stability and isolation phenomena for yang mills fields in this article a series of results concerning yang mills fields over the euclidean sphere and other locally homogeneous spaces are proved using differential geometric methods one of our main results is to prove that any weakly stable yang mills field overs4 with groupg su2 su3 oru2 is either self dual or anti self dual the analogous statement for so4 bundles is also proved the other main series of results concerns gap phenomena for yang mills fields as a consequence of the non linearity of the yang mills equations we can give explicitc0 neighbourhoods of the minimal yang mills fields which contain no other yang mills fields in this part of the study the nature of the groupg does not matter neither is the dimension of the base manifold constrained to be four

critical behavior of the one dimensional diffusive pair contact process the phase transition of the one dimensional diffusive pair contact process is investigated by n cluster mean field approximations and high precision simulations the n 3 4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate d with beta 2 2 mean field order parameter exponent of the pair density this contradicts with former n 2 results where two different mean field behavior was found along the transition line extensive dynamical simulations on l 10 5 lattices give estimates for the order parameter exponents of the particles for 0 05 or d or 0 7 these data may support former two distinct class findings however the gap between low and high d exponents is narrower than previously estimated and the possibility for interpreting numerical data as a single class behavior with exponents alpha 0 21 1 beta 0 40 1 assuming logarithmic corrections is shown finite size scaling results are also presented

approximate probabilistic cellular automata for the dynamics of single species populations under discrete logisticlike growth with and without weak allee effects we investigate one dimensional elementary probabilistic cellular automata pca whose dynamics in first order mean field approximation yields discrete logisticlike growth models for a single species unstructured population with nonoverlapping generations beginning with a general six parameter model we find constraints on the transition probabilities of the pca that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof several possible models display a negative cubic term that can be interpreted as a weak allee factor we also investigate the conditions under which a one parameter pca derived from the more general six parameter model can generate valid population growth dynamics numerical simulations illustrate the behavior of some of the pca found

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2

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

critical exponents for the restricted sandpile i report large scale monte carlo studies of a one dimensional height restricted stochastic sandpile using the quasistationary simulation method results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems but are consistent with recent predictions derived from a langevin equation for stochastic sandpiles ramasco phys rev e 69 045105 r 2004 this suggests that apparent violations of universality in one dimensional sandpiles are due to strong corrections to scaling and finite size effects

evolutionary games in economics evolutionary games are introduced as models for repeated anonymous strategic interaction actions or behaviors which are more fit given the current distribution of behaviors tend over time to displace less fit behaviors cone fields characterize the continuous time processes compatible with a given fitness or payoff function for large classes of dynamics it is shown that all stable steady states are nash equilibria and that all nash equilibria are steady states the biologists evolutionarily stable strategy condition is shown to be less closely related to the dynamic equilibria economic examples and a literature survey are also provided copyright 1991 by the econometric society

presentation functions fixed points and a theory of scaling function dynamics presentation functions provide the time ordered points of the forward dynamics of a system as successive inverse images they generally determine objects constructed on trees regular or otherwise and immediately determine a functional form of the transfer matrix of these systems presentation functions for regular binary trees determine the associated forward dynamics to be that of a period doubling fixed point they are generally parametrized by the trajectory scaling function of the dynamics in a natural way the requirement that the forward dynamics be smooth with a critical point determines a complete set of equations whose solution is the scaling function these equations are compatible with a dynamics in the space of scalings which is conjectured with numerical and intuitive support to possess its solution as a unique globally attracting fixed point it is argued that such dynamics is to be sought as a program for the solution of chaotic dynamics in the course of the exposition new information pertaining to universal mode locking is presented

boundary height correlations in a two dimensional abelian sandpile boundary height distributions of the two dimensional abelian sandpile model are studied in the self organized critical state all height probabilities are calculated explicitly both at open and closed boundaries the leading asymptotic term of the corresponding correlation functions is observed to behave as r 4 when r to infinity on the basis of conformal field theory predictions the bulk height correlators are shown to have the same critical exponents as boundary ones all heights seem to be identified with appropriate counterparts of the local energy operator in the zero component potts model

