internal diffusion limited aggregation parallel algorithms and complexity the computational complexity of internal diffusion limited aggregation dla is examined from both a theoretical and a practical point of view we show that for two or more dimensions the problem of predicting the cluster from a given set of paths is complete for the complexity class cc the subset of p characterized by circuits composed of comparator gates cc completeness is believed to imply that in the worst case growing a cluster of size n requires polynomial time in n even on a parallel computer a parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths and then corrects defects in the guessed cluster through a nonlocal annihilation process the parallel running time of the relaxation algorithm for two dimensional internal dla is studied by simulating it on a serial computer the numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n thus the computational resources needed to grow large clusters are significantly less on average than the worst case analysis would suggest for a parallel machine with k processors we show that random clusters in d dimensions can be generated in mathcal o n k logk n 2 d steps this is a significant speedup over explicit sequential simulation which takes mathcal o n 1 2 d time on average finally we show that in one dimension internal dla can be predicted in mathcal o logn parallel time and so is in the complexity class nc

parity law for population dynamics of n species with cyclic advantage competitions we study population dynamics on lattice space with n species n 3 4 5 and 6 with cyclic competitive advantage having both a weaker species and a stronger one the steady state with equal population densities is the globally stable fixed point for the biased rate cyclic advantage population we can observe the different features of the steady states and their stabilities for even n and for odd n and we call it as parity law we obtain the following results on the parity law i for odd number n all the species can coexist following the biased rate and we have the counterintuition for the change of equilibrium densities ii for even n all the species cannot always coexist and it coincides with our intuition we also analyzed mean field approximation it is revealed that most of the results of monte carlo simulation can be understood by mean field approximation dynamics however equilibrium densities cannot be always predicted by mean field approximation because of the spatial fixation

low complexity k dimensional taylor forms a low cost algorithm for the taylor expansion of the rational function in several variables is presented the algorithm is applied to compute the first two terms of a sample rational function in two variables

role of noise in population dynamics cycles noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase forgetting quasicycles by converting damped into sustained oscillations this function of noise becomes evident when considering langevin equations whose deterministic part yields only damped oscillations we formulate here a consistent and systematic approach to population dynamics leading to a fokker planck equation and the associate langevin equations in accordance with this conceptual framework founded on stochastic lattice gas models that describe spatially structured predator prey systems langevin equations in the population densities and predator prey pair density are derived in two stages first a birth and death stochastic process in the space of prey and predator numbers and predator prey pair number is obtained by a contraction method that reduces the degrees of freedom second a van kampen expansion in the inverse of system size is then performed to get the fokker planck equation we also study the time correlation function the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence

analytic solutions to the inverse problem of the newtonian potential let g be a homogeneous body whose shape in r3 is unknown we want to determine the figure of g from measurements of the newtonian potential created by this body on a spherical surface surrounding g we prove the existence of a local analytic solution to the stated problem

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

cyclical interactions with alliance specific heterogeneous invasion rates we study a six species lotka volterra type system on different two dimensional lattices when each species has two superior and two inferior partners the invasion rates from predator sites to a randomly chosen neighboring prey site depend on the predator prey pair whereby cyclic symmetries within the two three species defensive alliances are conserved monte carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival on the difference of alliance specific invasion rates this behavior is qualitatively reproduced by a four point mean field approximation the study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences

on the plane problem of the flow around a submerged beam abstract we consider the problem of the steady flow of an ideal heavy fluid around a submerged beam the problem is obtained from the free boundary problem of the flow past a submerged obstacle in the limit of bodies of vanishing thickness we introduce a special sobolev space formulation of the problem in term of a perturbed stream function and prove its unique solvability for every value of the unperturbed flow velocity with the possible exception of a discrete set depending on the geometry of the domain the asymptotic properties of the solutions are discussed

vortex generation in the rsp game on the triangular lattice abstract a new model of population dynamics on lattices is proposed the model consists of players on lattice points each of which plays the rsp game with neighboring players each player copies the next hand from the hand of the neighbouring player with the maximum point the model exhibits a steady pattern with pairs of vortices and sinks on the triangular lattice it is shown that the stationary vortex is due to the frustrations on the triangular lattice a frustration is the three sided situation where each of the three players around a triangle chooses the rock the scissors and the paper respectively

majority versus minority dynamics phase transition in an interacting two state spin system we introduce a simple model of opinion dynamics in which binary state agents evolve due to the influence of agents in a local neighborhood in a single update step a fixed size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1 p for group size g 3 there is a phase transition at p c 2 3 in all spatial dimensions for p p c the global majority quickly predominates while for p p c the system is driven to a mixed state in which the densities of agents in each state are equal for p p c the average magnetization the difference in the density of agents in the two states is conserved and the system obeys classical voter model dynamics in one dimension and within a kirkwood decoupling scheme the final magnetization in a finite length system has a nontrivial dependence on the initial magnetization for all p not equal p c in agreement with numerical results at p c the exact two spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model

