Stochastic tunneling STUN is an approach to global optimization based on the Monte Carlo method Sampling signal processing sampling of the function to be minimized. Idea image stun.jpg thumb 400px Schematic one dimensional test function black and STUN effective potential red & blue , where the minimum indicated by the arrows is the best minimum found so far. All Potential well well s that lie above the best minimum found are suppressed. If the dynamical process can escape the well around the current minimum estimate it will not be trapped by other local minima that are higher. Wells with deeper minima are enhanced. The dynamical process is accelerated by that. Monte Carlo method based optimization techniques sample the objective function by randomly hopping from the current solution vector to another with a difference in the function value of math Delta E math . The acceptance probability of such a trial jump is in most cases chosen to be math min left 1 exp left beta cdot Delta E right right math Nicholas Metropolis Metropolis criterion with an appropriate parameter math beta math . The general idea of STUN is to circumvent the slow dynamics of ill shaped energy functions that one encounters for example in spin glass es by tunneling through such barriers. This goal is achieved by Monte Carlo sampling of a transformed function that lacks this slow dynamics. In the standard form the transformation reads math f STUN 1 exp left gamma cdot left f x f o right right math where math f o math is the lowest function value found so far. This transformation preserves the Locus mathematics ... author K. Hamacher title Adaptation in Stochastic Tunneling Global Optimization of Complex Potential ... i2006 10058 0 Cite journal author K. Hamacher and W. Wenzel title The Scaling Behaviour of Stochastic ... title A Stochastic tunneling approach for global minimization journal Phys. Rev. Lett. volume 82 issue .....21.1087M Category Stochastic optimization de Stochastisches Tunneln ... more details
Infobox equilibrium name Epsilon equilibrium supersetof Nash Equilibrium usedfor stochastic game s In game theory , an epsilon equilibrium , or near Nash equilibrium, is a strategy profile that approximately satisfies the condition of Nash equilibrium . Definition Given a game and a real non negative parameter , a strategy profile is said to be an equilibrium if it is not possible for any player to gain more than in expected payoff by unilaterally deviating from his strategy Citation needed date March 2012 . Every Nash Equilibrium is equivalent to a equilibrium where 0. Formally, let math G N,A A 1 times cdots times A N, u A rightarrow reals N math be a N player game with action sets math A i math for each player and utility function u. A vector of strategies math sigma in Delta Delta 1 times cdots times Delta N math is an math epsilon math Nash Equilibrium for G if math u i sigma geq u i sigma i , sigma i epsilon math for all math sigma i in Delta i, i in N math Example The notion of equilibria is important in the theory of stochastic game s of potentially infinite duration. There are simple examples of stochastic games with no Nash equilibrium but with an equilibrium for any strictly bigger than 0. Perhaps the simplest such example is the following variant of Matching Pennies , suggested by Everett. Player 1 hides a penny and Player 2 must guess if it is heads up or tails up. If Player 2 guesses correctly, he wins the penny from Player 1 and the game ends. If Player 2 incorrectly guesses that the penny is heads up, the game ends with payoff zero to both players ... from previous stages is an equilibrium for the game. The expected payoff of Player 2 ... 2 that can guarantee an expected payoff of exactly 1. Therefore, the game has no Nash equilibrium ... prisoner s dilemma for T periods, where the payoff is averaged over the T periods. The only Nash equilibrium ..., 23 , 225 237, 1981. Game theory DEFAULTSORT Epsilon Equilibrium Category Game theory he ... more details
A population is in Malthusian equilibrium when all of its Production, costs, and pricing production is used only for subsistence . Malthusian equilibrium is a stability theory locally stable and a dynamicequilibrium . See also Thomas Malthus &mdash See this article for further exposition. An Essay on the Principle of Population Malthusian growth model Malthusian trap Population dynamics References Citation last Pingle first Mark title Introducing Dynamic Analysis Using Malthus s Principle of Population journal Journal of Economic Education date Winter 2003 volume 34 pages 3&ndash 20 issue 1 doi 10.1080 00220480309595196 Category Population Category Demography Category Mathematical modeling economics stub ... more details
In sociology , a system is said to be social equilibrium when there is a dynamic working balance among its interdependent parts Davis & Newstrom Clarify date January 2012 , 1985 . Each subsystem will adjust to any change in the other subsystems and will continue to do so until an equilibrium is retained. The process of achieving equilibrium will only work if the changes happen slowly, but for rapid changes it would throw the social system into wikt chaos chaos , unless and until a new equilibrium can be reached. References Gilboa, Itzhak & Matsui, Akihiko, 1991. http ideas.repec.org a ecm emetrp v59y1991i3p859 67.html Social Stability and Equilibrium , Econometrica , Econometric Society , vol. 59 3 , pages 859 67, May. Further reading Batchelor, George, Social Equilibrium and Other Problems Ethical and Religious , G. H. Ellis, 1887 Canning, David, http econpapers.repec.org paper fthcambri 150.htm Social Equilibrium , Working Papers from Cambridge Risk, Information & Quantity Signals, 1990 de C rdoba, Gonzalo Fern ndez, http www.ingentaconnect.com content els 01651765 1997 00000055 00000003 art00093 On the existence of a beliefs social equilibrium , Economics Letters , Volume 55, Issue 3, 12 September 1997, Pages 431 433 See also Open Society Category Sociodynamics sociology stub ... more details