on klauder s pseudo free oscillator studies the quantum oscillator on the half line defined by the hamiltonian h 1 2 delta 2 delta x2 1 2x2 together with vanishing boundary conditions at 0 the authors derives and discusses a new operator equation of motion of the form x x a for this system this equation is used to verify j r klauder s conjecture 1979 that x satisfy x x x 0 it is also used to obtain systematic results on the set of n point functions omega mod x t1 x t2 x tn mod omega it is suggested that these methods and results will act as a source of conjectures about the analogous pseudo free field theories postulated by klauder in his program for handling non renormalisable field theories

waves of topplings in an abelian sandpile abstract we study the structure of the avalanche process in the 2d abelian sandpile model an avalanche may be represented as a sequence of waves each consisting of sites that toppled only once in that wave it is shown that the waves are in one to one correspondence with the set of two rooted spanning trees and can be described in terms of green functions we argue that the probability distribution of waves of size s varies as 1 s for large s we prove also that the avalanches started at the open boundary consist of only one wave and find the asymptotic distribution of their sizes which varies as s 3 2 we establish the equivalence between waves and inverse avalanches introduced by dhar and manna and reproduce their result 11 8 for the critical exponent of the size distribution of the first inverse avalanche or in our terms the last wave

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

quantum instantons with classical moduli spaces we introduce a quantum minkowski space time based on the quantum group su 2 q extended by a degree operator and formulate a quantum version of the anti self dual yang mills equation we construct solutions of the quantum equations using the classical adhm linear data and conjecture that up to gauge transformations our construction yields all the solutions we also find a deformation of penrose s twistor diagram giving a correspondence between the quantum minkowski space time and the classical projective space p 3

oslo model hyperuniformity and the quenched edwards wilkinson model we present simulations of the one dimensional oslo rice pile model in which the critical height at each site is randomly reset after each toppling we use the fact that the stationary state of this sand pile model is hyperuniform to reach system of sizes 10 7 most previous simulations were seriously flawed by important finite size corrections we find that all critical exponents have values consistent with simple rationals 4 3 for the correlation length exponent d 9 4 for the fractal dimension of avalanche clusters and z 10 7 for the dynamical exponent in addition we relate the hyperuniformity exponent to the correlation length exponent finally we discuss the relationship with the quenched edwards wilkinson model where we find in particular that the local roughness exponent is loc 1

on a construction of coordinates at infinity on manifolds with fast curvature decay and maximal volume growth on etudie le comportement asymptotique de varietes de riemann on construit des coordonnees a l infini sous certaines conditions intrinseques

a hierarchical classification of cellular automata abstract a central issue in the theory of cellular automata is classification a classification is a structure imposed on the space of automata which groups together cellular automata with related properties in this paper a classification based on the action of cellular automata on n step markov measures is presented this classification is hierarchical and parametric an algorithm is described which efficiently constructs all rules in a given class at a given level of the hierarchy the utility of the classification is explored in the study of the invariant statistical properties of next nearest neighbor cellular automata on two states per cell

crossovers from parity conserving to directed percolation universality the crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean field method in case of models exhibiting z 2 symmetric absorbing phases the cellular automaton version of the nonequilibrium kinetic ising model nekimca and a stochastic cellular automaton invented by grassberger krause and von der twer j phys a 17 l105 1984 the introduction of an external symmetry breaking field causes a crossover to kink parity conserving models characterized by dynamical scaling of the directed percolation dp and the crossover exponent 1 phi approximately equal to 0 53 2 in the case of a branching and annihilating random walk model with an even number of offspring dual to nekimca the introduction of spontaneous particle decay destroys the parity conservation and results in a crossover to the dp class characterized by the crossover exponent 1 phi approximately equal to 0 205 5 the two different kinds of crossover operators cannot be mapped onto each other and the resulting models show a diversity within the dp universality class in one dimension these subclasses differ in cluster scaling exponents

