noise induced escape from bifurcating attractors symplectic approach in the weak noise limit the effect of noise is studied in one dimensional maps undergoing transcritical tangent and pitchfork bifurcations the attractors of the noiseless map become metastable states in the presence of noise in the weak noise limit a symplectic two dimensional map is associated with the original one dimensional map the consequences of their noninvertibility on the phase space structures are discussed heteroclinic orbits are identified which play a key role in the determination of the escape rates from the metastable states near bifurcations the critical slowing down justifies the use of a continuous time approximation replacing maps by flows which allows the analytic calculation of the escape rates this method provides the universal scaling behavior of the escape rates at the bifurcations

traces and determinants of strongly stochastic operators periodic orbit theory allows calculations of long time properties of chaotic systems from traces dynamical zeta functions and spectral determinants of deterministic evolution operators which are in turn evaluated in terms of periodic orbits for the case of stochastic dynamics a direct numerical evaluation of the trace of an evolution operator is possible as a multidimensional integral techniques for evaluating such path integrals are discussed using as an example the logistic map f x lambdax 1 x with moderate to strong additive gaussian noise rapid convergence is demonstrated for all values of lambda with strong noise as well as at fixed lambda 5 for all noise levels

signatures of noise enhanced stability in metastable states the lifetime of a metastable state in the transient dynamics of an overdamped brownian particle is analyzed both in terms of the mean first passage time and by means of the mean growth rate coefficient both quantities feature nonmonotonic behaviors as a function of the noise intensity and are independent signatures of the noise enhanced stability effect they can therefore be alternatively used to evaluate and estimate the presence of this phenomenon which characterizes metastability in nonlinear physical systems

delay fokker planck equations perturbation theory and data analysis for nonlinear stochastic systems with time delays we study nonlinear stochastic systems with time delayed feedback using the concept of delay fokker planck equations introduced by guillouzic l heureux and longtin we derive an analytical expression for stationary distributions using first order perturbation theory we demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data in addition we show that the fokker planck perspective for stochastic systems with time delays is consistent with the so called extended phase space approach to time delayed systems

small delay approximation of stochastic delay differential equations delay differential equations evolve in an infinite dimensional phase space in this paper we consider the effect of external fluctuations noise on delay differential equations involving one variable thus leading to univariate stochastic delay differential equations sdde s for small delays a univariate nondelayed stochastic differential equation approximating such a sdde is presented another approximation complementary to the first is also obtained using an average of the sdde s drift term over the delayed dynamical variable which defines a conditional average drift this second approximation is characterized by the fact that the diffusion term is identical to that of the original sdde for small delays our approach yields a steady state probability density and a conditional average drift which are in close agreement with numerical simulations of the original sdde we illustrate this scheme with the delayed linear langevin equation and a stochastic version of the delayed logistic equation the technique can be used with any type of noise and is easily generalized to multiple delays s1063 651x 99 08304 x

bi criteria and approximation algorithms for restricted matchings abstract in this work we study approximation algorithms for the restricted matching problem which is defined as follows given a graph in which each edge e has a color c e and a profit p e q we want to compute a maximum cardinality or profit matching in which no more than w j z edges of color c j are present this kind of problems beside the theoretical interest on its own right emerges in multi fiber optical networking systems where we interpret each unique wavelength that can travel through the fiber as a color class and we would like to establish communication between pairs of systems we study approximation and bi criteria algorithms for this problem which are based on linear programming techniques and in particular on polyhedral characterizations of the natural linear formulation of the problem in our setting we allow violations of the bounds w j and we can model our problem as a bi criteria problem we have two objectives that we want to optimize namely a to maximize the profit maximum matching while b minimizing the violation of the color bounds we prove how we can beat the integrality gap of the natural linear programming formulation of the problem by allowing only a slight violation of the color bounds in particular our main result is constant approximation bounds for both criteria of the corresponding bi criteria optimization problem

role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials we present a study of the noise driven escape of an overdamped brownian particle moving in a cubic potential profile with a metastable state we analyze the role of the initial conditions of the particle on the enhancement of the average escape time as a function of the noise intensity for fixed and fluctuating potentials we observe the noise enhanced stability effect for all the initial unstable states investigated for a fixed potential we find a peculiar initial condition xc which separates the set of the initial unstable states in two regions those which give rise to divergences from those which show nonmonotonic behavior of the average escape time for fluctuating potential at this particular initial condition and for low noise intensity we find large fluctuations of the average escape time