efficient exhaustive listings of reversible one dimensional cellular automata this paper looks at an algebraic formulation of one dimensional cellular automata using the formulation connections to combinatorial structures and graph theory become clear strong results about uniqueness and isomorphism allows us to outline effective algorithms for the generation of exhaustive lists of reversible one dimensional cellular automata and to count the number of distinct examples that exist these algorithms use the orderly algorithm methods to avoid the pitfalls of brute force searches

turbulent pattern bases for cellular automata abstract unpredictable patterns generated by cellular automata ca can be decomposed with respect to a turbulent positive entropy rate pattern basis the resulting filtered patterns uncover significant structural organization in a ca s dynamics and information processing capabilities we illustrate the decompostion technique by analyzing a binary range 2 cellular automaton having two invariant chaotic domains of different complexities and entropies once identified the domains are seen to organize the ca s state space and to dominate its evolution starting from the domains structures we show how to construct a finite state transducer that performs nonlinear spatial filtering such that the resulting space time patterns reveal the domains and the intervening walls and dislocations to show the statistical consequences of domain detection we compare the entropy and complexity densities of each domain with the globally averaged quantities a more graphical comparison uses difference patterns and difference plumes which trace the space time influence of a single site perturbation we also investigate the diversity of walls and particles emanating from the interface between two adjacent domains

species segregation in a model of interacting populations abstract we investigate segregation and spatial organization in a one dimensional system of n competing species forming a cyclic food chain for n

vertex dynamics during domain growth in three state models topological aspects of interfaces are studied by comparing quantitatively the evolving three color patterns in three different models such as the three state voter potts and extended voter models the statistical analysis of some geometrical features allows us to explore the role of different elementary processes during distinct coarsening phenomena in the above models

graph theoretical characterization of invertible cellular automata abstract a cellular automaton is defined to be invertible if its induced global rule is surjective on the set of all finite configurations it is shown that all one dimensional invertible cellular automata are obtainable from invertible nearest pair ones i e cellular automata given by a rule matrix for these an algorithm is proposed which runs in a time which is a polynomial function of the number of letters of the alphabet the result is expressed in a graph theoretical way the cellular automaton is invertible if and only if two graphs constructed by the algorithm have no edges in common it follows that if the number of letters in the alphabet is a prime the only invertible cellular automata are those for which every row or column of the rule matrix is a permutation of the alphabet for composite alphabet cardinalities several methods analytical and computational ones to obtain more complicated invertible cellular automata are proposed and used to construct examples all four letter invertible automata are constructed

cellular automata as an alternative to rather than an approximation of differential equations in modeling physics abstract cellular automata are models of distributed dynamical systems whose structure is particularly well suited to ultrafast exact numerical simulation on the other hand they constitute a radical departure from the traditional partial differential equation approach to distributed dynamics here we discuss the problem of encoding the state variables and evolution laws of a physical system into this new setting and of giving suitable correspondence rules for interpreting the model s behavior

saddles arrows and spirals deterministic trajectories in cyclic competition of four species population dynamics in systems composed of cyclically competing species has been of increasing interest recently here we investigate a system with four or more species using mean field theory we study in detail the trajectories in configuration space of the population fractions we discover a variety of orbits shaped like saddles spirals and straight lines many of their properties are found explicitly most remarkably we identify a collective variable that evolves simply as an exponential q e t where is a function of the reaction rates it provides information on the state of the system for late times as well as for t we discuss implications of these results for the evolution of a finite stochastic system a generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems

phase transitions and spatio temporal fluctuations in stochastic lattice lotka volterra models we study the general properties of stochastic two species models for predator prey competition and coexistence with lotka volterra type interactions defined on a d dimensional lattice introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical deterministic mean field picture already within mean field theory however spatial constraints modeling locally limited resources lead to the emergence of a continuous active to absorbing state phase transition field theoretic arguments supported by monte carlo simulation results indicate that this transition which represents an extinction threshold for the predator population is governed by the directed percolation universality class in the active state where predators and prey coexist the classical center singularities with associated population cycles are replaced by either nodes or foci in the vicinity of the stable nodes the system is characterized by essentially stationary localized clusters of predators in a sea of prey near the stable foci however the stochastic lattice lotka volterra system displays complex correlated spatio temporal patterns of competing activity fronts correspondingly the population densities in our numerical simulations turn out to oscillate irregularly in time with amplitudes that tend to zero in the thermodynamic limit yet in finite systems these oscillatory fluctuations are quite persistent and their features are determined by the intrinsic interaction rates rather than the initial conditions we emphasize the robustness of this scenario with respect to various model perturbations