Refimprove date December 2009 Stochastic cooling is a form of particle beam cooling . It is used in some particle accelerator s and storage ring s to control the Beam emittance emittance of the particle beam s in the machine. This process uses the Signal electrical engineering electrical signals that the individual charged particle s generate in a feedback loop to reduce the tendency of individual particles to move away from the other particles in the beam. It is accurate to think of this as thermodynamic cooling, or the reduction of entropy , in much the same way that a refrigerator or an air conditioner cools its contents. The technique was invented and applied at the Intersecting Storage Rings , ref name overview Citation arxiv physics 0308044 title Stochastic Cooling Overview author John Marriner arxiv physics.acc ph 0308044 doi 10.1016 j.nima.2004.06.025 date 2003 08 11 journal Nuclear Instruments and Methods A volume 532 issue 1 2 pages 11 18 bibcode 2004NIMPA.532...11M ref and later the Super Proton Synchrotron , at CERN in Geneva, Switzerland by Simon van der Meer , ref http www.nytimes.com ... National Accelerator Laboratory continues to use stochastic cooling in its antiproton source. The accumulated ... Detector at Fermilab CDF and the D0 experiment . Stochastic cooling in the Tevatron at Fermilab ... RHIC . Technical details This section needs to be edited for clarity by a stochastic cooling expert. Stochastic cooling uses the electrical signals produced by individual particles in a group of particles ... on the depth of the cooling that is required. Stochastic cooling is used to reduce the transverse ... spread of each bunch is not affected by this damping. The key to stochastic cooling is to address individual ... and gets smaller. The word stochastic in the title stems from the fact that usually only some of the particles ..., in general, has to wait until the bunch returns to make the correction. The detector and the kicker ... reflist Accelerator stub DEFAULTSORT Stochastic Cooling Category Accelerator physics de Stochastische ... more details
otheruses4 journal named after the subject matter the article regarding the models themselves stochastic processes Infobox journal title Stochastic Models cover discipline Stochastic calculus Stochastic models formernames Communications in Statistics. Stochastic Models editor Peter Taylor publisher Taylor & Francis country abbreviation Stoch. Model. history 1985 present frequency Quarterly openaccess impact 0.449 impact year 2010 website http www.tandf.co.uk journals LSTM link1 http www.tandfonline.com toc lstm20 current link1 name Online access link2 http www.tandfonline.com loi lstm20 link2 name Online archive ISSN 1532 6349 eISSN 1532 4214 LCCN 00212884 OCLC 48483352 JSTOR CODEN SMTOBE Stochastic Models is a peer review peer reviewed scientific journal that publishes papers on stochastic process stochastic models . It is published by Taylor & Francis . It was established in 1985 under the title Communications in Statistics. Stochastic Models and obtained its current name in 2001. According to the Journal Citation Reports , the journal has a 2010 impact factor of 0.449. ref name WoS cite book year 2011 chapter Stochastic Models title 2010 Journal Citation Reports publisher Thomson Reuters edition Science accessdate 2011 11 30 work Web of Science postscript . ref The founding editor in chief was Marcel Neuts Marcel F. Neuts , ref cite doi 10.1109 90.298435 ref the current editor is Peter Taylor University of Melbourne . References Reflist External links Official website http www.tandf.co.uk journals LSTM Category Taylor & Francis academic journals Category Publications established in 1985 Category Quarterly journals Category Mathematics journals Category English language journals ... more details
Primary sources date January 2012 relies entirely on Collani and Wurzburg affiliates Stochastic thinking may be looked upon as the opposite of causal thinking , however, the term stochastic thinking is rather ambiguous, because the meaning of stochastics is not clear. It can be looked upon as a branch of mathematics, or as a cocktail of statistical ideas and probabilistic ideas , ref Andreas Eichler, Maria Gabriella Ottaviani, Floriane Wozniak and Dave Pratt, Introduction on Stochastic Thinking , Proceedings of CERME 6, January 28th February 1st 2009, Lyon France INRP 2010, http www.inrp.fr publications ... . Here stochastic thinking is explained in the sense of Bernoulli Stochastics. ref Elart von ... solving by stochastic thinking Stochastic thinking for problem solving proceeds in three steps Stochastic thinking as basis for making decisions starts with observing an effect or problem which ... the Promising Alternative. ref The second step in stochastic thinking consists of identifying ... the relation between past and future which are to be changed. The third step of stochastic thinking is to verify that the system changes are effective. The main difference between stochastic thinking and the prevailing causal thinking is the focus Stochastic thinking focus on improving the whole, while causal thinking focus on improving parts. Stochastic thinking means to think in sets and structures ... of the occurrence of problems. Effect of stochastic thinking Stochastic thinking focus ... words stochastic thinking results in a continual examination and improvement of the whole to prevent the recurrence of problems. Thus, stochastic thinking results in proactive strategies in contrast ... by a Bernoulli space which represents the basis for stochastic thinking. The Bernoulli space shows ... Stochastic thinking is oriented towards long term effects by means of continual improvement of the system ..., http www.stochastikon.com Categories Category Stochastic processes ... more details