solution of the boundary value problem for optimal escape in continuous stochastic systems and maps topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps a topological method is introduced that simplifies the solution of boundary value problems the activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path the method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps

reactive dynamics of inertial particles in nonhyperbolic chaotic flows anomalous kinetics of infective e g autocatalytic reactions in open nonhyperbolic chaotic flows are important for many applications in biological chemical and environmental sciences we present a scaling theory for the singular enhancement of the production caused by the universal underlying fractal patterns the key dynamical invariant quantities are the effective fractal dimension and effective escape rate which are primarily determined by the hyperbolic components of the underlying dynamical invariant sets the theory is general as it includes all previously studied hyperbolic reactive dynamics as a special case we introduce a class of dissipative embedding maps for numerical verification

approximate bayesian analysis of censored survival data summary the bayesian analysis of data arising from a location scale regression model and which may include a number of right censored observations is considered the posterior distributions of the suitably normalized precision parameter and regression coefficient vector are shown to be well approximated by x2 and multivariate t distributions respectively the ideas are illustrated using some clinical survival data

biased diffusion inside regular islands under random symplectic perturbations we study the random concatenation of slightly different two dimensional hamiltonian maps with a mixed phase space we consider a regular island whose fixed point is identical for all maps trajectories of the concatenated maps near this fixed point are no longer confined to invariant tori we derive a stochastic model for the distance from the fixed point which turns out to be a biased random walk with multiplicative noise we give an analytical prediction of the survival probability of trajectories inside the regular island which asymptotically is the product of a power law and an exponential we confirm these results numerically for the parametrically perturbed standard map

minimax regret spanning arborescences under uncertain costs abstract the paper considers a classical optimization problem on a network whose arc costs are partially known it is assumed that an interval estimate is given for each arc cost and no further information about the statistical distribution of the truth value of the arc cost is known in this context given a spanning arborescence in the network its cost can take on different values according to the choice of each individual arc cost that is according to the different cost scenarios we analyze the problem of finding which spanning arborescence better approaches the optimal one under each possible scenario the minimax regret criterion is proposed in order to obtain such a robust solution to the problem in the paper it is shown that a greedy type algorithm can compute an optimal solution of this problem on acyclic networks for general networks the problem becomes np hard in this case the special structure of the optimization problem allows us to design a bounding process for the optimum value that will result in a heuristic algorithm described at the end of the paper

fluctuational transitions across different kinds of fractal basin boundaries we study fluctuational transitions in discrete and continuous dynamical systems that have two coexisting attractors in phase space separated by a fractal basin boundary which may be either locally disconnected or locally connected theoretical and numerical evidence is given to show that in each case the transition occurs via a unique accessible point on the boundary both in discrete systems and in flows the complicated structure of the escape paths inside the locally disconnected fractal basin boundary is determined by a hierarchy of homoclinic points the interrelation between the mechanism of transitions and the hierarchy is illustrated by consideration of fluctuational transitions in dynamical systems demonstrating fractal fractal basin boundary metamorphosis at some value of a control parameter the most probable escape path from an attractor which can be either regular or chaotic is found for each type of boundary using both statistical analysis of fluctuational trajectories and the hamiltonian theory of fluctuations

paths and trails in edge colored weighted graphs abstract let g c w be an edge colored weighted graph where g is a nontrivial connected graph c is an edge coloring of g and w is an edge weighting of g a path a trail a cycle or a closed trail of g say f is called proper under the edge coloring c if every two consecutive edges of f receive different colors in c let s and t be two specified nonadjacent vertices in g in this paper we study the problems for finding in g c w the minimum weighted proper s t path the minimum weighted proper s t trail the minimum weighted proper cycle the minimum weighted proper closed trail the maximum weighted proper s t path and the maximum weighted proper s t trail when the minimization problems are considered we assume that g c w has no negative proper cycle and when the maximization problems are considered we assume that g c w has no proper closed trail we show that all these problems are solvable in polynomial time

