loop star decomposition of basis functions in the discretization of the efie a general and readily applicable scheme is presented for the determination of the basis functions that allow the decomposition of the surface current into a solenoidal part and a nonsolenoidal remainder the proposed approach brings into correspondence these two parts with two scalar functions and generates the known loop and star basis functions the completeness of the loop star basis is discussed employing the presented scheme the issue of the irrotational property of the nonsolenoidal functions is addressed

additive one dimensional cellular automata are chaotic according to devaney s definition of chaos abstract we study the chaotic behavior of a particular class of dynamical systems cellular automata we specialize the definition of chaos given by devaney for general dynamical systems to the case of cellular automata a dynamical system x f is chaotic according to devaney s definition of chaos if its transition map f is sensitive to the initial conditions topologically transitive and has dense periodic orbits on x our main result is the proof that all the additive one dimensional cellular automata defined on a finite alphabet of prime cardinality are chaotic in the sense of devaney

consistent relations in the method of reducibility in the cluster variation method a redundancy is noted in the set of lagrange multipliers effective fields and effective interactions used in the expressions of the reduced density matrices given by morita 4 in some problems with less symmetry 6 the expressions of the reduced density matrices without this redundancy are given an argument showing that a certain expression of the free energy in terms of the lagrange multipliers is stationary with respect to the variations of these is presented

transition phenomena in cellular automata rule space abstract we define several qualitative classes of cellular automata ca behavior based on various statistical measures and describe how the space of all cellular automata is organized as a cellular automaton is changed by varying entries in its rule table abrupt changes in qualitative behavior may occur these abrupt changes have the character of bifurcations in smooth dynamical systems or of phase transitions in statistical mechanical systems the most complex ca rules exhibit many of the characteristics of second order transitions suggesting an association between computation complexity and critical phenomena

upper bounds for survival probability of the contact process a precise description of the nontrivial upper invariant measure for c is still an open problem for the basic contact process which is a self dual attractive but nonreversible markov process of an interacting particle system by its self duality to identify the invariant measure is equivalent to determining the initial state dependence of the survival probability of the process a procedure to give rigorous upper bounds for the survival probability is presented based on a lemma given by harris two new bounds are given improving the simple branching process bound in the one dimensional case the present procedure can be viewed as a trial to make approximate measures by generalized markov extensions

on some variational approximations in two dimensional classical lattice systems a new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster variation methods among them the well known bethe peierls and kramers wannier approximations the limiting behavior of a hierarchical sequence of cluster variation approximations the so calledc hierarchy is discussed it is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsfn on the free energy per lattice sitef and thatfn f asn our results are based on extension theorems for states given on subsets of the lattice which might be of some independent interest and on an application of transfer matrix concepts to the variational characterization of translation invariant equilibrium states

evolving cellular automata to perform computations mechanisms and impediments abstract we present results from experiments in which a genetic algorithm ga was used to evolve cellular automata cas to perform a particular computational task one dimensional density classification we look in detail at the evolutionary mechanisms producing the ga s behavior on this task and the impediments faced by the ga in particular we identify four epochs of innovation in which new ca strategies for solving the problem are discovered by the ga describe how these strategies are implemented in ca rule tables and identify the ga mechanisms underlying their discovery the epochs are characterized by a breaking of the task s symmetries on the part of the ga the symmetry breaking results in a short term fitness gain but ultimately prevents the discovery of the most highly fit strategies we discuss the extent to which symmetry breaking and other impediments are general phenomena in any ga search

entropy and global markov properties we extend refine and give simple proofs of some recent results on the validity of global markov properties for classical spin systems one of the new results is that there is a global markov property that is satisfied by equilibrium states in general the proof of this establishes formulas for the entropy and free energy that show that these quantities are ford dimensional systems given in terms of d 1 dimensional systems furthermore we show that global markov properties imply the absence of some types of symmetry breaking

mean field theory of avalanches in self organized critical states abstract a new mean field approximation is proposed for the sandpile model of bak tang and wiesenfeld and the distribution of heights in the self organized critical state is calculated we treat several series of successive topples to approximate various avalanches in contrast to the previous mean field theory given by tang and bak which assumes the stationary condition among topples in an avalanche out theory takes into account long term behavior of the system the results are in good agreement with the values estimated by computer simulations even in low dimensions d 2 and 3 higher approximations obtained by including local correlations or by imposing a reducibility condition which is used in the cluster variation method are also shown