Technical date September 2011 Stochastic resonance SR is a phenomenon that occurs in a threshold measurement ... non zero level of stochastic input noise thereby lowering the response threshold ref name MossReview cite journal author Moss F, Ward LM, Sannita WG title Stochastic resonance and sensory information ... resonate s at a particular noise level. Definition Stochastic resonance is observed when noise added ... ratio as a function of noise intensity shows a shape. Strictly speaking, stochastic resonance occurs ... wide band stochastic force noise . The system response is driven by the combination of the two ... switch rate induced by the sole noise the stochastic time scale . citation needed date December 2010 Thus the term stochastic resonance . Stochastic resonance was discovered and proposed for the first ... author Benzi R, Parisi G, Sutera A, Vulpiani A title Stochastic resonance in climatic ... has been applied in a wide variety of systems. Nowadays stochastic resonance is commonly invoked when ... stochastic resonance Suprathreshold stochastic resonance is a particular form of stochastic resonance ... systems where stochastic resonance occurs, suprathreshold stochastic resonance occurs not only ..., hence the qualifier, suprathreshold, in suprathreshold stochastic resonance. Neuroscience psychology and biology Main Stochastic resonance sensory neurobiology Stochastic resonance has been observed ... title Neural synchrony in stochastic resonance, attention, and consciousness journal Can J Exp Psychol ... Gammaitoni L, H nggi P, Jung P, Marchesoni F title Stochastic resonance journal Review of Modern Physics ... overview of stochastic resonance. Signal analysis A related phenomenon is dither ing applied to analog ... Gammaitoni L title Stochastic resonance and the dithering effect in threshold physical systems journal ... SR and dithering p4691 1.pdf doi 10.1103 PhysRevE.52.4691 bibcode 1995PhRvE..52.4691G ref Stochastic ... C title Measurement of weak transmittances by stochastic resonance journal Optics Letters volume ... more details
of consumer s are constant. This makes analysis much simpler than in a generalequilibrium model which includes an entire economy. Here the dynamic process is that prices adjust until supply equals demand. It is a powerfully simple technique that allows one to study economic equilibriumequilibrium ... of the three rectangles. ref name Suranovic Difference between Partial and GeneralEquilibrium class wikitable collapsible Partial EquilibriumGeneralEquilibrium Developed by Alfred Marshall ...Economics sidebar Partial equilibrium is a condition of economic equilibrium which takes into consideration only a part of the market, ceteris paribus , to attain equilibrium. As defined by George Stigler , A partial equilibrium is one which is based on only a restricted range of data, a standard example ... model is a partial equilibrium model where the clearance on the market of some specific good economics ... which, while seemingly precise, do not effectively model real world economic phenomena. Partial equilibrium analysis examines the effects of policy action in creating equilibrium only in that particular ... in constricted markets. L on Walras first formalized the idea of a one period economic equilibrium of the general economic system, but it was French economist Antoine Augustin Cournot and English ... equilibrium discusses, when does an individual, a firm , an industry , factors of production attain their equilibrium points A consumer is in a state of equilibrium when he achieves maximum aggregate ... and preferences, income, price and supply of the commodity etc. Producers equilibrium occurs when he maximizes his net profit subject to a given set of economic situations. A firm s equilibrium point ... Cost and in long run LMC MR AR LAC at its minimum are the conditions of equilibrium. ref cite book ... profit and has no intension to leave the industry . 4. Equilibrium for an industry happens when there is normal ..., i.e. land, Labor economics labor , capital and entrepreneurs are in equilibrium when they are paid ... more details
Solubility equilibrium is a type of dynamicequilibrium . It exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged .... Definitions A solubility equilibrium exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The equilibrium is an example of dynamicequilibrium ... or alkali. Each type of equilibrium is characterized by a temperature dependent equilibrium constant ... another. When equilibrium is established, the solution is said to be saturated. The concentration of the solute ... . A supersaturated solution may be induced to come to equilibrium by the addition .... This is characteristic of salts . The equilibrium constant is known in this case as a solubility ... s or weak base s in aqueous media of varying pH . In each case an equilibrium constant can be specified as a quotient of activity chemistry activities . This equilibrium constant is dimensionless as activity is a dimensionless quantity. However, use of activities is very inconvenient, so the equilibrium ... of concentrations. See equilibrium chemistry Equilibrium constant for details. Moreover, the concentration of solvent is usually taken to be constant and so is also subsumed into the equilibrium constant. For these reasons, the constant for a solubility equilibrium has dimensions related to the scale ... enters a true equilibrium. Particle size effect The thermodynamic solubility constant is defined for large ... strength of the solution and hence on activity coefficient s, so that the equilibrium constant, expressed ... water than cool water. It occurs because solubility constants, like other types of equilibrium constants ... temperature. ref name pauling450 Pauling, Linus General Chemistry , Dover Publishing, 1970, p 450 ref ... as an equilibrium between the substance in its solid and dissolved forms. For example, when ... C 12 H 22 O 11 aq math . An equilibrium expression for this reaction can be written, as for any ... more details