growing 1d and quasi 2d unstable manifolds of maps we present a new 1d algorithm for computing the global one dimensional unstable manifold of a saddle point of a map our method can be generalized to compute two dimensional unstable manifolds of maps with three dimensional state spaces this is shown here with a quasi 2d q2d algorithm for the special case of a quasiperiodically forced map which allows for a substantial simplification of the general case described in krauskopf and osinga 1998 the key idea is to grow the manifold in steps which consist of finding a new point on the manifold at a prescribed distance from the last point the speed of growth is determined only by the curvature of the manifold and not by the dynamics the performance of the 1d algorithm is demonstrated with a constructed test example and it is then used to compute one dimensional manifolds of a map modeling mixing in a stirring tank with the q2d algorithm we compute two dimensional unstable manifolds in the quasiperiodically forced henon map

random fluctuation leads to forbidden escape of particles a great number of physical processes are described within the context of hamiltonian scattering previous studies have rather been focused on trajectories starting outside invariant structures since the ones starting inside are expected to stay trapped there forever this is true though only for the deterministic case we show however that under finitely small random fluctuations of the field trajectories starting inside kolmogorov arnold moser kam islands escape within finite time the nonhyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field as a consequence trajectories which are started inside kam curves escape with hyperboliclike time decay distribution and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems we show a universal quadratic power law relating the exponential decay to the amplitude of noise we present a random walk model to relate this distribution to the amplitude of noise and investigate these phenomena with a numerical study applying random maps

escape from attracting sets in randomly perturbed systems the dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science previous studies of escape in chaotic systems have rather focused on the case of unbounded noise usually assumed to have gaussian distribution in this paper we address the problem of escape induced by bounded noise we show that the dynamics of escape from an attractor s basin is equivalent to that of a closed system with an appropriately chosen hole using this equivalence we show that there is a minimum noise amplitude above which escape takes place and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition we verify our analytical predictions through numerical simulations of two well known two dimensional maps with noise

faster scaling algorithms for general graph matching problems an algorithm for minimum cost matching on a general graph with integral edge costs is presented the algorithm runs in time close to the fastest known bound for maximum cardinality matching specifically let n m and n denote the number of vertices number of edges and largest magnitude of a cost respectively the best known time bound for maximum cardinal ity matching m 0 am the new algorithm for minimum cost matching has time bound 0 in a m n iog n m log nn a slight modification of the new algorithm finds a maximum cardinality matching in 0 fire time other applications of the new algorlthm are given mchrding an efficient implementa tion of christofides traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching

rare event statistics in reaction diffusion systems we present an efficient method to calculate probabilities of large deviations from the typical behavior rare events in reaction diffusion systems this method is based on a semiclassical treatment of an underlying quantum hamiltonian encoding the system s evolution to this end we formulate the corresponding canonical dynamical system and investigate its phase portrait this method is presented for a number of pedagogical examples

spectrum of stochastic evolution operators local matrix representation approach a matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum in the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits the evaluation of perturbative corrections is easier to implement in this framework than in the standard feynman diagram perturbation theory the results are perturbative corrections to a stochastic analog of the gutzwiller semiclassical spectral determinant computed to several orders beyond what has so far been attainable in stochastic and quantum mechanical applications

linear time approximation for maximum weight matching the maximum cardinality and maximum weight matching problems can be solved in o m n time a bound that has resisted improvement despite decades of research here m and n are the number of edges and vertices in this article we demonstrate that this m n barrier can be bypassed by approximation for any e 0 we give an algorithm that computes a 1 e approximate maximum weight matching in o me 1 log e 1 time that is optimal linear time for any fixed e our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error

weak noise approach to the logistic map using a nonperturbative weak noise approach we investigate the interference of noise and chaos in simple 1d maps we replace the noise driven 1d map by an area preserving 2d map modelling the poincare sections of a conserved dynamical system with unbounded energy manifolds we analyze the properties of the 2d map and draw conclusions concerning the interference of noise on the nonlinear time evolution we apply this technique to the standard period doubling sequence in the logistic map from the 2d area preserving analogue we in addition to the usual period doubling sequence obtain a series of period doubled cycles which are elliptic in nature these cycles are spinning off the real axis at parameters values corresponding to the standard period doubling events

escape times in fluctuating metastable potential and acceleration of diffusion in periodic fluctuating potentials abstract the problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered for the overdamped brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first passage time as a function of the potential parameters the noise intensity and the mean rate of switchings of the dichotomous noise we find noise enhanced stability phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed for the diffusion of the overdamped brownian particle in a fast fluctuating symmetric periodic potential we obtain that the effective diffusion coefficient depends on the mean first passage time as discovered for fixed periodic potential the effective diffusion coefficients for sawtooth sinusoidal and piecewise parabolic potentials are calculated in closed analytical form

