spectral formulation and wkb approximation for rare event statistics in reaction systems we develop a spectral formulation and a stationary wkb approximation for calculating the probabilities of rare events large deviations from the mean in systems of reacting particles with infinite range interaction describable by a master equation we compare the stationary wkb approximation to a recent time dependent semiclassical approximation developed for the same class of problems by elgart and kamenev phys rev e 70 41106 2004 as a benchmark we use an exactly solvable problem of the binary annihilation reaction 2a 0

how colored environmental noise affects population extinction environmental noise can cause an exponential reduction in the mean time to extinction mte of an isolated population we study this effect on an example of a stochastic birth death process with rates modulated by a colored that is correlated gaussian noise a path integral formulation yields a transparent way of evaluating the mte and finding the optimal realization of the environmental noise that determines the most probable path to extinction the population size dependence of the mte changes from exponential in the absence of the environmental noise to a power law for a short correlated noise and to no dependence for long correlated noise we also establish the validity domains of the white noise limit and adiabatic limit

the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

a tabu search approach to the constraint satisfaction problem as a general problem solver many combinatorial problems including a variety of combinatorial optimization problems can be naturally formulated as a constraint satisfaction problem csp we develop in this paper a tabu search based algorithm for the csp as a foundation for a general problem solver in addition to the basic components of tabu search we develop a number of elaborations such as an automatic control mechanism for the tabu tenure modification of the penalty function to handle objective functions and enlargement of the neighborhood by allowing swap operations computational results with our algorithm are reported for various problems selected from a wide range of applications i e graph coloring generalized assignment set covering timetabling and nurse scheduling our results appear to be competitive with those of existing algorithms specially developed for the respective problem domains

the equilibrium generalized assignment problem and genetic algorithm abstract the well known generalized assignment problem gap is to minimize the costs of assigning n jobs to m capacity constrained agents or machines such that each job is assigned to exactly one agent this problem is known to be np hard and it is hard from a computational point of view as well in this paper follows from practical point of view in real systems the gap is extended to the equilibrium generalized assignment problem egap and the equilibrium constrained generalized assignment problem ecgap a heuristic equilibrium strategy based genetic algorithm ga is designed for solving the proposed egap finally to verify the computational efficiency of the designed ga some numerical experiments are performed on some known benchmarks the test results show that the designed ga is very valid for solving egap

lagrangian relaxation guided problem space search heuristics for generalized assignment problems we develop and test a heuristic based on lagrangian relaxation and problem space search to solve the generalized assignment problem gap the heuristic combines the iterative search capability of subgradient optimization used to solve the lagrangian relaxation of the gap formulation and the perturbation scheme of problem space search to obtain high quality solutions to the gap we test the heuristic using different upper bound generation routines developed within the overall mechanism using the existing problem data sets of various levels of difficulty and sizes including the challenging largest instances we observe that the heuristic with a specific version of the upper bound routine works well on most of the benchmark instances known and provides high quality solutions quickly an advantage of the approach is its generic nature simplicity and implementation flexibility

degree dispersion increases the rate of rare events in population networks there is great interest in predicting rare and extreme events in complex systems and in particular understanding the role of network topology in facilitating such events in this letter we show that degree dispersion the fact that the number of local connections in networks varies broadly increases the probability of large rare fluctuations in population networks generically we perform explicit calculations for two canonical and distinct classes of rare events network extinction and switching when the distance to threshold is held constant and hence stochastic effects are fairly compared among networks we show that there is a universal exponential increase in the rate of rare events proportional to the variance of a network s degree distribution over its mean squared

extinction rates for fluctuation induced metastabilities a real space wkb approach the extinction of a single species due to demographic stochasticity is analyzed the discrete nature of the individual agents and the poissonian noise related to the birth death processes result in local extinction of a metastable population as the system hits the absorbing state the fokker planck formulation of that problem fails to capture the statistics of large deviations from the metastable state while approximations appropriate close to the absorbing state become in general invalid as the population becomes large to connect these two regimes a real space wkb method based on the master equation is presented and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to the absorbing state the details of the underlying microscopic process smeared out in a mean field treatment are shown to be crucial for an exact determination of the extinction exponent this general scheme is shown to reproduce the known results in the field to yield new corollaries and to fit quite precisely the numerical solutions moreover it allows for systematic improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable state

