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

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

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

random geometric graphs we analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present the critical connectivity is found numerically by examining the size of the largest cluster we derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs even for infinite dimensionality insights relevant for graph bipartitioning are included

discrete proportional hazards models for mismeasured outcomes la mesure erronee du critere de jugement peut conduire a des estimations biaisees dans plusieurs contextes magder et hughes 1997 ont montre que l absence de prise en compte de l erreur sur le critere de jugement dans une analyse logistique peut biaiser de facon conservatrice l estimation des effets des covariables meme lorsque le taux d erreur est le meme pour chaque valeur de la covariable d autres auteurs se sont interesses a la necessite de prendre en compte l erreur dans le recueil du critere de jugement dans les etudes de survie dans des cas particuliers snapinn 1998 gelfand et wang 2000 balasubramanian et lagakos 2001 nous proposons une methode ajustee a risques proportionnels generale plus largement utilisable pour l estimation de la survie cumulee et des risques relatifs dans un contexte de temps discret quand le critere de jugement est recueilli avec erreur nous montrons que le fait de recueillir l evenement avec erreur dans un modele a risques proportionnels standard peut biaiser les estimations des risques relatifs de facon conservatrice et que l inference dans la plupart des situations est plus severement influencee par une mauvaise specificite que par une mauvaise sensibilite cependant dans des simulations portant sur des situations tres variees la methode proposee avec des taux d erreurs bien specifies a de tres bonnes performances

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

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

criticality in cellular automata abstract using recent results obtained for the transition to turbulence via spatiotemporal intermittency in extended dynamical systems critical cellular automata rules are built thanks to a systematic procedure the continuous phase transition observed in a coupled map lattice is translated into a sequence of cellular automata rules for which the critical properties of the original system are reproduced as precisely as desired it is shown that criticality as understood from the point of view of statistical mechanics is intimately related to the various characteristics of wolfram s class iv rules this suggests in turn the picture of a critical surface in the space of rules and provides the basis for a discussion of the problem of classification schemes we review recent cellular automata studies where questions linked to criticality arise and argue that they are unified in light of our results leaving the relationship between computational and statistical characterizations of critical rules as the central problem for future studies on this subject

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

survival analysis with uncertain endpoints summary in some survival analysis applications the endpoint of interest has a degree of uncertainty associated with it these events are typically classified by the investigator or by an endpoint committee as true or false according to some decision rule and the analysis proceeds using only the true endpoints this procedure has two drawbacks the cutpoint for the decision rule is somewhat arbitrary and the information contained in the level of certainty is lost this paper introduces a modification of the cox regression model that allows all potential endpoints to be included in the analysis along with the level of certainty of each simulation results show this procedure to considerably increase the power of the standard procedure in a wide range of situations

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

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

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

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

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

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

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

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

morphology of technological levels in an innovation propagation model we study the dynamical properties of the propagation of innovation on a two dimensional lattice random network scale free network and cayley tree in order to investigate the diversity of technological level we study the scaling property of width w n t which represents the root mean square of the technological level of agents here n is the total number of agents from the numerical simulations we find that the steady state value of w n t w sat n scales as w sat n n 1 2 when the system is in a flat ordered phase for d 2 in the flat ordered phase most of the agents have the same technological level on the other hand when the system is in a smooth disordered phase the value of w sat n does not depend on n these behaviors are completely different from those observed on a one dimensional 1d lattice by considering the effect of the underlying topology on the propagation dynamics for d 2 we also provide a mean field analysis for w sat n which agrees very well with the observed behaviors of w sat n this directly shows that the morphological properties in order disorder transition on a 1d lattice is completely different from that on higher dimensions it also provides an evidence that the upper critical dimension for the roughening transition of the propagation of innovation is d u 2

coupling induced statistical cycling in two diffusively coupled maps abstract this paper discusses the effects of diffusively coupling two identical one dimensional maps attention is focused on situations where the local isolated maps are statistically stable but where the coupled system is not a biologically motivated map and the quadratic map are numerically shown to display this behavior the piecewise linear tent map is then investigated analytically and we give a phase diagram of this system which displays the location of nonequilibrium phase transitions it is conjectured that the diffusive coupling of two chaotic but statistically stable maps i e with asymptotically stable perron frobenius operators can yield a two dimensional system which is not statistically stable whose associated perron frobenius operator is asymptotically periodic

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

statistical properties of turbulent dynamical systems abstract we give an example of the use of stochastic models to describe turbulent systems this is the so called transition to spatio temporal intermittency whose connection to directed percolation has been an open question for a number of years we discuss the recent finding 1 that an asynchronously updated coupled map lattice seems to be in this universality class although the synchronous version is apparently not 2

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

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

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

nonparametric discrete survival function estimation with uncertain endpoints using an internal validation subsample when a true survival endpoint cannot be assessed for some subjects an alternative endpoint that measures the true endpoint with error may be collected which often occurs when obtaining the true endpoint is too invasive or costly we develop an estimated likelihood function for the situation where we have both uncertain endpoints for all participants and true endpoints for only a subset of participants we propose a nonparametric maximum estimated likelihood estimator of the discrete survival function of time to the true endpoint we show that the proposed estimator is consistent and asymptotically normal we demonstrate through extensive simulations that the proposed estimator has little bias compared to the naive kaplan meier survival function estimator which uses only uncertain endpoints and more efficient with moderate missingness compared to the complete case kaplan meier survival function estimator which uses only available true endpoints finally we apply the proposed method to a dataset for estimating the risk of developing alzheimer s disease from the alzheimer s disease neuroimaging initiative

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

nonparametric estimation of the survival function when cause of death is uncertain summary a nonparametric estimator for the survival function accommodating censored survival times and uncertainty in the assignment of cause of death is proposed for example in a carcinogenicity experiment the data on each animal may consist of an observed age at death and some indication of the probability that the tumor type under study caused death an estimator of the net survival function for time to death due to the cause of interest is developed under certain assumptions the proposed estimator is consistent and asymptotically normally distributed monte carlo simulations were used to compare this estimator with the kaplan meier estimator forcing the cause of death to be specified with certainty as required by the kaplan meier estimator may result in substantial biases

ising model on networks with an arbitrary distribution of connections we find the exact critical temperature t c of the nearest neighbor ferromagnetic ising model on an equilibrium random graph with an arbitrary degree distribution p k we observe an anomalous behavior of the magnetization magnetic susceptibility and specific heat when p k is fat tailed or loosely speaking when the fourth moment of the distribution diverges in infinite networks when the second moment becomes divergent t c approaches infinity the phase transition is of infinite order and size effect is anomalously strong

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

self organized evolution in a socioeconomic environment we propose a general scenario to analyze technological changes in socio economic environments we illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and at the same time sufficiently complex to display a rich dynamic behavior our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical in the sense that the distribution of events follow power laws computer simulations show that in addition the system always self organizes to achieve the optimal performance in the stationary state

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

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

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

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

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

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

analysis of time to event data with incomplete event adjudication in many multicenter randomized clinical trials the primary outcome is the time to the first of a number of possible clinical events an event classification committee may be convened to determine whether events that have been reported by investigators meet the predetermined criteria for primary endpoint events when interim analyses are performed in such trials the final classification for many reported events will not be known failure to account for the uncertain status of these events may result in incorrect interim analysis the probability that an unadjudicated event will be confirmed as a primary event can typically be estimated from those events for which adjudication is complete we show that if each unadjudicated event is weighted according to the probability that it will be the first primary event then consistent estimates of survival probabilities and regression parameters can be obtained and unbiased log rank tests of treatment differences performed moderate sample consistency of point es

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

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

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