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

algorithmic applications of baur strassen s theorem shortest cycles diameter and matchings consider a directed or an undirected graph with integral edge weights from the set w w that does not contain negative weight cycles in this article we introduce a general framework for solving problems on such graphs using matrix multiplication the framework is based on the usage of baur strassen s theorem and of strojohann s determinant algorithm it allows us to give new and simple solutions to the following problems finding shortest cycles we give a simple o wn time algorithm for finding shortest cycles in undirected and directed graphs for directed graphs and undirected graphs with nonnegative weights this matches the time bounds obtained in 2011 by roditty and williams on the other hand no algorithm working in o wn time was previously known for undirected graphs with negative weights furthermore our algorithm for a given directed or undirected graph detects whether it contains a negative weight cycle within the same running time computing diameter and radius we give a simple o wn time algorithm for computing a diameter and radius of an undirected or directed graphs to the best of our knowledge no algorithm with this running time was known for undirected graphs with negative weights finding minimum weight perfect matchings we present an o wn time algorithm for finding minimum weight perfect matchings in undirected graphs this resolves an open problem posted by sankowski 2009 who presented such an algorithm but only in the case of bipartite graphs these three problems that are solved in the full generality demonstrate the utility of this framework hence we believe that it can find applications for solving larger spectra of related problems as an illustrative example we apply it to the problem of computing a set of vertices that lie on cycles of length at most t for some given t we give a simple o wn time algorithm for this problem that improves over the o wn t time algorithm given by yuster in 2011 besides giving this flexible framework the other main contribution of this article is the development of a novel combinatorial interpretation of the dual solution for the minimum weight perfect matching problem despite the long history of the matching problem such a combinatorial interpretation was not known previously this result sheds a new light on the problem as there exist many structural theorems about unweighted matchings but almost no results that could cope with the weighted case

effect of time delay in fitzhugh nagumo neural model with correlations between multiplicative and additive noises abstract we study the effect of time delay in the fitzhugh nagumo neural model with correlations between multiplicative and additive noise terms based on the corresponding fokker planck equation the explicit expressions of the stationary probability distribution function spdf the mean first passage time mfpt and the signal to noise ratio snr are obtained respectively research results show that i the system undergoes a succession of two phase transitions i e the reentrance phenomenon as the noise correlation parameter is increased and a single phase transition as the time delay is increased ii the mfpt as a function of the multiplicative noise intensity exhibits a maximum this maximum for mfpt identifies the noise enhanced stability nes effect the noise correlation parameter intensifies the nes effect while the time delay and the additive noise intensity weakens it iii the existence of a maximum in the snr as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance sr phenomenon the noise correlation parameter enhances the sr while the time delay and the additive noise intensity weaken it

decay of unstable equilibrium and nonequilibrium states with inverse probability current taken into account we study the causes of noise delayed decay of unstable states in nonlinear dynamic systems within the framework of the overdamped brownian motion model for the analysis we use the exact expressions for the decay times of unstable states which take into account the inverse probability current in contrast to the well known mean first passage time method these expressions are valid for any intensity of fluctuations and for arbitrary potential profiles the effect of delay is shown to arise under the decay of unstable nonequilibrium states due to the action of two different mechanisms these mechanisms are caused by the inverse probability current and by the nonlinearity of potential describing an unstable state

approximate inference in location scale regression models abstract it is shown that 2 and multivariate t distributions provide good approximations to posterior distributions arising in location scale regression models in the case of a linear regression model bayesian inferences based on an improper prior have conditional frequency as well as fiducial structural interpretation so the results are also applicable in a non bayesian context numerical support for the approximations is presented for the case of a weibull regression model and a regression with t distributed errors

