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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 winn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."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, . This number is often expressed as a percentage (%), ranging from 0% to 100%. 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 as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Physics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in a wide variety of fields such as biology, neuroscience, computer science, information theory and sociology. Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions. While classical thermodynamics is primarily concerned with thermodynamic equilibrium, statistical mechanics has been applied in non-equilibrium stat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hopfield Network
A Hopfield network (or associative memory) is a form of recurrent neural network, or a spin glass system, that can serve as a content-addressable memory. The Hopfield network, named for John Hopfield, consists of a single layer of neurons, where each neuron is connected to every other neuron except itself. These connections are bidirectional and symmetric, meaning the weight of the connection from neuron ''i'' to neuron ''j'' is the same as the weight from neuron ''j'' to neuron ''i''. Patterns are associatively recalled by fixing certain inputs, and dynamically evolve the network to minimize an energy function, towards local energy minimum states that correspond to stored patterns. Patterns are associatively learned (or "stored") by a Hebbian learning algorithm. One of the key features of Hopfield networks is their ability to recover complete patterns from partial or noisy inputs, making them robust in the face of incomplete or corrupted data. Their connection to statistical mech ... [...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. Thermodynamic quantities Critical energy per particle: h_c = \sqrt. Critical inverse temperature \beta_c = 2\sqrt. Partition function Z(\beta) = \sum_s e^, which at large N becomes 2^N \mathbb E_E ^/math> when \beta denotes the av ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metastability
In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's 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 to the system (unique "absolu ... [...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'' : Itō diffusion">, +∞) × 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'' → R su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French National Centre For Scientific Research
The French National Centre for Scientific Research (, , 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. Organization The CNRS operates on the basis of research units, which are of two kinds: "proper units" (UPRs) are operated solely by the CNRS, and Joint Research Unit, Joint Research Units (UMRs – ) are run in association with other institutions, such as List of colleges and universities in France, universities or INSERM. Members of Joint Research Units may be either CNRS researchers or university employees (Academic ranks in France, ''maîtres de conférences'' or ''professeurs''). Each ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aix-Marseille University
Aix-Marseille University (AMU; ; formally incorporated as ) is a Public university, public research university located in the Provence region of southern France. It was founded in 1409 when Louis II of Anjou, List of rulers of Provence, Count of Provence, petitioned the Council of Pisa, Pisan Antipope Alexander V to establish the University of Provence, making it one of the List of oldest universities in continuous operation, oldest university-level institutions in the Francophone world. 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 List of countries and territories where French is an official language, French-speaking world in terms of its student body, its faculty and staff, and its budget that currently stands at €750 million. The university is or ... [...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 List of public universities in France by academy#Academy of Aix and Marseille, 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. Academic programs The university was 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 comprised the faculties of Medicine, Pharmacy and Dentistry. In addition, there were a number of institutes: *Institut de Mécanique de Marseille (Institute of mechanics at Marseille) *École de Journalisme et de Communication (School of Journalism and Communications) *Institut universitair ... [...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 by volume (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. His father, 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 began to add the name of this hamlet to his name, following a custom of the Ancien Régime. Towards the year 1803, father and son formally adopted the name Gay-Lussac. During the Revolution, under the Law of Suspects, his father, former king's attorney, was imprisoned in Saint Léo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bonn
The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick William III, as the linear successor of the () 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. Bonn has 6 Clusters of Excellence, the most of any German university; the Hausdorff Center for Mathematics, the Matter and Light for Quantum Computing cluster, Bonn Center for Dependency and Slavery Studies, PhenoRob: Research for the Future of Crop Production, the Immune Sensory System cluster, and ECONtribute: M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year is a unit of time based on how long it takes the Earth to orbit the Sun. In scientific use, the tropical year (approximately 365 solar days, 5 hours, 48 minutes, 45 seconds) and the sidereal year (about 20 minutes longer) are more exact. The modern calendar year, as reckoned according to the Gregorian calendar, approximates the tropical year by using a system of leap years. The term 'year' is also used to indicate other periods of roughly similar duration, such as the lunar year (a roughly 354-day cycle of twelve of the Moon's phasessee lunar calendar), as well as periods loosely associated with the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