distinguished material surfaces and coherent structures in three dimensional fluid flows we prove analytic criteria for the existence of finite time attracting and repelling material surfaces and lines in three dimensional unsteady flows the longest lived such structures define coherent structures in a lagrangian sense our existence criteria involve the invariants of the velocity gradient tensor along fluid trajectories an alternative approach to coherent structures is shown to lead to their characterization as local maximizers of the largest finite time lyapunov exponent field computed directly from particle paths both approaches provide effective tools for extracting distinguished lagrangian structures from three dimensional velocity data we illustrate the results on steady and unsteady abc type flows

an iterative action minimizing method for computing optimal paths in stochastic dynamical systems abstract we present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations sdes in particular we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic hamiltonian system the numerical method presented here involves using an iterative scheme for solving a two point boundary value problem for the hamiltonian system we validate our method by applying it to both continuous stochastic systems such as nonlinear oscillators governed by the duffing equation and finite discrete systems such as epidemic problems which are governed by a set of master equations furthermore we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations

an effective vns for the capacitated p median problem in the capacitated p median problem cpmp a set of n customers is to be partitioned into p disjoint clusters such that the total dissimilarity within each cluster is minimized subject to constraints on maximum cluster capacity dissimilarity of a cluster is the sum of the dissimilarities between each customer who belongs to the cluster and the median associated with the cluster an effective variable neighbourhood search heuristic for this problem is proposed the heuristic is characterized by the use of easily computed lower bounds to assess whether undertaking computationally expensive calculation of the worth of moves within the neighbourhood search is necessary the small proportion of moves that need to be assessed fully are then evaluated by an exact solution of a relatively small subproblem computational results on five standard sets of benchmark problem instances show that the heuristic finds all the best known solutions for one instance the previously best known solution is improved if only marginally

evolution of a fluctuating population in a randomly switching environment environment plays a fundamental role in the competition for resources and hence in the evolution of populations here we study a well mixed finite population consisting of two strains competing for the limited resources provided by an environment that randomly switches between states of abundance and scarcity assuming that one strain grows slightly faster than the other we consider two scenarios one of pure resource competition and one in which one strain provides a public good and investigate how environmental randomness external noise coupled to demographic internal noise determines the population s fixation properties and size distribution by analytical means and simulations we show that these coupled sources of noise can significantly enhance the fixation probability of the slower growing species we also show that the population size distribution can be unimodal bimodal or multimodal and undergoes noise induced transitions between these regimes when the rate of switching matches the population s growth rate

principles of scatter search scatter search is an evolutionary method that has been successfully applied to hard optimization problems the fundamental concepts and principles of the method were first proposed in the 1970s based on formulations dating back to the 1960s for combining decision rules and problem constraints in contrast to other evolutionary methods like genetic algorithms scatter search is founded on the premise that systematic designs and methods for creating new solutions afford significant benefits beyond those derived from recourse to randomization it uses strategies for search diversification and intensification that have proved effective in a variety of optimization problems this paper provides the main principles and ideas of scatter search and its generalized form path relinking we first describe a basic design to give the reader the tools to create relatively simple implementations more advanced designs derive from the fact that scatter search and path relinking are also intimately related to the tabu search ts metaheuristic and gain additional advantage by making use of ts adaptive memory and associated memory exploiting mechanisms capable of being tailored to particular contexts these and other advanced processes described in the paper facilitate the creation of sophisticated implementations for hard problems that often arise in practical settings due to their flexibility and proven effectiveness scatter search and path relinking can be successfully adapted to tackle optimization problems spanning a wide range of applications and a diverse collection of structures as shown in the papers of this volume

stochastic dynamics and logistic population growth the verhulst model is probably the best known macroscopic rate equation in population ecology it depends on two parameters the intrinsic growth rate and the carrying capacity these parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources respectively we investigate analytically and numerically the simplest possible microscopic scenarios that give rise to the logistic equation in the deterministic mean field limit we provide a definition of the two parameters of the verhulst equation in terms of microscopic parameters in addition we derive the conditions for extinction or persistence of the population by employing either the momentum space spectral theory or the real space wentzel kramers brillouin approximation to determine the probability distribution function and the mean time to extinction of the population our analytical results agree well with numerical simulations