special issue on control and optimization in cooperative networks this special issue of the siam journal on control and optimization is motivated by the emerging disciplines of multi agent networks distributed motion coordination and cooperative control it is foreseen that in the near future large numbers of coordinated devices communicating through ad hoc networks will perform a variety of challenging sensing tasks the potential advantages of employing arrays of sensors are numerous certain tasks are difficult if not impossible when performed by a single agent and a group of agents inherently provides robustness to failures of single agents or communication links although the individual components of these networked systems are increasingly sophisticated we lack a fundamental understanding of how to assemble and coordinate the individual physical devices into a coherent whole as a consequence of this limitation there exists a strong need for the integration of the sensing computing and networking aspects of coordinated control of networks this special issue gathers recent developments aimed at providing new sets of control and distributed optimization tools to address the research challenges posed by multi agent networks this volume presents 16 papers that deal with a wide range of coordination tasks such as consensus connectivity maintenance spatial process estimation formation stabilization localization coverage and target detection the topics considered include the characterization of convergence speeds the design of algorithms that tolerate delays noisy measurements and packet drops and the study of the controllability of graph structures and the influence of the interconnection topology in the control design collectively the papers detail deep connections between a wide variety of scientific disciplines including cooperative distributed and decentralized control theory distributed algorithms and systems communication networks graph theory geometric optimization differential and computational geometry game and learning theory and process estimation we believe this special issue contains an excellent sample of current research on multi agent networks and we envision that it will be of great interest to the broad readership of the siam journal on control and optimization a million thanks are due to all the authors who submitted their work to this special issue we would also like to thank the proficient and timely editorial support provided by brian fauth and mitch chernoff and the insightful and gracious advice that we received from the editor in chief john baillieul

cyclic cellular automata and related processes abstract a cyclic cellular automaton is a discrete time process defined on the state space 0 1 n 1 zd starting from a random initial condition at each time step each site looks at its nearest neighbors if the state at site x is i then site x will change state to i 1 mod n if it locates state i 1 mod n among its neighbors otherwise site x will remain in state i cyclic cellular automata have properties akin to cyclic particle systems introduced by bramson and griffeath which are continuous time markov processes on 0 1 n 1 zd with a stochastic evolution rather than a deterministic one in one dimension some clustering results about cyclic cellular automata are presented the analogous problems in the context of cyclic particle systems are still unresolved also we discuss the consequences of these clustering results in the context of one dimensional systems of particles with various interaction mechanisms finally we touch upon the work currently being done on two dimensional cyclic particle systems and cellular automata

stable and unstable manifolds for hyperbolic bi semigroups we show the existence of local lipschitzian stable and unstable manifolds for the ill posed problem of perturbations of hyperbolic bi semigroups we do not assume backward nor forward uniqueness of solutions we do not use cut off functions because we do not assume global smallness conditions on the nonlinearities we introduce what we call dichotomous flows which recovers the symmetry between the past and the future thus we need to prove only a stable manifold theorem we modify the conley mcgehee moeckel approach to avoid appealing to wazewski principle and brouwer degree theory hence we allow both the stable and unstable directions to be infinite dimensional we apply our theorem to the elliptic system u u g u u in an infinite cylinder r

coexistence versus extinction in the stochastic cyclic lotka volterra model cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity see e g b kerr m a riley m w feldman and b j m bohannan nature 418 171 2002 and b kirkup and m a riley nature 428 412 2004 through analytical methods supported by numerical simulations we address this issue by studying the properties of a paradigmatic non spatial three species stochastic system namely the rock paper scissors or cyclic lotka volterra model while the deterministic approach rate equations predicts the coexistence of the species resulting in regular yet neutrally stable oscillations of the population densities we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction after long enough time two of the three species die out as main findings we provide analytic estimates and numerical computation of the extinction probability at a given time we also discuss the implications of our results for a broad class of competing population systems

nonequilibrium phase transition in a lattice prey predator system abstract we study a lattice model of a prey predator system mean field approximation predicts that the active phase i e one with a finite fraction of preys and predators is a generic phase of this model moreover within this approximation the model exhibits quasi oscillations resembling lotka volterra systems however monte carlo simulations for a one two and three dimensional versions of this model do not support this scenario and predict that at a certain value of some parameter the model enters the absorbing state i e a state where the entire population of predators dies out and the model is invaded by preys simulations for the one dimensional version indicate that the transition into the absorbing state belongs to the directed percolation universality class

a circular splitting search algorithm for systems of complex equations the results of moore and jones on finding safe starting regions for iterative methods for real functions are extended to finding safe starting discs for iteration methods for complex functions in one or more variables the methods is based on the splitting of circular discs a simple numerical example is given

multiplicative cellular automata on nilpotent groups structure entropy and asymptotics if mathbb m mathbb z d and mathcal b is a finite nonabelian group then mathcal b mathbb m is a compact group a multiplicative cellular automaton mca is a continuous transformation mathfrak g b mathbb m to b mathbb m which commutes with all shift maps and where nearby coordinates are combined using the multiplication operation of mathcal b we characterize when mca are group endomorphisms of mathcal b mathbb m and show that mca on mathcal b mathbb m inherit a natural structure theory from the structure of mathcal b we apply this structure theory to compute the measurable entropy of mca and to study convergence of initial measures to haar measure