switching path distribution in multidimensional systems we explore the distribution of paths followed in fluctuation induced switching between coexisting stable states we introduce a quantitative characteristic of the path distribution in phase space that does not require a priori knowledge of system dynamics the theory of the distribution is developed and its direct measurement is performed in a micromechanical oscillator driven into parametric resonance the experimental and theoretical results on the shape and position of the distribution are in excellent agreement with no adjustable parameters in addition the experiment provides the first demonstration of the lack of time reversal symmetry in switching of systems far from thermal equilibrium the results open the possibility of efficient control of the switching probability based on the measured narrow path distribution

theoretical analysis of destabilization resonances in time delayed stochastic second order dynamical systems and some implications for human motor control a linear stochastic delay differential equation of second order is studied that can be regarded as a kramers model with time delay an analytical expression for the stationary probability density is derived in terms of a gaussian distribution in particular the variance as a function of the time delay is computed analytically for several parameter regimes strikingly in the parameter regime close to the parameter regime in which the deterministic system exhibits hopf bifurcations we find that the variance as a function of the time delay exhibits a sequence of pronounced peaks these peaks are interpreted as delay induced destabilization resonances arising from oscillatory ghost instabilities on the basis of the obtained theoretical findings reinterpretations of previous human motor control studies and predictions for future human motor control studies are provided 2006 the american physical society

escape problem for irreversible systems the problem of noise induced escape from a metastable state arises in physics chemistry biology systems engineering and other areas the problem is well understood when the underlying dynamics of the system obey detailed balance when this assumption fails many of the results of classical transition rate theory no longer apply and no general method exists for computing the weak noise asymptotic behavior of fundamental quantities such as the mean escape time in this paper we present a general technique for analyzing the weak noise limit of a wide range of stochastically perturbed continuous time nonlinear dynamical systems we simplify the original problem which involves solving a partial differential equation into one in which only ordinary differential equations need be solved this allows us to resolve some old issues for the case when detailed balance holds when it does not hold we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path we also present results on short time behavior and discuss the possibility of ital focusing along the escape path

scale parameters a bayesian treatment a definition of a scale parameter is given which includes the usual definition of a scale parameter in the exponential family some suggestions for the estimation of and approximations to the marginal posterior distribution of a vector valued parameter of primary interest are made in particular the possibility of a 2 approximation to the posterior distribution of leading to h p d regions for based on the f distribution is explored two examples are discussed where observations are from a normal and gamma distribution

stochastic time delayed systems driven by correlated noises steady state analysis abstract in the present paper a class of stochastic time delayed systems driven by correlated gaussian white noises are considered novikov s theorem is used to derive delay fokker planck equations in the case of small time delays approximate stationary solutions are obtained as a special case the delay fokker planck equation and the approximate stationary probability density function is obtained for a bistable system numerical simulations show that the small delay approximation is a good approximation in the case of small delay furthermore the effects of the correlated noises and the feedback are investigated the critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by the degree of the correlation of the noises and e the strength of the feedback both and e can change the curve of the stationary probability density function from a bimodal to a unimodal structure

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

effects of time delay on transient behavior of a time delayed metastable system subjected to cross correlated noises abstract the effects of time delay on the transient properties of a time delayed metastable system subjected to cross correlated noises are studied by means of a stochastic simulation method it is found that i both additive noise and multiplicative noise can produce the noise enhanced stability nes effect ii the time delay induces critical behavior on the nes i e there is a critical value of the delay time c 1 2 2 above which the time delay increases the stability of the system enhanced by the additive noise and below which the nes effect induced by the additive noise disappears iii there exists another critical value of the delay time c 2 3 0 above which the time delay increases the stability of the system enhanced by the multiplicative noise and below which the time delay decreases it