intrinsic noise in systems with switching environments we study individual based dynamics in finite populations subject to randomly switching environmental conditions these are inspired by models in which genes transition between on and off states regulating underlying protein dynamics similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread existing piecewise deterministic markov process approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear noise approximation specifically we derive the stationary distributions of a number of model systems in good agreement with simulations this improves existing approaches which are limited to the regimes of fast and slow switching

taming the diffusion approximation through a controlling factor wkb method the diffusion approximation da is widely used in the analysis of stochastic population dynamics from population genetics to ecology and evolution the da is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied this failure becomes severe in situations where the direction of selection switches sign here we employ the wkb wentzel kramers brillouin large deviations method which requires only the logarithm of a given quantity to be smooth over its state space combining the wkb scheme with asymptotic matching techniques we show how to derive the diffusion approximation in a controlled manner and how to produce better approximations applicable for much wider regimes of parameters we also introduce a scalable independent of population size wkb based numerical technique the method is applied to a central problem in population genetics and evolution finding the chance of ultimate fixation in a zero sum two types competition

a path relinking approach with ejection chains for the generalized assignment problem the generalized assignment problem is a classical combinatorial optimization problem known to be np hard it can model a variety of real world applications in location allocation machine assignment and supply chains the problem has been studied since the late 1960s and computer codes for practical applications emerged in the early 1970s we propose a new algorithm for this problem that proves to be more effective than previously existing methods the algorithm features a path relinking approach which is a mechanism for generating new solutions by combining two or more reference solutions it also features an ejection chain approach which is embedded in a neighborhood construction to create more complex and powerful moves computational comparisons on benchmark instances show that the method is not only effective in general but is especially effective for types d and e instances which are known to be very difficult

disease extinction in the presence of random vaccination we investigate disease extinction in an epidemic model described by a birth death process we show that in the absence of vaccination the effective entropic barrier for extinction displays scaling with the distance to the bifurcation point with an unusual critical exponent even a comparatively weak poisson distributed random vaccination leads to an exponential increase in the extinction rate with the exponent that strongly depends on the vaccination parameters

colonization of a territory by a stochastic population under a strong allee effect and a low immigration pressure we study the dynamics of colonization of a territory by a stochastic population at low immigration pressure we assume a sufficiently strong allee effect that introduces in deterministic theory a large critical population size for colonization at low immigration rates the average precolonization population size is small thus invalidating the wkb approximation to the master equation we circumvent this difficulty by deriving an exact zero flux solution of the master equation and matching it with an approximate nonzero flux solution of the pertinent fokker planck equation in a small region around the critical population size this procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization for a wide range of immigration rates at sufficiently high immigration rates our results agree with wkb results obtained previously at low immigration rates the results can be very different

population extinction risk in the aftermath of a catastrophic event we investigate how a catastrophic event modeled as a temporary fall of the reproduction rate increases the extinction probability of an isolated self regulated stochastic population using a variant of the verhulst logistic model as an example we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction probability caused by the catastrophe this quantity is given by the eikonal action computed over the optimal path instanton of an effective classical hamiltonian system with a time dependent hamiltonian for a general catastrophe the eikonal equations can be solved numerically for simple models of catastrophic events analytic solutions can be obtained one such solution becomes quite simple close to the bifurcation point of the verhulst model the eikonal results for the increase in the extinction probability caused by a catastrophe agree well with numerical solutions of the master equation

extinction of an infectious disease a large fluctuation in a nonequilibrium system we develop a theory of first passage processes in stochastic nonequilibrium systems of birth death type using two closely related epidemiological models as examples our method employs the probability generating function technique in conjunction with the eikonal approximation in this way the problem is reduced to finding the optimal path to extinction a heteroclinic trajectory of an effective multidimensional classical hamiltonian system we compute this trajectory and mean extinction time of the disease numerically and uncover a nonmonotone spiral path to extinction of a disease we also obtain analytical results close to a bifurcation point where the problem is described by a hamiltonian previously identified in one species population models

