on the stochastic pendulum with ornstein uhlenbeck noise we study a frictionless pendulum subject to multiplicative random noise because of destructive interference between the angular displacement of the system and the noise term the energy fluctuations are reduced when the noise has a non zero correlation time we derive the long time behaviour of the pendulum in the case of ornstein uhlenbeck noise by a recursive adiabatic elimination procedure an analytical expression for the asymptotic probability distribution function of the energy is obtained and the results agree with numerical simulations lastly we compare our method with other approximation schemes

geometrical treatment of systems driven by coloured noise the authors use geometrical methods and functional derivative techniques to analyse the stochastic behaviour of multidegree of freedom nonlinear systems driven by gaussian noises with arbitrary correlation functions the method has the advantage of being also applicable to systems with an infinite number of degrees of freedom partial differential equations with some kind of hamiltonian structure and gives some insight into the nature of the approximations that lead to some of the main effective fokker planck equations used in the literature

the projection approach to the fokker planck equation i colored gaussian noise it is shown that the fokker planck operator can be derived via a projection perturbation approach using the repartition of a more detailed operator into a perturbation 1 and an unperturbed part 0 the standard fokker planck structure is recovered at the second order in 1 whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure to get rid of these higher order terms a key approximation local linearization ll is made in general to evaluate at the second order in 1 the exact expression of the diffusion coefficient which simulates the influence of a gaussian noise with a finite correlation time a resummation up to infinite order in must be carried out leading to what other authors call the best fokker planck approximation bfpa it is shown that due to the role of terms of higher order in 1 the bfpa leads to predictions on the equilibrium distributions that are reliable only up to the first order in t the ll on the contrary in addition to making the influence of terms of higher order in 1 vanish results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the fox theory the corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady state distributions therefore over the whole range 0 the ll turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in 1 vanish in the short region the ll leads to results virtually coincident with those of the bfpa in the large region the ll is a more accurate approximation than the bfpa itself these theoretical arguments are supported by the results of both analog and digital simulation

external non white noise theory and experiment abstract we consider a system under the influence of an external gaussian noise with a flat spectrum and finite cut off frequency the stationery properties of the system are studied as a function of the correlation time of the noise theoretical predictions based on an expansion in powers of the correlation time are corroborated by experimental measurements on an electric circuit with a digital noise generator the two main qualitative properties experimentally observed which can not be explained in a white noise limit theory are i appearance of relative extrema of the stationery distribution for high noise intensity when the correlation time is not too small ii dependence on the noise characteristics of the position of the maximum of the stationary distribution for low noise intensity

anharmonic oscillator driven by additive ornstein uhlenbeck noise we present an analytical study of a nonlinear oscillator subject to an additive ornstein uhlenbeck noise known results are mainly perturbative and are restricted to the large dissipation limit obtained by neglecting the inertial term or to a quasi white noise i e a noise with vanishingly small correlation time here in contrast we study the small dissipation case we retain the inertial term and consider a noise with finite correlation time our analysis is non perturbative and based on a recursive adiabatic elimination scheme a reduced effective langevin dynamics for the slow action variable is obtained after averaging out the fast angular variable in the conservative case we show that the physical observables grow algebraically with time and calculate the associated anomalous scaling exponents and generalized diffusion constants in the case of small dissipation we derive an analytic expression of the stationary probability distribution function pdf which differs from the canonical boltzmann gibbs distribution our results are in excellent agreement with numerical simulations

brownian dynamics time averaging and colored noise we propose a method to obtain the equilibrium distribution for positions and velocities of a one dimensional particle via time averaging and laplace transformations we apply it to the case of a damped harmonic oscillator in contact with a thermal bath the present method allows us to treat among other cases a gaussian noise function exponentially correlated in time e g gaussian colored noise we obtain the exact equilibrium solution and study some of its properties

no hypersignaling principle a paramount topic in quantum foundations rooted in the study of the einstein podolsky rosen epr paradox and bell inequalities is that of characterizing quantum theory in terms of the spacelike correlations it allows here we show that to focus only on spacelike correlations is not enough we explicitly construct a toy model theory that while not contradicting classical and quantum theories at the level of spacelike correlations still displays an anomalous behavior in its timelike correlations we call this anomaly quantified in terms of a specific communication game the hypersignaling phenomena we hence conclude that the principle of quantumness if it exists cannot be found in spacelike correlations alone nontrivial constraints need to be imposed also on timelike correlations in order to exclude hypersignaling theories

