noise induced drift in stochastic differential equations with arbitrary friction and diffusion in the smoluchowski kramers limit we consider the dynamics of systems with arbitrary friction and diffusion these include as a special case systems for which friction and diffusion are connected by einstein fluctuation dissipation relation e g brownian motion we study the limit where friction effects dominate the inertia i e where the mass goes to zero smoluchowski kramers limit using the ito stochastic integral convention we show that the limiting effective langevin equations has different drift fields depending on the relation between friction and diffusion alternatively our results can be cast as different interpretations of stochastic integration in the limiting equation which can be parametrized by interestingly in addition to the classical ito 0 stratonovich 0 5 and anti ito 1 integrals we show that position dependent x and even stochastic integrals with 0 1 arise our findings are supported by numerical simulations

the analysis of activity networks under generalized precedence relations gprs we present a model for activity networks under generalized precedence relations gprs discuss its temporal analysis and the issues that may arise relative to inconsistency among the specified relations and the activity durations we also give more precise definition to the concept of criticality of an activity and introduce the new concept of flexibility of an activity which is akin to the traditional concept of activity floats in regular cpm with the latter taking on different meaning from its common interpretation in standard cpm issues of optimization are raised when one assumes for each activity a piecewise linear time cost function that permits positive and negative deviations from its least cost duration between specified lower and upper bounds on that duration we seek the optimal activity durations subject to the specified gprs and a given due date we also seek the construction of the complete project duration cost function between the project minimum duration and its least cost duration when the due date is interpreted first as a deadline and second as a target date with rewards for early and penalties for late completion the relations between the problems posed and the uncapacitated minimum cost flow problems are revealed and are utilized in the algorithmic solution of the problems

critical patch size reduction by heterogeneous diffusion population survival depends on a large set of factors and on how they are distributed in space due to landscape heterogeneity species can occupy particular regions that provide the ideal scenario for development working as a refuge from harmful environmental conditions survival occurs if population growth overcomes the losses caused by adventurous individuals that cross the patch edge in this work we consider a single species dynamics in a patch with a space dependent diffusion coefficient we show analytically within the stratonovich framework that heterogeneous diffusion reduces the minimal patch size for population survival when contrasted with the homogeneous case with the same average diffusivity furthermore this result is robust regardless of the particular choice of the diffusion coefficient profile we also discuss how this picture changes beyond the stratonovich framework particularly the ito case which is nonanticipative can promote the opposite effect while hanggi klimontovich interpretation reinforces the reduction effect

a small delay and correlation time limit of stochastic differential delay equations with state dependent colored noise we consider a general stochastic differential delay equation sdde with state dependent colored noises and derive its limit as the time delays and the correlation times of the noises go to zero the work is motivated by an experiment involving an electrical circuit with noisy delayed feedback an ornstein uhlenbeck process is used to model the colored noise the main methods used in the proof are a theorem about convergence of solutions of stochastic differential equations by kurtz and protter and a maximal inequality for sums of a stationary sequence of random variables by peligrad and utev

marcus versus stratonovich for systems with jump noise the famous ito stratonovich dilemma arises when one examines a dynamical system with a multiplicative white noise in physics literature this dilemma is often resolved in favour of the stratonovich prescription because of its two characteristic properties valid for systems driven by brownian motion i it allows physicists to treat stochastic integrals in the same way as conventional integrals and ii it appears naturally as a result of a small correlation time limit procedure on the other hand the marcus prescription ieee trans inform theory 24 164 1978 stochastics 4 223 1981 should be used to retain i and ii for systems driven by a poisson process levy flights or more general jump processes in present communication we present an in depth comparison of the ito stratonovich and marcus equations for systems with multiplicative jump noise by the examples of a real valued linear system and a complex oscillator with noisy frequency the kubo anderson oscillator we compare solutions obtained with the three prescriptions

