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Véronique Gayrard
Véronique Gayrard is a French mathematician specializing in probability and statistical physics, with research topics including Hopfield networks, the long-term behavior of the random energy model and similar glassy systems, and metastability in reversible diffusion. She is a director of research for the French National Centre for Scientific Research (CNRS), affiliated with the Marseille Institute of Mathematics (I2M) operated jointly by CNRS and Aix-Marseille University. At I2M, she is affiliated with the research group on the mathematics of randomness (ALEA), which she headed from 2015 to 2021. Education Gayrard earned her doctorate in 1993 through the University of the Mediterranean Aix-Marseille II, now part of Aix-Marseille University. Her dissertation, ''Contribution à l'étude rigoureuse des modèles de Hoppfiel'' 'Contributions to the rigorous study of Hopfield models'' was supervised by Pierre Picco. Recognition In December 2021, Gayrard was named as one of the winner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Physics
Statistical physics is a branch of physics that evolved from a foundation of statistical mechanics, which uses methods of probability theory and statistics, and particularly the Mathematics, mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, and neuroscience. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics develop the Phenomenology (particle physics), phenomenological results of thermodynamics from a probabilistic examination of the underlying microscopic systems. Historically, one of the first topics in physics where statistical methods were applied was the field of classical mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hopfield Network
A Hopfield network (or Ising model of a neural network or Ising–Lenz–Little model) is a form of recurrent artificial neural network and a type of spin glass system popularised by John Hopfield in 1982 as described earlier by Little in 1974 based on Ernst Ising's work with Wilhelm Lenz on the Ising model. Hopfield networks serve as content-addressable ("associative") memory systems with binary threshold nodes, or with continuous variables. Hopfield networks also provide a model for understanding human memory. Origins The Ising model of a neural network as a memory model was first proposed by William A. Little in 1974, which was acknowledged by Hopfield in his 1982 paper. Networks with continuous dynamics were developed by Hopfield in his 1984 paper. A major advance in memory storage capacity was developed by Krotov and Hopfield in 2016 through a change in network dynamics and energy function. This idea was further extended by Demircigil and collaborators in 2017. The contin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Energy Model
In the statistical physics of disordered systems, the random energy model is a toy model of a system with quenched disorder, such as a spin glass, having a first-order phase transition. It concerns the statistics of a collection of N spins (''i.e.'' degrees of freedom \boldsymbol\sigma\equiv \_^N that can take one of two possible values \sigma_i=\pm 1) so that the number of possible states for the system is 2^N. The energies of such states are independent and identically distributed Gaussian random variables E_x \sim \mathcal(0,N/2) with zero mean and a variance of N/2. Many properties of this model can be computed exactly. Its simplicity makes this model suitable for pedagogical introduction of concepts like quenched disorder and replica symmetry. Comparison with other disordered systems The r-spin infinite-range model, in which all r-spin sets interact with a random, independent, identically distributed interaction constant, becomes the random energy model in a suitably defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metastability
In chemistry and physics, metastability denotes an intermediate Energy level, energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy. During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation: *the state of least energy is the only one the system will inhabit for an indefinite length of time, until more external energy is added ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Diffusion
In mathematics, a reversible diffusion is a specific example of a reversible stochastic process. Reversible diffusions have an elegant characterization due to the Russian mathematician Andrey Nikolaevich Kolmogorov. Kolmogorov's characterization of reversible diffusions Let ''B'' denote a ''d''-dimensional standard Brownian motion; let ''b'' : R''d'' → R''d'' be a Lipschitz continuous vector field. Let ''X'' : , +∞) × Ω → R''d'' be an Itō diffusion defined on a probability space (Ω, Σ, P) and solving the Itō stochastic differential equation \mathrm X_ = b(X_) \, \mathrm t + \mathrm B_ with square-integrable initial condition, i.e. ''X''0 ∈ ''L''2(Ω, Σ, P; R''d''). Then the following are equivalent: * The process ''X'' is reversible with stationary distribution ''μ'' on R''d''. * There exists a scalar potential Φ : R''d'' & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French National Centre For Scientific Research
