exclusion and persistence in deterministic and stochastic chemostat models abstract we first introduce and analyze a variant of the deterministic single substrate chemostat model in this model microbe removal and growth rates depend on biomass concentration with removal terms increasing faster than growth terms using a comparison principle we show that persistence of all species is possible in this scenario then we turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation in particular we show that random effects may lead to extinction in scenarios where the deterministic model predicts persistence on the other hand we also establish some stochastic persistence results

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

langevin approach for the dynamics of the contact process on annealed scale free networks we study the dynamics of the contact process one of the simplest nonequilibrium stochastic processes taking place on a scale free network we consider the network topology as annealed i e all links are rewired at each microscopic time step so that no dynamical correlation can build up this is a practical implementation of the absence of correlations assumed by mean field approaches we present a detailed analysis of the contact process in terms of a langevin equation including explicitly the effects of stochastic fluctuations in the number of particles in finite networks this allows us to determine analytically the survival time for spreading experiments and the density of active sites in surviving runs the fluctuations in the topological structure induce anomalous scaling effects with respect to the system size when the degree distribution has a hard upper bound when the upper bound is soft the presence of outliers with huge connectivity perturbs the picture even more inducing an apparent shift of the critical point in light of these findings recent theoretical and numerical results in the literature are critically reviewed

seislet transform and seislet frame we introduce a digital waveletlike transform which is tailored specifically for representing seismic data the transform provides a multiscale orthogonal basis with basis functions aligned along seismic events in the input data it is defined with the help of the wavelet lifting scheme combined with local plane wave destruction in the 1d case the seislet transform is designed to follow locally sinusoidal components in the 2d case it is designed to follow local plane wave components with smoothly variable slopes if more than one component is present the transform turns into an overcomplete representation or a tight frame in these terms the classic digital wavelet transform is simply a seislet transform for a zero frequency in one dimension or zero slope in two dimensions the main objective of the new transform is an effective seismic data compression for designing efficient data analysis algorithms traditional signal processing tasks such as noise attenuation and trace interpolation become simply defined in the seislet domain when applied in the offset direction on common midpoint or common image point gathers the seislet transform finds an additional application in optimal stacking of seismic records

mathematical morphological filtering for linear noise attenuation of seismic data abstractlinear coherent noise attenuation is a troublesome problem in a variety of seismic exploration areas traditional methods often use the differences in frequency wavenumber or amplitude to separate the useful signal and coherent noise however the application of traditional methods is limited or even invalid when the aforementioned differences between useful signal and coherent noise are too small to be distinguished for this reason we have managed to develop a new algorithm from the differences in the shape of seismic waves and thus introduce mathematical morphological filtering mmf into coherent noise attenuation the morphological operation is calculated in the trace direction of a rotating coordinate system this rotating coordinate system is along the direction of the trajectory of coherent noise to make the energy of the coherent noise distributed along the horizontal direction the mmf approach is more effective than mean and median filters in rejecting abnormal values and causes fe

distribution of infected mass in disease spreading in scale free networks we use scale free networks to study properties of the infected mass m of the network during a spreading process as a function of the infection probability q and the structural scaling exponent we use the standard sir model and investigate in detail the distribution of m we find that for dense networks this function is bimodal while for sparse networks it is a smoothly decreasing function with the distinction between the two being a function of q we thus recover the full crossover transition from one case to the other this has a result that on the same network a disease may die out immediately or persist for a considerable time depending on the initial point where it was originated thus we show that the disease evolution is significantly influenced by the structure of the underlying population

analysis of stochastic multimolecular biochemical reaction model with levy jumps abstract in this paper a stochastic multimolecular biochemical reaction model with levy jumps is investigated firstly we prove the existence and uniqueness of the global positive solution then we derive the conditions when the reaction will end and when the reaction will proceed moreover the existence of positive recurrence to the solutions is studied by constructing suitable lyapunov functions results show that the end and persistence of the reaction are closely related to the intensity of levy noise finally numerical simulations are carried out to illustrate the theoretical results

shaping regularization in geophysical estimation problems regularization is a required component of geophysical estimation problems that operate with insufficient data the goal of regularization is to impose additional constraints on the estimated model i introduce shaping regularization a general method for imposing constraints by explicit mapping of the estimated model to the space of admissible models shaping regularization is integrated in a conjugate gradient algorithm for iterative least squares estimation it provides the advantage of better control on the estimated model in comparison with traditional regularization methods and in some cases leads to a faster iterative convergence simple data interpolation and seismic velocity estimation examples illustrate the concept

analytically solvable model of probabilistic network dynamics we present a simple model of network dynamics that can be solved analytically for fully connected networks we obtain the dynamics of response of the system to perturbations the analytical solution is an excellent approximation for random networks a comparison with the scale free network though qualitatively similar shows the effect of distinct topology

spreading and shortest paths in systems with sparse long range connections spreading according to simple rules e g of fire or diseases and shortest path distances are studied on d dimensional systems with a small density p per site of long range connections small world lattices the volume v t covered by the spreading quantity on an infinite system is exactly calculated in all dimensions as a function of time t from this the average shortest path distance l r can be calculated as a function of euclidean distance r it is found that l r approximately r for r r c the characteristic length r c which governs the behavior of shortest path lengths diverges logarithmically with l for all p 0