a branch and bound procedure for the resource constrained project scheduling problem with generalized precedence relations abstract we present an optimal solution procedure for the resource constrained project scheduling problem rcpsp with generalized precedence relations rcpsp gpr with the objective of minimizing the project makespan the rcpspgpr extends the rcpsp to arbitrary minimal and maximal time lags between the starting and completion times of activities the proposed procedure is suited for solving a general class of project scheduling problems and allows for arbitrary precedence constraints activity ready times and deadlines multiple renewable resource constraints with time varying resource requirements and availabilities several types of permissible and mandatory activity overlaps and multiple projects it can be extended to other regular and non regular measures of performance essentially the procedure is a depth first branch and bound algorithm in which the nodes in the search tree represent the original project network extended with extra precedence relations to resolve a number of resource conflicts these conflicts are resolved using the concept of minimal delaying modes which is an extension of the notion of minimal delaying alternatives for the rcpsp several bounds and dominance rules are used to fathom large portions of the search tree extensive computational experience is reported

mapping multiplicative to additive noise the langevin formulation of a number of well known stochastic processes involves multiplicative noise in this work we present a systematic mapping of a process with multiplicative noise to a related process with additive noise which may often be easier to analyse the mapping is easily understood in the example of the branching process in a second example we study the random neighbour or infinite range contact process which is mapped to an ornstein uhlenbeck process with absorbing wall the present work might shed some light on absorbing state phase transitions in general such as the role of conditional expectation values and finite size scaling and elucidate the meaning of the noise amplitude while we focus on the physical interpretation of the mapping we also provide a mathematical derivation

data driven approach to decomposing complex enzyme kinetics with surrogate models the temporal autocorrelation ac function associated with monitoring order parameters characterizing conformational fluctuations of an enzyme is analyzed using a collection of surrogate models the surrogates considered are phenomenological stochastic differential equation sde models it is demonstrated how an ensemble of such surrogate models each surrogate being calibrated from a single trajectory indirectly contains information about unresolved conformational degrees of freedom this ensemble can be used to construct complex temporal acs associated with a non markovian process the ensemble of surrogates approach allows researchers to consider models more flexible than a mixture of exponentials to describe relaxation times and at the same time gain physical information about the system the relevance of this type of analysis to matching single molecule experiments to computer simulations and how more complex stochastic processes can emerge from a mixture of simpler processes is also discussed the ideas are illustrated on a toy sde model and on molecular dynamics simulations of the enzyme dihydrofolate reductase

brownian motion with multiplicative noises revisited the langevin equation with multiplicative noise and a state dependent transport coefficient should always complemented with the proper interpretation rule of the noise such as the ito and stratonovich conventions although the mathematical relationship between the different rules and how to translate from one rule to another are well established the subject of which is a more physically natural rule still remains controversial in this communication we derive the overdamped langevin equation with multiplicative noise for brownian particles by systematically eliminating the fast degrees of freedom of the underdamped langevin equation the langevin equations obtained here vary depending on the choice of the noise conventions but they are different representations for an identical phenomenon the results apply to multi variable nonequilibrium non stationary systems and other general settings

on no wait and no idle flow shops with makespan criterion the paper deals with the np hard problems of minimizing the makespan in m machine no wait and no idle permutation flow shops we identify networks whose longest path lengths represent the makespans these networks reveal the duality between the two problems and show graphical explanations of the fact that under no wait and no idle conditions the makespan can be a decreasing function of some job processing times moreover they also lead to a natural reduction of the no wait flow shop problem to the traveling salesman problem some lower bounds on the shortest makespan and new efficiently solvable special cases