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

large negative velocity gradients in burgers turbulence we consider one dimensional burgers equation driven by large scale white in time random force the tails of the velocity gradients probability distribution function pdf are analyzed by saddle point approximation in the path integral describing the velocity statistics the structure of the saddle point instanton that is the velocity field configuration realizing the maximum of probability is studied numerically in details the numerical results allow us to find analytical solution for the long time part of the instanton its careful analysis confirms the result of balkovsky et al phys rev lett 78 1452 1997 based on short time estimations that the left tail of pdf has the form mathrm ln mathcal p u x ensuremath propto ensuremath u x 3 2

tabu search for the multilevel generalized assignment problem abstract the multilevel generalized assignment problem mgap differs from the classical gap in that agents can perform tasks at more than one efficiency level important manufacturing problems such as lot sizing can be formulated as mgaps however the large number of variables in the related 0 1 integer program makes the use of commercial optimization packages impractical in this paper we present a heuristic approach to the solution of the mgap which consists of a novel application of tabu search ts our ts method employs neighborhoods defined by ejection chains that produce moves of greater power without significantly increasing the computational effort

extinction of metastable stochastic populations we investigate the phenomenon of extinction of a long lived self regulating stochastic population caused by intrinsic demographic noise extinction typically occurs via one of two scenarios depending on whether the absorbing state n 0 is a repelling scenario a or attracting scenario b point of the deterministic rate equation in scenario a the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n 0 in scenario b there is an intermediate repelling point n n 1 between the attracting point n 0 and another attracting point n n 2 in the vicinity of which the metastable population resides the crux of the theory is a dissipative variant of wkb wentzel kramers brillouin approximation which assumes that the typical population size in the metastable state is large starting from the master equation we calculate the quasistationary probability distribution of the population sizes and the exponentially long mean time to extinction for each of the two scenarios when necessary the wkb approximation is complemented i by a recursive solution of the quasistationary master equation at small n and ii by the van kampen system size expansion valid near the fixed points of the deterministic rate equation the theory yields both entropic barriers to extinction and pre exponential factors and holds for a general set of multistep processes when detailed balance is broken the results simplify considerably for single step processes and near the characteristic bifurcations of scenarios a and b

chemical langevin equation a path integral view of gillespie s derivation in 2000 gillespie rehabilitated the chemical langevin equation cle by describing two conditions that must be satisfied for it to yield a valid approximation of the chemical master equation cme in this work we construct an original path integral description of the cme and show how applying gillespie s two conditions to it directly leads to a path integral equivalent to the cle we compare this approach to the path integral equivalent of a large system size derivation and show that they are qualitatively different in particular both approaches involve converting many sums into many integrals and the difference between the two methods is essentially the difference between using the euler maclaurin formula and using riemann sums our results shed light on how path integrals can be used to conceptualize coarse graining biochemical systems and are readily generalizable

a hybrid tabu search branch bound approach to solving the generalized assignment problem a new approach for solving the generalized assignment problem gap is proposed that combines the exact branch bound approach with the heuristic strategy of tabu search ts to produce a hybrid algorithm for solving gap the algorithm described uses commercial software to solve sub problems generated by the ts guiding strategy the ts approach makes use of the concept of referent domain optimisation and introduces novel add drop strategies in addition the linear programming relaxation of gap that forms part of the branch bound approach is itself helpful in suggesting which variables might take binary values computational results on benchmark test instances are presented and compared with results obtained by the standard branch bound approach and also several other heuristic approaches from the literature the results show the new algorithm performs competitively against the alternatives and is able to find some new best solutions for several benchmark instances

a tabu search heuristic for the generalized assignment problem abstract this paper considers the generalized assignment problem gap it is a well known np hard combinatorial optimization problem that is interesting in itself and also appears as a subproblem in other problems of practical importance a tabu search heuristic for the gap is proposed the algorithm uses recent and medium term memory to dynamically adjust the weight of the penalty incurred for violating feasibility the most distinctive features of the proposed algorithm are its simplicity and its flexibility these two characteristics result in an algorithm that compared to other well known heuristic procedures provides good quality solutions in competitive computational times computational experiments have been performed in order to evaluate the behavior of the proposed algorithm

molecular evolution under fitness fluctuations molecular evolution is a stochastic process governed by fitness mutations and reproductive fluctuations in a population here we study evolution where fitness itself is stochastic with random switches in the direction of selection at individual genomic loci as the correlation time of these fluctuations becomes larger than the diffusion time of mutations within the population fitness changes from an annealed to a quenched random variable we show that the rate of evolution has its maximum in the crossover regime where both time scales are comparable adaptive evolution emerges in the quenched fitness regime evidence for such fitness fluctuations has recently been found in genomic data the joint statistical theory of reproductive and fitness fluctuations establishes a conceptual connection between evolutionary genetics and statistical physics of disordered systems