dynamical analysis of a iwsr rumor spreading model with considering the self growth mechanism and indiscernible degree abstract propagation of rumor as one of the most important aspects of spreading dynamics on networks which is often accompanied by the self growth of individuals and indiscernible degree of events and the analysis of this phenomenon can help us to better understand the information dissemination in the social network here with the wiseman supplemented to the classical ignorant spreader stifler i s r rumor spreading model a modified ignorant wiseman spreader stifler i w s r model is established with self growth mechanism by considering indiscernible degree of events by mean field equations of i w s r model the spreading threshold c is calculated to describe the theory of steady state dynamics of the rumor spreading numerical simulation is performed to assess the influence of self growth of individual and indiscernible degree of events on dynamic spreading process the results show that when the spreading rate is smaller than the threshold c the rumor will not spread in the population the stronger the self growth ability of the individual is the smaller the range of rumor will be the higher the indiscernible degree of events is the greater influence of the rumor these obtained findings in the present study could not only elaborate our understandings of spreading dynamics in network but also provide us with an insight to develop effective strategies of inhibiting rumor propagation

a connection between a system of random walks and rumor transmission abstract we establish a relationship between the phenomenon of rumor transmission on a population and a probabilistic model of interacting particles on the complete graph more precisely we consider variations of the maki thompson epidemic model and the frog model of random walks which were introduced in the scientific literature independently and in different contexts we analyze the markov chains which describe these models and show a coupling between them our connection shows how the propagation of a rumor in a closed homogeneously mixing population can be described by a system of random walks on the complete graph additionally we discuss further applications of the random walk model which are relevant to the modeling of different biological dynamics

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

threshold behavior of a stochastic sis model with levy jumps in this paper the dynamics of a stochastic sis model with levy jumps are investigated we first prove that this model has a unique global positive solution starting from the positive initial value then taking the accumulated jump size into account we find a threshold of the model denoted by r 0 which completely determines the extinction and prevalence of the disease if r 0 1 the disease dies out exponentially with probability one if r 0 1 the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease from the view of epidemiology the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics moreover we find that levy noise can suppress disease outbreak finally we introduce some numerical simulations to support the main results obtained

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

two group sir epidemic model with stochastic perturbation a stochastic two group sir model is presented in this paper the existence and uniqueness of its nonnegative solution is obtained and the solution belongs to a positively invariant set furthermore the globally asymptotical stability of the disease free equilibrium is deduced by the stochastic lyapunov functional method if r 0 1 which means the disease will die out while if r 0 1 we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average in addition the intensity of the fluctuation is proportional to the intensity of the white noise when the white noise is small we consider the disease will prevail at last we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments

shir competitive information diffusion model for online social media abstract in online social media opinion divergences and differentiations generally exist as a result of individuals extensive participation and personalization in this paper a susceptible hesitated infected removed shir model is proposed to study the dynamics of competitive dual information diffusion the proposed model extends the classical sir model by adding hesitators as a neutralized state of dual information competition it is both hesitators and stable spreaders that facilitate information dissemination researching on the impacts of diffusion parameters it is found that the final density of stiflers increases monotonically as infection rate increases and removal rate decreases and the advantage information with larger stable transition rate takes control of whole influence of dual information the density of disadvantage information spreaders slightly grows with the increase of its stable transition rate while whole spreaders of dual information and the relaxation time remain almost unchanged moreover simulations imply that the final result of competition is closely related to the ratio of stable transition rates of dual information if the stable transition rates of dual information are nearly the same a slightly reduction of the smaller one brings out a significant disadvantage in its propagation coverage additionally the relationship of the ratio of final stiflers versus the ratio of stable transition rates presents power characteristic

iterative deblending of simultaneous source seismic data using seislet domain shaping regularization abstractwe used a novel iterative estimation scheme for separation of blended seismic data from simultaneous sources the scheme is based on an augmented estimation problem that can be solved by iteratively constraining the deblended data using shaping regularization in the seislet domain we formulated the forward modeling operator in the common receiver domain in which two sources were assumed to be blended using a random time shift dithering approach the nonlinear shaping regularization framework offered some freedom in designing a shaping operator to constrain the model in an underdetermined inverse problem we designed the backward operator and the shaping operator for the shaping regularization framework the backward operator can be optimally chosen as half of the identity operator in the two source case and the shaping operator can be chosen as coherency promoting operator the high performance deblending effect of the iterative framework was tested on three numerically blended synthetic data s

fingerprint image postprocessing a combined statistical and structural approach abstract for complex patterns such as fingerprints it is difficult to describe the dactylotype by using a set of feature vectors as well as to construct and parse all of the individual fingerprint pattern with a syntactical approach in this paper which is different from the conventional methods we present an approach in which the statistical and structural approaches are combined to represent the fingerprint false minutia patterns based on the proposed approach a fingerprint image postprocessing algorithm is developed to eliminate the false minutiae in fingerprint images because a global minutia relation is considered on the whole image experimental results demonstrate the advantages of the combined approach