moduli spaces of self dual connections over asymptotically locally flat gravitational instantons we investigate yang mills instanton theory over four dimensional asymptotically locally flat alf geometries including gravitational instantons of this type by exploiting the existence of a natural smooth compactification of these spaces introduced by hausel hunsicker mazzeo first referring to the codimension 2 singularity removal theorem of sibner sibner and rade we prove that given a smooth finite energy self dual su 2 connection over a complete alf space its energy is congruent to a chern simons invariant of the boundary three manifold if the connection satisfies a certain holonomy condition at infinity and its curvature decays rapidly then we introduce framed moduli spaces of self dual connections over ricci flat alf spaces we prove that the moduli space of smooth irreducible rapidly decaying self dual connections obeying the holonomy condition with fixed finite energy and prescribed asymptotic behaviour on a fixed bundle is a finite dimensional manifold we calculate its dimension by a variant of the gromov lawson relative index theorem as an application we study yang mills instantons over the flat mathbb r 3 times s 1 the multi taub nut family and the riemannian schwarzschild space

a note on the rule classification for square homogeneous cellular automata abstract we give the dynamical sense for the qualitative ideas of wolfram s and stauffer s classifications for the elementary two dimensional cellular automata with four nearest neighbours the new sense arises from the attracting role of the so called subshifts

path connected yang mills moduli spaces on utilise des techniques de min max dans le calcul des variations pour demontrer que les espaces modules des connexions auto duales sur des fibres principaux su 2 ou su 3 sur s 4 sont chemin connexe

effects of pair correlation on mean field theory of btw sand pile model we extend the mean field calculation of btw sand pile model to one that includes the correlation between pairs of nearest neighbors specifically we derive dynamical equations of both one site and two site densities and solve the equations order by order starting with the mean field solution the investigation provides analytical results for both stationary and dynamic states of the sand pile near the critical point which are valid in the regime where h e2 1h e2 1 h incoming rate of sand grains e bulk dissipation rate of sand grainse bulk dissipation rate of sand grains in the stationary case we evaluate the pair correlation and the correction to the mean field single site densities due to the correlation the correction is found to be of the same order as the mean field solution in the dynamic case the initial state deviates from the stationary state by a small fluctuation which subsequently decays exponentially with the time constant being reduced from the corresponding mean field value again the correction to the time constant in this case is found comparable to the mean field value itself

quaternion structure on the moduli space of yang mills connections soit m h un 2 tore complexe avec une metrique plate ou une surface k3 a metrique de ricciplate soit p un fibre g principal sur m g est un groupe de lie compact simple et l espace des modules des connexions irreductibles anti auto duales sur p alors la variete de rieman admet une structure de quaternion constante de facon covariante son groupe d holonomie est contenu dans sp n 4n dim r

n site approximations and coherent anomaly method analysis for a stochastic sandpile n site cluster approximations for a stochastic sandpile in one dimension are developed a height restriction is imposed to limit the number of states each site can harbor at most two particles height z i l 2 this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded on the basis of results for nl 11 sites the critical particle density as ensuremath zeta c 0 930 1 is estimated in good agreement with simulations a coherent anomaly analysis yields estimates for the order parameter exponent ensuremath beta 0 41 1 and the relaxation time exponent ensuremath nu ensuremath simeq 2 5