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

inclusion functions and global optimization 11 inclusion functions combined with special subdivision strategies are an effective means of solving the global unconstrained optimization problem although these techniques were determined and numerically tested about ten years ago they are nearly unknown and scarcely used in order to make the role of inclusion functions and subdivision strategies more widespread and transparent we will discuss a related simplified basic algorithm it computes approximations of the global minimum and at the same time bounds the absolute approximation error we will show that the algorithm works and converges under more general assumptions than it has been known hitherto that is only appropriate inclusion functions are expected to exist the number of minimal points finite or infinite is not of importance lipschitz conditions or continuity are not assumed as shown in the appendix the required inclusion functions can be constructed and programmed without difficulty in a natural way using interval analysis

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

quasilinear cellular automata abstract simulating a cellular automaton ca for t time steps into the future requires t 2 serial computation steps or t parallel ones however certain cas based on an abelian group such as addition mod 2 are termed linear because they obey a principle of superposition this allows them to be predicted efficiently in serial time o t robinson 1987 or o log t in parallel in this paper we generalize this by looking at cas with a variety of algebraic structures including quasigroups non abelian groups steiner systems and other structures we show that in many cases an efficient algorithm exists even though these cas are not linear in the previous sense we term them quasilinear we find examples which can be predicted in serial time proportional to t t log t t log 2 t and t for t log t log log t and log 2 t we also discuss what algebraic properties are required or implied by the existence of scaling relations and principles of superposition and exhibit several novel vector valued cas

coexistence and survival in conservative lotka volterra networks analyzing coexistence and survival scenarios of lotka volterra lv networks in which the total biomass is conserved is of vital importance for the characterization of long term dynamics of ecological communities here we introduce a classification scheme for coexistence scenarios in these conservative lv models and quantify the extinction process by employing the pfaffian of the network s interaction matrix we illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time

clustering in the one dimensional three color cyclic cellular automaton cyclic cellular automaton the author has previously shown that this process fluctuates meaning that each lattice site changes color infinitely often so that there is no final state for the system the focus of the current work is on the clustering properties of this system this paper demonstrates that the one dimensional three color cyclic cellular automaton clusters and the mean cluster size as a function of time t is asymptotic to ct1 2 where c is an explicitly calculable constant the method of proof also allows us to compute asymptotic estimates of the mean interparticle distance for a one dimensional system of particles which undergo deterministic motion and which annihilate upon collision no clustering results are known about the four color process but evidence is presented to suggest that the mean cluster size of such systems grows at a rate different from t1 2

deterministic soluble model of coarsening we investigate a three phase deterministic one dimensional phase ordering model in which interfaces move ballistically and annihilate upon colliding we determine analytically the autocorrelation function a t this is done by computing generalized first passage type probabilities mathrm p mathrm n t which measure the fraction of space crossed by exactly n interfaces during the time interval 0 t and then expressing the autocorrelation function via mathrm p mathrm n s we further reveal the spatial structure of the system by analyzing the domain size distribution

recurrence and ergodicity of interacting particle systems an important technical result proposition 2 3 and its proof present in the original submission was erroneously omitted when this paper was published in 2000 the missing text which should have appeared on page 243 directly before section 3 is included in this erratum together with a short account of its context simultaneously with the publication of this erratum the electronic version of the paper in vol 116 no 2 2000 will be completed by insertion of the missing text readers of probability theory and related fields who have access to the electronic version of this erratum will also have access via a url to the full intact paper

a cyclically catalytic super brownian motion in generalization of the mutually catalytic super brownian motion in r of dawson and perkins and mytnik a function valued cyclically catalytic model x is constructed as a strong markov solution to a martingale problem starting with a finite population x 0 each pair of neighboring types will globally segregate in the long term limit noncoexistence of neighboring types also finer extinction survival properties depending on x 0 are studied in the spirit of mueller and perkins in fact x 0 can be chosen in such a way that all types survive for all finite times on the other hand sufficient conditions on x 0 are stated for the following situation given a type k and a positive time t the kth subpopulation x k dies by time t with a large probability provided that its initial value x k 0 was sufficiently small