complex dynamic behavior of a rumor propagation model with spatial temporal diffusion terms a spatial temporal rumor propagation model with discrete and non local delays is regarded stability and hopf bifurcation are proved in a strict mathematical way sensitivity analysis is applied to search active parameters hopf bifurcation causes an oscillation phenomenon in this model numerical simulations provide a new insight into rumor spreading in online social networks rumor propagation as a typical form of social communication in online social networks has had a significant negative impact on a harmonious and stable society with the rapid development of mobile communication equipments traditional rumor propagation models which depend on ordinary differential equations ode may not be suitable for describing rumor propagation in an online social network in this paper based on reaction diffusion equations we propose a novel epidemic like model with both discrete and nonlocal delays for investigating the spatial temporal dynamics of rumor propagation by analyzing the corresponding characteristic equations of this model the local stability conditions of a boundary equilibrium point and a positive equilibrium point are established by applying the linear approximation method of nonlinear systems sufficient conditions are derived for the existence of hopf bifurcation at the above two kinds of equilibrium points moreover a sensitivity analysis method based on the density of spreading users is proposed and then in theoretical and experimental aspect we identify some sensitive parameters in the process of rumor propagation finally numerical simulations are performed to illustrate the theoretical results

noise reduction by vector median filtering abstractthe scalar median filter smf is often used to reduce noise in scalar geophysical data we present an extension of the smf to a vector median filter vmf for suppressing noise contained in geophysical data represented by multidimensional multicomponent vector fields although the smf can be applied to each component of a vector field individually the vmf is applied to all components simultaneously like the smf the vmf intends to suppress random noise while preserving discontinuities in the vector fields preserving such discontinuities is essential for exploration geophysics because discontinuities often manifest important geologic features such as faults and stratigraphic channels the vmf is applied to synthetic and field data sets the results are compared to those generated by using smf f x deconvolution and mean filters our results indicate that the vmf can reduce noise while preserving discontinuities more effectively than the alternatives in addition a fast vmf algorithm is descr

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

damped multichannel singular spectrum analysis for 3d random noise attenuation abstractmultichannel singular spectrum analysis mssa is an effective algorithm for random noise attenuation in seismic data which decomposes the vector space of the hankel matrix of the noisy signal into a signal subspace and a noise subspace by truncated singular value decomposition tsvd however this signal subspace actually still contains residual noise we have derived a new formula of low rank reduction which is more powerful in distinguishing between signal and noise compared with the traditional tsvd by introducing a damping factor into traditional mssa to dampen the singular values we have developed a new algorithm for random noise attenuation we have named our modified mssa as damped mssa the denoising performance is controlled by the damping factor and our approach reverts to the traditional mssa approach when the damping factor is sufficiently large application of the damped mssa algorithm on synthetic and field seismic data demonstrates superior performance compared with the conve

the maki thompson rumor model on infinite cayley trees in this paper we study the maki thompson rumor model on infinite cayley trees the basic version of the model is defined by assuming that a population represented by a graph is subdivided into three classes of individuals ignorants spreaders and stiflers a spreader tells the rumor to any of its nearest ignorant neighbors at rate one at the same rate a spreader becomes a stifler after a contact with other nearest neighbor spreaders or stiflers in this work we study this model on infinite cayley trees which is formulated as a continuous times markov chain and we extend our analysis to the generalization in which each spreader ceases to propagate the rumor right after being involved in a given number of stifling experiences we study sufficient conditions under which the rumor either becomes extinct or survives with positive probability

critical behavior of propagation on small world networks we report numerical evidence that an epidemiclike model which can be interpreted as the propagation of a rumor exhibits critical behavior at a finite randomness of the underlying small world network the transition occurs between a regime where the rumor dies in a small neighborhood of its origin and a regime where it spreads over a finite fraction of the whole population critical exponents are evaluated through finite size scaling analysis and the dependence of the critical randomness with the network connectivity is studied the behavior of this system as a function of the small network randomness bears noticeable similarities with an epidemiological model reported recently m kuperman and g abramson phys rev lett 86 2909 2001 in spite of substantial differences in the respective dynamical rules

stationary distribution and extinction of a stochastic seir epidemic model with standard incidence abstract in this paper we consider a stochastic seir epidemic model with standard incidence by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of ergodic stationary distribution to the model our result does not depend on the positive endemic equilibrium e of the deterministic system which improves the previous result to a greater extent moreover we also establish sufficient conditions for extinction of the disease

stability of a stochastic sir system abstract we propose a stochastic sir model with or without distributed time delay and we study the stability of disease free equilibrium the numerical simulation of the stochastic sir model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found

beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data we propose a robust interpolation scheme for aliased regularly sampled seismic data that uses the curvelet transform in a first pass the curvelet transform is used to compute the curvelet coefficients of the aliased seismic data the aforementioned coefficients are divided into two groups of scales alias free and alias contaminated scales the alias free curvelet coefficients are upscaled to estimate a mask function that is used to constrain the inversion of the alias contaminated scale coefficients the mask function is incorporated into the inversion via a minimum norm least squares algorithm that determines the curvelet coefficients of the desired alias free data once the alias free coefficients are determined the curvelet synthesis operator is used to reconstruct seismograms at new spatial positions the proposed method can be used to reconstruct regularly and irregularly sampled seismic data we believe that our exposition leads to a clear unifying thread between f x and f k beyond alias interpo