the geometric minimum action method a least action principle on the space of curves freidlin wentzell theory of large deviations for the description of the effect of small random perturbations on dynamical systems is exploited as a numerical tool specifically a numerical algorithm is proposed to compute the quasi potential in the theory which is the key object to quantify the dynamics on long time scales when the effect of the noise becomes ubiquitous the equilibrium distribution of the system the pathways of transition between metastable states and their rate etc can all be expressed in terms of the quasi potential we propose an algorithm to compute these quantities called the geometric minimum action method gmam which is a blend of the original minimum action method mam and the string method it is based on a reformulation of the large deviations action functional on the space of curves that allows one to easily perform the double minimization of the original action required to compute the quasi potential the theoretical background of the gmam in the context of large deviations theory is discussed in detail as well as the algorithmic aspects of the method the gmam is then illustrated on several examples a finite dimensional system displaying bistability and modeled by a nongradient stochastic ordinary differential equation an infinite dimensional analogue of this system modeled by a stochastic partial differential equation and an example of a bistable genetic switch modeled by a markov jump process

sharp asymptotics for the quasi stationary distribution of birth and death processes we study a general class of birth and death processes with state space mathbb n that describes the size of a population going to extinction with probability one this class contains the logistic case the scale of the population is measured in terms of a carrying capacity k when k is large the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes extinct our aim is to quantify the behavior of the process and the mean time to extinction in the quasi stationary distribution as a function of k for large k we also give a quantitative description of this quasi stationary distribution it turns out to be close to a gaussian distribution centered about the deterministic long time equilibrium when k is large our analysis relies on precise estimates of the maximal eigenvalue of the corresponding eigenvector and of the spectral gap of a self adjoint operator associated with the semigroup of the process

on approximate solution of hammerstein integral equations in the space l p p 1 this paper deals with an approximate method for solving hammerstein integral equation this method is based on the replacement of the kernel of the given equation by degenerate kernel and which it has a solution equivalent to the solution of a system of nonlinear algebraic equations suitable numerical technique can be used to obtain the results of that problem at the end of this paper numerical examples were presented

stability measures in metastable states with gaussian colored noise we present a study of the escape time from a metastable state of an overdamped brownian particle in the presence of colored noise generated by ornstein uhlenbeck process we analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity we observe the noise enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau c investigated we can distinguish two dynamical regimes characterized by weak and strong correlated noises depending on the value of tau c with respect to the relaxation time of the system

phase diagram for logistic systems under bounded stochasticity extinction is the ultimate absorbing state of any stochastic birth death process hence the time to extinction is an important characteristic of any natural population here we consider logistic and logisticlike systems under the combined effect of demographic and bounded environmental stochasticity three phases are identified an inactive phase where the mean time to extinction t increases logarithmically with the initial population size an active phase where t grows exponentially with the carrying capacity n and a temporal griffiths phase with a power law relationship between t and n the system supports an exponential phase only when the noise is bounded in which case the continuum diffusion approximation breaks down within the griffiths phase this breakdown is associated with a crossover between qualitatively different survival statistics and decline modes to study the power law phase we present a new wkb scheme which is applicable both in the diffusive and in the nondiffusive regime

a branch and price algorithm for the generalized assignment problem the generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents a new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem

population switching under a time varying environment we study the switching dynamics of a stochastic population subjected to a deterministically time varying environment our approach is demonstrated on a problem of population establishment which is important in ecology at the deterministic level the model we study gives rise to a critical population size beyond which the system experiences establishment notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental variations here we consider two prototypical examples of a time varying environment a temporary change in the environment and a periodically varying environment by employing a semiclassical approximation we compute within exponential accuracy the change in the establishment probability and mean establishment time of the population due to the environmental variability our analytical results are verified by using a modified gillespie algorithm which accounts for explicitly time dependent reaction rates importantly our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under external variations