spirals and coarsening patterns in the competition of many species a complex ginzburg landau approach in order to model real ecological systems one has to consider many species that interact in complex ways however most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions the few studies dealing with larger number of species and or more complex interaction schemes are mostly restricted to numerical explorations in this paper we determine starting from the deterministic mean field rate equations for large classes of systems the space of coexistence fixed points at which biodiversity is maximal for systems with a single coexistence fixed point we derive complex ginzburg landau equations that allow to describe space time pattern realized in two space dimensions for selected cases we compare the theoretical predictions with the pattern observed in numerical simulations

the computational complexity of sandpiles given an initial distribution of sand in an abelian sandpile what final state does it relax to after all possible avalanches have taken place in d 3 we show that this problem is p complete so that explicit simulation of the system is almost certainly necessary we also show that the problem of determining whether a sandpile state is recurrent is p complete in d 3 and briefly discuss the problem of constructing the identity in d 1 we give two algorithms for predicting the sandpile on a lattice of size n both faster than explicit simulation a serial one that runs in time mathcal o n log n and a parallel one that runs in time mathcal o log3n i e the class nc3 the latter is based on a more general problem we call additive ranked generability this leaves the two dimensional case as an interesting open problem

symmetric two particle exclusion eating processes we consider infinite particle systems on a countable set s with two particle exclusion eating motion determined by a symmetric transition function p x y this is in a certain sense a mixture of the exclusion process and the voter model we discuss the dual process of this process and use the dual process to give a description of the set of invariant measures and to prove an ergodic theorem

exact solution of the wave resistance problem for a submerged cylinder ii the non linear problem we study the problem of wave resistance for a slender cylinder submerged in a heavy fluid of finite depth with the cylinder moving at uniform supercritical speed in the direction orthogonal to its generators we look for a divergence free irrotational flow the boundary of the region occupied by the fluid consisting of the free surface the bottom and the obstacle profile is assumed to belong to streamlines and the bernoulli condition is taken on the free surface the problem is transformed via the hodograph map into a problem set in a strip with a cut by using a hard version of the inverse function theorem and by taking account of the results obtained in part i which we recall here we prove the existence of a complex velocity function satisfying all the requirements of the problem in particular this function is continuous up to the surface of the obstacle and the only possible singularities appear at the end points where the boundary is not smooth moreover two stagnation points appear near to the extremities of the submerged body

interplay between partnership formation and competition in generalized may leonard games in order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized may leonard models with n species these models have a very rich structure characterized by different types of space time patterns interesting partnership formations emerge following the maxim that the enemy of my enemy is my friend in specific cases cyclic dominance within coarsening clusters yields a peculiar coarsening behavior with intriguing pattern formation we classify the different types of dynamics through the analysis of the square of the adjacency matrix the dependence of the population densities on emerging pattern and propagating wave fronts is elucidated through a fourier analysis finally after having identified collaborating teams we study interface fluctuations where we initially populate different parts of the system with different teams

circular centered forms for rational functions in several complex variables abstract as a continuation of rokne this journal 1987 this paper considers the explicit representation and inclusion properties as well as convergence of circular centered forms for rational complex functions in several variables

stable oscillations of a predator prey probabilistic cellular automaton a mean field approach we analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator prey system the individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the lotka volterra model two levels of mean field approximations are set up the simple approximation is equivalent to an extended patch model a simple metapopulation model with patches colonized by prey patches colonized by predators and empty patches this approximation is capable of describing the limited available space for species occupancy the pair approximation is moreover able to describe two types of coexistence of prey and predators one where population densities are constant in time and another displaying self sustained time oscillations of the population densities the oscillations are associated with limit cycles and arise through a hopf bifurcation they are stable against changes in the initial conditions and in this sense they differ from the lotka volterra cycles which depend on initial conditions in this respect the present model is biologically more realistic than the lotka volterra model

centered forms for functions in several variables abstract r e moore 3 has introduced the centered form of a rational function f for obtaining good and easily computable approximations which include the exact range of f over an interval x moore s definition is implicit while explicit formulas for the centered form are given in 8 and 9 in 9 centered forms of higher order for functions of one variable are developed which lead to better estimations than the centered forms defined originally in this paper centered forms of higher order for rational functions in several variables are explicitly defined they also give better approximations than the centered forms defined originally

dynamic of cyclic automata over z2 abstract let k be the two dimensional grid let q be an integer greater than 1 and let q 0 q 1 let s q q be defined by s 1 mod q q in this work we study the following dynamic f on q z 2 for x q z 2 we define fv x s xv if the state s xv appears in one of the four neighbors of v in k and fv x xv otherwise for x q z 2 such that v z 2 x v 0 is finite we prove that there exists a finite family of cycles such that the period of every vertex of k divides the lcm of their lengths this is a generalization of the same result known for finite graphs moreover we show that this upper bound is sharp we prove that for every n 1 and every collection k1 kn of non negative integers there exists y n q z 2 such that v z 2 y n v 0 o k 1 2 k n 2 and the period of the vertex 0 0 is p lcm k1 kn for some even integer p

steady flows of inviscid fluids under localized perturbations on essaie d obtenir tous les ecoulements stationnaires dans un canal avec un petit obstacle pour des nombres de froude proches de la valeur critique fo