curl flux induced drift in stochastic differential equations in the zero mass limit abstract we consider the nonlinear stochastic dynamics of dissipative hamiltonian systems with state dependent friction and diffusion connected by the fluctuation dissipation relation in high dimensions the system under study has a close connection to ao s framework in constructing a dynamical potential for non equilibrium processes without detailed balance we study the limiting case where the mass approaches zero and give a new and complete derivation of effective stochastic differential equations using the ito stochastic integral convention we show that the limiting effective langevin equations have a new drift term this extra term happens to be identical to the corresponding anti ito or isothermal integral requiring constant temperature in one dimension we however cannot obtain this additional drift term using conventional stochastic integrals in high dimension it is interesting to note that in a high dimensional system a curl flux induced drift may appear even if the diffusion matrix is constant our findings are supported by numerical simulations we further analyze and discuss the role of this new drift term in calculating the classic escape time for the first time to our knowledge the relation between the escape rate and the anti ito integral is presented we also demonstrate that the derived diffusion equations give a new sampling algorithm which can increase convergence speed in a simple two dimensional example

on the complexity of project scheduling to minimize exposed time we consider project scheduling where the project manager s objective is to minimize the time from when an adversary discovers the project until the completion of the project we analyze the complexity of the problem identifying both polynomially solvable and np hard versions of the problem the complexity of the problem is seen to be dependent on the nature of renewable resource constraints precedence constraints and the ability to crash activities in the project

a mathematical framework for stochastic climate models there has been a recent burst of activity in the atmosphere ocean sciences community in utilizing stable linear langevin stochastic models for the unresolved degrees of freedom in stochastic climate prediction here a systematic mathematical strategy for stochastic climate modeling is developed and some of the new phenomena in the resulting equations for the climate variables alone are explored the new phenomena include the emergence of both unstable linear langevin stochastic models for the climate mean variables and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances all of these phenomena are derived from a systematic self consistent mathematical framework for eliminating the unresolved stochastic modes that is mathematically rigorous in a suitable asymptotic limit the theory is illustrated for general quadratically nonlinear equations where the explicit nature of the stochastic climate modeling procedure can be elucidated the feasibility of the approach is demonstrated for the truncated equations for barotropic flow with topography explicit concrete examples with the new phenomena are presented for the stochastically forced three mode interaction equations the conjecture of smith and waleffe phys fluids 11 1999 1608 1622 for stochastically forced three wave resonant equations in a suitable regime of damping and forcing is solved as a byproduct of the approach examples of idealized climate models arising from the highly inhomogeneous equilibrium statistical mechanics for geophysical flows are also utilized to demonstrate self consistency of the mathematical approach with the predictions of equilibrium statistical mechanics in particular for these examples the reduced stochastic modeling procedure for the climate variables alone is designed to reproduce both the climate mean and the energy spectrum of the climate variables c 2001 john wiley sons inc

anomalous diffusion in systems driven by the stable levy noise with a finite noise relaxation time and inertia dynamical systems driven by a general levy stable noise are considered the inertia is included and the noise represented by a generalized ornstein uhlenbeck process has a finite relaxation time a general linear problem the additive noise is solved the resulting distribution converges with time to the distribution for the white noise massless case moreover a multiplicative noise is discussed it can make the distribution steeper and the variance which is finite depends sublinearly on time subdiffusion for a small mass a white noise limit corresponds to the stratonovich interpretation on the other hand the distribution tails agree with the ito interpretation if the inertia is very large an escape time from the potential well is calculated

ito versus stratonovich white noise limits for systems with inertia and colored multiplicative noise we consider the dynamics of systems in the presence of inertia and colored multiplicative noise we study the limit where the particle relaxation time and the correlation time of the noise both tend to zero we show that the limiting equation for the particle position depends on the magnitude of the particle relaxation time relative to the noise correlation time in particular the limiting equation should be interpreted either in the ito or stratonovich sense with a crossover occurring when the two fast time scales are of comparable magnitude at the crossover the limiting stochastic differential equation is neither of ito nor of stratonovich type this means that after adiabatic elimination the governing equations have different drift fields leading to different physical behavior depending on the relative magnitude of the two fast time scales our findings are supported by numerical simulations