of the reactant and product. This process is called dynamicequilibrium . ref name aj ref GoldBookRef title chemical equilibrium file C01023 ref Introduction File Burette.svg thumb right 100px A burette , an apparatus for carrying out e.g. acid base titration , is an important part of equilibrium chemistry. The concept of chemical equilibrium was developed after Berthollet 1803 found .... This is an example of dynamicequilibrium . Equilibria, like the rest of thermodynamics, are statistical ... of the behavior of an equilibrium system when changes to its reaction conditions occur. If a dynamic ... ref In general an equilibrium system is defined by writing an equilibrium equation for the reaction .... It is also general practice to use the term equilibrium constant instead of the more accurate concentration ... Applying the general formula for an equilibrium constant to the specific case of acetic acid one obtains ... approaches to the general calculation of the composition of a mixture at equilibrium. The most basic ...Refimprove date March 2009 In a chemical reaction , chemical equilibrium is the state in which both reactants ... at equilibrium, the reaction rate rates of the forward and backward reverse reactions are equal. In the following chemical equation with arrows pointing both ways to indicate equilibrium, A and B are reactant ... A beta B rightleftharpoons sigma S tau T math The equilibrium position of a reaction is said to lie far to the right if, at equilibrium, nearly all the reactants are consumed. Conversely the equilibrium ... sub sub and k sub sub are rate constant s. Since at equilibrium forward and backward rates are equal ... of the rate constants is also a constant, now known as an equilibrium constant . math K frac k k ... state and is not valid in general because reaction rate Rate equation rate equations do not, in general ... conditions necessary condition for chemical equilibrium, though it is not Necessary and sufficient conditions sufficient to explain why equilibrium occurs. Despite the failure of this derivation ... more details
In probability theory , stochastic drift is the change of the average value of a stochastic process stochastic random process . A related term is the drift rate which is the rate at which the average changes. This is in contrast to the random fluctuations about this average value. For example, the process which counts the number of heads in a series of math n math coin toss es has a drift rate of 1 2 per toss. Stochastic drifts in population studies Longitudinal studies of secular events are frequently conceptualized as consisting of a trend component fitted by a polynomial , a cyclical component often fitted by an analysis based on autocorrelation s or on a Fourier series , and a random component stochastic drift to be removed. In the course of the time series analysis , identification of cyclical and stochastic drift components is often attempted by alternating autocorrelation analysis and differencing of the trend. Autocorrelation analysis helps to identify the correct phase of the fitted model while the successive differencing transforms the stochastic drift component into white noise . Stochastic drift can also occur in population genetics where it is known as Genetic drift . A finite population of randomly reproducing organisms would experience changes from generation to generation in the frequencies of the different genotypes. This may lead to the fixation of one of the genotypes, and even the emergence of a speciation new species . In sufficiently small populations, drift can also neutralize the effect of deterministic natural selection on the population. Stochastic ... variable. In this case the stochastic drift can be removed from the data by regressing math y t math ... where math u t math is a zero long run mean stationary random variable here c is a non stochastic ... any stochastic change to the price level permanently affects the expected values of the price level ... analysis Category Stochastic processes Category Economics Category Finance ... more details
about iterative method s the modeling and optimization of decisions under uncertainty stochastic programming Stochastic optimization SO methods are optimization mathematics optimization iterative method method s that generate and use random variable s. For stochastic problems, the random variables appear ... s or random constraints, for example. Stochastic optimization methods also include methods with random iterates. Some stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. ref name spall2003 Cite book author Spall, J. C. title Introduction to Stochastic Search and Optimization year 2003 publisher Wiley url http www.jhuapl.edu ISSO isbn 0471330523 ref Stochastic optimization methods generalize deterministic system mathematics deterministic methods for deterministic problems. Methods for stochastic functions Partly random ... decisions about the next steps. Methods of this class include stochastic approximation SA , by Herbert ..., S. title A Stochastic