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Jacques Neveu
Jacques Jean-Pierre Neveu (14 November 193217 May 2016) was a Belgian (and then French) mathematician, specializing in probability theory. He is one of the founders of the French school (post WW II) of probability and statistics. Education and career Jacques Neveu received in 1955 from the Sorbonne his doctorate in mathematics under Robert Fortet with dissertation ''Étude des semi-groupes de Markov''. In 1960, Neveu was, with Robert Fortet, one of the first two members of the Laboratoire de Probabilités et Modèles Aléatoires (LPMA). He was the LPMA's director from 1980 until 1989 when Jean Jacod became the director. In 1962, Neveu was a ''chargé de cours'' (university lecturer) at the Collège de France. He taught at the Sorbonne and, after the reorganization of the University of Paris, at the University of Paris VI at the Laboratory for Probability of the . He was a professor at the École Polytechnique. In 1976, he gave a course at l'école d'été de Saint-Flour (a summe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Paris VI
Pierre and Marie Curie University (french: link=no, Université Pierre-et-Marie-Curie, UPMC), also known as Paris 6, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, France. UPMC merged with Paris-Sorbonne University into a new combined Sorbonne University. It was ranked as the best university in France in medicine and health sciences by ''Times Higher Education'' in 2018. History Paris VI was one of the inheritors of the faculty of Sciences of the University of Paris, which was divided into several universities in 1970 after the student protests of May 1968. In 1971, the five faculties of the former University of Paris (Paris VI as the Faculty of Sciences) were split and then re-formed into thirteen universities by the Faure Law. The campus of Paris VI was built in the 1950s and 1960s, on a site previously occupied by wine storehouses. The Dean, Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
São Paulo
São Paulo (, ; Portuguese for 'Saint Paul') is the most populous city in Brazil, and is the capital of the state of São Paulo, the most populous and wealthiest Brazilian state, located in the country's Southeast Region. Listed by the GaWC as an alpha global city, São Paulo is the most populous city proper in the Americas, the Western Hemisphere and the Southern Hemisphere, as well as the world's 4th largest city proper by population. Additionally, São Paulo is the largest Portuguese-speaking city in the world. It exerts strong international influences in commerce, finance, arts and entertainment. The city's name honors the Apostle, Saint Paul of Tarsus. The city's metropolitan area, the Greater São Paulo, ranks as the most populous in Brazil and the 12th most populous on Earth. The process of conurbation between the metropolitan areas around the Greater São Paulo (Campinas, Santos, Jundiaí, Sorocaba and São José dos Campos) created the São Paulo Macrometr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emilie Kaufmann
Emilie Kaufmann (born 1987) is a French statistician and computer scientist specializing in machine learning, and particularly known for her research on the multi-armed bandit problem. She is a researcher for the French National Centre for Scientific Research (CNRS), associated with the Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) at the University of Lille. Education and career Kaufmann studied mathematics at the University of Strasbourg, earning a bachelor's degree in 2009, and she passed the agrégation in mathematics in 2010. In 2011 she earned a master's degree in statistical learning from the École normale supérieure Paris-Saclay, and she completed her Ph.D. in 2014 at Télécom Paris. Her dissertation was ''Analyse de stratégies bayésiennes et fréquentistes pour l’allocation séquentielle de ressources'', supervised by Olivier Cappé and Aurélien Garivier. After postdoctoral research in the project on Dynamics of Geometric Network ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Measure
In mathematics, a Dirac measure assigns a size to a set based solely on whether it contains a fixed element ''x'' or not. It is one way of formalizing the idea of the Dirac delta function, an important tool in physics and other technical fields. Definition A Dirac measure is a measure on a set (with any -algebra of subsets of ) defined for a given and any (measurable) set by :\delta_x (A) = 1_A(x)= \begin 0, & x \not \in A; \\ 1, & x \in A. \end where is the indicator function of . The Dirac measure is a probability measure, and in terms of probability it represents the almost sure outcome in the sample space . We can also say that the measure is a single atom at ; however, treating the Dirac measure as an atomic measure is not correct when we consider the sequential definition of Dirac delta, as the limit of a delta sequence. The Dirac measures are the extreme points of the convex set of probability measures on . The name is a back-formation from the Dirac delta fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Tree
In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: *Uniform spanning tree, a spanning tree of a given graph in which each different tree is equally likely to be selected *Random minimal spanning tree, spanning trees of a graph formed by choosing random edge weights and using the minimum spanning tree for those weights *Random binary tree, binary trees with a given number of nodes, formed by inserting the nodes in a random order or by selecting all possible trees uniformly at random *Random recursive tree, increasingly labelled trees, which can be generated using a simple stochastic growth rule. *Treap or randomized binary search tree, a data structure that uses random choices to simulate a random binary tree for non-random update sequences * Rapidly exploring random tree, a fractal space-filling pattern used as a data structure for searching high-dimensional spaces *Brownian tree, a frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ergodic Theory
Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems. The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics. Ergodic theory, like probability theory, is based on general notions of measure theory. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincaré recurrence theorem, which claims that almost all points in any subset of the ... [...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] |
Gaussian Process
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space. The concept of Gaussian processes is named after Carl Friedrich Gauss because it is based on the notion of the Gaussian distribution (normal distribution). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions. Gaussian processes are useful in statistical modelling, benefiting from properties inherited from the normal distribution. For example, if a random process is modelled as a Gaussian process, the distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Process
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
