multiplicative noise induced coherence resonance via two different mechanisms in bistable neural models the bistable fitzhugh nagumo fhn neural model driven by two multiplicative noises and one additive noise is investigated two different potential mechanisms for enhancing coherence of bistable fhn model are presented that is the first multiplicative noise changes the system from the bistable to the oscillatory regime and the second multiplicative noise can enhance the symmetry of two stable states of the system the two mechanisms are analytically or numerically explained at any level of the second multiplicative noise a maximal coherence have been found at some intermediate noise intensity of the first multiplicative noise only when the first multiplicative noise intensity is less than 0 0001 can a maximal coherence be obtained at some intermediate noise intensity of the second multiplicative noise these coherence resonance phenomena have been understood in terms of the presented mechanisms

linear response theory applied to stochastic resonance in models of ensembles of oscillators we apply linear response theory to a parallel ensemble of stochastic resonators we show that for a large number of elements the system can be used to process broadband signals without frequency distortions both conventional stochastic resonance and aperiodic stochastic resonance are studied

control of cardiac function and noise from a decaying power spectrum evidence is presented that adds to the debate surrounding the question to what extent does neural control of cardiac output exploit noise the transduction capability of cardiac afferent neurons situated in and adjacent to the heart is vital to feedback in control of cardiac function an analysis of in situ cardiac afferent activity shows evidence of independent and exponentially distributed interspike intervals an anatomical basis for such memoryless interspike intervals ultimately derives from the fact that each afferent neuron is associated with a field of sensory neurites or bare nerve endings that transduce local chemical and mechanical stimuli in a many to one fashion as such cardiac afferent neurons and their sensory neurite inputs are respectively modeled here by the hodgkin huxley equations forced by red noise decaying power spectrum perturbing an otherwise constant subthreshold input a variable barrier competition model is derived from these equations in order to address the question how are noisy inputs being processed by sensory neurons to cause each spike it is found that ion channels are responsible for significant input whitening increased spectral power at higher frequency through differentiation of the inputs such whitening is a means to distinguish low frequency control signals from otherwise red noise fluctuations furthermore spiking occurs when backward moving averages of the whitened inputs over a window of the order of the sodium activation time scale exceed an approximately constant barrier

competition model for aperiodic stochastic resonance in a fitzhugh nagumo model of cardiac sensory neurons regional cardiac control depends upon feedback of the status of the heart from afferent neurons responding to chemical and mechanical stimuli as transduced by an array of sensory neurites emerging experimental evidence shows that neural control in the heart may be partially exerted using subthreshold inputs that are amplified by noisy mechanical fluctuations this amplification is known as aperiodic stochastic resonance asr neural control in the noisy subthreshold regime is difficult to see since there is a near absence of any correlation between input and the output the latter being the average firing spiking rate of the neuron this lack of correlation is unresolved by traditional energy models of asr since these models are unsuitable for identifying cause and effect between such inputs and outputs in this paper the competition between averages model is used to determine what portion of a noisy subthreshold input is responsible on average for the output of sensory neurons as represented by the fitzhugh nagumo equations a physiologically relevant conclusion of this analysis is that a nearly constant amount of input is responsible for a spike on average and this amount is approximately independent of the firing rate hence correlation measures are generally reduced as the firing rate is lowered even though neural control under this model is actually unaffected

schmitt trigger a solvable model of stochastic resonance an ideal schmitt trigger st is the simplest two state system available for realization of stochastic resonance sr an exact solution is found for the st driven by exponentially correlated gaussian noise plus a weak periodic signal the signal to noise ratio is shown to pass through a maximum at a specific value of the noise intensity a qualitative classification is given for a class of noise models which either exhibit sr or do not

metric based mathematical derivation of efficient airfoil design variables within an aerodynamic shape optimization framework an efficient shape parameterization and deformation scheme is critical to allow flexible deformation of the surface with the maximum possible design space coverage numerous approaches have been developed for the geometric representation of airfoils a fundamental approach is considered here from the geometric perspective and a method is presented to allow the derivation of efficient generic and orthogonal airfoil geometric design variables this is achieved by the mathematical decomposition of a training library the resulting geometric modes are independent of a parameterization scheme surface and volume mesh and flow solver thus they are generally applicable however these modes are dependent on the training library and so a benchmark performance measure called the airfoil technology factor has also been incorporated into the scheme to allow intelligent metric based filtering or design space reduction of the training library to ensure eff

