Combinatorial optimizationCombinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
UnimodalityIn mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. In statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal".
Multimodal distributionIn statistics, a multimodal distribution is a probability distribution with more than one mode. These appear as distinct peaks (local maxima) in the probability density function, as shown in Figures 1 and 2. Categorical, continuous, and discrete data can all form multimodal distributions. Among univariate analyses, multimodal distributions are commonly bimodal. When the two modes are unequal the larger mode is known as the major mode and the other as the minor mode. The least frequent value between the modes is known as the antimode.
.uk.uk is the Internet country code top-level domain (ccTLD) for the United Kingdom. It was first registered in July 1985, seven months after the original generic top-level domains such as .com and the first country code after .us. it is the fifth most popular top-level domain worldwide (after .com, .cn, .de and .net), with over 10 million registrations. uk has used OpenDNSSEC since March 2010. Internet in the United Kingdom#History and Nominet UK#History In October 1984, RFC 920 set out the creation of ccTLDs using country codes derived from the corresponding two-letter code in the ISO 3166-1 list.
Quasiconvex functionIn mathematics, a quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the of any set of the form is a convex set. For a function of a single variable, along any stretch of the curve the highest point is one of the endpoints. The negative of a quasiconvex function is said to be quasiconcave. All convex functions are also quasiconvex, but not all quasiconvex functions are convex, so quasiconvexity is a generalization of convexity.
Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
United KingdomThe United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Northwestern Europe, off the north-western coast of the continental mainland. It comprises England, Scotland, Wales, and Northern Ireland. It includes the island of Great Britain, the north-eastern part of the island of Ireland, and most of the smaller islands within the British Isles.
Mode (statistics)The mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e, x=argmaxxi P(X = xi)). In other words, it is the value that is most likely to be sampled. Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population.
Order of operationsIn mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression 1 + 2 × 3 is interpreted to have the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.
Operation (mathematics)In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant.
Program optimizationIn computer science, program optimization, code optimization, or software optimization, is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or to make it capable of operating with less memory storage or other resources, or draw less power. Although the word "optimization" shares the same root as "optimal", it is rare for the process of optimization to produce a truly optimal system.
Mathematical notationMathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, Albert Einstein's equation is the quantitative representation in mathematical notation of the mass–energy equivalence.
Golden ratioIn mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with , where the Greek letter phi ( or ) denotes the golden ratio. The constant satisfies the quadratic equation and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names.
Symmetric probability distributionIn statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function (for continuous probability distribution) or probability mass function (for discrete random variables) is reflected around a vertical line at some value of the random variable represented by the distribution. This vertical line is the line of symmetry of the distribution.
Labour Party (UK)The Labour Party is a political party in the United Kingdom that has been described as an alliance of social democrats, democratic socialists, and trade unionists. The Labour Party sits on the centre-left of the political spectrum. In all general elections since 1922, Labour has been either the governing party or the Official Opposition. There have been six Labour prime ministers and thirteen Labour ministries. Since the 2010 general election, it has been the second-largest UK political party by the number of votes cast, behind the Conservative Party and ahead of the Liberal Democrats.
LondonLondon ('lʌndən ) is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea and has been a major settlement for two millennia. The City of London, its ancient core and financial centre, was founded by the Romans as Londinium and retains its medieval boundaries. The City of Westminster, to the west of the City of London, has for centuries hosted the national government and parliament.
Evaluation strategyIn a programming language, an evaluation strategy is a set of rules for evaluating expressions. The term is often used to refer to the more specific notion of a parameter-passing strategy that defines the kind of value that is passed to the function for each parameter (the binding strategy) and whether to evaluate the parameters of a function call, and if so in what order (the evaluation order). The notion of reduction strategy is distinct, although some authors conflate the two terms and the definition of each term is not widely agreed upon.
Section d'OrThe Section d'Or ("Golden Section"), also known as Groupe de Puteaux or Puteaux Group, was a collective of painters, sculptors, poets and critics associated with Cubism and Orphism. Based in the Parisian suburbs, the group held regular meetings at the home of the Duchamp brothers in Puteaux and at the studio of Albert Gleizes in Courbevoie. Active from 1911 to around 1914, members of the collective came to prominence in the wake of their controversial showing at the Salon des Indépendants in the spring of 1911.