efficient implementation of graph algorithms using contraction the component merging problem is a new graph problem versions of this problem appear as bottlenecks in various graph algorithms a new data structure solves this problem efficiently and two special cases of the problem have even more efficient solutions based on other data structures the performance of the data structures is sped up by introducing a new algorithmic tool called packets the algorithms that use these solutions to the component merging problem also exploit new properties of two existing data structures specifically trees can be used simultaneously as a priority queue and a concatenable queue similarly f heaps support some kinds of split operations with no loss of efficiency an immediate application of the solution to the simplest version of the merging problem is an o t m n algorithm for finding minimum spanning trees in undirected graphs without using f heaps where t m n m log 2 log 2 log d n the graph has n vertices and m edges and d max m n 2 packets also improve the f heap minimum spanning tree algorithm giving the fastest algorithm currently known for this problem the efficient solutions to the merging problem and the new observation about f heaps lead to an o n t m n n log n algorithm for finding a maximum weighted matching in general graphs this settles an open problem posed by tarjan 15 p 123 where the weaker bound of o nm log n 2 m was conjectured

finding minimum cost circulations by successive approximation we develop a new approach to solving minimum cost circulation problems our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling we measure the accuracy of a solution by the amount that the complementary slackness conditions are violated we propose a simple minimum cost circulation algorithm one version of which runs in on3lognc time on an n vertex network with integer arc costs of absolute value at most c by incorporating sophisticated data structures into the algorithm we obtain a time bound of onm logn2 mlognc on a network with m arcs a slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of on lognc blocking flow problems a corollary of this result is an on2log nlognc time m processor parallel minimum cost circulation algorithm our approach also yields strongly polynomial minimum cost circulation algorithms our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem we believe that a suitable implementation of our method will perform extremely well in practice

new algorithms for maximum weight matching and a decomposition theorem we revisit the classical maximum weight matching problem in general graphs with nonnegative integral edge weights we present an algorithm that operates by decomposing the problem into w unweighted versions of the problem where w is the largest edge weight our algorithm has running time as good as the current fastest algorithms for the maximum weight matching problem when w is small one of the highlights of our algorithm is that it also produces an integral optimal dual solution thus our algorithm also returns an integral certificate corresponding to the maximum weight matching that was computed our algorithm yields a new proof to the total dual integrality of edmonds matching polytope and it also gives rise to a decomposition theorem for the maximum weight of a matching in terms of the maximum size of a matching in certain subgraphs we also consider the maximum weight capacitated b matching problem in bipartite graphs with nonnegative integral edge weights and show that it can also be decomposed i

an o ev log v algorithm for finding a maximal weighted matching in general graphs we define two generalized types of a priority queue by allowing some forms of changing the priorities of the elements in the queue we show that they can be implemented efficiently consequently each operation takes o log n time we use these generalized priority queues to construct an o ev log v algorithm for finding a maximal weighted matching in general graphs

a scaling theory of bifurcations in the symmetric weak noise escape problem we consider two dimensional overdamped double well systems perturbed by white noise in the weak noise limit the most probable fluctuational path leading from either point attractor to the separatrix the most probable escape path or mpep must terminate on the saddle between the two wells however as the parameters of a symmetric double well system are varied a unique mpep may bifurcate into two equally likely mpeps at the bifurcation point in parameter space the activation kinetics of the system become non arrhenius we quantify the non arrhenius behavior of a system at the bifurcation point by using the maslov wkb method to construct an approximation to the quasistationary probability distribution of the system that is valid in a boundary layer near the separatrix the approximation is a formal asymptotic solution of the smoluchowski equation our construction relies on a new scaling theory which yields critical exponents describing weak noise behavior at the bifurcation point near the saddle

noise enhanced stability of periodically driven metastable states we study the effect of noise enhanced stability of periodically driven metastable states in a system described by piecewise linear potential we find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system we analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations

effects of cross correlation on the relaxation time of a bistable system driven by cross correlated noise we study the effects of correlations between additive and multiplicative noise on relaxation time in a bistable system driven by cross correlated noise using the projection operator method we derived an analytic expression for the relaxation time t c of the system which is the function of additive ensuremath alpha and multiplicative d noise intensities correlation intensity ensuremath lambda of noise and correlation time ensuremath tau of noise after introducing a noise intensity ratio and a dimensionless parameter r d ensuremath alpha and then performing numerical computations we find the following i for the case of rl1 the relaxation time t c increases as r increases ii for the cases of rg 1 there is a one peak structure on the t c ensuremath r plot and the effects of cross correlated noise on the relaxation time are very notable iii for the case of rl1 t c almost does not change with both ensuremath lambda and ensuremath tau and for the cases of rg 1 t c decreases as ensuremath lambda increases however t c increases as ensuremath tau increases ensuremath lambda and ensuremath tau play opposite roles in t c i e ensuremath lambda enhances the fluctuation decay of dynamical variable and ensuremath tau slows down the fluctuation decay of dynamical variable