influence of the noise spectrum on the anomalous diffusion in a stochastic system we use an effective markovian description to study the long time behavior of a nonlinear second order langevin equation with a gaussian noise when dissipation is neglected the energy of the system grows as with time a power law with an anomalous scaling exponent that depends both on the confining potential and on the high frequency distribution of the noise the asymptotic expression of the probability distribution function in phase space is calculated analytically the results are extended to the case where small dissipative effects are taken into account

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

nonlinear proximal point algorithms using bregman functions with applications to convex programming a bregman function is a strictly convex differentiable function that induces a well behaved distance measure or d function on euclidean space this paper shows that for every bregman function there exists a nonlinear version of the proximal point algorithm and presents an accompanying convergence theory applying this generalization of the proximal point algorithm to convex programming one obtains the d function proximal minimization algorithm of censor and zenios and a wide variety of new multiplier methods these multiplier methods are different from those studied by kort and bertsekas and include nonquadratic variations on the proximal method of multipliers

a study on the action of non gaussian noise on a brownian particle abstract we analytically address the non equilibrium problem of a brownian particle in contact with a thermal reservoir by means of a non gaussian langevin noise term t the presence of noise kurtosis is akin to a second temperature reservoir acting on the system and we exploit its consequences by means of studying a converging exact form for the stationary probability distribution

extension of statistical replacement to systems with time correlated fluctuations nonlinear systems with correlated stochastic parameters are approximated by simpler systems this method is an extension of an earlier version of statistical replacement and statistical linearization the extended method is applicable to systems with correlated fluctuations we show how this general method reduces to the earlier methods in special cases

approximation solvability of a class of nonlinear set valued variational inclusions involving a η monotone mappings abstract a new class of nonlinear set valued variational inclusions involving a monotone mappings in a hilbert space setting is introduced and then based on the generalized resolvent operator technique associated with a monotonicity the existence and approximation solvability of solutions using an iterative algorithm is investigated

on a new system of nonlinear a monotone multivalued variational inclusions in this paper we introduce and study a new system of nonlinear a monotone multivalued variational inclusions in hilbert spaces by using the concept and properties of a monotone mappings and the resolvent operator technique associated with a monotone mappings due to verma we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated with a monotone mappings in hilbert spaces we also prove the existence of solutions for the nonlinear multivalued variational inclusions and the convergence of iterative sequences generated by the algorithm our results improve and generalize many known corresponding results

bounding the set of quantum correlations we introduce a hierarchy of conditions necessarily satisfied by any distribution p ensuremath alpha ensuremath beta representing the probabilities for two separate observers to obtain outcomes ensuremath alpha and ensuremath beta when making local measurements on a shared quantum state each condition in this hierarchy is formulated as a semidefinite program among other applications our approach can be used to obtain upper bounds on the quantum violation of an arbitrary bell inequality it yields for instance tight bounds for the violations of the collins et al inequalities

random oscillator with general gaussian noise we study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density or power spectrum that decays as a power law at high frequencies when the dissipation is negligible physical observables such as the amplitude the velocity and the energy of the oscillator grow as power laws with time we calculate the associated scaling exponents and we show that their values depend on the asymptotic behaviour of the external potential and on the high frequencies of the noise our results are generalized to include dissipative effects and additive noise

reduction of overdamped stochastic processes in the coherent state representation the adiabatic elimination of fast variables from overdamped stochastic processes by functional integration is demonstrated adiabatic elimination entails the evaluation of a reduced evolution operator from the full evolution equation for fokker planck processes the reduced evolution operator may be expressed as a ground state expectation and it is shown how this is represented as a coherent state path integral the elimination is then achieved by functionally integrating out all reference to the fast variables the end result is a decoupling of the full evolution equation into separate equations for the fast and slow variables the method is demonstrated for brownian motion and for a system with multiplicative colored noise

