the security of the fdh variant of chaum s undeniable signature scheme in this paper a new kind of adversarial goal called forge and impersonate in undeniable signature schemes is introduced note that forgeability does not necessarily imply impersonation ability the security of the full domain hash fdh variant of chaum s undeniable signature scheme is then classified according to three dimensions the goal of adversaries the attacks and the zero knowledge zk level of confirmation and disavowal protocols each security is then related to some well known computational problem in particular the security of the fdh variant of chaum s scheme with noninteractive zero knowledge nizk protocol confirmation and disavowal protocols is proven to be equivalent to the computational diffie hellman cdh problem as opposed to the gap diffie hellman gdh problem as claimed by okamoto and pointcheval

disordered one dimensional contact process new theoretical and numerical analysis of the one dimensional contact process with quenched disorder are presented we derive new scaling relations different from their counterparts in the pure model which are valid not only at the critical point but also away from it due to the presence of generic scale invariance all the proposed scaling laws are verified in numerical simulations in addition we map the disordered contact process into a non markovian contact process by using the so called run time statistic and write down the associated field theory this turns out to be in the same universality class as one derived by janssen for the quenched system with a gaussian distribution of impurities our findings here support the lack of universality suggested by the field theoretical analysis generic power law behaviors are obtained evidence is shown of the absence of a characteristic time away from the critical point and the absence of universality is put forward the intermediate sublinear regime predicted by bramsom et al is also found

epidemic analysis of the second order transition in the ziff gulari barshad surface reaction model we study the dynamic behavior of the ziff gulari barshad irreversible surface reaction model around its kinetic second order phase transition using both epidemic and poisoning time analyses we find that the critical point is given by p 1 0 3873682 ifmmode pm else textpm fi 0 0000015 which is lower than the previously determined value we also obtain precise values of the dynamical critical exponents z ensuremath delta and ensuremath eta which provide further numerical evidence that this transition is in the same universality class as directed percolation

spatial models for species area curves the relationship between species number and area is an old problem in biology we propose here an interacting particle system the multitype voter model with mutation as a mathematical model to study this problem we analyze the species area curves of this model as the mutation rate a tends to zero we obtain two basic types of behavior depending on the size of the spatial region under consideration if the region is a square with area r r 1 then for small the number of species is of order l r log 2 whereas if r 1 the number of species is bounded

stochastic lattice gas model for a predator prey system we propose a stochastic lattice gas model to describe the dynamics of two animal species population one being a predator and the other a prey this model comprehends the mechanisms of the lotka volterra model our analysis was performed by using a dynamical mean field approximation and computer simulations our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators for the sets of parameters used in our computer simulations these oscillations occur at a local level mean field results predict synchronized collective oscillations

critical attractive spin systems we study a class of attractive spin systems we prove that for these processes the system dies out when the parameters are on the critical surface we also prove that the supercritical process survives with positive probability in a sufficiently thick space time slab

stochastic p d e s arising from the long range contact and long range voter processes a long range contact process and a long range voter process are scaled so that the distance between sites decreases and the number of neighbors of each site increases the approximate densities of occupied sites under suitable tine scaling converge to continuous space time densities which solve stochastic p d e s for the contact process the limiting equation is the kolmogorov petrovskii piscuinov equation driven by branching white noise for the voter process the limiting equation is the heat equation driven by fisher wright white noise

density profile processes describing biological signaling networks almost sure convergence to deterministic trajectories we introduce jump processes in k called density profile processes to model biological signaling networks our modeling setup describes the macroscopic evolution of a finite size spin flip model with k types of spins with arbitrary number of internal states interacting through a non reversible stochastic dynamics we are mostly interested on the multi dimensional empirical magnetization vector in the thermodynamic limit and prove that within arbitrary finite time intervals its path converges almost surely to a deterministic trajectory determined by a first order non linear differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories as parameters of the spin flip dynamics change the associated dynamical system may go through bifurcations associated to phase transitions in the statistical mechanical setting we present a simple example of spin flip stochastic model associated to a synthetic biology model known as repressilator which leads to a dynamical system with hopf and pitchfork bifurcations depending on the parameter values the magnetization random path can either converge to a unique stable fixed point converge to one of a pair of stable fixed points or asymptotically evolve close to a deterministic orbit in k we also discuss a simple signaling pathway related to cancer research called p53 module