the state variable correlation function of the bistable system subject to the cross correlated noises abstract the effects of correlations between additive and multiplicative noises on the state variable correlation function of a bistable system driven by cross correlated noises were studied applying an approximate fokker planck equation to the system the analytic expression for the state variable correlation function of the system is derived by projection operator method from numerical computations we find that the normalized correlation function c s decreases exponentially as the decay time s increases and decreases with increasing cross correlated strength however c s increases with increasing cross correlated time and play opposing roles in the c i e enhances the rate of fluctuation decay of dynamical variable and the slows down the rate of fluctuation decay of dynamical variable

maximum skew symmetric flows and matchings the maximum integer skew symmetric flow problem msfp generalizes both the maximum flow and maximum matching problems it was introduced by tutte 28 in terms of self conjugate flows in antisymmetrical digraphs he showed that for these objects there are natural analogs of classical theoretical results on usual network flows such as the flow decomposition augmenting path and max flow min cut theorems we give unified and shorter proofs for those theoretical results we then extend to msfp the shortest augmenting path method of edmonds and karp 7 and the blocking flow method of dinits 4 obtaining algorithms with similar time bounds in general case moreover in the cases of unit arc capacities and unit node capacities our blocking skew symmetric flow algorithm has time bounds similar to those established in 8 21 for dinits algorithm in particular this implies an algorithm for finding a maximum matching in a nonbipartite graph in time which matches the time bound for the algorithm of micali and vazirani 25 finally extending a clique compression technique of feder and motwani 9 to particular skew symmetric graphs we speed up the implied maximum matching algorithm to run in time improving the best known bound for dense nonbipartite graphs also other theoretical and algorithmic results on skew symmetric flows and their applications are presented

pathways of activated escape in periodically modulated systems we investigate dynamics of activated escape in periodically modulated systems the trajectories followed in escape form diffusion broadened tubes which are periodically repeated in time we show that these tubes can be directly observed and find their shape quantitatively the tubes are characterized by the distribution of trajectories that after escape pass through a given point in phase space for a given modulation phase this distribution may display several peaks separated by the modulation period analytical results agree with the results of simulations of a brownian particle in a model modulated potential

bayes inference in the tobit censored regression model we consider the bayes estimation of the tobit censored regression model with normally distributed errors a simple condition for the existence of posterior moments is provided suitable versions of monte carlo procedures based on symmetric multivariate t distributions and laplacian approximations in a certain parametrization are developed and illustrated ideas involving data augmentation and gibbs sampling cf tanner and wong 1987 and gelfand and smith 1990 are also developed the methods are compared in two examples with diffuse priors and various combinations of sample sizes and degrees of censoring

multichannel image compression by bijection mappings onto zero trees a new approach to multichannel image compression is introduced where the intra and cross band correlations are jointly exploited in a surprisingly simple yet very effective manner the key component of the algorithm is a bijection mapping of the original multichannel image into a virtual two dimensional 2 d scalar image by optimally mapping the multichannel image set into a 2 d array and by subsequently applying a scalar image coding algorithm the spatial correlation and the spectral correlation of the multichannel data set are jointly exploited based on the statistical characteristics of the multichannel data the bijection mapping can be optimized to minimize the distortion introduced by the compression algorithm the optimization reduces to the maximization of a function of the second order statistics of the multichannel data at high compression rates the new algorithm outperforms traditional compression algorithms whenever the cross band correlation is high and it yields comparable performance at low compression rates

comment on nonstationary optimal paths and tails of prehistory probability density in multistable stochastic systems a possible criterion to select the optimal path when more than a nonstationary path is found in multistable stochastic systems is discussed under this criterion some of the nonstationary paths derived in phys rev e 55 5338 1997 would not be optimal