a rumor transmission model with incubation in social networks abstract in this paper we propose a rumor transmission model with incubation period and constant recruitment in social networks by carrying out an analysis of the model we study the stability of rumor free equilibrium and come to the local stable condition of the rumor equilibrium we use the geometric approach for ordinary differential equations for showing the global stability of the rumor equilibrium and when 0 1 the new model occurs a transcritical bifurcation furthermore numerical simulations are used to support the analysis at last some conclusions are presented

a rumor spreading model with variable forgetting rate abstract a rumor spreading model with the consideration of forgetting rate changing over time is examined in small world networks the mean field equations are derived to describe the dynamics of rumor spreading in small world networks further numerical solutions are conducted on livejournal an online social blogging platform to better understand the performance of the model results show that the forgetting rate has a significant impact on the final size of rumor spreading the larger the initial forgetting rate or the faster the forgetting speed the smaller the final size of the rumor spreading numerical solutions also show that the final size of rumor spreading is much larger under a variable forgetting rate compared to that under a constant forgetting rate

the dynamics of a stochastic vaccinated tuberculosis model with treatment abstract in this paper we study a stochastic model with vaccination and treatment to describe the transmission dynamics of tuberculosis firstly by using the stochastic lyapunov analysis method we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model then we obtain sufficient conditions for extinction of the diseases our work greatly improves the results of feng and qiu 2018 finally some examples and numerical simulations are introduced to illustrate our theoretical results

phase transition for the maki thompson rumour model on a small world network we consider the maki thompson model for the stochastic propagation of a rumour within a population in this model the population is made up of spreaders ignorants and stiflers any spreader attempts to pass the rumour to the other individuals via pair wise interactions and in case the other individual is an ignorant it becomes a spreader while in the other two cases the initiating spreader turns into a stifler in a finite population the process will eventually reach an equilibrium situation where individuals are either stiflers or ignorants we extend the original hypothesis of homogenously mixed population by allowing for a small world network embedding the model in such a way that interactions occur only between nearest neighbours this structure is realized starting from a k regular ring and by inserting in the average c additional links in such a way that k and c are tuneable parameters for the population architecture we prove that this system exhibits a transition between regimes of localization where the final number of stiflers is at most logarithmic in the population size and propagation where the final number of stiflers grows algebraically with the population size at a finite value of the network parameter c a quantitative estimate for the critical value of c is obtained via extensive numerical simulations

dynamics of a stochastic hiv 1 infection model with logistic growth abstract this paper is concerned with a stochastic hiv 1 infection model with logistic growth firstly by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the hiv 1 infection model then we obtain sufficient conditions for extinction of the infection the stationary distribution shows that the infection can become persistent in vivo

random noise attenuation using local signal and noise orthogonalization abstractwe have developed a novel approach to attenuate random noise based on local signal and noise orthogonalization in this approach we first removed from a seismic section using one of the conventional denoising operators and then applied a weighting operator to the initially denoised section to predict the signal leakage energy as well as retrieve it from the initial noise section the weighting operator was obtained by solving a least squares minimization problem via shaping regularization with a smoothness constraint next the initially denoised section and the retrieved signal were combined to form the final denoised section the proposed denoising approach corresponded to orthogonalizing the initially denoised signal and noise in a local manner we evaluated the denoising performance using local similarity to test the orthogonalization property of the estimated signal and noise we calculated the local similarity map between the denoised signal section and removed noise section low values o

blackmail propagation on small world networks abstract the dynamics of the blackmail propagation model based on small world networks is investigated it is found that for a given transmitting probability the dynamical behavior of blackmail propagation transits from linear growth type to logistical growth one with the network randomness p increases the transition takes place at the critical network randomness p c 1 n where n is the total number of nodes in the network for a given network randomness p the dynamical behavior of blackmail propagation transits from exponential decrease type to logistical growth one with the transmitting probability increases the transition occurs at the critical transmitting probability c 1 k where k is the average number of the nearest neighbors the present work will be useful for understanding computer virus epidemics and other spreading phenomena on communication and social networks

combining minutiae descriptors for fingerprint matching a novel minutiae based fingerprint matching algorithm is proposed a minutiae matching algorithm has to solve two problems correspondence and similarity computation for the correspondence problem we assign each minutia two descriptors texture based and minutiae based descriptors and use an alignment based greedy matching algorithm to establish the correspondences between minutiae for the similarity computation we extract a 17 d feature vector from the matching result and convert the feature vector into a matching score using support vector classifier the proposed algorithm is tested on fvc2002 databases and compared to all participators in fvc2002 according to equal error rate the proposed algorithm ranks 1st on db3 the most difficult database in fvc2002 and on the average ranks 2nd on all 4 databases

asymptotic behavior of stochastic multi group epidemic models with distributed delays abstract in this paper we introduce stochasticity into multi group epidemic models with distributed delays and general kernel functions the stochasticity in the model is a standard technique in stochastic population modeling when the perturbations are small by using the method of stochastic lyapunov functions we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number r 0 if r 0 1 the solution of the stochastic system oscillates around the disease free equilibrium e 0 while if r 0 1 the solution of the stochastic model fluctuates around the endemic equilibrium e moreover we also establish sufficient conditions of these results