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

a digital signature scheme secure against adaptive chosen message attacks we present a digital signature scheme based on the computational difficulty of integer factorization the scheme possesses the novel property of being robust against an adaptive chosen message attack an adversary who receives signatures for messages of his choice where each message may be chosen in a way that depends on the signatures of previously chosen messages cannot later forge the signature of even a single additional message this may be somewhat surprising since in the folklore the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosen message attack were considered to be contradictory more generally we show how to construct a signature scheme with such properties based on the existence of a claw free pair of permutations a potentially weaker assumption than the intractibility of integer factorization the new scheme is potentially practical signing and verifying signatures are reasonably fast and signatures are compact

on the dominance of roots of characteristic equations for neutral functional differential equations we present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type to be simple and dominant this knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations a simple characteristic equation arisen from the study of delay equations with small delay is analyzed in greater detail

dynamics of a contact process with ontogeny we propose a simple model of how sessile organisms grow disperse and die our model extends the contact process to include a spatially explicit representation of organismal growth in addition to the familiar terms denoting reproduction and mortality we develop a size structured mean field theory which predicts an oscillatory phase as a consequence of excess reproduction monte carlo simulations of a spatial implementation show instead a transition from a dilute to a ring like phase the ring like phase arises as a consequence of the competition for limited space among juvenile and mature organisms i e the ecological cost of reproduction we also calculate the phase transition between life and death in the spatial model and find that it is in the same universality class as directed percolation finally we analyze the onset of the ring like phase via a spatial autocorrelation and comment on the model s applicability to problems in the study of ecosystem structure and dynamics

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

extinction in the lotka volterra model birth death processes often exhibit an oscillatory behavior we investigate a particular case where the oscillation cycles are marginally stable on the mean field level an iconic example of such a system is the lotka volterra model of predator prey interaction fluctuation effects due to discreteness of the populations destroy the mean field stability and eventually drive the system toward extinction of one or both species we show that the corresponding extinction time scales as a certain power law of the population sizes this behavior should be contrasted with the extinction of models stable in the mean field approximation in the latter case the extinction time scales exponentially with size

vortices and strings in a model ecosystem we study the spatial pattern formation in a model ecosystem by the position fixed reaction method this ecosystem contains three biospecies whose competing powers are cyclic it is well known that this system is self organized into a quasistationary state and that the mean field approximation mfa never predicts such a pattern formation recently several authors applied the pair approximation pa and obtained considerable improvements however applying pa to our ecosystem fails to yield such an improvement as revealed by computer simulations the failures of mfa and pa may be attributed to the fact that both approximations neglect a long range correlation thus we introduce the concept of topological defects such as vortices or strings and demonstrate that the dynamics of these defects can at least qualitatively account for the observed pattern formation dynamics

large time behavior of a linear difference equation with rationally non related delays abstract we consider the linear difference equation x t j 1 n a j x t r j t 0 where a j 0 1 j n and the delays 0 r 1 r 2 r n are not rationally related in the sense that r j r k is irrational for some j and k it is shown that the large time behavior of the continuous solutions can be described in terms of the unique real root of the associated characteristic equation the proof is based on newman s tauberian theorem

exponential decay for subcritical contact and percolation processes we study the contact process together with a version of the percolation process with one continuously varying coordinate it is proved here that the radius of the infected cluster has an exponentially decaying tail throughout the subcritical phase the same is true of the lebesgue measure in space time of this cluster certain critical exponent inequalities are derived and the critical point of the percolation process in two dimensions is determined exactly