bees algorithm for generalized assignment problem bees algorithm ba is a new member of meta heuristics ba tries to model natural behavior of honey bees in food foraging honey bees use several mechanisms like waggle dance to optimally locate food sources and to search new ones this makes them a good candidate for developing new algorithms for solving optimization problems in this paper a brief review of ba is first given afterwards development of a ba for solving generalized assignment problems gap with an ejection chain neighborhood mechanism is presented gap is a np hard problem many meta heuristic algorithms were proposed for its solution so far ba is generally applied to continuous optimization in order to investigate the performance of ba on a complex integer optimization problem an attempt is made in this paper an extensive computational study is carried out and the results are compared with several algorithms from the literature

theory of time averaged neutral dynamics with environmental stochasticity competition is the main driver of population dynamics which shapes the genetic composition of populations and the assembly of ecological communities neutral models assume that all the individuals are equivalent and that the dynamics is governed by demographic shot noise with a steady state species abundance distribution sad that reflects a mutation extinction equilibrium recently many empirical and theoretical studies emphasized the importance of environmental variations that affect coherently the relative fitness of entire populations here we consider two generic time averaged neutral models in both the relative fitness of each species fluctuates independently in time but its mean is zero the first model a describes a system with local competition and linear fitness dependence of the birth death rates while in the second model b the competition is global and the fitness dependence is nonlinear due to this nonlinearity model b admits a noise induced stabilization mechanism that facilitates the invasion of new mutants a self consistent mean field approach is used to reduce the multispecies problem to two species dynamics and the large n asymptotics of the emerging set of fokker planck equations is presented and solved our analytic expressions are shown to fit the sads obtained from extensive monte carlo simulations and from numerical solutions of the corresponding master equations

definition and properties of lagrangian coherent structures from finite time lyapunov exponents in two dimensional aperiodic flows this paper develops the theory and computation of lagrangian coherent structures lcs which are defined as ridges of finite time lyapunov exponent ftle fields these ridges can be seen as finite time mixing templates such a framework is common in dynamical systems theory for autonomous and time periodic systems in which examples of lcs are stable and unstable manifolds of fixed points and periodic orbits the concepts defined in this paper remain applicable to flows with arbitrary time dependence and in particular to flows that are only defined computed or measured over a finite interval of time previous work has demonstrated the usefulness of ftle fields and the associated lcss for revealing the lagrangian behavior of systems with general time dependence however ridges of the ftle field need not be exactly advected with the flow the main result of this paper is an estimate for the flux across an lcs which shows that the flux is small and in most cases negligible for well defined lcss or those that rotate at a speed comparable to the local eulerian velocity field and are computed from ftle fields with a sufficiently long integration time under these hypotheses the structures represent nearly invariant manifolds even in systems with arbitrary time dependence the results are illustrated on three examples the first is a simplified dynamical model of a double gyre flow the second is surface current data collected by high frequency radar stations along the coast of florida and the third is unsteady separation over an airfoil in all cases the existence of lcss governs the transport and it is verified numerically that the flux of particles through these distinguished lines is indeed negligible

interfacial velocity corrections due to multiplicative noise the problem of velocity selection for reaction fronts has been intensively investigated leading to the successful marginal stability ms approach for propagation into an unstable state because the front velocity is controlled by the leading edge which perforce has low density it is interesting to study the role that finite particle number fluctuations have on this picture here we use the well known mapping of discrete markov processes to stochastic differential equations and focus on the front velocity in the simple a a ensuremath leftrightarrows a system our results are consistent with a recent heuristic proposal that v mathrm ms ensuremath v ensuremath sim 1 mathrm ln 2 n

dynamics of simple gene network motifs subject to extrinsic fluctuations cellular processes do not follow deterministic rules even in identical environments genetically identical cells can make random choices leading to different phenotypes this randomness originates from fluctuations present in the biomolecular interaction networks most previous work has been focused on the intrinsic noise in of these networks yet especially for high copy number biomolecules extrinsic or environmental noise en has been experimentally shown to dominate the variation here we develop an analytical formalism that allows for calculation of the effect of en on gene expression motifs we introduce a method for modeling bounded en as an auxiliary species in the master equation the method is fully generic and is not limited to systems with small en magnitudes we focus our study on motifs that can be viewed as the building blocks of genetic switches a nonregulated gene a self inhibiting gene and a self promoting gene the role of the en properties magnitude correlation time and distribution on the statistics of interest are systematically investigated and the effect of fluctuations in different reaction rates is compared due to its analytical nature our formalism can be used to quantify the effect of en on the dynamics of biochemical networks and can also be used to improve the interpretation of data from single cell gene expression experiments