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

is there a sharp phase transition for deterministic cellular automata abstract previous work has suggested that there is a kind of phase transition between deterministic automata exhibiting periodic behavior and those exhibiting chaotic behavior however unlike the usual phase transitions of physics this transition takes place over a range of values of the parameter rather than at a specific value the present paper asks whether the transition can be made sharp either by taking the limit of an infinitely large rule table or by changing the parameter in terms of which the space of automata is explored we find strong evidence that for the class of automata we consider the transition does become sharp in the limit of an infinite number of symbols the size of the neighborhood being held fixed our work also suggests an alternative parameter in terms of which it is likely that the transition will become fairly sharp even if one does not increase the number of symbols in the course of our analysis we find that mean field theory which is our main tool gives surprisingly good predictions of the statistical properties of the class of automata we consider

instantons and geometric invariant theory we show that the yang mills instantons can be described in terms of certain holomorphic bundles on the projective plane the proof uses explicit matrix descriptions arising from monads and an analysis of the corresponding groups of symmetries

critical behavior of a one dimensional fixed energy stochastic sandpile we study a one dimensional fixed energy version that is with no input or loss of particles of manna s stochastic sandpile model the system has a continuous transition to an absorbing state at a critical value of the particle density and exhibits the hallmarks of an absorbing state phase transition including finite size scaling critical exponents are obtained from extensive simulations which treat stationary and transient properties and an associated interface representation these exponents characterize the universality class of an absorbing state phase transition with a static conserved density in one dimension they differ from those expected at a linear interface depinning transition in a medium with point disorder and from those of directed percolation

the geometry of the yang mills moduli space for definite manifolds on etudie la geometrie riemannienne de l espace des modules des connexions auto duales su 2 k 1 sur une classe tres generale de 4 varietes des 4 varietes compactes orientees simplement connexe m a forme d intersection definie positive

phase diagrams for an evolutionary prisoner s dilemma game on two dimensional lattices the effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner s dilemma game with players located on the sites of different two dimensional lattices this system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive using monte carlo simulations and the generalized mean field approximations we have determined the phase boundaries critical points separating the two phases on the plane of the temperature noise and temptation to choose defection in the zero temperature limit the cooperation can be sustained only for those connectivity structures where three site clique percolation occurs

instanton moduli as a novel map from tori to k3 surfaces a map is constructed from the moduli of hyper kahler tori to hyper kahler k3 surfaces which does not coincide with the kummer map the map takes a torus to the moduli space of so 3 connections on a bundle with nontrivial first stiefel whitney class and first pontrjagin class equal to 4 this map is shown to intersect the kummer moduli and also certain subvarieties of singular k3 surfaces our map is shown to satisfy the local torelli theorem and the k3 surfaces in its image are shown to carry a natural metric which is calabi yau

cooperation in the noisy case prisoner s dilemma game on two types of regular random graphs we have studied an evolutionary prisoner s dilemma game with players located on two types of random regular graphs with a degree of 4 the analysis is focused on the effects of payoffs and noise temperature on the maintenance of cooperation when varying the noise level and or the highest payoff the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive for the random regular graph and bethe lattice the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions although the measure of cooperation is enhanced by the absence of loops in the connectivity structure for low noise the optimal connectivity structure is built up from randomly connected triangles

an instanton invariant for 3 manifolds to an oriented closed 3 dimensional manifoldm withh1 m 0 we assign a 8 graded homology groupi m whose euler characteristic is twice casson s invariant the definition uses a construction on the space of instantons onm

evolutionary prisoner s dilemma game on a square lattice a simplified prisoner s game is studied on a square lattice when the players interacting with their neighbors can follow two strategies to cooperate c or to defect d unconditionally the players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference using monte carlo simulations and dynamical cluster techniques we study the density c of cooperators in the stationary state this system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect in the limits stackrel ensuremath rightarrow c 0 and 1 we have observed critical transitions belonging to the universality class of directed percolation

fourier decomposition of payoff matrix for symmetric three strategy games in spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries for the two strategy games this decomposition reproduces interactions characteristic to the ising model for the three strategy symmetric games the fourier components can be classified into four types representing games with self dependent and cross dependent payoffs variants of three strategy coordinations and the rock scissors paper rsp game in the absence of the rsp component the game is a potential game the resultant potential matrix has been evaluated the general features of these systems are analyzed when the game is expressed by the linear combinations of these components