certificateless undeniable signatures from bilinear maps certificateless public key cryptosystem avoids the inherent key escrow problem in identity based public key cryptosystem and does not need expensive certificates in the public key infrastructure this cryptographic primitive has received a significant attention since it was introduced and lots of certificateless schemes have been proposed in the past years in this paper we propose an certificateless undeniable signature scheme based on bilinear maps to formally analyze the security of the proposed scheme we extend security notions of undeniable signatures in the traditional public key infrastructure to the certificateless setting under the formally defined security models we prove that our proposed scheme satisfies all the security properties under certain standard assumptions in the random oracle model compared with existed certificateless undeniable signatures the sign algorithm of our scheme is more efficient the weakness is that the unforgeability of our scheme is proved in a weak model

a competition model for size structured species the asymptotic dynamics of a system of ordinary differential equations describing the dynamics of nsize structured species competing for a single unstructured resource are studied the system is

super brownian limits of voter model clusters the voter model is one of the standard interacting particle systems two related problems for this process are to analyze its behavior after large times t for the sets of sites 1 sharing the same opinion as the site 0 and 2 having the opinion that was originally at 0 results on the sizes of these sets were given by sawyer 1979 and bramson and griffeath 1980 here we investigate the spatial structure of these sets in d 2 which we show converge to quantities associated with super brownian motion after suitable normalization the main theorem from cox durrett and perkins 2000 serves as an important tool for these results

stochastic spatial models in the models we will consider space is represented by a grid of sites that can be in one of a finite number of states and that change at rates that depend on the states of a finite number of sites our main aim here is to explain an idea of durrett and levin 1994 the behavior of these models can be predicted from the properties of the mean field ode i e the equations for the densities of the various types that result from pretending that all sites are always independent we will illustrate this picture through a discussion of eight families of examples from statistical mechanics genetics population biology epidemiology and ecology some of our findings are only conjectures based on simulation but in a number of cases we are able to prove results for systems with fast stirring by exploiting connections between the spatial model and an associated reaction diffusion equation

diffusive clustering in the two dimensional voter model on donne des resultats de simulation et une enquete concernant les resultats connus sur le modele du votant dans trois cas distincts trois ou plusieurs dimensions une dimension et deux dimensions

ergodic theorems for the multitype contact process this paper studies a process involving competition of two types of particles 1 and 2 for the empty space 0 each site of the latticez d is therefore in one of three possible states 0 1 or 2 particles of each type die with rate 1 while an empty site becomes occupied by a particle of typei with rate i proportion of neighbors of typei the set of neighbors of a sitex is of the form y x y j for a positive integerj and a norm assuming there are only 0 s and 1 s present at the beginning the process reduces to the contact process with the critical rate of survival of 1 s being c the basic problem we address is the existence of equilibria in which both types of particles coexist without loss of generality one can restrict to the case 2 1 c and in this case we show 1 if 2 1 and the initial state is translation invariant and contains infinitely many 2 s then the 1 s go away and the process approaches the invariant measure of the contact process with only 2 s and 0 s present 2 if 2 1 andd 2 then clustering occurs starting from a translation invariant initial measure with no mass on all 0 s the process converges weakly to a convex combination of the two invariant measures obtained with only one type of particles present and 3 if 2 1 andd 3 then there is a one parameter family of invariant measures including both types

concurrent signature without random oracles a concurrent signature provides an efficient way to exchange digital signatures between parties in a fair manner since its introduction in eurocrypt 2004 removing the random oracle heuristic in the security analysis of a concurrent signature scheme has become an open problem and the security of all the existing provably secure schemes could have only been done in the random oracle model while it has been known that the security in the random oracle model may not be guaranteed when the underlying random oracles are replaced by real life hash functions in this paper we solve this open problem by proposing a new concurrent signature scheme which allows us to prove its security without random oracles the security model we consider in this paper also slightly differs from previous works signatures before revealing the keystone are strongly ambiguous or anonymous in the sense that everyone is able to produce signatures that are indistinguishable from those generated honestly by the parties involved in the exchange while signatures after revealing the keystone remain unforgeable without sacrificing the fairness property in the multi user setting and without random oracles we prove the security of our scheme based on the intractability of computational diffie hellman cdh problem and collision resistance of hash functions