analytical approach to the stochastic fitzhugh nagumo system and coherence resonance we consider the fitzhugh nagumo system under the influence of white gaussian noise in the excitable regime we present an analytical approximation in the limit of fast activator time scale marginal probability densities of a reduced system and dynamical quantities such as the pulse rate are found and the mean interspike interval and its relative standard deviation are investigated the latter quantities allow a quantitative description of the phenomenon of coherence resonance as comparisons with simulations show

noisy fitzhugh nagumo model from single elements to globally coupled networks we study the noisy fitzhugh nagumo model representative of the dynamics of excitable neural elements and derive a fokker planck equation for both a single element and for a network of globally coupled elements we introduce an efficient way to numerically solve this fokker planck equation especially for large noise levels we show that contrary to the single element the network can undergo a hopf bifurcation as the coupling strength is increased furthermore we show that an external sinusoidal driving force leads to a classical resonance when its frequency matches the underlying system frequency this resonance is also investigated analytically by exploiting the different time scales in the problem

stochastic sensitivity of systems driven by colored noise abstract we study a response of the general nonlinear dynamic system to the colored noise a stochastic sensitivity analysis of equilibria forced by small exponentially correlated gaussian noise is carried out for the stochastic sensitivity matrix of the equilibrium a system of matrix equations is derived and explicit solution is found in 2d case applying these theoretical results we study a response of fitzhugh nagumo model to colored noise we analyze how dispersion of random states near the deterministic equilibrium depends on the characteristic time of the power limited colored noise the effect of the colored noise induced excitability is discussed

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

dynamic journeying under uncertainty abstract we introduce a journey planning problem in multi modal transportation networks under uncertainty the goal is to find a journey possibly involving transfers between different transport services from a given origin to a given destination within a specified time horizon due to uncertainty in travel times the arrival times of transport services at public transport stops are modeled as random variables if a transfer between two services is rendered unsuccessful the commuter has to reconsider the remaining path to the destination the problem is modeled as a markov decision process in which states are defined as paths in the transport network the main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time by assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination the proposed approximations may be useful for practical purposes due to their computational simplicity in addition to on time arrival probability we show how travel and overdue costs can be taken into account making the model applicable to freight transportation problems

excitable systems with noise and delay with applications to control renewal theory approach we present an approach for the analytical treatment of excitable systems with noise induced dynamics in the presence of time delay an excitable system is modeled as a bistable system with a time delay while another delay enters as a control term taken after pyragas k pyragas phys lett a 170 421 1992 as a difference between the current system state and its state tau time units before this approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term

synchronization and desynchronization in a network of locally coupled wilson cowan oscillators a network of wilson cowan wc oscillators is constructed and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis the network is a 2d matrix where each oscillator is coupled only to its neighbors we show analytically that a chain of locally coupled oscillators the piecewise linear approximation to the wc oscillator synchronizes and we present a technique to rapidly entrain finite numbers of oscillators the coupling strengths change on a fast time scale based on a hebbian rule a global separator is introduced which receives input from and sends feedback to each oscillator in the matrix the global separator is used to desynchronize different oscillator groups unlike many other models the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding gestalt principles of feature grouping the ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure ground segregation based on oscillatory correlation

analytical approach to an integrate and fire model with spike triggered adaptation the calculation of the steady state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale the theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron i a membrane potential distribution with a convex shape ii a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation and iii a maximized variability associated with the adaptation current at a finite adaptation time scale

control of noise induced oscillations by delayed feedback abstract we propose a method to control noise induced motion based on using delayed feedback in the form of the difference between the delayed and the current states of the system the method is applied to two different types of systems namely a self oscillator near andronov hopf bifurcation and a threshold system in both cases we demonstrate that by variation of time delay one can effectively control coherence and timescales of stochastic oscillations the entrainment of the basic period of oscillations by time delay is discovered we give explanations of the phenomena observed and provide a theory for the system near bifurcation