Approximation Method journal Annals of Mathematical Statistics year 1951 volume 22 pages 400 407 doi 10.1214 aoms 1177729586 issue 3 ref stochastic gradient descent inventor and reference needed finite difference stochastic approximation finite difference SA by Kiefer and Wolfowitz ... J. Wolfowitz title Stochastic Estimation of the Maximum of a Regression Function journal Annals ... ref simultaneous perturbation stochastic approximation simultaneous perturbation SA by Spall 1992 ref name spall1992 cite journal author Spall, J. C. title Multivariate Stochastic Approximation Using ... ref Holger H. Hoos and Thomas St tzle, http www.sls book.net Stochastic Local Search Foundations and Applications ... performance uniformly across many data sets, for many sorts of problems. Stochastic optimization ... Random Search year 1991 publisher Kluwer Academic isbn 0792311221 ref stochastic tunneling ref name wenz1999 cite journal author W. Wenzel coauthors K. Hamacher title Stochastic tunneling approach ... more details
. When the pressing force is removed the spring attains its original state. See also Dynamicequilibrium ...Image Stable unstable pendulum.svg right thumb A pendulum in a stable equilibrium left and unstable equilibrium right A standard definition of static equilibrium is A system of particles is in static equilibrium ... Corben & Philip Stehle url http books.google.com ?id 1gxk4oq9trYC&pg PA113&dq 22static equilibrium ... ref This is a strict definition, and often the term static equilibrium is used in a more relaxed manner interchangeably with mechanical equilibrium , as defined next. ref name Rao cite book title Engineering ...&pg PA90&dq 22static equilibrium 22 PPA6,M1 page 6 year 2004 ref A standard definition of mechanical equilibrium for a particle is The necessary and sufficient conditions for a particle to be in mechanical equilibrium is that the net force acting upon the particle is zero. ref name Synge cite book ... year 1949 page 45 46 ref The necessary conditions for mechanical equilibrium for a system of particles ... conditions become A rigid body is in mechanical equilibrium when the sum of all force physics forces ... is zero. ref http physics.tamuk.edu suson html 2325 MechanicalEquilibrium.html Mechanical Equilibrium ... body in mechanical equilibrium is undergoing neither linear nor rotational acceleration however ... gives no information as to one of the most important and interesting aspects of equilibrium states &ndash their Stability theory stability . An alternative definition of equilibrium that applies to conservative ... 201 02918 9 ref A system is in mechanical equilibrium if its position in configuration space is a point ... about the stability of the equilibrium state. For example, from elementary calculus , we know ... to the stability of the equilibrium state are as follows File vratka rovnovazna poloha.svg thumb This is an unstable equilibrium. Second derivative < 0 The potential energy is at a local maximum, which means that the system is in an unstable equilibrium state. If the system is displaced ... more details
Other uses Dominance disambiguation Dominance Stochastic dominance ref Hadar and Russell, Rules for Ordering ... is a form of stochastic ordering . The term is used in decision theory and decision analysis to refer ... aversion is a factor only in second order stochastic dominance. Stochastic dominance does not give a order .... A related concept not included under stochastic dominance is deterministic dominance , which ... outcome of gamble B. Statewise dominance The simplest case of stochastic dominance is statewise dominance ... dominant gamble. First order stochastic dominance Statewise dominance is a special case of the canonical first order stochastic dominance , defined as follows gamble A has first order stochastic dominance ... toss outcome by value won, but gamble C has first order stochastic dominance over B without statewise ... to stochastic dominance simply by comparing the means of their probability distributions. Every ... will prefer gamble A over gamble B if A first order stochastically dominates B. First order stochastic ..., pushing some of the probability mass to the left. Second order stochastic dominance The other commonly used type of stochastic dominance is second order stochastic dominance . Roughly speaking, for two gambles A and B, gamble A has second order stochastic dominance over gamble B if the former is more ... for all nondecreasing and concave utility functions math U math . Second order stochastic dominance ... to the fixed number 0 , then B is a mean preserving spread of A. Second order stochastic dominance ... other portfolio. See modern portfolio theory and marginal conditional stochastic dominance . Sufficient conditions for second order stochastic dominance First order stochastic dominance is a sufficient condition. Necessary conditions for second order stochastic dominance math E A x geq E B x math ... order stochastic dominance Let math F A math and math F B math be the cumulative distribution functions ... a positive third derivative throughout . Sufficient condition for third order stochastic dominance ... more details