certificateless undeniable signature scheme in this paper we present the first certificateless undeniable signature scheme the scheme does not suffer from the key escrow problem which is inherent in identity based cryptosystems also it can avoid the onerous management of certificates particularly by using some cryptographic and mathematical techniques we guarantee that the scheme s two component protocols satisfy the properties of zero knowledge proofs to address the security issues we extend security notions of undeniable signatures to the complex certificateless setting and consider two different types of adversaries based on these formally defined security notions we prove that in the random oracle model the certificateless undeniable signature scheme is secure in the sense of existential unforgeability under the bilinear diffie hellman assumption and is secure in the sense of invisibility under the decisional bilinear diffie hellman assumption

large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order the spectral theory for linear autonomous neutral functional differential equations fde yields explicit formulas for the large time behaviour of solutions our results are based on resolvent computations and dunford calculus applied to establish explicit formulas for the large time behaviour of solutions of fde we investigate in detail a class of two dimensional systems of fde

a phase transition for a stochastic pde related to the contact process we consider the one dimensional heat equation with a semilinear term and with a nonlinear white noise term r durrett conjectured that this equation arises as a weak limit of the contact process with longrange interactions we show that our equation possesses a phase transition to be more precise we assume that the initial function is nonnegative with bounded total mass if a certain parameter in the equation is small enough then the solution dies out to 0 in finite time with probability 1 if this parameter is large enough then the solution has a positive probability of never dying out to 0 this result answers a question of durett

convergence of markov processes near saddle fixed points we consider sequences xtn t 0 of markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form xt b xt where for some 0 and x o x 2 here the processes are indexed so that the variance of the fluctuations of xtn is inversely proportional to n the simplest example arises from the ok corral gunfight model which was formulated by williams and mcilroy bull london math soc 30 1998 166 170 and studied by kingman bull london math soc 31 1999 601 606 these processes exhibit their most interesting behavior at times of order logn so it is necessary to establish a fluid limit that is valid for large times we find that this limit is inherently random and obtain its distribution using this it is possible to derive scaling limits for the points where these processes hit straight lines through the origin and the minimum distance from the origin that they can attain the power of n that gives the appropriate scaling is surprising for example if t is the time that xtn first hits one of the lines y x or y x then n 2 xtn z for some zero mean gaussian random variable z

self organized critical forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f ensuremath rightarrow 0 provided that the time scales of tree growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system we show that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

coexistence results for catalysts in this paper we consider a modification of ziff gulari and barshad s 1986 model of oxidation of carbon monoxide on a catalyst surface in which the reactants are mobile on the catalyst surface we find regions in the parameter space in which poisoning occurs the catalyst surface becomes completely occupied by one type of atom and another in which there is a translation invariant stationary distribution in which the two atoms have positive density the last result is proved by exploiting a connection between the particle system with fast stirring and a limiting system of reaction diffusion equations

critical dynamics of the contact process with quenched disorder we study critical spreading in monte carlo simulations of the two dimensional contact process cp with quenched disorder in the form of random dilution in the pure model spreading from a single particle at the critical point ensuremath lambda c follows power laws with the critical exponents of directed percolation with disorder critical spreading is logarithmic not power law below ensuremath lambda c there is a griffiths phase in which the time dependence is governed by nonuniversal power laws the effects of disorder are also apparent above ensuremath lambda c in the active phase where the relaxation of the survival probability is algebraic rather than exponential as in the pure model our results support the conjecture by bramson durrett and schonmann ann prob 19 960 1991 that in two or more dimensions the disordered cp has only a single phase transition

improved upper bounds for the contact process critical value the best known upper bound for the critical value c of the basic one dimensional contact process is 2 most techniques for finding bounds on critical values have the property that they can be modified in order to obtain improved bounds this seemed not to be the case for the approach which yielded c 2 for the basic contact process in this paper we propose a technique for generating better bounds in this context to illustrate its use we carry out the full program in one case with the conclusion that c 1 942