the generalized wiener process ii finite systems a class of langevin like equations non markovian processes are studied in the presence of non natural boundary conditions exact results for all cumulants and the corresponding kolmogorov hierarchy of distributions are given in terms of our functional approach we previously reported 1997 j phys a math gen 30 8427 the generalized wiener processes on finite domains are completely characterized for reflecting and periodic boundary conditions some examples are given to show the behaviour of the moments and the probability distributions for different noises the interplay between the boundary conditions and the structure of the noises is also pointed out

temporal quantum correlations and leggett garg inequalities in multilevel systems we show that the quantum bound for temporal correlations in a leggett garg test analogous to the tsirelson bound for spatial correlations in a bell test strongly depends on the number of levels n that can be accessed by the measurement apparatus via projective measurements we provide exact bounds for small n that exceed the known bound for the leggett garg inequality and we show that in the limit n the leggett garg inequality can be violated up to its algebraic maximum

mixed equilibrium problems sensitivity analysis and algorithmic aspect abstract the aim of this paper is twofold first it is to extend the sensitivity analysis framework developed recently for variational inequalities to mixed equilibrium problems the second is to propose iterative methods for solving this kind of problems in the process we establish an equivalence between an extended version of wiener hopf equations and the given problems relying on a generalization of the yosida approximation notion our results generalize results obtained for optimization variational inequalities complementarity problems and problems of nash equilibria

theory of nonlinear langevin equation with quadratic noise a generalized langevin equation with a multiplicative linear and quadratic ornstein uhlenbeck stochastic noise is investigated an exact generalized fokker planck equation for this langevin equation is obtained this generalized fokker planck equation has the form of an integro differential equation an exact form of the integral kernel is given in terms of an operator valued matrix continued fraction in the limit of small fluctuations and short coherence time of the noise a standard fokker planck equation with drift and diffusion is derived in a systematic way

computing a non maxwellian velocity distribution from first principles we investigate a family of single particle anomalous velocity distribution by solving a particular class of stochastic liouville equations the stationary state is obtained analytically and the maxwell boltzmann distribution is reobtained in a particular limit we discuss the comparison with other different methods to obtain the stationary state extensions when the models cannot be solved in an exact way are also pointed out in connection with the one ficton approximation

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

a new system of variational inclusions with h η monotone operators in hilbert spaces in this paper we introduce and study a new system of variational inclusions involving h h monotone operators in hilbert space using the resolvent operator associated with h h monotone operators we prove the existence and uniqueness of solutions for this new system of variational inclusions we also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm

sequences of projective measurements in generalized probabilistic models we define a simple rule that allows us to describe sequences of projective measurements for a broad class of generalized probabilistic models this class embraces quantum mechanics and classical probability theory but for example also the hypothetical popescu rohrlich box for quantum mechanics the definition yields the established luders rule which is the standard rule for updating the quantum state after a measurement for the general case it can be seen as being the least disturbing or most coherent way of performing sequential measurements we show as an example that the spekkens toy model spekkens 2007 phys rev a 75 032110 provides an instance of our definition we also demonstrate the possibility of strong postquantum correlations as well as the existence of triple slit correlations for certain nonquantum toy models

a new method of analysis of the effect of weak colored noise in nonlinear dynamical systems a systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed it is based on the search of wkb solutions to the fokker planck equation for the joint probability density of the system and noise in which the perturbation expansion is continued to the first correction beyond the hamilton jacobi limit the method can be applied to noise with correlation time of order unity it is illustrated on the normal form of a pitchfork bifurcation where it is pointed out that additive noise can induce a shift of the most probable value this prediction is confirmed by numerical simulation of the stochastic differential equations

statistical replacement for systems with delta correlated fluctuations nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement this method is an extension of the previously developed agree which was restricted to systems with additive fluctuations statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable

applications of splitting algorithm to decomposition in convex programming and variational inequalities recently han and lou proposed a highly parallelizable decomposition algorithm for minimizing a strongly convex cost over the intersection of closed convex sets it is shown that their algorithm is in fact a special case of a splitting algorithm analyzed by gabay for finding a zero of the sum of two maximal monotone operators gabay s convergence analysis for the splitting algorithm is sharpened and new applications of this algorithm to variational inequalities convex programming and the solution of linear complementarily problems are proposed for convex programs with a certain separable structure a multiplier method that is closely related to the alternating direction method of multipliers of gabay mercier and of glowinski marrocco but which uses both ordinary and augmented lagrangians is obtained