ricci curvature bounds and einstein metrics on compact manifolds where f mo m1 is a homeomorphism and dil f is the dilatation of f given by dil f supx x2 dist f x f x2 dist x1 x2 if mo and m1 are not homeomorphic define dl mo mi oo gromov 20 proves the remarkable result that the space of compact riemannian manifolds f a 3 d of sectional curvature iki 3 0 and diameter dm v and diameter dm c iki dm vm1 in particular gromov s compactness theorem may be strengthened to the statement that f a v d is c1 l compact in the lipschitz topology in this paper we study the question of lipschitz convergence of compact riemannian manifolds with bounds imposed on the ricci curvature ric in

mean field approximation with coherent anomaly method for a non equilibrium model a mean field approximation for a 1d non equilibrium lattice model known as model a is considered allowing the authors to compute the probability of a configuration of a given cluster of sites the mean field equations are numerically solved in the stationary regime for different cluster sizes l or 15 from a finite size analysis and the application of the coherent anomaly method cam they compute the critical parameter of the model the correlation length critical exponent nu perpendicular to and the order parameter critical exponent beta the results are in agreement with those obtained by other methods

nontrivial path integrals for nonrenormalizable fields multicomponent ultralocal models a nontrivial lattice space path integral formulation of nonrenormalizable multicomponent ultralocal models is constructed from the nonperturbative operator solutions presented in a recent paper the indefinite nonclassical singular potential required for the nontriviality has different effects on distributions compared to the single component case however the essential property of reweighting the distribution at the origin is similar the appearance of additional nonclassical singular potentials suggests that we cannot always place the classical lagrangian or classical hamiltonian directly into the path integral formulation or in other words a straightforward canonical quantization of fields with infinite degrees of freedom does not always apply

operator analysis of nonrenormalizable multicomponent ultralocal field models a nontrivial nonperturbative quantum field theory of o n invariant multicomponent nonrenormalizable ultralocal models is developed along lines presented earlier for single component models the additional nonclassical repulsive potential that is always present in the solution of the single component case becomes indefinite and may even vanish in the multicomponent case the disappearance of the nonclassical and singular potential does not mean a return to a conventional quantum field theory and the operator solution of multicomponent ultralocal fields remains noncanonical nontrivial i e non gaussian results hold for any number n of components and suitable nontrivial behavior persists even in the infinite component n case as well

removable singularities in yang mills fields we show that a field satisfying the yang mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite we obtain the result that every yang mills field overr4 with bounded functional l2 norm may be obtained from a field ons4 r4 hodge or coulomb gauges are constructed for general small fields in arbitrary dimensions including 4

comment on garden of eden states in a traffic model revisited recently huang and lin suggested a combination of two successful mean field theories the 2 cluster approximation and paradisical mean field for the nagel schreckenberg cellular automaton model of traffic flow we argue that this new approximation is inconsistent since it violates the kolmogorov conditions

re entrant behaviour in the domany kinzel cellular automaton we present numerical and analytical results for a special kind of one dimensional probabilistic cellular automaton the so called domany kinzel automaton it is shown that the phase boundary separating the active and the recently found chaotic phase exhibits re entrant behaviour furthermore exact results for the p2 0 line are discussed

gauge theory on asymptotically periodic 4 manifolds il existe une famille non denombrable de classes de diffeomorphismes des 4 varietes orientees homeomorphes a r 4

reflection functors for quiver varieties and weyl group actions we introduce reflectionfunctors on quiver varieties they are hyper kahler isometries between quiver varieties with different parameters related by elements in the weyl group the definition is motivated by the origial reflection functor given by bernstein gelfand ponomarev 1 but they behave much nicely they are isomorphisms and satisfy the weyl group relations as an application we define weyl group representations of homology groups of quiver varieties they are analogues of slodowy s construction of springer representations of the weyl group