enhancement of large fluctuations to extinction in adaptive networks during an epidemic individual nodes in a network may adapt their connections to reduce the chance of infection a common form of adaption is avoidance rewiring where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible infected susceptible model focusing on the largest fluctuations that result in extinction of infection using techniques from large deviation theory combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state we are able to predict and analyze large fluctuations and extinction in adaptive networks we find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption furthermore we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate even when holding the average number of infected nodes constant

noise driven unlimited population growth demographic noise causes unlimited population growth in a broad class of models which without noise would predict a stable finite population we study this effect on the example of a stochastic birth death model which includes immigration binary reproduction and death the unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution mpd of the population we develop a systematic wkb theory complemented by the van kampen system size expansion for the mpd and for the decay time important signatures of the mpd are a power law tail such that all the distribution moments except the zeroth one diverge and the presence in the solution of two different wkb modes

a chebyshev approximation for solving optimal control problems abstract this paper presents a numerical solution for solving optimal control problems and the controlled duffing oscillator a new chebyshev spectral procedure is introduced control variables and state variables are approximated by chebyshev series then the system dynamics is transformed into systems of algebraic equations the optimal control problem is reduced to a constrained optimization problem results and comparisons are given at the end of the paper

population extinction under bursty reproduction in a time modulated environment in recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations for example nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size or environmental variability in the form of time varying reaction rates have been separately found to dramatically impact the extinction risk of isolated populations in this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation using the so called momentum space wentzel kramers brillouin wkb approach and accounting for the explicit time dependence in the reaction rates we arrive at a set of time dependent hamilton equations to this end we evaluate the population s extinction risk by finding the instanton of the time perturbed hamiltonian numerically whereas analytical expressions are presented in particular limits using various perturbation techniques we focus on two classes of time varying environments periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe all our theoretical results are tested against numerical monte carlo simulations with time dependent rates and also against a numerical solution of the corresponding time dependent hamilton equations

field theory of branching and annihilating random walks we develop a systematic analytic approach to the problem of branching and annihilating random walks equivalent to the diffusion limited reaction processes 2a and a m 1 a where m 1 starting from the master equation a field theoretic representation of the problem is derived and fluctuation effects are taken into account via diagrammatic and renormalization group methods for d 2 the mean field rate equation which predicts an active phase as soon as the branching process is switched on applies qualitatively for both even and odd m but the behavior in lower dimensions is shown to be quite different for these two cases for even m and d near 2 the active phase still appears immediately but with nontrivial crossover exponents which we compute in an expansion in 2 d and with logarithmic corrections in d 2 however there exists a second critical dimension d c 4 3 below which a nontrivial inactive phase emerges with asymptotic behavior characteristic of the pure annihilation process this is confirmed by an exact calculation in d 1 the subsequent transition to the active phase which represents a new nontrivial dynamic universality class is then investigated within a truncated loop expansion which appears to give a correct qualitative picture the model with m 2 is also generalized to n species of particles which provides yet another universality class and which is exactly solvable in the limit n for odd m we show that the fluctuations of the annihilation process are strong enough to create a nontrivial inactive phase for all d 2 in this case the transition to the active phase is in the directed percolation universality class finally we study the modification when the annihilation reaction is 3a when m 0 mod 3 the system is always in its active phase but with logarithmic crossover corrections for d 1 while the other cases should exhibit a directed percolation transition out of a fluctuation driven inactive phase

on existence of unique solution to non linear integral equations of the second kind this paper we employ the technique of degenerate kernel method by using the linear polynomial operator which plays an important role in study of numerical technique can be used to obtain the results of that problem a numerical example is reported at the end of this paper to illustrate our technique

reducing the extinction risk of stochastic populations via nondemographic noise we consider nondemographic noise in the form of uncertainty in the reaction step size and reveal a dramatic effect this noise may have on the stability of self regulating populations employing the reaction scheme ma ka but allowing e g the product number k to be a priori unknown and sampled from a given distribution we show that such nondemographic noise can greatly reduce the population s extinction risk compared to the fixed k case our analysis is tested against numerical simulations and by using empirical data of different species we argue that certain distributions may be more evolutionary beneficial than others