functional characterization of generalized langevin equations we present an exact functional formalism to deal with linear langevin equations with arbitrary memory kernels and driven by an arbitrary noise structure characterized through its characteristic functional no other hypothesis is assumed over the noise neither do we use the fluctuation dissipation theorem we find that the characteristic functional of the linear process can be expressed in terms of noise functional and the green function of the deterministic memory like dissipative dynamics this yields a procedure for calculating the full kolmogorov hierarchy of the non markov process as examples we have characterized through the 1 time probability a noise induced interplay between the dissipative dynamics and the structure of different noises conditions that lead to non gaussian statistics and distributions with long tails are analysed the introduction of arbitrary fluctuations in fractional langevin equations has also been pointed out

how ψ epistemic models fail at explaining the indistinguishability of quantum states we study the extent to which epistemic models for quantum measurement statistics models where the quantum state does not have a real ontic status can explain the indistinguishability of nonorthogonal quantum states this is done by comparing the overlap of any two quantum states with the overlap of the corresponding classical probability distributions over ontic states in a epistemic model it is shown that in hilbert spaces of dimension d 4 the ratio between the classical and quantum overlaps in any epistemic model must be arbitrarily small for certain nonorthogonal states suggesting that such models are arbitrarily bad at explaining the indistinguishability of quantum states for dimensions d 3 and 4 we construct explicit states and measurements that can be used experimentally to put stringent bounds on the ratio of classical to quantum overlaps in epistemic models allowing one in particular to rule out maximally epistemic models more efficiently than previously proposed

smooth methods of multipliers for complementarity problems this paper describes several methods for solving nonlinear complementarity problems a general duality framework for pairs of monotone operators is developed and then applied to the monotone complementarity problem obtaining primal dual and primal dual formulations we derive bregman function based generalized proximal algorithms for each of these formulations generating three classes of complementarity algorithms the primal class is well known the dual class is new and constitutes a general collection of methods of multipliers or augmented lagrangian methods for complementarity problems in a special case it corresponds to a class of variational inequality algorithms proposed by gabay by appropriate choice of bregman function the augmented lagrangian subproblem in these methods can be made continuously differentiable the primal dual class of methods is entirely new and combines the best theoretical features of the primal and dual methods some preliminary computation shows that this class of algorithms is effective at solving many of the standard complementarity test problems

ordered cumulant technique and differential equations for probability density abstract this paper is concerned with stochastic differential equations of langevin type in which the stochastic forces are gaussian and not of white noise type the problem of finding explicitly the differential equation for the probability density of the process is solved by means of an expansion in the small correlation time of the noise for this purpose we will use the cumulant technique different situations are studied such as markovian or fokker planck equation first correction to the markovian approximation but with the fokker planck form and the corrections of non fokker planck form

is a time symmetric interpretation of quantum theory possible without retrocausality huw price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal i e it must involve influences that travel backwards in time one of price s assumptions is that the quantum state is a state of reality however one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no go theorems including recent proofs of the reality of the quantum state here we show that this assumption can be replaced by a different assumption called mediation that plausibly holds independently of the status of the quantum state we also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely we show that our assumptions imply a timelike analogue of bell s local causality criterion and in doing so give a new interpretation of timelike violations of bell inequalities namely they show the impossibility of a non retrocausal time symmetric ontology

effective potential and weak noise transitions we review the notion of effective potential for stochastic processes and discuss its possible applications we calculate this function up to first order in a parameter measuring the intensity of the noise for a general nonlinear system the result is applied exhibiting a transition induced by weak noise

geometrical derivation of the intrinsic fokker planck equation and its stationary distribution starting from an intrinsic langevin equation we give a geometrical derivation of the fokker planck equation we also present a method for obtaining a stationary distribution and for deriving potential conditions when the diffusion matrix is singular