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

representations of geometrical and topological quantities in cellular automata abstract this paper addresses the problem of finding novel representations of analogs of physical field variables in cellular automata several examples illustrate how this might be done 1 a manifestly covariant vector law for diffusion 2 a model for potential energy and exact one forms 3 a counting algorithm using a winding number density and 4 fields which support topological charges in order to combine the advantages of cellular automata and continuum analysis it is necessary to have representations which involve more than one cell

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

three state potts model in combination with the rock scissors paper game we study a three state potts model extended by allowing cyclic dominance between the states as exemplified in the rock scissors paper game monte carlo simulations are performed on a square lattice while varying the temperature and the strength of cyclic dominance it is shown that the critical phase transition from the disordered state to the ordered one is destroyed by the cyclic dominance which yields a self organizing pattern even at low temperatures the differences and similarities are discussed between the present model and half filled driven lattice gases with repulsive interaction

three and four state rock paper scissors games with diffusion cyclic dominance of three species is a commonly occurring interaction dynamics often denoted the rock paper scissors rps game such a type of interactions is known to promote species coexistence here we generalize recent results of reichenbach et al nature london 448 1046 2007 of a four state variant of the rps game we show that spiral formation takes place only without a conservation law for the total density nevertheless in general fast diffusion can destroy species coexistence we also generalize the four state model to slightly varying reaction rates this is shown both analytically and numerically not to change pattern formation or the effective wavelength of the spirals and therefore not to alter the qualitative properties of the crossover to extinction

exit probability in generalised kinetic ising model in this paper we study generalised ising glauber models with inflow of information in one dimension and derive expressions for the exit probability using well established analytical methods the analytical expressions agree very well with the results obtained from numerical simulation only when the interaction is restricted to the nearest neighbor but as the range of interaction is increased the analytical results deviate from simulation results systematically the reasons for the deviation as well as some related open questions are discussed

growth behavior of helical cellular automata a helical cellular automata hca model constructed on a two dimensional grid of cells with a helical structure is presented and the pattern formation of this model studied by numerous computer simulations it is found that the evolutions of the hca are sensitive to the circumference of the helix p with various p the initial growth of the model generates various patterns ranging from sierpinski triangle gasket complex textured pattern to lateral quasiperiodic structure a sudden transition from regular fractal to compact pattern occurs near the point where p is equal to a positive integer power of 2 with increasing height of the patterns increasing growth time the model also exhibits different growth behaviors in the vertical direction for various p including the formation of regular periodic patterns and the evolution from initial regular patterns to eventual random structures fractal dimension analysis is used to characterize these different evolution processes quantitatively

interval approximation of higher order to the ranges of functions the bernstein and b spline forms are generalized to multivariate polynomials these forms are combined with a type of taylor form for multivariate functions to generate realizable forms for multivariate functions

exponents appearing in the zero temperature dynamics of the 1d potts model for the glauber dynamics of the one dimensional q state potts model at zero temperature the fraction of spins which have never flipped up to time t decreases as t theta q where the exponent theta q varies continuously with q the calculation of the q dependence of this exponent can be reduced to the study of a simple reaction diffusion model using finite size scaling this allows one to obtain accurate estimates of b q for all values of q one can also show that for 1 1 epsilon the expansion of theta y is given by theta 1 2 pi epsilon o epsilon 2

a family of centered forms for rational functions abstract a family of centered forms for rational functions dependent on a parameter is investigated particular choices of the parameter are investigated in further detail it is also shown that a centered form of minimum width can be chosen from the family these centered forms are then generalized to a family of forms of higher order

the neumann kelvin problem for a beam abstract we discuss existence uniqueness and regularity of the solution of the plane neumann kelvin problem in a strip in the case of a beam the problem is obtained by linearization of the equations of the wave resistance problem for a slender cylinder semisubmerged in a heavy fluid and moving at uniform supercritical speed in the direction orthogonal to its generators the results obtained may be relevant for the resolution of the nonlinear wave resistance problem