fingerprint matching based on global comprehensive similarity this paper introduces a novel algorithm based on global comprehensive similarity with three steps to describe the euclidean space based relative features among minutiae we first build a minutia simplex that contains a pair of minutiae as well as their associated textures with its transformation variant and invariant relative features employed for the comprehensive similarity measurement and parameter estimation respectively by the second step we use the ridge based nearest neighborhood among minutiae to represent the ridge based relative features among minutiae with these ridge based relative features minutiae are grouped according to their affinity with a ridge the euclidean space based and ridge based relative features among minutiae reinforce each other in the representation of a fingerprint finally we model the relationship between transformation and the comprehensive similarity between two fingerprints in terms of histogram for initial parameter estimation through these steps our experiment shows that the method mentioned above is both effective and suitable for limited memory afis owing to its less than 1k byte template size

the extinction and persistence of the stochastic sis epidemic model with vaccination abstract in this paper we discuss the dynamics of a stochastic sis epidemic model with vaccination when the noise is large the infective decays exponentially to zero regardless of the magnitude of r 0 when the noise is small sufficient conditions for extinction exponentially and persistence in the mean are established the results are illustrated by computer simulations

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

multisource encoding and decoding using the signal apparition technique signal apparition is a method for encoding sources in simultaneous multisource seismic acquisition and decoding the multisource response of the earth into its single source responses for m sources encoding is performed by applying periodic sequences of period m to each of the sources along source lines decoding is achieved in the wavenumber domain for each frequency by solving an m m linear system of equations the system s matrix is the product of a fourier matrix and an encoding matrix the latter containing the information of the codes the solution of the system is unique when the encoding matrix is invertible when the encoding sequences consist of time delays applied to sources firing times the determinant of the encoding matrix becomes a polynomial a unique solution to decoding then exists if the roots of the polynomial avoid the unit circle periodic time shift sequences for two three four and six sources are discussed a model example of simultaneous four source data acquisition illustrates the performance of the encoding decoding technique for the spatially nonaliased case less

shot domain deblending using least squares inversion abstractsimultaneous source acquisition which allows a temporal overlap between shot records has significant advantages to improve data quality e g denser shooting and reduce acquisition cost e g efficient wide azimuth shooting we have developed a novel shot domain deblending approach for a wide azimuth simultaneous shooting survey based on an inversion scheme the inverse problem is formulated by introducing two convolution operators that can respectively destruct the signal and interference and is solved by a conjugate gradient algorithm in the least squares sense our approach breaks down the limit that source separation can only be implemented in some domains other than the shot domain based on the incoherency principle our shot domain approach does not require the random dithering time thus it is very flexible to use in a wide azimuth simultaneous shooting survey three numerically blended synthetic examples were developed to demonstrate the excellent performance of our method the feas

lamellar pattern formation in small world media abstract numerical and analytical techniques are used to investigate the effects of quenched disorder of small world networks on the phase ordering dynamics of lamellar patterns as modeled by the swift hohenberg equation morphologies for small and large values of the network randomness are quite different it is found that addition of shortcuts to an underlying regular lattice makes the growth of domains evolving from random initial conditions much slower at late times as the randomness increases the evolution is eventually frozen

dynamical behavior of a stochastic svir epidemic model with vaccination abstract in this paper we investigate the dynamical behavior of svir models in random environments firstly we show that if r 0 s 1 the disease of stochastic autonomous svir model will die out exponentially if r 0 s 1 the disease will be prevail moreover this system admits a unique stationary distribution and it is ergodic when r 0 s 1 results show that environmental white noise is helpful for disease control secondly we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic svir model with periodic parameters finally numerical simulations validate the analytical results

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

optimization as a result of the interplay between dynamics and structure abstract in this work we study the interplay between the dynamics of a model of diffusion governed by a mechanism of imitation and its underlying structure the dynamics of the model can be quantified by a macroscopic observable which permits the characterization of an optimal regime we show that dynamics and underlying network cannot be considered as separated ingredients in order to achieve an optimal behavior

the long time behavior of di sir epidemic model with stochastic perturbation in this paper we present a di sir epidemic model with two categories stochastic perturbations the long time behavior of the two stochastic systems is studied mainly we show how the solution goes around the infection free equilibrium and the endemic equilibrium of deterministic system under different conditions

the susceptible infected recovered model on a euclidean network we consider a susceptible infected recovered sir epidemic model on a euclidean network in one dimension in which nodes at a distance l are connected with probability p l l in addition to nearest neighbors the topology of the network changes as is varied and its effect on the sir model is studied r t the recovered fraction of population up to time t and the total duration of the epidemic are calculated for different values of the infection probabilities q and a threshold behavior is observed for all up to 2 0 above the threshold value q qc the saturation value rsat attains a finite value both rsat and show scaling behavior in a finite system of size n and qc is constant for 0 qc the results are compared to static percolation phenomena and also to mean field results for finite systems discussions on the properties of the euclidean network are made in the light of the present results

exponential extinction of a stochastic predator prey model with allee effect abstract in this paper we study a stochastic predator prey model with beddington deangelis functional response and allee effect whose coefficients are dependent on expectations we prove that there is a unique global positive solution to the system with the positive initial value moreover sufficient conditions for exponential extinction are established