harmonic potential driven by long range correlated noise the probability distribution of a particle in a quadratic potential driven by gaussian long range correlated noise has been obtained the long time asymptotic relaxation of the stochastic process has been characterized in terms of the long range correlated noise appearing in the corresponding stochastic differential equation defining the process the particular case when the particle is driven by a gaussian color noise has also been revisited in this way giving its exact probability distribution for all time by using a characteristic functional technique reported previously results for a non gaussian long range correlated noise are also shown emphasis has been placed on solving the plane rotator in the presence of arbitrary random torques having long range correlations in order to show strong and weak non markovian effects coming from different sources of noise the undamped free particle under the influence of arbitrary accelerations has been analyzed we also analyze in detail the structure of the trajectories of the overdamped and undamped free particle

a new approximate stationary probability distribution for processes driven by ornstein uhlenbeck noise a novel approximate probability distribution for a class of nonlinear processes driven by multiplicative linear ornstein uhlenbeck noise is presented a comparison is made with other approximate distributions reported in the literature

the generalized ornstein uhlenbeck process langevin like equations have been studied in the presence of arbitrary noise the characteristic functional of the generalized langevin process has been built up exact results for all cumulants are given particular stress has been put on the campbell dichotomous and radioactive decay noises transient relaxation susceptibility and diffusion constants for different noisy media have been sketched in order to exemplify the theory the generalized ornstein uhlenbeck and wiener processes have been completely characterized the generalized kubo oscillator has been worked out and all its 1 time moments have been calculated for different noise structures

linear convergence of epsilon subgradient descent methods for a class of convex functions this paper establishes a linear convergence rate for a class of epsilon subgradient descent methods for minimizing certain convex functions currently prominent methods belonging to this class include the resolvent proximal point method and the bundle method in proximal form considered as a sequence of serious steps other methods such as the recently proposed descent proximal level method may also fit this framework depending on implementation the convex functions covered by the analysis are those whose conjugates have subdifferentials that are locally upper lipschitzian at the origin a class introduced by zhang and treiman we argue that this class is a natural candidate for study in connection with minimization algorithms

a nonlinear oscillator with parametric coloured noise some analytical results the asymptotic behaviour of a nonlinear oscillator subject to a multiplicative ornstein uhlenbeck noise is investigated when the dynamics is expressed in terms of energy angle coordinates it is observed that the angle is a fast variable as compared to the energy thus an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out however the standard elimination procedure performed earlier for a gaussian white noise fails when the noise is coloured because of correlations between the noise and the fast angular variable we develop here a specific averaging scheme that retains these correlations this allows us to calculate the probability distribution function pdf of the system and to derive the behaviour of physical observables in the long time limit

finite correlation time effects in nonequilibrium phase transitions i dynamic equation and steady state properties abstract we determine an approximate renormalized equation of evolution for an arbitrary nonlinear single degree of freedom system externally driven by gaussian parametric fluctuations of finite correlation time the renormalization scheme used here gives a second order equation with a time and state dependent diffusion coefficient we are able to calculate the diffusion coefficient in closed form the steady state distribution can easily be obtained from the evolution equation we are thus able to determine the parameter dependence of the steady state distribution and in particular the influence of a correlation time of the fluctuations which does not vanish on the steady state distribution

levy noise levy flights levy fluctuations this paper is concerned with a levy noise characterized for t 0 by the functional with 0 2 then levy flights can be defined through a stochastic differential equations rather than the usual chapmann kolmogorov equation we have used this functional approach to solve a plane rotor in the presence of levy noise the linear damped stochastic process driven by levy noise is revisited and its non autonomous and non markovian generalizations have been solved in the context of our functional analysis

langevin like equation with colored noise consider a stochastic differential equation of the form of a langevin equation but in which the noise source is not white if it is nearly white i e its autocorrelation time is short a systematic approximation method is known it leads to a fokker planck equation with successive higher order corrections to obtain the coefficients more explicitly a secondary expansion may be employed the validity of the resulting double series approximation is discussed and confronted with the various results given in the literature in addition an alternative approximation method is obtained using the technique for eliminating fast variables it produces the same terms in a different sequence

inexact variants of the proximal point algorithm without monotonicity this paper studies convergence properties of inexact variants of the proximal point algorithm when applied to a certain class of nonmonotone mappings the presented algorithms allow for constant relative errors in the line of the recently proposed hybrid proximal extragradient algorithm the main convergence result extends a recent work of the second author where exact solutions for the proximal subproblems were required we also show that the linear convergence property is preserved in the case when the inverse of the operator is locally lipschitz continuous near the origin as an application we give a convergence analysis for an inexact version of the proximal method of multipliers for a rather general family of problems which includes variational inequalities and constrained optimization problems