adiabatic elimination for systems of brownian particles with nonconstant damping coefficients we discuss the problem of eliminating the momentum variable in the phase space langevin equations for a system of brownian particles in two related situations i position dependent damping and ii existence of hydrodynamic interactions we discuss the problems associated with the conventional elimination and we develop an alternative elimination procedure in the lagevin framework which leads to the correct smoluchowski equation we give a heuristic argument on the basis of stochastic differential equations for the smoluchowski limit and establish rigorously the limit for the general case of position dependent friction and diffusion coefficents

a path enumeration approach for the analysis of critical activities in fuzzy networks this paper addresses the problem of determining the degree of possible and necessary criticality of activities as well as determining paths in networks that have fuzzy activity durations in such networks activities and paths are reported in a fuzzy representation as being critical with certain degrees of possibility and necessity instead of being declared critical or not in a binary way although the problem of computing the possibility and necessity degrees of criticality for paths have been investigated in the literature those problems for activities have not yet been addressed herein an efficient algorithm that relies on a path enumeration technique is proposed to compute the possibility degrees of criticality of activities additionally the proposed algorithm computes paths with maximum and minimum degrees for the necessity of criticality which correspond to activities real world project networks were used to evaluate the performance of the algorithm

a time oriented branch and bound algorithm for resource constrained project scheduling with generalised precedence constraints resource constrained project scheduling with generalised precedence constraints is a very general scheduling model with applications in areas such as make to order production planning we describe a time oriented branch and bound algorithm that uses constraint propagation techniques which actively exploit the temporal and resource constraints of the problem in order to reduce the search space extensive computational experiments with systematically generated test problems show that the algorithm solves more problems to optimality than other exact solution procedures which have recently been proposed and that the truncated version of the algorithm is also a very good heuristic

from dynamical systems to the langevin equation abstract it is shown that some dynamical systems which in microscopic time are fully deterministic exhibit a long time stochastic behavior governed by the langevin equation the limit in which this becomes a precise statement is obtained by an appropriate scaling of time and force the results are exemplified by a computer experiment

white noise limits for discrete dynamical systems driven by fast deterministic dynamics abstract we study a class of singularly perturbed dynamical systems that have fast and slow components e 1 being the fast to slow timescale ratio the fast components are governed by a strongly mixing discrete map which is iterated at time intervals e the slow components are governed by a first order finite difference equation that uses a time step e as e tends to zero the fast components may be eliminated giving rise to sdes for the slow components the emerging stochastic calculus is in the general case of neither ito nor stratonovich type but depends on the correlation time of the mixing process

homogenization for deterministic maps and multiplicative noise a recent paper of melbourne stuart a note on diffusion limits of chaotic skew product flows nonlinearity 24 2011 1361 1367 gives a rigorous proof of convergence of a fast slow deterministic system to a stochastic differential equation with additive noise in contrast to other approaches the assumptions on the fast flow are very mild in this paper we extend this result from continuous time to discrete time moreover we show how to deal with one dimensional multiplicative noise this raises the issue of how to interpret certain stochastic integrals it is proved that the integrals are of stratonovich type for continuous time and neither

calculating differential galois groups of parametrized differential equations with applications to hypertranscendence the main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations via the parameterized and differential galois theories to achieve this we expand the representation theory of linear differential algebraic groups and develop new algorithms that calculate unipotent radicals of parameterized differential galois groups for differential equations whose coefficients are rational functions berman and singer presented an algorithm calculating the differential galois group for differential equations without parameters whose differential operator is a composition of two completely reducible differential operators we use their algorithm as a part of our algorithm as a result we find an effective criterion for the algebraic independence of the solutions of parameterized differential equations and all of their derivatives with respect to the parameter