detection and characterization of transport barriers in complex flows via ridge extraction of the finite time lyapunov exponent field this paper proposes an algorithm to detect and characterize ridges in the finite time lyapunov exponent ftle field obtained from a continuous dynamical system or flow these ridges represent time dependent separatrices of the flow and are also called lagrangian coherent structures lcs lcs have been demonstrated to be an effective way to analyze realistic time chaotic flows although they can be quite complex therefore in order to exploit the information that lcs can provide it is important to locate and characterize these structures in a systematic way this can be accomplished by interpreting the ftle as a height field and detecting the lcs as ridges of this graph methodologies developed in the image processing framework are integrated with dynamical system inspired approaches in order to characterize ridge strength and location the main novel contribution of the proposed algorithm is a scheme to connect sets of points into curves or surfaces rather than distributions of points around a ridge axis and classify these curves or surfaces using a dynamical systems measure of strength this approach provides the capability to track ranked lcs in space and time the results are presented for a simple analytical model and noisy lcs from realistic three dimensional geophysical fluid data copyright 2010 john wiley sons ltd

epidemic threshold for the sirs model on the networks abstract we study the phase transition from the persistence phase to the extinction phase for the sirs susceptible infected refractory susceptible model of diseases spreading on the networks we derive an analytical expression for the probability of the descendants to reinfect their ancestors we find that in the case of the recovery time r is larger than the infection time i the infection will flow directionally from the ancestors to descendants however the descendants will be unable to reinfect their ancestors during the time of their illness this behavior leads us to deduce that if the infection rate is high enough so that any infected node on the network infects all its neighbors during its infection time then the sirs model on the network evolves to extinction state where all the nodes on the network become susceptible moreover we assert that in order to the disease spreads frequently throughout the nodes of the networks the loops on the network are necessary which means the clustering coefficient will play an important role in this model hence unlike the other models such as sis model and sir model the sirs model has two critical thresholds which separate the persistence phase from the extinction phase when i r i e for fixed values of i and r there are two critical points for infection rate 1 and 2 where epidemic persists in between of those two points we confirm those results numerically with the simulation of a regular one dimensional sirs system and small world network

mean field solution of the small world network model the small world network model is a simple model of the structure of social networks which possesses characteristics of both regular lattices and random graphs the model consists of a one dimensional lattice with a low density of shortcuts added between randomly selected pairs of points these shortcuts greatly reduce the typical path length between any two points on the lattice we present a mean field solution for the average path length and for the distribution of path lengths in the model this solution is exact in the limit of large system size and either a large or small number of shortcuts

the threshold of a stochastic delayed sir epidemic model with temporary immunity abstract this paper is concerned with the asymptotic properties of a stochastic delayed sir epidemic model with temporary immunity sufficient conditions for extinction and persistence in the mean of the epidemic are established the threshold between persistence in the mean and extinction of the epidemic is obtained compared with the corresponding deterministic model the threshold affected by the white noise is smaller than the basic reproduction number r 0 of the deterministic system

asymptotic behavior of a stochastic delayed seir epidemic model with nonlinear incidence abstract this paper is concerned with a stochastic delayed seir epidemic model with nonlinear incidence firstly we verify that there exists a unique global positive solution of the system then by constructing some suitable lyapunov functions we study the asymptotic behaviors of the disease free equilibrium and the endemic equilibrium respectively

fast dual domain reduced rank algorithm for 3d deblending via randomized qr decomposition abstractwe have developed a fast dual domain algorithm based on matrix rank reduction for separating simultaneous source seismic data our algorithm operates on 3d common receiver gathers or offset midpoint gathers at a given monochromatic frequency slice in the x y domain the spatial data of the ideal unblended common receiver or offset midpoint gather could be represented via a low rank matrix the interferences from the randomly and closely fired shots increased the rank of the aforementioned matrix therefore we could minimize the misfit between the blended observation and the predicted blended data subject to a low rank constraint that was applied to the data in the x y domain the low rank constraint could be implemented via the classic truncated singular value decomposition svd or via a randomized qr decomposition rqrd the rqrd yielded nearly one order of processing time improvement with respect to the truncated svd we have also discovered that the rqrd was less stringent on the select

dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size abstract in this paper we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system

deblending by direct inversion deblending of simultaneous source data is usually considered to be an underdetermined inverse problem which can be solved by an iterative procedure assuming additional constraints like sparsity and coherency by exploiting the fact that seismic data are spatially band limited deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constraints we applied the method with numerically modeled data and it suppressed the crosstalk well when the blended data consisted of responses to adjacent densely sampled sources

preserving the discontinuities in least squares reverse time migration of simultaneous source data abstractthe simultaneous source shooting technique can accelerate field acquisition and improve spatial sampling but it will cause strong interferences in the recorded data and artifacts in the final image the previously proposed structural smoothing operator can effectively attenuate artifacts for relatively simple reflection structures during least squares inversion but it will cause damage to complicated reflection events such as discontinuities to preserve discontinuities in a seismic image we apply the singular spectrum analysis ssa operator to attenuate artifacts during least squares inversion considering that global ssa cannot deal with overcomplicated data very well we use local ssa to remove noise and to better preserve the steeply dipping components the local ssa operator corresponds to a local low rank constraint applied in the inversion process the migration operator used in the study is the reverse time migration rtm operator tests using the marmousi model showed the superior per