a stochastic sirs epidemic model with nonlinear incidence rate a stochastic sirs model with ratio dependent incidence rate is developed the global dynamics of the deterministic model is shown the stochastic dynamics of the sde model is given the existence of a unique stationary distribution of the sde model is displayed in this paper we investigate the global dynamics of a general sirs epidemic model with a ratio dependent incidence rate and its corresponding stochastic differential equation version for the deterministic model we show that the basic reproduction number r0 determines whether there is an endemic outbreak or not if r0 1 the disease persists for the stochastic model we show that its related reproduction number r0s can determine whether there is a unique disease free stationary distribution or a unique endemic stationary distribution in addition we provide analytic results regarding the stochastic boundedness and permanence extinction one of the most interesting findings is that random fluctuations introduced in our stochastic model can suppress disease outbreak which can provide us some useful control strategies to regulate disease dynamics

a spatial model for the abundance of species the voter model with mutations occurring at a positive rate has a unique equilibrium distribution we investigate the logarithms of the relative abundance of species for these distributions in d 2 we show that as 0 the limiting distribution is right triangular in d 2 and uniform in d 3 we also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions

stationary distribution and extinction of the ds i a model disease with periodic parameter function and markovian switching this paper introduces the ds i a model with periodic parameter function and markovian switching first we will prove that the solution of the system is positive and global furthermore we draw a conclusion that there exists nontrivial positive periodic solution for the stochastic system and we establish sufficient conditions for extinction of system moreover we construct stochastic lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the solution to ds i a model perturbed by white and telephone noises and we also establish sufficient conditions for extinction of system with regime switching finally we test our theory conclusion by simulations

criticality and oscillatory behavior in non markovian contact process a non markovian generalization of a one dimensional contact process is being introduced in which every particle has an age and will be annihilated at its maximum age tau there is an absorbing state phase transition which is controlled by this parameter the model can demonstrate oscillatory behavior in its approach to the stationary state these oscillations are also present in the mean field approximation which is a first order differential equation with time delay studying dynamical critical exponents suggests that the model belongs to the direct percolation universality class

the critical contact process dies out by producing a finite box criterion for survival in a slab we show that the critical contact process dies out and that in two and more dimensions the critical parameter value coincides with the limit of slab thresholds using the techniques developed in this paper one may obtain the complete convergence and shape theorems for contact processes in all dimensions and for all infection rates our results apply also to the discrete time analogue of the contact process viz oriented percolation

stationary distribution and extinction of a stochastic sirs epidemic model with standard incidence abstract in this paper we consider a stochastic sirs epidemic model with standard incidence by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of ergodic stationary distribution of the model moreover we also establish sufficient conditions for extinction of the disease

contact processes in several dimensions this paper deals primarily with the basic contact processes introduced and studied by harris 12t4 these are random evolutions on the state space s a l l subsets of z a zd the d dimensional integer lattice with extremely simple local dynamics namely if we think of the contact process as representing the spread of an infection t es denoting the set of infected sites at time t then x e it becomes healthy at exponential rate 1 while x z a t is infected at a rate proport ional to the number of sites neighboring x where infection is present the proportionali ty constant 2 is called the infection parameter contact processes are perhaps the simplest s valued markov processes which exhibit a critical phenomenon infection emanating from a single site dies out with probabili ty one for small positive 2 but has positive probability of surviving for all time when is large there is a critical value 2 d where the transition occurs principal objectives of analysis are the precise formulation of the critical phenomenon and detailed description of the ergodic behavior both below and above a c our recent survey articles 10 and i 6 provide introductions to contact processes and to the general field of interacting s valued systems respectively we will make constant use of notation and techniques from the surveys assuming that the reader is familiar with thern the article 10 describes in some detail the current state of knowledge concerning one dimensional contact processes the theory for d 1 is now fairly complete with two major exceptions 1 is not even determined to one decimal place 1 18 2 e there is an