In probability theory and statistics , a stochastic order quantifies the concept of one random variable being bigger than another. These are usually partial order s, so that one random variable math A math may be neither stochastically greater than, less than nor equal to another random variable math B math . Many different orders exist, which have different applications. Usual stochastic order A real random variable math A math is less than a random variable math B math in the usual stochastic order if math Pr A x le Pr B x text for all x in infty, infty , math where math Pr cdot math denotes the probability of an event. This is sometimes denoted math A preceq B math or math A le st B math . If additionally math Pr A x Pr B x math for some math x math , then math A math is stochastically strictly ... in distribution. Stochastic dominance Stochastic dominance ref http www.mcgill.ca files economics stochasticdominance.pdf ref is a stochastic ordering used in decision theory . Several orders of stochastic dominance are defined. Zeroth order stochastic dominance consists of simple inequality math A preceq 0 B math if math A le B math for all state of nature states of nature . First order stochastic dominance is equivalent to the usual stochastic order above. Higher order stochastic dominance is defined in terms of integrals of the distribution function . Lower order stochastic dominance implies higher order stochastic dominance. Multivariate stochastic order Empty section date July 2010 Other stochastic orders Hazard rate order The hazard rate of a non negative random variable math X math ... are. This is captured to a limited extent by the variance , but more fully by a range of stochastic .... The converse is not true. See also Stochastic dominance References refimprove date February 2012 M. Shaked and J. G. Shanthikumar, Stochastic Orders and their Applications , Associated Press, 1994. E ... 419, 1955. reflist DEFAULTSORT Stochastic Ordering Category Theory of probability distributions de ... more details
, chromatography and redox equilibria. Thermodynamic equilibrium main dynamicequilibrium thermodynamic equilibrium A chemical system is said to be in equilibrium when the quantities of the chemical entities ... way so that the macroscopic quantities do not change. Chemical equilibrium is a dynamic state ... equilibrium can be written as ref group note The general expression is not used much in chemistry ... on the analytical concentrations and equilibrium constants. A general computational procedure has ... of concentrations. The equilibrium potential for a general redox half reaction See Equilibrium ...Equilibrium chemistry is a concerned with systems in chemical equilibrium . The unifying principle is that the thermodynamic free energy free energy of a system at equilibrium is the minimum possible, so ... last Denbeigh first K title The principles of chemical equilibrium publisher Cambridge University Press ... first N. title Physical and Chemical Equilibrium for Chemical Engineers year 2002 isbn 978 0 471 07170 9 ref This principle, applied to mixtures at equilibrium provides a definition of an equilibrium ... a system in chemical equilibrium is in a stable state. The system at chemical equilibrium ... or volume constitutes an external influence and the equilibrium quantities will change as a result ... equilibrium can be expressed symbolically as reactant s eqm product s The sign eqm means are in equilibrium ... is constant. Thus, equilibrium sign eqm symbolizes the fact that reactions occur in both ... 250px right A Steady state chemistry steady state , on the other hand, is not necessarily an equilibrium ... equilibrium because the decay process occurs in one direction only. Thermodynamic equilibrium is characterized by the free energy for the whole closed system being a minimum. For systems ... positive. ref Atkins, p 149 ref ref cite journal last Schultz first M.J. year 1999 title Why Equilibrium ... value. math delta G r left frac partial G partial xi right T,P delta G r Eq 0 math Equilibrium constant ... more details
Quantum mechanics cTopic Interpretation of quantum mechanics Interpretations The stochastic interpretation is an interpretation of quantum mechanics . The modern application of stochastics to quantum mechanics involves the assumption of spacetime stochasticity , the idea that the small scale structure of spacetime is undergoing both metric and topological fluctuations John Archibald Wheeler s quantum foam , and that the averaged result of these fluctuations recreates a more conventional looking metric at larger scales that can be described using classical physics, along with an element of nonlocality that can be described using quantum mechanics. A stochastic interpretation of quantum mechanics due to persistent vacuum fluctuations is suggested by Roumen Tsekov. The main idea is that vacuum or spacetime fluctuations are the reason for quantum mechanics and not a result of it how it is usually considered. See also Quantum foam Interpretation of quantum mechanics Interpretations of quantum mechanics References cite journal author Edward Nelson title Derivation of the Schr dinger Equation from Newtonian Mechanics journal Physical Review volume 150 page 1079 1085 year 1966 bibcode 1966PhRv..150.1079N doi 10.1103 PhysRev.150.1079 cite book author Khavtain Namsrai title Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics publisher Springer year 1985 isbn 9027720010 cite journal author Roumen Tsekov title Dissipative and Quantum Mechanics journal New Adv. Phys. volume 3 page 35 44 year 2009 Category Interpretations of quantum mechanics quantum stub ... more details
