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Godfried Toussaint
Godfried Theodore Patrick Toussaint (1944 – July 2019) was a Canadian computer scientist, a professor of computer science, and the head of the Computer Science Program at New York University Abu Dhabi (NYUAD) in Abu Dhabi, United Arab Emirates. He is considered to be the father of computational geometry in Canada. He did research on various aspects of computational geometry, discrete geometry, and their applications: pattern recognition (k-nearest neighbor algorithm, cluster analysis), motion planning, visualization (computer graphics), knot theory (stuck unknot problem), linkage (mechanical) reconfiguration, the art gallery problem, polygon triangulation, the largest empty circle problem, unimodality ( unimodal function), and others. Other interests included meander (art), compass and straightedge constructions, instance-based learning, music information retrieval, and computational music theory. He was a co-founder of the Annual ACM Symposium on Computational Geometr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meander (art)
__NOTOC__ A meander or meandros ( el, Μαίανδρος) is a decorative border constructed from a continuous line, shaped into a repeated motif. Among some Italians, these patterns are known as "Greek Lines". Such a design also may be called the Greek fret or Greek key design, although these terms are modern designations even though the decorative motif appears thousands of years before that culture, thousands of miles away from Greece, and among cultures that are continents away from it. Usually the term is used for motifs with straight lines and right angles and the many versions with rounded shapes are called running scrolls or, following the entomological origin of the term, may be identified as water wave motifs. On one hand, the name "meander" recalls the twisting and turning path of the Maeander River in Asia Minor (present day Turkey) that is typical of river pathways. On another hand, as Karl Kerenyi pointed out, "the meander is the figure of a labyrinth in linear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making predicti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relative Neighborhood Graph
In computational geometry, the relative neighborhood graph (RNG) is an undirected graph defined on a set of points in the Euclidean plane by connecting two points p and q by an edge whenever there does not exist a third point r that is closer to both p and q than they are to each other. This graph was proposed by Godfried Toussaint in 1980 as a way of defining a structure from a set of points that would match human perceptions of the shape of the set.. Algorithms showed how to construct the relative neighborhood graph of n points in the plane efficiently in O(n\log n) time. It can be computed in O(n) expected time, for random set of points distributed uniformly in the unit square. The relative neighborhood graph can be computed in linear time from the Delaunay triangulation of the point set.. Generalizations Because it is defined only in terms of the distances between points, the relative neighborhood graph can be defined for point sets in any and for non-Euclidean metrics. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis Of Algorithms
In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it takes (its time complexity) or the number of storage locations it uses (its space complexity). An algorithm is said to be efficient when this function's values are small, or grow slowly compared to a growth in the size of the input. Different inputs of the same size may cause the algorithm to have different behavior, so best, worst and average case descriptions might all be of practical interest. When not otherwise specified, the function describing the performance of an algorithm is usually an upper bound, determined from the worst case inputs to the algorithm. The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of a br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Hull
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting half-spaces, are fundamental problems of co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Hull Algorithms
Algorithms that construct convex hulls of various objects have a broad range of applications in mathematics and computer science. In computational geometry, numerous algorithms are proposed for computing the convex hull of a finite set of points, with various computational complexities. Computing the convex hull means that a non-ambiguous and efficient representation of the required convex shape is constructed. The complexity of the corresponding algorithms is usually estimated in terms of ''n'', the number of input points, and sometimes also in terms of ''h'', the number of points on the convex hull. Planar case Consider the general case when the input to the algorithm is a finite unordered set of points on a Cartesian plane. An important special case, in which the points are given in the order of traversal of a simple polygon's boundary, is described later in a separate subsection. If not all points are on the same line, then their convex hull is a convex polygon whose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Selim Akl
Selim G. Akl (Ph.D., McGill University, 1978) is a professor at Queen's University in the Queen's School of Computing, where he leads the Parallel and Unconventional Computation Group. His research interests are primarily in the area of algorithm design and analysis, in particular for problems in parallel computing and unconventional computing. Activities Akl is currently Director of the School of Computing at Queen's University. He is editor in chief of ''Parallel Processing Letters'' published by World Scientific Publishing in 1991 and an editor of several major computing journals including: *''International Journal of Unconventional Computing'' (Old City Publishing; 2011) *''Computational Geometry'' (Elsevier; 1993) *''International Journal of Parallel, Emergent, and Distributed Systems'' (Taylor and Francis; 2004) Akl is the founding editorial board member of ''International Journal of High Performance Computing and Networking'' (Inderscience Publishers; 2003 ), and a pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symposium On Computational Geometry
The International Symposium on Computational Geometry (SoCG) is an academic conference in computational geometry. It was founded in 1985, and was originally sponsored by the SIGACT and SIGGRAPH Special Interest Groups of the Association for Computing Machinery (ACM). It dissociated from the ACM in 2014, motivated by the difficulties of organizing ACM conferences outside the United States and by the possibility of turning to an open-access Open access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. With open access strictly defined (according to the 2001 definition), or libre op ... system of publication. Since 2015 the conference proceedings have been published by the Leibniz International Proceedings in Informatics instead of by the ACM. Since 2019 the conference has been organized under the auspices of the newly-formed Society for Computational Geometry. A 2010 assessment o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McGill University
McGill University (french: link=no, Université McGill) is an English-language public research university located in Montreal, Quebec Montreal ( ; officially Montréal, ) is the second-most populous city in Canada and most populous city in the Canadian province of Quebec. Founded in 1642 as '' Ville-Marie'', or "City of Mary", it is named after Mount Royal, the triple-pe ..., Canada. Founded in 1821 by royal charter granted by George IV, King George IV,Frost, Stanley Brice. ''McGill University, Vol. I. For the Advancement of Learning, 1801–1895.'' McGill-Queen's University Press, 1980. the university bears the name of James McGill, a Scottish merchant whose bequest in 1813 formed the university's precursor, University of McGill College (or simply, McGill College); the name was officially changed to McGill University in 1885. McGill's main campus is on the slope of Mount Royal in downtown Montreal in the borough of Ville-Marie, Montreal, Ville-Marie, with a Macdona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Music Theory
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the " rudiments", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built." Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. Because of the ever-expanding conception of what constitutes music, a more inclusive definition could be the consideration of any sonic phenomena, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