synchronization of stochastic oscillations due to long range diffusion we investigate the effect of long range diffusive mixing on stochastic processes taking place on low dimensional catalytic supports as a working example the cyclic lattice lotka volterra llv model is used which is conservative at the mean field level and demonstrates fractal patterns and local oscillations when realized on low dimensional lattice supports we show that the local oscillations are synchronized when a weak long range diffusive process is added to llv and global oscillations of limit cycle type emerge this phenomenon is demonstrated as a nonequilibrium phase transition and takes place when the mixing to reaction rate p order parameter is above a critical point p c the value of the critical point is shown to depend on the kinetic parameters the global oscillations in this case emerge as a result of phase synchronization between local oscillations on sublattices

exact theory of secondary supercritical solutions for steady surface waves over a bump abstract two dimensional steady surface waves on an ideal fluid over a small and symmetric bump are studied when the froude number f of the uniform flow far upstream is greater than unity recent numerical results for a symmetric bump indicate that corresponding to f 1 there may exist two solutions for the problem one approaches the uniform flow and the other a solitary wave as the bump size goes to zero in this paper we use a two parameter asymptotic expansion to derive an explicit approximate expression for the later solution and show that the expansion is indeed an asymptotic approximation to the solution of the exact nonlinear equations

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

fixation in a cyclic lotka volterra model we study a cyclic lotka volterra model of n interacting species populating a d dimensional lattice in the realm of a kirkwood approximation a critical number of species nc d above which the system fixates is determined analytically we find nc d 5 14 23 in dimensionsdd 1 2 3 in remarkably good agreement with simulation results in two dimensions a cyclic variant of the lotka volterra model of interacting populations originally introduced by vito volterra for the description of the struggle for existence among species 1 2 has then appeared in a number of apparently unrelated fields ranging from plasma physics 3 to integrable systems 4 5 recently the cyclic lotka volterra model also known as the cyclic voter model has attracted considerable interest as it was realized that introduction of the spatial structure drastically enriches the dynamics 6 11 namely if species live on a one dimensional 1d lattice a homogeneous initial state evolves into a coarsening mosaic of interacting species this heterogeneous spatial structure spontaneously develops when the number of species is sufficiently small n nc fixation occurs i e the system approaches a frozen state little is known in higher dimensions not even the existence of nc has yet been established theoretically or numerically in simulations on two dimensional 2d lattices with n 6 10 species no sign of fixation has been found and instead a reactive steady state has been observed 6 11 in this letter we investigate the cyclic lotka volterra model in the framework of a kirkwood like approximation this approach predicts a finite nc in all spatial dimensions in the following we shall use the language of the voter model 12 consider the cyclic voter model with n possible opinions each site of a d dimensional cubic lattice is occupied by a voter which has an opinion labelled by with d 1 n voters can change their opinions in a cyclic manner 1 modulo n according to the opinions of their neighbourhood specifically the following sequential dynamics is implemented i we randomly choose a site of opinion say and one of its 2d nearest neighbours of opinion ii if d 1 then the chosen site changes its opinion from to d 1 and iii otherwise opinion does not change we set the timescale so that in unit time each site of the lattice is chosen once on average when nd 2 the cyclic voter model is

synchronization of finite state pulse coupled oscillators abstract we propose a novel generalized cellular automaton gca model for discrete time pulse coupled oscillators and study the emergence of synchrony given a finite simple graph and an integer n 3 each vertex is an identical oscillator of period n with the following weak coupling along the edges each oscillator inhibits its phase update if it has at least one neighboring oscillator at a particular blinking state and if its state is ahead of this blinking state we obtain conditions on initial configurations and on network topologies for which states of all vertices eventually synchronize we show that our gca model synchronizes arbitrary initial configurations on paths trees and with random perturbation any connected graph in particular our main result is the following local global principle for tree networks for n 3 4 5 6 any n periodic network on a tree synchronizes arbitrary initial configuration if and only if the maximum degree of the tree is less than the period n

reachability and recurrence in a modular generalization of annihilating random walks and lights out games to hypergraphs we study a discrete asynchronous dynamical system on hypergraphs that can be regarded as a natural extension of annihilating walks along two directions first the interaction topology is a hypergraph second the number of particles at a vertex of the hypergraph is an element of a finite ring z p of integers modulo an odd number p 3 equivalently particles move on a hypergraph with a moving particle at a vertex being replaced by one indistinguishable copy at each neighbor in a given hyperedge particles at a vertex collectively annihilate when their number reaches p the boolean version of this system arose in earlier work 22 motivated by the statistical physics of social balance 3 2 generalizes certain lights out games 31 to finite fields and also has some applications to the complexity of local search procedures 23 our result shows that under a liberal sufficient condition on the nature of the interaction hypergraph there exists a polynomial time algorithm based on linear algebra over z p for deciding reachability and recurrence of this dynamical system interestingly we provide a counterexample that shows that this connection does not extend to all graphs