band ordering in lossless compression of multispectral images in this paper we consider a model of lossless image compression in which each band of a multispectral image is coded using a prediction function involving values from a previously coded band of the compression and examine how the ordering of the bands affects the achievable compression we present an efficient algorithm for computing the optimal band ordering for a multispectral image this algorithm has time complexity o n sup for an n band image while the naive algorithm takes time spl omega n a slight variant of the optimal ordering problem that is motivated by some practical concerns is shown to be np hard and hence computationally infeasible in all cases except for the most trivial possibility in addition we report on our experimental findings using the algorithms designed in this paper applied to real multispectral satellite data the results show that the techniques described here hold great promise for application to real world compression needs

limiting exit location distributions in the stochastic exit problem consider a two dimensional continuous time dynamical system with an attracting fixed point s if the deterministic dynamics are perturbed by white noise random perturbations of strength epsilon the system state will eventually leave the domain of attraction omega of s we analyze the case when as epsilon to0 the exit location on the boundary partial omega is increasingly concentrated near a saddle point h of the deterministic dynamics we show using formal methods that the asymptotic form of the exit location distribution on partial omega is generically non gaussian and asymmetric and classify the possible limiting distributions a key role is played by a parameter mu equal to the ratio lambda s h lambda u h of the stable and unstable eigenvalues of the linearized deterministic flow at h if mu 1 then the exit location distribution is generically asymptotic as epsilon to0 to a weibull distribution with shape parameter 2 mu on the cal o epsilon mu 2

reactions in flows with nonhyperbolic dynamics we study the reaction dynamics of active particles that are advected passively by 2d incompressible open flows whose motion is nonhyperbolic this nonhyperbolicity is associated with the presence of persistent vortices near the wake wherein fluid is trapped we show that the fractal equilibrium distribution of the reactants is described by an effective dimension d mathit eff which is a finite resolution approximation to the fractal dimension furthermore d mathit eff depends on the resolution and on the reaction rate 1 ensuremath tau as ensuremath tau is increased the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly these transitions are determined by the complex structure of cantori surrounding the kolmogorov arnold moser kam islands

incremental assignment problem in this paper we introduce the incremental assignment problem in this problem a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known and the maximum weighted matching of the extended graph is sought we propose an o v 2 algorithm for the problem

stability properties of nonhyperbolic chaotic attractors with respect to noise we study local and global stability of nonhyperbolic chaotic attractors contaminated by noise the former is given by the maximum distance of a noisy trajectory from the noisefree attractor while the latter is provided by the minimal escape energy necessary to leave the basin of attraction calculated with the hamiltonian theory of large fluctuations we establish the important and counterintuitive result that both concepts may be opposed to each other even when one attractor is globally more stable than another one it can be locally less stable our results are exemplified with the holmes map for two different sets of parameter and with a juxtaposition of the holmes and the ikeda maps finally the experimental relevance of these findings is pointed out

noise enhanced stability in fluctuating metastable states we derive general equations for the nonlinear relaxation time of brownian diffusion in randomly switching potential with a sink for piece wise linear dichotomously fluctuating potential with metastable state we obtain the exact average lifetime as a function of the potential parameters and the noise intensity our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential we find noise enhanced stability phenomenon in the system investigated the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise we obtain the parameter region of the fluctuating potential where the effect can be observed the system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential

trace formula for noisy flows a trace formula is derived for the fokker planck equation associated with ito stochastic differential equations describing noisy time continuous nonlinear dynamical systems in the weak noise limit the trace formula provides estimations of the eigenvalues of the fokker planck operator on the basis of the pollicott ruelle resonances of the noiseless deterministic system which is assumed to be non bifurcating at first order in the noise amplitude the effect of noise on a periodic orbit is given in terms of the period and the derivative of the period with respect to the pseudo energy of the onsager machlup freidlin wentzell scheme

stochastic perturbations in open chaotic systems random versus noisy maps we investigate the effects of random perturbations on fully chaotic open systems perturbations can be applied to each trajectory independently white noise or simultaneously to all trajectories random map we compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time dependent conditionally map invariant measure for the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map in random maps we show that the escape rate ensuremath kappa and dimensions d of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation we discuss the accuracy bias and precision variance of finite size estimators of ensuremath kappa and d and show that the improvement of the precision of the estimations with the number of trajectories n is extremely slow ensuremath propto 1 mathrm ln n we also argue that the finite size d estimators are typically biased general theoretical results are combined with analytical calculations and numerical simulations in area preserving baker maps