asymmetric chirplet transform for sparse representation of seismic data abstractfor a fast and accurate extraction of important information in seismic signals a sparse representation based on the physical parameters of the given data is crucial we have used the asymmetric gaussian chirplet model agcm and established a dictionary free variant of the orthogonal matching pursuit a greedy algorithm for sparse approximation the atoms of agcm so called chirplets display asymmetric oscillation attenuation properties which make the agcm very suitable for sparse representation of absorption decay seismic signals unlike the fourier transform which assumes that the seismic signals consist of plane waves the agcm assumes that the seismic signal consists of nonstationary compressed plane waves i e symmetric or asymmetric chirplets thus agcm is a general model for seismic wave simulation and its model parameters include an envelope part and a phase part we have mainly concentrated on the parameters of the envelope part such as the envelope amplitude and arrival time we

majority vote model on a dynamic small world network abstract dynamic small world networks combine short range interactions within a fixed neighborhood with stochastic long range interactions the probability of a long range link occurring instead of a short range one is a measure of the mobility of a population here the critical properties of the majority vote model with noise on a two dimensional dynamic small world lattice are investigated via monte carlo simulation and finite size scaling analyses we construct the order disorder phase diagram and find the critical exponents associated with the continuous phase transition findings are consistent with previous results indicating that a model s transitions on static and dynamic small world networks are in the same universality class

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

global stability of two group sir model with random perturbation abstract in this paper we discuss the two group sir model introduced by guo li and shuai h b guo m y li z shuai global stability of the endemic equilibrium of multigroup sir epidemic models can appl math q 14 2006 259 284 allowing random fluctuation around the endemic equilibrium we prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large in addition the stability condition is obtained by the construction of lyapunov function finally numerical simulations are presented to illustrate our mathematical findings

theory of rumour spreading in complex social networks we introduce a general stochastic model for the spread of rumours and derive mean field equations that describe the dynamics of the model on complex social networks in particular those mediated by the internet we use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks random graphs uncorrelated scale free networks and scale free networks with assortative degree correlations we show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system in the case of scale free networks on the other hand this threshold becomes vanishingly small in the limit of infinite system size we find that the initial rate at which a rumour spreads is much higher in scale free networks than in random graphs and that the rate at which the spreading proceeds on scale free networks is further increased when assortative degree correlations are introduced the impact of degree correlations on the final fraction of nodes that ever hears a rumour however depends on the interplay between network topology and the rumour spreading rate our results show that scale free social networks are prone to the spreading of rumours just as they are to the spreading of infections they are relevant to the spreading dynamics of chain emails viral advertising and large scale information dissemination algorithms on the internet

separation and reconstruction of simultaneous source data via iterative rank reduction abstractwe have developed a rank reduction algorithm based on singular spectrum analysis ssa that is capable of suppressing the interferences generated by simultaneous source acquisition we evaluated an inversion scheme that minimizes the misfit between predicted and observed blended data in t x domain subject to a low rank constraint that is applied to data in the f x domain in particular we developed an iterative algorithm by adopting the projected gradient method with the ssa filter acting as the projection operator this method entails extracting small patches of data from a common receiver gather and organizing the spatial data at a given monochromatic frequency into a hankel matrix for the ideal unblended data hankel matrices extracted from the data are of low rank the incoherent interferences in common receiver domain caused by simultaneously fired shots increase the rank of the aforementioned hankel matrices therefore rank reduction filtering is an effective way to annihilate source inte

dynamic analysis of a stochastic rumor propagation model abstract the rapid development of the internet especially the emergence of the social networks leads rumor propagation into a new media era in this paper we are concerned with a stochastic rumor propagation model sufficient conditions for extinction and persistence in the mean of the rumor are established the threshold between persistence in the mean and extinction of the rumor is obtained compared with the corresponding deterministic model the threshold affected by the white noise is smaller than the basic reproduction number r 0 of the deterministic system

rumor spreading in complex networks under stochastic node activity abstract the research on rumor spreading has a long history and its wanton flooding has brought huge impact on people s life in the process of its spreading the individual s activity plays an important role however in the complex and changeable environment randomness cannot be ignored not to mention its influence on individual activity based on the i s r model of individual activity this paper explores the stochastic version of the rumor model including fluctuations in the activity then the influence of stratonovich stochastic noise on the asymptotic behavior of non linear rumor spreading model is studied through the mathematical analysis we get the critical values to measure whether the deterministic and stochastics models spread or not as well as the threshold conditions for rumor to spread wantonly at the same time the effects of stratonovich stochastic noise on the asymptotic behavior of rumor free equilibrium point e 0 and endemic equilibrium point e are obtained respectively and the condition that the rumor free equilibrium is globally asymptotically stable in the presence of noise is given finally the theoretical results are verified by numerical simulation

two stage predictions of evolutionary dynamics during the rumor dissemination abstract the spreading of rumor is the common type of collective actions as a macro social phenomenon the rumor spreading should be supported by the micro level actions and interactions of people agents therefore the agent based modeling is applied to modeling the micro level mechanism of rumor spreading which has more significance in the big data age the outcomes of simulations indicate that there exist a stage transfer and the turning point d which divides the whole spreading process into the linear od and nonlinear de stages in the linear stage od the spreading percentage increases rapidly into a relatively high level of spreading percentage however after the turning point d it increases slowly until the 100 is reached in the nonlinear stage de for the linear stage od we estimated the linear dynamics with the linear ols regression and it suggests that the adjusted r2 is as high as over 98 99 which is infinitely close to 100 for the nonlinear stage de we estimated the nonlinear stage via adding the quadratic term of time into the regression model it suggests that the adjusted r2 is as high as over 98 as well which is also close to 100 based on the predictions of linear and nonlinear stages with the highest accuracies we combined the linear and nonlinear stages oe od de to predict the whole process of rumor spreading eventually the smooth predicted curves spcs can be obtained to better fit the evolutionary dynamic of spreading curves in reality