mixed mode oscillations in a stochastic piecewise linear system abstract we analyse a piecewise linear fitzhugh nagumo model the system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist the addition of small noise induces mixed mode oscillations mmos in the vicinity of the canard point we determine the effect of each model parameter on the stochastically driven mmos in particular we show that any parameter variation such as a modification of the piecewise linear function in the model that leaves the ratio of noise amplitude to time scale separation unchanged typically has little effect on the width of the interval of the primary bifurcation parameter over which mmos occur in that sense the mmos are robust furthermore we show that the piecewise linear model exhibits mmos more readily than the classical fitzhugh nagumo model for which a cubic polynomial is the only nonlinearity by studying a piecewise linear model we are able to explain results using analytical expressions and compare these with numerical investigations

noise induced escape in an excitable system we consider the stochastic dynamics of escape in an excitable system the fitzhugh nagumo fhn neuronal model for different classes of excitability we discuss first the threshold structure of the fhn model as an example of a system without a saddle state we then develop a nonlinear nonlocal stability approach based on the theory of large fluctuations including a finite noise correction to describe noise induced escape in the excitable regime we show that the threshold structure is revealed via patterns of most probable optimal fluctuational paths the approach allows us to estimate the escape rate and the exit location distribution we compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli unlike the commonly used local analysis of the stable state our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the langevin equation

gradient limiting shape control for efficient aerodynamic optimization local shape control methods such as b spline surfaces are well conditioned such that they allow high fidelity design optimization however this comes at the cost of degraded optimization converg

noise driven switching between limit cycles and adaptability in a small dimensional excitable network with balanced coupling we study a system of globally coupled fitzhugh nagumo equations each unit is either excitatory or inhibitory if the numbers of units of both types are in a specific ratio we observe the presence of multistable oscillatory states with different excitation or firing rates in the presence of noise there is noise driven switching between these states and the resultant firing pattern is long range correlated the choice between higher and lower frequency oscillations depends on the input which results in increasing adaptability of the system s output to the periodic input

technical note a note on the stochastic shortest route problem an optimality index for choosing the shortest route in an acyclic stochastic network has recently been proposed the present note identifies certain anomalies in using that index and proposes another optimality index the results of using these indices are compared in a simple example

arc reduction and path preference in stochastic acyclic networks the paper presents a heuristic for determining the path that maximizes the expected utility of a stochastic acyclic network the focus is on shortest route problems where a general nonlinear utility function is used to measure outcomes for such problems enumerating all feasible paths is the only way to guarantee that the global optimum has been found alternatively we develop a reduction algorithm based on stochastic dominance to speed up the computations monte carlo simulation is used to evaluate the approach in all 70 test problems comprising 20 to 60 nodes are randomly generated and analyzed the results indicate that the heuristic produces significant computational saving as the size of the network grows and that the quality of the reduced network solutions are better than those obtained from the original formulation

a priori optimization consider a complete graph g v e in which each node is present with probability p we are interested in solving combinatorial optimization problems on subsets of nodes which are present with a certain probability we introduce the idea of a priori optimization as a strategy competitive to the strategy of reoptimization under which the combinatorial optimization problem is solved optimally for every instance we consider four problems the traveling salesman problem tsp the minimum spanning tree vehicle routing and traveling salesman facility location we discuss the applicability of a priori optimization strategies in several areas and show that if the nodes are randomly distributed in the plane the a priori and reoptimization strategies are very close in terms of performance we characterize the complexity of a priori optimization and address the question of approximating the optimal a priori solutions with polynomial time heuristics with provable worst case guarantees finally we use the tsp as an example to find practical solutions based on ideas of local optimality

geometry parameterization method for multidisciplinary applications a technique is described for parameterizing geometries in a manner suitable for numerical simulations used in design optimization the new methodology referred to as control grids is flexible easy to use extendable and applicable to multidisciplinary design optimization although significantly different than free form deformation the present method provides many similar capabilities comparisons between the current technique and free form deformation are provided to highlight the advantages and disadvantages of each method the new parameterization technology is described and demonstrated in both two and three dimensions for single and multidisciplinary applications

drift and diffusion in periodically driven renewal processes we consider the drift and diffusion properties of periodically driven renewal processes these processes are defined by a periodically time dependent waiting time distribution which governs the interval between subsequent events we show that the growth of the cumulants of the number of events is asymptotically periodic and develop a theory which relates these periodic growth coefficients to the waiting time distribution defining the periodic renewal process the first two coefficients which are the mean frequency and effective diffusion coefficient of the number of events are considered in greater detail they may be used to quantify stochastic synchronization

