after every loss so that the first win would recover all previous losses plus win a profit equal to the original stake. As the gambler's wealth and available time jointly approach infinity, their probability of eventually flipping heads approaches 1, which makes the martingale betting strategy seem like a sure thing. However, the exponential growth of the bets eventually bankrupts its users due to f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Problems
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Control
Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise. The context may be either discrete time or continuous time. Certainty equivalence An extremely well-studied formulation in stochastic control is that of linear quadratic Gaussian control. Here the model is linear, the objective function is the expected value of a quadratic form, and the disturbances are purely additive. A basic result for discrete-time centralized systems with only additive uncertainty is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_Peredur.jpg "Click for more on -> Peredur Son Of Efrawg")
.svg "Click for more on -> Probability Problems")