brownian motion from deterministic dynamics abstract certain deterministic dynamical systems exhibit a transition from non gaussian chaotic to brownian motion behavior when a suitable scaling limit is applied for a simple hyperbolic model system we analyze the structure of the corresponding strange attractor determine the invariant measure and elucidate the transition scenario leading to a gaussian stochastic process

rate of convergence in the weak invariance principle for deterministic systems we obtain the first results on convergence rates in the prokhorov metric for the weak invariance principle functional central limit theorem for deterministic dynamical systems our results hold for uniformly expanding hyperbolic axiom a systems as well as nonuniformly expanding hyperbolic systems such as dispersing billiards henon like attractors viana maps and intermittent maps as an application we obtain convergence rates for deterministic homogenization in multiscale systems

singular perturbations to semilinear stochastic heat equations we consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof the interesting feature of these perturbations is that as the small parameter e tends to zero their solutions converge to the wrong limit i e they do not converge to the solution obtained by simply setting e 0 a similar effect is also observed for some formally small stochastic perturbations of a deterministic semilinear parabolic pde our proofs are based on a detailed analysis of the spatially rough component of the equations combined with a judicious use of gaussian concentration inequalities

prescription induced jump distributions in multiplicative poisson processes generalized langevin equations gle with multiplicative white poisson noise pose the usual prescription dilemma leading to different evolution equations master equations for the probability distribution contrary to the case of multiplicative gaussian white noise the stratonovich prescription does not correspond to the well known mid point or any other intermediate prescription by introducing an inertial term in the gle we show that the ito and stratonovich prescriptions naturally arise depending on two time scales the one induced by the inertial term and the other determined by the jump event we also show that when the multiplicative noise is linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution we apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white poisson noise whose features are tailored to the characters of the daily precipitation a method is finally suggested to infer the most appropriate prescription from the data

optimal potentials for temperature ratchets in a spatially periodic temperature profile directed transport of an overdamped brownian particle can be induced along a periodic potential with a load force applied to the particle this setup can perform as a heat engine for a given load the optimal potential maximizes the current and thus the power output of the heat engine we calculate the optimal potential for different temperature profiles and show that in the limit of a periodic piecewise constant temperature profile alternating between two temperatures the optimal potential leads to a divergent current this divergence being an effect of both the overdamped limit and the infinite temperature gradient at the interface would be cut off in any real experiment

stochastic algorithms for discontinuous multiplicative white noise stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral this fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories moreover if the multiplicative noise function is not continuous then the standard algorithms cannot be used we present an explicit algorithm to avoid this problem and we apply it to a well controlled example finally we discuss on the existence of higher order algorithms for this specific situation

the smoluchowski kramers limit of stochastic differential equations with arbitrary state dependent friction we study a class of systems of stochastic differential equations describing diffusive phenomena the smoluchowski kramers approximation is used to describe their dynamics in the small mass limit our systems have arbitrary state dependent friction and noise coefficients we identify the limiting equation and in particular the additional drift term that appears in the limit is expressed in terms of the solution to a lyapunov matrix equation the proof uses a theory of convergence of stochastic integrals developed by kurtz and protter the result is sufficiently general to include systems driven by both white and ornstein uhlenbeck colored noises we discuss applications of the main theorem to several physical phenomena including the experimental study of brownian motion in a diffusion gradient

parameterized picard vessiot extensions and atiyah extensions abstract generalizing atiyah extensions we introduce and study differential abelian tensor categories over differential rings by a differential ring we mean a commutative ring with an action of a lie ring by derivations in particular these derivations act on a differential category a differential tannakian theory is developed the main application is to the galois theory of linear differential equations with parameters namely we show the existence of a parameterized picard vessiot extension and therefore the galois correspondence for many differential fields with possibly non differentially closed fields of constants that is fields of functions of parameters other applications include a substantially simplified test for a system of linear differential equations with parameters to be isomonodromic which will appear in a separate paper this application is based on differential categories developed in the present paper and not just differential algebraic groups and their representations