forward and backward equations for a nonmarkovian process a cumulant approach abstract this paper deals with nonmarkovian processes induced by colored noise the forward equations of motion for both the single and joint probability distribution functions are derived at the same time the backward equation for the probability density of a nonmarkovian process is for the first time deduced these results are obtained by means of the systematic use of the ordered cumulant technique

numerical method for solving stochastic differential equations with dichotomous noise we propose a numerical method for solving stochastic differential equations with dichotomous markov noise the numerical scheme is formulated such that i the stochastic formula used follows the stratonovichtaylor form over the entire range of noise correlation times including the gaussian white noise limit and ii the method is readily applicable to dynamical systems driven by arbitrary types of noise provided there exists a way to describe the random increment of the stochastic process expressed in the stratonovich taylor form we further propose a simplified taylor scheme that significantly reduces the computation time while still satisfying the moment properties up to the required order the accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions

new separations in zero error channel capacity through projective kochen specker sets and quantum coloring we introduce two generalizations of kochen specker ks sets projective ks sets and generalized ks sets we then use projective ks sets to characterize all graphs for which the chromatic number is strictly larger than the quantum chromatic number here the quantum chromatic number is defined via a nonlocal game based on graph coloring we further show that from any graph with separation between these two quantities one can construct a classical channel for which entanglement assistance increases the one shot zero error capacity as an example we exhibit a new family of classical channels with an exponential increase

approximation solvability of a class of a monotone implicit variational inclusion problems in semi inner product spaces abstract this paper deals with the existence of solutions for a class of nonlinear implicit variational inclusion problems in semi inner product spaces we construct an iterative algorithm for approximating the solution for the class of implicit variational inclusions problems involving a monotone and h monotone operators by using the generalized resolvent operator technique

local hidden variable models for entangled quantum states while entanglement and violation of bell inequalities were initially thought to be equivalent quantum phenomena we now have different examples of entangled states whose correlations can be described by local hidden variable models and therefore do not violate any of the bell inequalities we provide an up to date overview of the existing literature regarding local hidden variable models for entangled quantum states in both the bipartite and multipartite cases and discuss some of the most relevant open questions in this context our review covers twenty five years of this line of research beginning with the seminal work by werner 1989 phys rev a 40 8 which provided the first example of an entangled state with a local model werner s work in turn appeared twenty five years after the seminal work by bell 1964 physics 1 195 about the impossibility of recovering the predictions of quantum mechanics using a local hidden variable theory this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

phase diagram of the random frequency oscillator the case of ornstein uhlenbeck noise abstract we study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an ornstein uhlenbeck noise this system undergoes a noise induced bifurcation when the amplitude of the noise grows the critical curve that separates the absorbing phase from an extended non equilibrium steady state corresponds to the vanishing of the lyapunov exponent that measures the asymptotic logarithmic growth rate of the energy we derive various expressions for this lyapunov exponent by using different approximation schemes this allows us to study quantitatively the phase diagram of the random parametric oscillator

generalized eckstein bertsekas proximal point algorithm based on a maximal monotonicity design a general design for the eckstein bertsekas proximal point algorithm using the notion of the a maximal monotonicity is developed convergence analysis for the generalized eckstein bertsekas proximal point algorithm in the context of solving a class of nonlinear inclusion problems is explored some auxiliary results of interest involving a maximal monotone mappings are also included the obtained results generalize investigations on general maximal monotonicity and beyond

a general scheme for studying the stochastic dynamics of a parametric oscillator driven by coloured noise the stochastic dynamics of a classical parametric oscillator driven by coloured noise with exponential correlation is studied both by analytical and numerical methods the critical strength of the parametric modulation at which the motion of the oscillator becomes unbounded and the dependence of this critical strength on the magnitude and the correlation length of the noise are investigated the results show that the critical strength does not depend on either the strength or the correlation length of the coloured noise but that the squeezing induced by the parametric oscillation is enhanced by increasing the correlation length of the noise

weak noise expansions through functional integrals for colored noise we use path integral methods to obtain expansions for the correlation functions of the non markovian stochastic processes generated by stochastic differential equations with colored noise