routing optimization under uncertainty we consider a class of routing optimization problems under uncertainty in which all decisions are made before the uncertainty is realized the objective is to obtain optimal routing solutions that would as much as possible adhere to a set of specified requirements after the uncertainty is realized these problems include finding an optimal routing solution to meet the soft time window requirements at a subset of nodes when the travel time is uncertain and sending multiple capacitated vehicles to different nodes to meet the customers uncertain demands we introduce a precise mathematical framework for defining and solving such routing problems in particular we propose a new decision criterion called the requirements violation rv index which quantifies the risk associated with the violation of requirements taking into account both the frequency of violations and their magnitudes whenever they occur the criterion can handle instances when probability distributions are known and ambiguity when dis

a data based approach for fast airfoil analysis and optimization airfoils are of great importance in aerodynamic design and various tools have been developed to evaluate and optimize their performance existing tools are usually either accurate or efficient bu

shortest paths in stochastic networks with correlated link costs the objective is to minimize expected travel time from any origin to a specific destination in a congestible network with correlated link costs each link is assumed to be in one of two possible conditions conditional probability density functions for link travel times are assumed known for each condition conditions over the traversed links are taken into account for determining the optimal routing strategy for the remaining trip this problem is treated as a multistage adaptive feedback control process each stage is described by the physical state the location of the current decision point and the information state the service level of the previously traversed links proof of existence and uniqueness of the solution to the basic dynamic programming equations and a solution procedure are provided

a geometric comparison of aerofoil shape parameterisation methods a comprehensive review of aerofoil shape parameterization methods that can be used for aerodynamic shape optimization is presented seven parameterization methods are considered for a range of desi

predicting the coherence resonance curve using a semianalytical treatment emergence of noise induced regularity or coherence resonance in nonlinear excitable systems is well known we explain theoretically why the normalized variance v n of interspike time intervals which is a measure of regularity in such systems has a unimodal profile our semianalytic treatment of the associated spiking process produces a general yet simple formula for v n which we show is in very good agreement with numerics in two test cases namely the fitzhugh nagumo model and the chemical oscillator model

frequency analysis of binary oscillators triggered by a random noise abstract the frequency analysis of a bistable binary oscillator triggered by a stationary random signal is performed by analyzing the expression for the power spectrum of its output the oscillator state changes when the input noise exceeds a fixed threshold which occurs in correspondence of the events produced by an ordinary renewal process after each state change a fixed refractory time t is to be passed before the output performs a new transition a theoretical study shows that a coherence resonance cr effect appears in the output square wave if the threshold is lower than a positive real value when the overcoming of the input threshold occurs according to a poisson process with exponential parameter the regularity is present at the output only if the product t exceeds 2 1 the value of the characteristic frequency increases rapidly with t towards its asymptotic value 1 2 t the same probabilistic approach is then adopted to perform the spectral analysis of a set of uncoupled binary oscillators sharing the same refractory time t and the same input random signal under mild assumptions the whole system behaves as a single oscillator whose output is amplified proportionally to the number of elements involved

geometric filtration using proper orthogonal decomposition for aerodynamic design optimization when carrying out design searches traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables this is particularly true when only a small number of simulations is combined with a parameterization which results in a large number of variables of seemingly equal importance here the authors present a variable reduction technique which employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process unlike traditional screening techniques the presented method operates at the geometric level instead of the variable level the filtering process uses the designs which result from a geometry parameterization instead of the variables which control the parameterization the method is shown to perform well in the optimization of a two dimensional airfoil for the minimization of drag to lift ratio producing designs better than those resulting from traditional kriging based surrogate model optimization and with a significant reduction in surrogate tuning cost

domain element method for aerodynamic shape optimization applied to a modern transport wing generic wraparound aerodynamic shape optimization technology is presented and applied to a modern commercial aircraft wing in transonic cruise the wing geometry is parameterized by a novel domain element method which uses efficient global interpolation functions to deform both the surface geometry and corresponding computational fluid dynamics volume mesh the technique also provides a method that allows geometries to be parameterized at various levels ranging from global three dimensional planform alterations to detailed local surface changes combining all levels of parameterization allows for free form design control with very few design variables the method provides an efficient combined shape parameterization and high quality mesh deformation technique that is totally independent of mesh type structured or unstructured optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient based optimizer by finite differences the entire optimization suite has also been parallelized to allow optimization with highly flexible parameterization in practical times results are presented for highly constrained optimizations of the modern aircraft wing in transonic cruise using three levels of parameterization number of design variables to assess the effect of parameterization level on the optimization the highest level optimization results in a totally shock free geometry with an associated substantial reduction in drag