Hatnote See also Volatility finance . Stochastic Volatility finance volatility models are used in the field of mathematical finance to evaluate derivative finance derivative securities , such as option finance options . The name derives from the models treatment of the underlying security s volatility ... process itself, among others. Stochastic volatility models are one approach to resolve a shortcoming ... price is a stochastic process rather than a constant, it becomes possible to model derivatives more ... Wiener process with zero mean and unit rate of variance . The explicit solution of this stochastic differential ... stochastic volatility models such as Black Scholes and Cox Ross Rubinstein . For a stochastic volatility ... between volatility and price, introducing stochastic volatility math dS t mu S t d t sigma S t gamma ... 1 math . Some argue that because the CEV model does not incorporate its own stochastic process for volatility, it is not truly a stochastic volatility model. Instead, they call it a local volatility model. SABR volatility model Main SABR Volatility Model The SABR model Stochastic Alpha, Beta, Rho ... or equity under stochastic volatility math sigma math math dF t sigma t F beta t , dW t, math math ... model for estimating stochastic volatility. It assumes that the randomness of the variance process ..., mean reverting and volatility of variance parameters, are stochastic quantities given by math theta ... developed the first stochastic mean and stochastic volatility model, Chen model . Specifically, the dynamics of the instantaneous interest rate are given by following the stochastic differential ... and ambiguity Black Scholes References http www.wilmott.com detail.cfm?articleID 245 Stochastic Volatility ... Heston original.pdf A closed form solution for options with stochastic volatility , SL Heston, 1993 ... of Stochastic Volatility Models , Kilin, Fiodar 2006 . cite book title Stochastic Mean and Stochastic Volatility A Three Factor Model of the Term Structure of Interest Rates and Its Application ... more details
A stochastic grammar statistical grammar is a grammar framework with a probabilistic notion of grammaticality Stochastic context free grammar Statistical parsing Data oriented parsing Hidden Markov model Estimation theory Statistical natural language processing uses stochastic , probabilistic and statistical methods, especially to resolve difficulties that arise because longer sentences are highly ambiguous when processed with realistic grammars, yielding thousands or millions of possible analyses. Methods for disambiguation often involve the use of corpus linguistics corpora and Markov model s. A probabilistic model consists of a non probabilistic model plus some numerical quantities it is not true that probabilistic models are inherently simpler or less structural than non probabilistic models. ref John Goldsmith. 2002. Probabilistic Models of Grammar Phonology as Information Minimization. Phonological Studies 5 21&ndash 46. ref The technology for statistical NLP comes mainly from machine learning and data mining , both of which are fields of artificial intelligence that involve learning from data. See also Colorless green ideas sleep furiously Computational linguistics Refimprove date March 2011 More footnotes date March 2011 References references Further reading Christopher D. Manning, Hinrich Sch tze Foundations of Statistical Natural Language Processing , MIT Press 1999 , ISBN 978 0262133609. Stefan Wermter, Ellen Riloff, Gabriele Scheler eds. Connectionist, Statistical and Symbolic Approaches to Learning for Natural Language Processing , Springer 1996 , ISBN 978 3540609254. Category Grammar frameworks Category Statistical natural language processing Category Probabilistic models ling stub nl Stochastische grammatica ... more details
In estimation theory in statistics , stochastic equicontinuity is a property of estimator s or of estimation procedures that is useful in dealing with their Asymptotic theory statistics asymptotic behviour as the amount of data increases. It is a version of equicontinuity used in the context of functions of random variables that is, random function s. The property relates to the rate of convergence of random variables convergence of sequences of random variables and requires that this rate is essentially the same within a region of the parameter space being considered. For instance, stochastic equicontinuity, along with other conditions, can be used to show uniform weak convergence, which can be used to prove the convergence of random variables convergence of extremum estimator s. ref Newey, Whitney K. 1991 Uniform Convergence in Probability and Stochastic Equicontinuity , Econometrica , 59 4 , 1161 1167 jstor 2938179 ref Definition Let math H n theta n geq 1 math be a family of random functions defined from math Theta rightarrow reals math , where math Theta math is any normed metric space. Here math H n theta math might represent a sequence of estimators applied to datasets of size n , given that the data arises from a population for which the parameter indexing the statistical model for the data is &theta . The randomness of the functions arises from the data generating process under which a set of observed data is considered to be a realisation of a probabilistic or statistical model. However, in math H n theta math , &theta relates to the model currently being postulated or fitted rather than to an underlying model which is supposed to represent the mechanism generating the data. Then math H n math is stochastically equicontinuous if, for every math epsilon 0 math , there is a math delta 0 math such that math lim n rightarrow infty Pr left sup theta in Theta sup theta in B theta, delta H n theta H n theta epsilon right delta . math Here B &theta , &delta represents ... more details