dynamical properties of non markovian stochastic differential equations we study nonstationary non markovian processes defined by langevin type stochastic differential equations with an ornstein uhlenbeck driving force we concentrate on the long time limit of the dynamical evolution we derive an approximate equation for the correlation function of a nonlinear nonstationary non markovian process and we discuss its consequences non markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the markovian limit several examples are discussed in which the relaxation time increases with respect to the markovian limit for a brownian harmonic oscillator with fluctuating frequency the non markovicity of the process decreases the domain of stability of the system and it can change an infradamped evolution into an overdamped one

alternating projection proximal methods for convex programming and variational inequalities we consider a mixed problem composed in part of finding a zero of a maximal monotone operator and in part of solving a monotone variational inequality problem we propose a solution method for this problem that alternates between a proximal step for the maximal monotone operator part and a projection type step for the monotone variational inequality part and analyze its convergence and rate of convergence this method extends a decomposition method of chen and teboulle math programming 64 1994 pp 81 101 for convex programming and yields as a by product new decomposition methods

the over relaxed proximal point algorithm based on h maximal monotonicity design and applications first the general framework for a generalized over relaxed proximal point algorithm using the notion of h maximal monotonicity also referred to as h monotonicity is developed and then the convergence analysis for this algorithm in the context of solving a general class of nonlinear inclusion problems is examined along with some auxiliary results on the resolvent operators corresponding to h maximal monotonicity

composition duality and maximal monotonicity this paper shows how the attouch thera duality principle for operator inclusions can be extended to compositions of multifunctions so that the primal and dual inclusions may involve operators between different pairs of spaces we first present the extension and give an example from computational economics to demonstrate that it has practical utility then we consider a particular case often found in applications involving real hilbert spaces and maximal monotone operators we show that in this case our duality framework includes those previously developed by rockafellar mosco and gabay finally we demonstrate that in this case under very simple hypotheses the duality transformation preserves the maximal monotonicity of the operators involved this proof uses an apparently new criterion for maximal monotonicity of operators of the form l tl where t is maximal monotone and l is linear and continuous with adjoint l

a computable evolution equation for the joint response excitation probability density function of stochastic dynamical systems by using functional integral methods we determine a computable evolution equation for the joint response excitation probability density function of a stochastic dynamical system driven by coloured noise this equation can be represented in terms of a superimposition of differential constraints i e partial differential equations involving unusual limit partial derivatives the first one of which was originally proposed by sapsis athanassoulis a connection with the classical response approach is established in the general case of random noise with arbitrary correlation time yielding a fully consistent new theory for non markovian systems we also address the question of computability of the joint response excitation probability density function as a solution to a boundary value problem involving only one differential constraint by means of a simple analytical example it is shown that in general such a problem is undetermined in the sense that it admits an infinite number of solutions this issue can be overcome by completing the system with additional relations yielding a closure problem which is similar to the one arising in the standard response theory numerical verification of the equations for the joint response excitation density is obtained for a tumour cell growth model under immune response

ψ epistemic models are exponentially bad at explaining the distinguishability of quantum states the status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory is it an epistemic state state of knowledge or an ontic state state of reality in realist models of quantum theory the epistemic view asserts that nonorthogonal quantum states correspond to overlapping probability measures over the true ontic states this naturally accounts for a large number of otherwise puzzling quantum phenomena for example the indistinguishability of nonorthogonal states is explained by the fact that the ontic state sometimes lies in the overlap region in which case there is nothing in reality that could distinguish the two states for this to work the amount of overlap of the probability measures should be comparable to the indistinguishability of the quantum states in this letter i exhibit a family of states for which the ratio of these two quantities must be 2de cd in hilbert spaces of dimension d that are divisible by 4 this implies that for large hilbert space dimension the epistemic explanation of indistinguishability becomes implausible at an exponential rate as the hilbert space dimension increases

an approximate master equation for systems driven by linear ornstein uhlenbeck noise abstract by use of an operator method we construct a novel approximate evolution equation for a one dimensional probability distribution of a single degree of freedom system driven by ornstein uhlenbeck noise this equation is an integro differential equation of the time convolutionless type and its steady state solution is presented a class of non linear equations with multiplicative noise is considered