|
Weber Problem
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation costs from this point to ''n'' destination points, where different destination points are associated with different costs per unit distance. The Weber problem generalizes the geometric median, which assumes transportation costs per unit distance are the same for all destination points, and the problem of computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although the same name has also been used for the unweighted geometric median problem. The Weber problem is in turn generalized by the attraction–repulsion problem, which allows some of the costs to be negative, so that greater distance from some points is better. Definition and history of the Fermat, Weber, and attraction-repulsion problems In th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Simpson
Thomas Simpson Fellow of the Royal Society, FRS (20 August 1710 – 14 May 1761) was a British mathematician and inventor known for the :wikt:eponym, eponymous Simpson's rule to approximate definite integrals. The attribution, as often in mathematics, can be debated: this rule had been found 100 years earlier by Johannes Kepler, and in German it is called :de:Keplersche Fassregel, Keplersche Fassregel. Biography Simpson was born in Sutton Cheney, Leicestershire. The son of a weaver, Simpson taught himself mathematics. At the age of nineteen, he married a fifty-year old widow with two children. As a youth, he became interested in astrology after seeing a solar eclipse. He also dabbled in divination and caused fits in a girl after 'raising a devil' from her. After this incident, he and his wife had to flee to Derby. He moved with his wife and children to London at age twenty-five, where he supported his family by weaving during the day and teaching mathematics at night. From 17 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nobel Memorial Prize
The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered by the Nobel Foundation. Although not one of the five Nobel Prizes which were established by Alfred Nobel's will in 1895, it is commonly referred to as the Nobel Prize in Economics. The winners of the Nobel Memorial Prize in Economic Sciences are chosen in a similar way, are announced along with the Nobel Prize recipients, and the prize is presented at the Nobel Prize Award Ceremony. The award was established in 1968 by an endowment "in perpetuity" from Sweden's central bank, Sveriges Riksbank, to commemorate the bank's 300th anniversary. It is administered and referred to along with the Nobel Prizes by the Nobel Foundation. Laureates in the Memorial Prize in Economics are selected by the Royal Swedish Academy of Sciences. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Krugman
Paul Robin Krugman ( ; born February 28, 1953) is an American economist, who is Distinguished Professor of Economics at the Graduate Center of the City University of New York, and a columnist for ''The New York Times''. In 2008, Krugman was the winner of the Nobel Memorial Prize in Economic Sciences for his contributions to New Trade Theory and New Economic Geography. The Prize Committee cited Krugman's work explaining the patterns of international trade and the geographic distribution of economic activity, by examining the effects of economies of scale and of consumer preferences for diverse goods and services. Krugman was previously a professor of economics at MIT, and later at Princeton University. He retired from Princeton in June 2015, and holds the title of professor emeritus there. He also holds the title of Centennial Professor at the London School of Economics. Krugman was President of the Eastern Economic Association in 2010, and is among the most influential economi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Geography
Economic geography is the subfield of human geography which studies economic activity and factors affecting them. It can also be considered a subfield or method in economics. There are four branches of economic geography. There is, primary sector, Secondary sector, Tertiary sector, & Quaternary sector. Economic geography takes a variety of approaches to many different topics, including the location of industries, economies of agglomeration (also known as "linkages"), transportation, international trade, development, real estate, gentrification, ethnic economies, gendered economies, core-periphery theory, the economics of urban form, the relationship between the environment and the economy (tying into a long history of geographers studying culture-environment interaction), and globalization. Theoretical background and influences There are varied methodological approaches. Neoclassical location theorists, following in the tradition of Alfred Weber, tend to focus on industria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bid Rent Theory
The bid rent theory is a geographical economic theory that refers to how the price and demand for real estate change as the distance from the central business district (CBD) increases. It states that different land users will compete with one another for land close to the city centre. This is based upon the idea that retail establishments wish to maximize their profitability, so they are much more willing to pay more for land close to the CBD and less for land further away from this area. This theory is based upon the reasoning that the more accessible an area (i.e., the greater the concentration of customers), the more profitable. Explanation Land users all compete for the most accessible land within the CBD. The amount they are willing to pay is called "bid rent". The result is a pattern of concentric rings of land use, creating the concentric zone model. It could be assumed that, according to this theory, the poorest houses and buildings would be on the very outskirts of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brigitte Jaumard
Brigitte Jaumard is a computer scientist and expert on mathematical programming. She earned a doctorate in 2006 from ENSTA ParisTech under the supervision of Michel Minoux, after previously teaching at Polytechnique Montréal. She is a professor of computer science and software engineering at Concordia University Concordia University ( French: ''Université Concordia'') is a public research university located in Montreal, Quebec, Canada. Founded in 1974 following the merger of Loyola College and Sir George Williams University, Concordia is one of the t ..., where she is the holder of an Honorary Concordia Research Chair in Optimization of Communication Networks. References External links * Canadian women computer scientists Canadian computer scientists Academic staff of Concordia University Year of birth missing (living people) Living people {{compu-scientist-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Varignon Frame
The Varignon frame, named after Pierre Varignon, is a mechanical device which can be used to determine an optimal location of a warehouse for the destribution of goods to a set of shops. Optimal means that the sum of the ''weighted distances'' of the shops to the warehouse should be minimal. The frame consists of a board with n holes corresponding to the n shops at the locations \mathbf x_1, ...\mathbf x_n, n strings are tied together in a knot at one end, the loose ends are passed, one each, through the holes and are attached to weights below the board (see diagram). If the influence of friction and other odds of the real world are neglected, the knot will take a position of equilibrium \mathbf v. It can be shown (see below), that point \mathbf v is the optimal location which minimizes the weighted sum of distances :(1): \ D(\mathbf x)=\sum_^n m_i\, \mathbf x_i-\mathbf x\, . The optimization problem is called Weber problem. Mechanical Problem - Optimization Problem If the holes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weiszfeld's Algorithm
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the ''L''1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation. The special case of the problem for three points in the plane (that is, = 3 and = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iteratively Reweighted Least Squares
The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form of a ''p''-norm: :\underset \sum_^n \big, y_i - f_i (\boldsymbol\beta) \big, ^p, by an iterative method in which each step involves solving a weighted least squares problem of the form:C. Sidney Burrus, Iterative Reweighted Least Squares' :\boldsymbol\beta^ = \underset \sum_^n w_i (\boldsymbol\beta^) \big, y_i - f_i (\boldsymbol\beta) \big, ^2. IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set. For example, by minimizing the least absolute errors rather than the least square errors. One of the advantages of IRLS over linear programming and convex programming is that it can be used with Gauss–Newton and Levenberg–Marquardt numerical algorithms. E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