refimprove date March 2011 Stochastic screening or FM screening is a halftone process based on Pseudorandomness pseudo random distribution of halftone dots, using frequency modulation FM to change the density of dots according to the gray level desired. Traditional amplitude modulation halftone screening is based on a geometric and fixed spacing of dots, which vary in size depending on the tone color represented for example, from 10 to 200 micrometre s . The stochastic screening or FM screening instead uses a fixed size of dots for example, about 25 micrometres and a distribution density that varies depending on the color s tone. The technique of stochastic screening, which has existed since the seventies, Citation needed date March 2011 has had a revival in recent times thanks to increased use of Computer to plate computer to plate CTP techniques. In previous techniques, computer to film , during the exposure there could be a drastic variation in the quality of the plate. It was a very delicate and difficult procedure that was not much used. Today, with CTP during the creation of the plate you just need to check a few parameters on the density and tonal correction curve. When you make a plate with stochastic screening you must use a tone correction curve, this curve allows one to align the tone reproduction of an FM screen to that of an industry standard. Given the same final presswork tone value, an FM screen utilizes more halftone dots than an AM XM screen. The result is that more light is filtered by the ink and less light simply reflects off the surface of the substrate. The result is that FM screens exhibit a greater color gamut than conventional AM XM halftone screen frequencies. The creation of a plate with stochastic screening is done the same way as is done with an AM XM screen. A tone reproduction compensation curve is typically applied to align the stochastic screening to conventional AM FM tone reproductions targets e.g. ISO 12647 2 . Advantages The screening ... more details
Radner equilibrium is an economic concept defined by economist Roy Radner in the context of generalequilibrium . The concept is an extension of the Arrow Debreu equilibrium and the base for the first consistent incomplete markets framework. The departure from the Arrow Debreu framework are two fold 1 uncertainty is explicitly modelled through a tree structure or equivalent filtration rending passage of time and resolution of uncertainty explicit, 2 budget feasibility is no longer defined as affordability but through explicit trading of financial instruments. Financial instruments are used to allow insurance and inter temporal wealth transfers across spot markets at each nodes of the tree. Economic agents face a sequence of budget sets, one at each date state. Item 2 introduces the concept of incomplete markets, formulated in terms of net trade, the budget set is contained in a half space intersecting the positive cone of contingent goods at zero net trade only this is called absence of arbitrage . This is because without transaction cost agents will demand an infinite amount of any trade promising positive consumption in some state and no negative net trade against that in any other good and state. This half space, containing the budget set and separating it from the free lunch cone, corresponds to a half line of positive prices. However potentially if not enough instruments are present, the full half space may not be spanned by trading the instruments and the budgets set may be strictly smaller. In such a configuration markets are said to be incomplete, and there are several ways to separate the budget set from the positive cone sometimes called the free lunch cone . This means that several price systems become admissible. At a Radner equilibrium like the Arrow Debreu equilibrium under uncertainty, perfect consensual foresight is used. It is what is called a rational ... equilibrium econ stub Category Generalequilibrium and disequilibrium ... more details
In technical analysis of security finance securities trading, the stochastic Oscillator technical analysis oscillator is a momentum technical analysis momentum indicator that uses support and resistance levels. George Lane technical analysis Dr. George Lane promoted this indicator in the 1950s. The term stochastic refers to the location of a current price in relation to its price range over a period of time. ref Murphy, John J. 1999 . http stockcharts.com school doku.php?id chart school trading strategies john murphy s ten laws John Murphy s Ten Laws of Technical Trading . ref This method attempts to predict price turning points by comparing the closing price of a security to its price range. The indicator is defined as follows math K 100 frac text closing price text L text H text L , math where H and L are respectively the highest and the lowest price over the last math n math periods, and math D text 3 period exponential moving average of K. math In working with D it is important to remember that there is only one valid signal a divergence between D and the analyzed security. ref name Lane Lane, George M.D. May June 1984 Lane s Stochastics, second issue of Technical Analysis of Stocks ... of the recent range before turning points. The Stochastic oscillator is calculated Where ... analyst, is one of the first to publish on the use of stochastic oscillators to forecast prices ... prices will start to retreat from the upper boundaries of the range, causing the stochastic indicator ... John L year 2004 publisher Wiley location Hoboken, NJ isbn 0 471 58455 X pages 144 145 ref File Stochastic divergence.jpg thumb right 250px Stochastic divergence. An alert or set up is present when the D .... An event known as stochastic pop occurs when prices break out and keep going. This is interpreted ... links http www.investopedia.com terms s stochasticoscillator.asp Stochastic Oscillator at Investopedia technical analysis DEFAULTSORT Stochastic Oscillator Category Technical indicators ceb Osilador ... more details
Equilibrium temperature may refer to Thermal equilibrium , for questions of heat transfer. Gliese 581 g , for temperatures of extrasolar planets. disambig ... more details
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