spreading of families in cyclic predator prey models we study the spreading of families in two dimensional multispecies predator prey systems in which species cyclically dominate each other in each time step randomly chosen individuals invade one of the nearest sites of the square lattice eliminating their prey initially all individuals get a family name which will be carried on by their descendants monte carlo simulations show that the systems with several species n 3 4 5 are asymptotically approaching the behavior of the voter model i e the survival probability of families the mean size of families and the mean square distance of descendants from their ancestor exhibits the same scaling behavior the scaling behavior of the survival probability of families has a logarithmic correction in case of the voter model this correction depends on the number of species while cyclic predator prey models behave like the voter model with infinite species it is found that changing the rates of invasions does not change this asymptotic behavior as an application a three species system with a fourth species intruder is also discussed

phase transitions for rock scissors paper game on different networks monte carlo simulations and dynamical mean field approximations are performed to study the phase transitions in the rock scissors paper game on different host networks these graphs are originated from lattices by introducing quenched and annealed randomness simultaneously in the resulting phase diagrams three different stationary states are identified for all structures the comparison of results on different networks suggests that the value of the clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase the critical behavior of phase transitions seems to be universal and can be described by the same exponents

collective behavior of random activated mobile cellular automata abstract dynamical properties of 2d cellular automata with mobile elements are examined qualitatively results show that a system containing elements with local interactions but with no fixed connections due to movement and connection breaking are able to display periodic oscillations by collective synchronization of non periodical randomly activated elements the system studied is found to be robust spatial dynamics is shown to generate interesting spatial structures suggesting the presence of self organization moreover maximum lyapunov exponents and fractal dimension of attractors have been calculated in order to show that the dynamics of interaction among elements is chaotic

coarsening and persistence in the voter model the voter model is a simple model for coarsening with a nonconserved scalar order parameter we investigate coarsening and persistence in the voter model by introducing the quantity pn t defined as the fraction of voters who changed their opinion n times up to time t we show that pn t exhibits scaling behavior that strongly depends on the dimension as well as on the initial opinion concentrations exact results are obtained for the average number of opinion changes n and the autocorrelation function a t 21 n pn t 2d 2 in arbitrary dimension d these exact results are complemented by a mean field theory heuristic arguments and numerical simulations for dimensions d 2 the system does not coarsen and the opinion changes follow a nearly poissonian distribution in agreement with mean field theory for dimensions d 2 the distribution is given by a different scaling form which is characterized by nontrivial scaling exponents for unequal opinion concentrations an unusual situation occurs where different scaling functions correspond to the majority and the minority as well as for even and odd n

exact solution of the wave resistance problem for a submerged cylinder i linearized theory we consider the problem of finding a holomorphic function in a strip with a cut cal a x y x in re 0 y h backslash x y x le x 0 y y 0 satisfying some prescribed linear conditions on the boundary the problem has a one parameter family of solutions in the class of sectionally holomorphic functions in vanishing for x to infty a special solution can be selected by fixing the value of the circulation around the cut the problem is obtained by linearization of the equations of the wave resistance problem for a slender cylinder submerged in a heavy fluid and moving at uniform speed in the direction orthogonal to its generators the results obtained besides their own interest are a crucial step for the resolution of the non linear problem

on the evaluation of rational functions in interval arithmetic we discuss some new expressions for rational functions for which the hausdorff distance between the range over a given interval and the interval arithmetic evaluation has the order of the square of the width of the given interval

vortex dynamics in a three state model under cyclic dominance the evolution of domain structure is investigated in a two dimensional voter model with three states under cyclic dominance the study focus on the dynamics of vortices defined by the points where the three states domains meet we can distinguish vortices and antivortices which walk randomly and annihilate each other the domain wall motion can create vortex antivortex pairs at a rate that is increased by the spiral formation due to cyclic dominance this mechanism is contrasted with a branching annihilating random walk barw in a particle antiparticle system with density dependent pair creation rate numerical estimates for the critical indices of the vortex density beta 0 29 4 and of its fluctuation gamma 0 34 6 improve an earlier monte carlo study k tainaka and y itoh europhys lett 15 399 1991 of the three state cyclic model in two dimensions

rational circular complex centered forms abstract a discussion is given of the problem of computing including estimates of the range of a complex rational function over a circular complex interval for this purpose rational circular complex centered forms are defined explicit formulas are given for the first few forms and these formulas are used to prove that forms of higher order are an improvement over the forms of lower order the forms are furthermore shown to be quadratically convergent a semi centered form is also discussed this form is shown to be quadratically convergent depending on some conditions on the coefficients of the polynomials defining the complex rational function finally a number of numerical examples are given showing the improvements obtained using the circular centered forms as compared to simple circular complex rational function estimations