BRS-inequality
BRS-inequality is the short name for Bruss-Robertson-Steele inequality. This inequality gives a convenient upper bound for the expected maximum number of non-negative random variables one can sum up without exceeding a given upper bound s > 0. For example, suppose 100 random variables X_1, X_2,..., X_ are all uniformly distributed on , 1/math>, not necessarily independent, and let s= 10, say. Let N , s:= N 00, 10/math> be the maximum number of X_j one can select in \ such that their sum does not exceed s= 10. N 00, 10/math> is a random variable, so what can one say about bounds for its expectation? How would an upper bound for E(N , s behave, if one changes the size n of the sample and keeps s fixed, or alternatively, if one keeps n fixed but varies s? What can one say about E(N , s, if the uniform distribution is replaced by another continuous distribution? In all generality, what can one say if each X_k may have its own continuous distribution function F_k? General problem Let ...
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Online
In computer technology and telecommunications, online indicates a state of connectivity and offline indicates a disconnected state. In modern terminology, this usually refers to an Internet connection, but (especially when expressed "on line" or "on the line") could refer to any piece of equipment or functional unit that is connected to a larger system. Being online means that the equipment or subsystem is connected, or that it is ready for use. "Online" has come to describe activities performed on and data available on the Internet, for example: "online identity", "online predator", "online gambling", "online game", "online shopping", "online banking", and "online learning". Similar meaning is also given by the prefixes "cyber" and "e", as in the words " cyberspace", "cybercrime", "email", and "ecommerce". In contrast, "offline" can refer to either computing activities performed while disconnected from the Internet, or alternatives to Internet activities (such as shopping in br ...
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Point Process
In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Kallenberg, O. (1986). ''Random Measures'', 4th edition. Academic Press, New York, London; Akademie-Verlag, Berlin. , .Daley, D.J, Vere-Jones, D. (1988). ''An Introduction to the Theory of Point Processes''. Springer, New York. , . Point processes can be used for spatial data analysis,Diggle, P. (2003). ''Statistical Analysis of Spatial Point Patterns'', 2nd edition. Arnold, London. . which is of interest in such diverse disciplines as forestry, plant ecology, epidemiology, geography, seismology, materials science, astronomy, telecommunications, computational neuroscience, economics and others. There are different mathematical interpretations of a point process, such as a random counting measure or a random set. Some authors regard a point process and stochastic process as two different objects ...
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Selection Algorithm
In computer science, a selection algorithm is an algorithm for finding the ''k''th smallest number in a list or array; such a number is called the ''k''th ''order statistic''. This includes the cases of finding the minimum, maximum, and median elements. There are O(''n'')-time (worst-case linear time) selection algorithms, and sublinear performance is possible for structured data; in the extreme, O(1) for an array of sorted data. Selection is a subproblem of more complex problems like the nearest neighbor and shortest path problems. Many selection algorithms are derived by generalizing a sorting algorithm, and conversely some sorting algorithms can be derived as repeated application of selection. The simplest case of a selection algorithm is finding the minimum (or maximum) element by iterating through the list, keeping track of the running minimum – the minimum so far – (or maximum) and can be seen as related to the selection sort. Conversely, the hardest case of a selection ...
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Knapsack Problem
The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision-makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating as far back as 1897. The name "knapsack problem" dates back to the early works of the mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage. Applications Knapsack problems ap ...
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Tiling
Tiling may refer to: *The physical act of laying tiles *Tessellations Computing *The compiler optimization of loop tiling *Tiled rendering, the process of subdividing an image by regular grid *Tiling window manager People *Heinrich Sylvester Theodor Tiling (1818–1871), physician and botanist *Reinhold Tiling (1893–1933), German rocket pioneer Other uses *Neuronal tiling *Tile drainage, an agriculture practice that removes excess water from soil *Tiling (crater), a small, undistinguished crater on the far side of the Moon See also *Brickwork *Packing (other) *Tiling puzzle Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps). Some tiling puzzles ask you to dissect a given ...