The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 engineers and technical staff, and 7,085 contractual workers. It is headquartered in Paris and has administrative offices in Brussels, Beijing, Tokyo, Singapore, Washington, D.C., Bonn, Moscow, Tunis, Johannesburg, Santiago de Chile, Israel, and New Delhi. From 2009 to 2016, the CNRS was ranked No. 1 worldwide by the SCImago Institutions Rankings (SIR), an international ranking of research-focused institutions, including universities, national research centers, and companies such as Facebook or Google. The CNRS ranked No. 2 between 2017 and 2021, then No. 3 in 2022 in the same SIR, after the Chinese Academy of Sciences and before universities such as Harvard University, MIT, or Stanford ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aix-Marseille University
Aix-Marseille University (AMU; french: Aix-Marseille Université; formally incorporated as ''Université d'Aix-Marseille'') is a public research university located in the Provence region of southern France. It was founded in 1409 when Louis II of Anjou, Count of Provence, petitioned the Pisan Antipope Alexander V to establish the University of Provence, making it one of the oldest university-level institutions in France. The institution came into its current form following a reunification of the University of Provence, the University of the Mediterranean and Paul Cézanne University. The reunification became effective on 1 January 2012, resulting in the creation of the largest university in the French-speaking world, with about 80,000 students. AMU has the largest budget of any academic institution in the Francophone world, standing at €750 million. It is consistently ranked among the top 200 universities in the world and is ranked within the top 4 universities in France ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of The Mediterranean
The University of the Mediterranean Aix-Marseille II was a French university in the Academy of Aix and Marseille. Historically, it was part of the University of Aix-Marseille based across the communes of Aix-en-Provence and Marseille in southern France. It had 24,000 students. On 1 January 2012 it merged with the University of Provence and Paul Cézanne University to become Aix-Marseille University, the youngest, but also the largest in terms of students, budgets and staff in France. Academic programs The university is particularly strong in sciences with faculties for science ( Faculté des Sciences de Luminy), sport sciences (Faculté des Sciences du Sport), engineering ( École supérieure d'ingénieurs de Luminy) and economic science and management (Faculté des Sciences Économiques et de Gestion). The medical school comprises the faculties of Medicine, Pharmacy and Dentistry. In addition, there are a number of institutes: * Institut de Mécanique de Marseille (Institute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gay-Lussac Humboldt Prize
Joseph Louis Gay-Lussac (, , ; 6 December 1778 – 9 May 1850) was a French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen (with Alexander von Humboldt), for two laws related to gases, and for his work on alcohol–water mixtures, which led to the degrees Gay-Lussac used to measure alcoholic beverages in many countries. Biography Gay-Lussac was born at Saint-Léonard-de-Noblat in the present-day department of Haute-Vienne. The father of Joseph Louis Gay, Anthony Gay, son of a doctor, was a lawyer and prosecutor and worked as a judge in Noblat Bridge. Father of two sons and three daughters, he owned much of the Lussac village and usually added the name of this hamlet of the Haute-Vienne to his name, following a custom of the Ancien Régime. Towards the year 1803, father and son finally adopted the name Gay-Lussac. During the Revolution, on behalf of the Law of Suspects, his father, former king's atto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bonn
The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine University) on 18 October 1818 by Frederick William III, as the linear successor of the ( en, Academy of the Prince-elector of Cologne) which was founded in 1777. The University of Bonn offers many undergraduate and graduate programs in a range of subjects and has 544 professors. The University of Bonn is a member of the U15 (German universities), German U15 association of major research-intensive universities in Germany and has the title of "University of Excellence" under the German Universities Excellence Initiative; it is consistently ranked amongst the best German universities in the world rankings and is one of the most research intensive universities in Germany. Bonn has 6 Clusters of Excellence, the most of any German university; t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year or annus is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars. For the Gregorian calendar, the average length of the calendar year (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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