the ergodicity and extinction of stochastically perturbed sir and seir epidemic models with saturated incidence abstract in this paper we include stochastic perturbations into sir and seir epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number r 0 the long time behavior of the two stochastic systems is studied mainly we utilize stochastic lyapunov functions to show under some conditions the solution has the ergodic property as r 0 1 while exponential stability as r 0 1 at last we make simulations to conform our analytical results

stability analysis of i2s2r rumor spreading model in complex networks abstract in this paper we propose i 2 s 2 r rumor spreading model with general incidence function in homogeneous networks and i 2 s 2 r rumor spreading model in heterogeneous network in the first model we establish a dynamic model for rumor propagation called i 2 s 2 r in which we consider two general incidence functions then the basic reproduction number the locally stability and the global stability of rumor free equilibrium are discussed in the second model we mainly consider another network structure i e heterogeneous network thus we propose a new dynamic model for rumor spreading by deriving the mean field equation the basic reproduction number is obtained moreover the global stability of rumor free equilibrium is established by comparison principle by using a monotone iterative algorithm the global attractivity of the positive equilibrium is proved finally we obtain some important conclusions with numerical simulations

a periodically varying code for improving deblending of simultaneous sources in marine acquisition abstractwe have designed a periodically varying code that can avoid the problem of the local coherency and make the interference distribute uniformly in a given range hence it was better at suppressing incoherent interference blending noise and preserving coherent useful signals compared with a random dithering code we have also devised a new form of the iterative method to remove interference generated from the simultaneous source acquisition in each iteration we have estimated the interference using the blending operator following the proposed formula and then subtracted the interference from the pseudodeblended data to further eliminate the incoherent interference and constrain the inversion the data were then transformed to an auxiliary sparse domain for applying a thresholding operator during the iterations the threshold was decreased from the largest value to zero following an exponential function the exponentially decreasing threshold aimed to gradually pass the deblended data to a more

dynamics of a stochastic sis model with double epidemic diseases driven by levy jumps abstract this paper is to investigate the dynamics of a stochastic sis epidemic model with saturated incidence rate and double epidemic diseases which make the research more complex the environment variability in this study is characterized by white noise and jump noise sufficient conditions for the extinction and persistence in the mean of two epidemic diseases are obtained it is shown that the two diseases can coexist under appropriate conditions finally numerical simulations are introduced to illustrate the results developed

rock scissors paper game on regular small world networks the spatial rock scissors paper game or cyclic lotka volterra system is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours degree at each site on the square lattice this system exhibits a self organizing pattern with equal concentration of the competing strategies species if the quenched background is constructed by substituting random links for the nearest neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value this transition can also be observed if the standard link is replaced temporarily by a random one with a probability p at each step of iteration above a second threshold value of p the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous absorbing states in this case the results of monte carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one two four and six site clusters

dynamics of three state excitable units on poisson vs power law random networks abstract the influence of the network topology on the dynamics of systems of coupled excitable units is studied numerically and demonstrates a lower dynamical variability for power law networks than for poisson ones this effect which reflects a robust collective excitable behavior is however lower than that observed for diffusion processes or network robustness instead the presence and number of triangles and larger loops in the networks appears as a parameter with strong influence on the considered dynamics

separation of blended data by iterative estimation and subtraction of blending interference noise seismic acquisition is a trade off between economy and quality in conventional acquisition the time intervals between successive records are large enough to avoid interference in time to obtain an efficient survey the spatial source sampling is therefore often too large however in blending or simultaneous acquisition temporal overlap between shot records is allowed this additional degree of freedom in survey design significantly improves the quality or the economics or both deblending is the procedure of recovering the data as if they were acquired in the conventional unblended way a simple least squares procedure however does not remove the interference due to other sources or blending noise fortunately the character of this noise is different in different domains e g it is coherent in the common source domain but incoherent in the common receiver domain this property is used to obtain a considerable improvement we propose to estimate the blending noise and subtract it from the blended data the estimate does not need to be perfect because our procedure is iterative starting with the least squares deblended data the estimate of the blending noise is obtained via the following steps sort the data to a domain where the blending noise is incoherent apply a noise suppression filter apply a threshold to remove the remaining noise ending up with part of the signal compute an estimate of the blending noise from this signal at each iteration the threshold can be lowered and more of the signal is recovered promising results were obtained with a simple implementation of this method for both impulsive and vibratory sources undoubtedly in the future algorithms will be developed for the direct processing of blended data however currently a high quality deblending procedure is an important step allowing the application of contemporary processing flows

emd seislet transform abstractthe seislet transform uses a prediction operator that is connected to the local slope or frequency of seismic events we have combined the 1d nonstationary seislet transform with empirical mode decomposition emd in the f x domain we used emd to decompose data into smoothly variable frequency components for the following 1d seislet transform the resultant representation showed remarkable sparsity we developed a detailed algorithm and used a field example to demonstrate the application of the new seislet transform for sparsity promoting seismic data processing