stochastic resonance in discrete time nonlinear ar 1 models this paper deals with stochastic resonance this nonlinear physical phenomenon generally occurs in bistable systems excited by random input noise plus a sinusoid through its internal dynamics such a system forces cooperation between the input noise and the input sine provided the existence of fine tuning between the power noise and the dynamics the system reacts periodically at the frequency of the sine of particular interest is the fact that the local output signal to noise ratio presents a maximum when plotted against the input noise power the system resounds stochastically continuous time systems have already been studied we study the ability of intrinsically discrete time systems general nonlinear ar 1 models to produce stochastic resonance it is then suggested that such discrete systems can be used in signal processing

dynamic shortest paths in acyclic networks with markovian arc costs we examine shortest path problems in acyclic networks in which arc costs are known functions of certain environment variables at network nodes each of these variables evolves according to an independent markov process the vehicle can wait at a node at a cost in anticipation of more favorable arc costs we first develop two recursive procedures for the individual arc case one based on successive approximations and the other on policy iteration we also solve the same problem via parametric linear programming we show that the optimal policy essentially classifies the state of the environment variable at a node into two categories green states for which the optimal action is to immediately traverse the arc and red states for which the optimal action is to wait we then extend these concepts for the entire network by developing a dynamic programming procedure that solves the corresponding problem the complexity of this method is shown to be o n2k nk3 where n is the number of network nodes and k

statistical pulse dynamics in a reaction diffusion system abstract we study a nonlinear response to random external stimuli in an excitable reaction diffusion system numerical simulations are carried out in one dimension to investigate formation of excited domains pulses in response to stimuli and pair annihilate upon collision our main concern is how the area of excited domains in the steady state depends on the strength of stimuli we have found three different stimuli response behaviors a power law dependence for sufficiently weak stimuli a logarithmic dependence for intermediate strength and an oscillatory behavior for strong stimuli the power law behavior can be understood by a theoretical analysis

metastable switching in a planar limit cycle system with additive noise abstract additive noise is known to produce counter intuitive behaviors in nonlinear dynamical systems previously it was shown that systems with a deterministic limit cycle can display switching between metastable states in the presence of asymmetric additive white noise here we systematically analyze the dynamics of this metastable behavior and show how the vector field away from the limit cycle influences the rate and directionality of the metastable switching using stochastic phase reduction methods as well as asymptotic approximations we identify mechanisms underlying different rates of switching and predict when the system will rotate in the opposite direction of the deterministic limit cycle thus this work presents an alternative mechanism for generating a range of metastable switch behaviors that have been observed in a number of physical systems

unified fluid structure interpolation and mesh motion using radial basis functions a multivariate interpolation scheme using radial basis functions is presented which results in a completely unified formulation for the fluid structure interpolation and mesh motion problems the method has several significant advantages primarily all volume mesh structural mesh and flow solver type dependence is removed and all operations are performed on totally arbitrary point clouds of any form hence all connectivity and user input requirements are removed from the computational fluid dynamics computational structural dynamics cfd csd coupling problem as only point clouds are required to determine the coupling also it may equally well be applied to structured and unstructured grids or structural and aerodynamic grids that intersect again because no connectivity information is required furthermore no expensive computations are required during an unsteady simulation just matrix vector multiplications since the required dependence relations are computed only once prior to any simulation and then remain constant this property means that the method is both perfectly parallel since only the data relevant to each structured block or unstructured partition are required to move those points and totally independent from the flow solver hence a completely generic black box tool can be developed which is ideal for use in an optimization approach aeroelastic behaviour of the brite euram mdo wing is analysed in terms of both static deflection and dynamic responses and it is demonstrated that responses are strongly dependent on the exact cfd csd interpolation used mesh quality is also examined during the motion resulting from a large surface deformation global grid quality is shown to be preserved well with local grid orthogonality also being maintained well particularly at and near the moving surface where the original orthogonality is retained copyright 2007 john wiley sons ltd

exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function in this paper the stochastic shortest path problem of determining a path that maximizes the expected utility is considered the nature of the utility function used to evaluate paths is of a decreasing deadline type the principal contribution of this paper is the development of exact algorithms that use two types of pruning techniques that are incorporated in labeling procedures one type of pruning makes use of the concept of local preference relations while the other type makes use of relaxations specifically two algorithms are developed each containing the same preference relation but two different relaxations our extensive computational testing indicate that both these algorithms are able to solve even large size problems quickly more importantly even for large problems both the algorithms solved them by enumerating a very small percentage of all paths

spectra and waiting time densities in firing resonant and nonresonant neurons the response of a neural cell to an external stimulus can follow one of two patterns nonresonant neurons monotonically relax to the resting state after excitation while resonant ones show subthreshold oscillations we investigate how these subthreshold properties of neurons affect their suprathreshold response conversely we ask the following can we distinguish between both types of neuronal dynamics using suprathreshold spike trains the dynamics of neurons is given by stochastic fitzhugh nagumo and morris lecar models either having a focus or a node as the stable fixed point we determine numerically the spectral power density as well as the interspike interval density in response to random noiselike signals we show that the information about the type of dynamics obtained from power spectra is of limited validity in contrast the interspike interval density provides a very sensitive instrument for the diagnostics of whether the dynamics has resonant or nonresonant properties for the latter value we formulate a fit formula and use it to reconstruct theoretically the spectral power density which coincides with the numerically obtained spectra we underline that the renewal theory is applicable to analysis of suprathreshold responses even of resonant neurons

dynamic shortest path in stochastic dynamic networks ship routing problem abstract in this paper we apply the stochastic dynamic programming to find the dynamic shortest path from the source node to the sink node in stochastic dynamic networks in which the arc lengths are independent random variables with exponential distributions in each node there is an environmental variable which evolves in accordance with a continuous time markov process the parameter of the exponential distribution of the transition time of each arc is also a function of the state of the environmental variable of its initiative node upon arriving at each node we can move toward the sink node through the best outgoing arc or wait at the beginning it is assumed that upon arriving at each node we know the state of its environmental variable and also the states of the environmental variables of its adjacent nodes then we extend this assumption such that upon arriving at each node we know the states of the environmental variables of all nodes in the ship routing problem which we focus in this paper the environmental variables of all nodes are known but it is shown that the complexity of the algorithm becomes exponential in this case

finding the shortest path in stochastic networks common network parameters such as number of nodes and arc lengths are frequently subjected to ambiguity as a result of probability law a number of authors have discussed the calculation of the shortest path in networks with random variable arc lengths generally only a subset of intermediate nodes chosen in accordance with a given probability law can be used to transition from source node to sink node the determination of a priori path of the minimal length in an incomplete network is defined as a probabilistic shortest path problem when arc lengths between nodes are randomly assigned variables in an incomplete network the resulting network is known as an incomplete stochastic network in this paper the computation of minimal length in incomplete stochastic networks when travel times between nodes are allowed to be exponentially distributed random variables is formulated as a linear programming problem a practical application of the methodology is demonstrated and the results and process compared to the kulkarni s v g kulkarni shortest paths in networks with exponentially distributed arc lengths networks 16 1986 255 274 method

analysis of excitability for the fitzhugh nagumo model via a stochastic sensitivity function technique we study excitability phenomena for the stochastically forced fitzhugh nagumo system modeling a neural activity noise induced changes in the dynamics of this model can be explained by the high stochastic sensitivity of its attractors computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of these attractors our method allows us to construct confidence ellipses and estimate a threshold value of a noise intensity corresponding to the neuron excitement on the basis of the proposed technique a supersensitive limit cycle is found for the fitzhugh nagumo model

coupled three state oscillators abstract we investigate globally coupled stochastic three state oscillators which we consider as general models of stochastic excitable systems we compare two situations in the first case the transitions between the three states of each unit 1 2 3 1 are determined by poissonian waiting time distributions in the second case only transition 1 2 is poissonian whereas the others are deterministic with a fixed delay when coupled the second system shows coherent oscillations whereas the first remains in a stable stationary state we show that the coherent oscillations are due to a hopf bifurcation in the dynamics of the occupation probabilities of the discrete states and discuss the bifurcation diagram