critical density of the abelian manna model via a multitype branching process a multitype branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the abelian manna model this branching process incorporates partially the spatiotemporal correlations of the activity which are essential for the dynamics in particular in low dimensions an analytical expression for the critical density in arbitrary dimensions is derived which significantly improves the results over mean field theories as confirmed by comparison to the literature on numerical estimates from simulations the method can easily be extended to lattices and dynamics other than those studied in the present work

long range correlations in chaotic cellular automata abstract one dimensional cellular automata of class 3 are studied as models for spatially extended chaotic systems their irreversible dynamics can generate weak but long range spatial correlations the one labelled 22 by wolfram is treated in an exemplary way its stationary state is approximated by a markov chain the regular grammar underlying the markov chain is chosen with care so that it includes a maximum amount of information on the stationary state the approximation can be performed without simulating the dynamics of the cellular automaton 22 and reproduces its long range correlations qualitatively their origin is explained intuitively and they are argued to be a frequent feature of cellular automata with more complicated rules

evolutionary matching pennies game on bipartite regular networks evolutionary games are studied here with two types of players located on a chessboard or on a bipartite random regular graph each player s income comes from matching pennies games played with the four neighbors the players can modify their own strategies according to a myopic strategy update resembling the glauber dynamics for the kinetic ising model this dynamical rule drives the system into a stationary state where the two strategies are present with the same probability without correlations between the nearest neighbors while a weak correlation is induced between the second and the third neighbors in stationary states the deviation from the detailed balance is quantified by the evaluation of entropy production finally our analysis is extended to evolutionary games where the uniform pair interactions are composed of an anticoordination game and a weak matching pennies game this system preserves the ising type order disorder transitions at a critical noise level decreasing with the strength of the matching pennies component for both networks

local structure theory for cellular automata abstract the mean field theory for cellular automata wolfram and schulman and seiden is generalized to the local structure theory the local structure theory is a sequence of finitely parameterized models of the statistical features of a cellular automaton s evolution the n th model in the sequence takes into account correlations in terms of the probability of blocks of n states a class of measures the n block measures is introduced the local structure operator of order n maps n block measures to n block measures in a manner which reflects the cellular automaton map on blocks of states the fixed points of the map on measures approximate the invariant measures of the cellular automaton the ability of the local structure theory to model evolution from uncorrelated initial distributions is studied the theory gives exact results in simple cases in more complex cases monte carlo numerical experiments suggest that an accurate statistical portrait of cellular automaton evolution is obtained the invariant measures of a cellular automaton and the stability of these measures may be obtained from the local structure theory the local structure theory appears to be a powerful method for characterization and classification of cellular automata nearest neighbor cellular automata with two states per cell are studied using this method

the construction of ale spaces as hyper kahler quotients on decrit la construction d une famille particuliere de 4 varietes hyper kahler les espaces asymptotiquement localement euclidiens ale on decrit une 4 variete de riemann avec juste une extremite qui a l infini ressemble au quotient r 4 de l espace euclidien r 4 par un groupe fini d identifications

stability in yang mills theories at a solution of the yang mills equations ons4 or the yang mills higgs equation on 3 the hessian of the action functional defines a natural second order elliptic operator the number of negative eigenvalues of this operator is bounded below by a multiple of the relevant topological charge the proof of this assertion requires a relative index theorem for dirac type operators on n n 3

the analysis of elliptic families i metrics and connections on determinant bundles in this paper we construct the quillen metric on the determinant bundle associated with a family of elliptic first order differential operators we also introduce a unitary connection on and calculate its curvature our results will be applied to the case of dirac operators in a forthcoming paper

nonclassical critical exponents out of mean field results abstract we consider a mean field systematic approach to study the critical behavior of cooperative models the sequence of approximate mean field results are analyzed by the introduction of a scaling hypothesis from which we can obtain the critical parameter as well as the nonclassical critical exponents the method is applied to the domany kinzel probabilistic cellular automaton and to the two dimensional glauber ising model

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

scaling behavior of the absorbing phase transition in a conserved lattice gas around the upper critical dimension we analyze numerically the critical behavior of a conserved lattice gas that was recently introduced as an example of the new universality class of absorbing phase transitions with a conserved field phys rev lett 85 1803 2000 we determine the critical exponent of the order parameter as well as the critical exponent of the order parameter fluctuations in d 2 3 4 5 dimensions a comparison of our results and those obtained from a mean field approach and a field theory suggests that the upper critical dimension of the absorbing phase transition is four

randomly evolving idiotypic networks modular mean field theory we develop a modular mean field theory for a minimalistic model of the idiotypic network the model comprises the random influx of new idiotypes and a deterministic selection it describes the evolution of the idiotypic network towards complex modular architectures the building principles of which are known the nodes of the network can be classified into groups of nodes the modules which share statistical properties each node experiences only the mean influence of the groups to which it is linked given the size of the groups and linking between them the statistical properties such as mean occupation mean lifetime and mean number of occupied neighbors are calculated for a variety of patterns and compared with simulations for a pattern which consists of pairs of occupied nodes correlations are taken into account

the classical limit of ultralocal scalar fields the classical limit of the quantum theory of ultralocal scalar fields is approached with the help of coherent state techniques in the limit 0 it is demonstrated that the coherent state expectation value of the heisenberg field operators coincide with the solutions of the corresponding classical canonical equations of motion

cellular automaton rules conserving the number of active sites this paper shows how to determine all of the unidimensional two state cellular automaton rules of a given number of inputs which conserve the number of active sites these rules have to satisfy a necessary and sufficient condition if the active sites are viewed as cells occupied by identical particles these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved some of these rules which allow motion in both directions mimic ensembles of one dimensional pseudorandom walkers numerical evidence indicates that the corresponding stochastic processes might be non gaussian

critical discontinuous phase transition in the threshold contact process we analyze a threshold contact process on a square lattice in which particles are created on empty sites with at least two neighboring particles and are annihilated spontaneously we show by means of monte carlo simulations that the process undergoes a discontinuous phase transition at a definite value of the annihilation parameter in accordance with the gibbs phase rule and that the discontinuous transition exhibits critical behavior the simulations were performed by using boundary conditions in which the sites of the border of the lattice are permanently occupied by particles

the abelian sandpile and related models abstract the abelian sandpile model is the simplest analytically tractable model of self organized criticality this paper presents a brief review of known results about the model the abelian group structure of the algebra of operators allows an exact calculation of many of its properties in particular when there is a preferred direction one can calculate all the critical exponents characterizing the distribution of avalanche sizes in all dimensions for the undirected case the model is related to q 0 state potts model this enables exact calculation of some exponents in two dimensions and there are some conjectures about others we also discuss a generalization of the model to a network of communicating reactive processors this includes sandpile models with stochastic toppling rules as a special case we also consider a nondashabelian stochastic variant which lies in a different universality class related to directed percolation

a torelli type theorem for gravitational instantons on montre que chaque 4 variete hyper kahler asymptotiquement localement euclidienne et isometrique a un membre d une des familles obtenues dans un article precedent

hyperkahler metrics and supersymmetry we describe two constructions of hyperkahler manifolds one based on a legendre transform and one on a sympletic quotient these constructions arose in the context of supersymmetric nonlinear models but can be described entirely geometrically in this general setting we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

moduli spaces of anti self dual connections on ale gravitational instantons we study the framed moduli space m of anti self dual connections on a principal bundle over an ale hyperkahler 4 manifold it has the natural riemannian metric g m and the hyperkahler structure i m j m k m induced from those on the base manifold

phenomenology of nonlocal cellular automata dynamical systems with nonlocal connections have potential applications to economic and biological systems this paper studies the dynamics of nonlocal cellular automata in particular all two state three input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings although it is observed that sometimes a rule can have different dynamical behaviors with different wirings the nonlocal cellular automata rule space is studied using a mean field parametrization which is ideal for the situation of random wiring nonlocal cellular automata can be considered as computers carrying out computation at the level of each component their computational abilities are studied from the point of view of whether they contain many basic logical gates in particular i ask the question of whether a three input cellular automaton rule contains the three fundamental logical gates two input rules and and or and one input rule not a particularly interesting edge of chaos nonlocal cellular automaton the rule 184 is studied in detail it is a system of coupled selectors or multiplexers it is also part of the fredkin s gate a proposed fundamental gate for conservative computations this rule exhibits irregular fluctuations of density large coherent structures and long transient times

structure of two dimensional sandpile i height probabilities the height probabilities of the two dimensional abelian sandpile model are the fractionial numbers of lattice sites having heights 1 2 3 4 a combinatorial method for evaluation of these quantities is proposed the method is based on mapping the set of allowed sandpile configurations onto the set of spanning trees covering a given lattice exact analytical expressions for all probabilities are obtained

the n site approximation for the triplet creation model the nonequilibrium phase transition of the one dimensional triplet creation model is investigated using the n site approximation scheme we find that the phase diagram in the space of parameters d where is the particle decay probability and d is the diffusion probability exhibits a tricritical point for n 4 however the fitting of the tricritical coordinates t dt using data for 4 n 13 predicts that t becomes negative for n 26 indicating thus that the phase transition is always continuous in the limit n however the large discrepancies between the critical parameters obtained in this limit and those obtained by monte carlo simulations as well as a puzzling non monotonic dependence of these parameters on the order of the approximation n argue for the inadequacy of the n site approximation to study the triplet creation model for computationally feasible values of n

sandpiles with height restrictions we study stochastic sandpile models with a height restriction in one and two dimensions a site can topple if it has a height of two as in manna s model but in contrast to previously studied sandpiles here the height or number of particles per site cannot exceed two this yields a considerable simplification over the unrestricted case in which the number of states per site is unbounded two toppling rules are considered in one the particles are redistributed independently while the other involves some cooperativity we study the fixedenergy system no input or loss of particles using cluster approximations and extensive simulations and find that it exhibits a continuous phase transition to an absorbing state at a critical value z c of the particle density the critical exponents agree with those of the unrestricted manna sandpile

how self organized criticality works a unified mean field picture we present a unified dynamical mean field theory based on the single site approximation to the master equation for stochastic self organized critical models in particular we analyze in detail the properties of sandpile and forest fire ff models in analogy with other nonequilibrium critical phenomena we identify an order parameter with the density of active sites and control parameters with the driving rates depending on the values of the control parameters the system is shown to reach a subcritical absorbing or supercritical active stationary state criticality is analyzed in terms of the singularities of the zero field susceptibility in the limit of vanishing control parameters the stationary state displays scaling characteristics of self organized criticality soc we show that this limit corresponds to the breakdown of space time locality in the dynamical rules of the models we define a complete set of critical exponents describing the scaling of order parameter response functions susceptibility and correlation length in the subcritical and supercritical states in the subcritical state the response of the system to small perturbations takes place in avalanches we analyze their scaling behavior in relation with branching processes in sandpile models because of conservation laws a critical exponents subset displays mean field values ensuremath nu frac 1 2 and ensuremath gamma 1 in any dimensions we treat bulk and boundary dissipation and introduce a critical exponent relating dissipation and finite size effects we present numerical simulations that confirm our results in the case of the forest fire model our approach can distinguish between different regimes soc ff and deterministic ff studied in the literature and determine the full spectrum of critical exponents