pair correlations and structure factor of the j1 j2 square lattice ising model in an external field abstract we compute the structure factor of the j 1 j 2 ising model in an external field on the square lattice within the cluster variation method we use a four point plaquette approximation which is the minimal one able to capture phases with broken orientational order in real space like the recently reported ising nematic phase in the model the analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against temperature and external field although the nematic susceptibility is not directly related to the structure factor we show that because of the close relationship between the nematic order parameter and the structure factor the latter shows unambiguous signatures of the presence of a nematic phase in agreement with results from direct minimization of a variational free energy the disorder variety of the model is identified and the possibility that the cvm four point approximation be exact on the disorder variety is discussed

nonequilibrium lattice models series analysis of steady states a perturbation theory for steady states of interacting particle systems is developed and applied to several lattice models with nonequilibrium critical points near an absorbing state the expansion is expressed directly in terms of the kinetic parameter creation rate rather than in powers of the interaction an algorithm for generating series expansions for local properties is described order parameter series 16 terms and precise estimates of critical properties are presented for the one dimensional contact process and several related models

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

aperiodicity in one dimensional cellular automata abstract cellular automata are a class of mathematical systems characterized by discreteness in space time and state values determinism and local interaction a certain class of one dimensional binary site valued nearest neighbor automata is shown to generate infinitely many aperiodic temporal sequences from arbitrary finite initial conditions on an infinite lattice the class of automaton rules that generate aperiodic temporal sequences are characterized by a particular form of injectivity in their interaction rules included are the nontrivial linear automaton rules that is rules for which the superposition principle holds certain nonlinear automata with injectivity properties similar to those of linear automata and a wider subset of nonlinear automata whose interaction rules satisfy a weaker form of injectivity together with certain symmetry conditions the evolution of this last subset of automata can be viewed as consisting of multiple domains within which behavior exactly mimics that of a linear automaton a linearization technique is used to establish that these domains coalesce in finite time to produce at most two domains and thereby to assert the aperiodicity of their temporal sequences

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

epidemic spreading of random walkers in metapopulation model on an alternating graph abstract much literature exists on temporal networks for epidemic spreading we present a metapopulation dynamic model on a temporal network a subpopulation patch is represented by a node on a graph and a link represents a migration path between patches we consider the alternating graph as a temporal network it alternates between star and complete graphs where the nodes do not change but links vary temporally and periodically mobile individuals move by random walk through a link between nodes each individual is either susceptible s or infected i the reaction diffusion equations are presented as ordinary differential equations with time dependent coefficients to evaluate the infection risk of each patch node we obtain the solutions of reaction diffusion equations numerically the temporal behavior of infected individuals depends highly on the frequency of the alternating graph at low frequency infected densities exhibit an oscillating behavior while they keep a constant value at high frequencies the crossover occurs from the oscillating state to the frozen state with increasing frequency the sis epidemic threshold is derived for the alternating graph the epidemic threshold is lower than that on the star graph and higher than that on the complete graph

lennard jones triangular lattice gas in the kikuchi approximation abstract the triangular lattice gas problem for a model with infinitely repulsive nearest neighbor and attractive second j 2 and third neighbor j 3 interactions is studied in the kikuchi approximation with a triangle of nearest neighbor sites as the basic cluster values of the ratio j 3 j 2 correspond to a lennard jones interaction in a model for commensurate phases of submonolayers of inert gases adsorbed on graphite a method of calculation is developed which allows a detailed study of the evolution of the phase diagrams in particular the location of the liquid gas critical end point and of the solid liquid gas triple point distinct liquid and gas phases are found to be stable for 0 9481

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

continuous sequence of mean field approximations and critical phenomena abstract the coherent anomaly method introduced by suzuki in 1986 provides in principle a remarkably simple approach to study critical phenomena within the framework of the mean field approximation unlike the renormalization group techniques commonly employed to investigate critical phenomena suzuki s method exploits the systematic behavior of a sequence of mean field approximations in order to extract critical temperature and exponents despite its conceptual simplicity actual implementation of the cam requires the ability to treat at least three levels of mean field approximations belonging to what suzuki has termed a cardinal sequence here we present a new method based on a continuous sequence of mean field approximations from which the implementation of the cam proceeds in a straightforward manner

susceptibility propagation by using diagonal consistency a susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for markov random fields herein we formulate an improved susceptibility propagation by using the concept of a diagonal matching method that is based on mean field approaches to inverse ising problems the proposed susceptibility propagation is robust for various network structures and it is reduced to the ordinary susceptibility propagation and to the adaptive thouless anderson palmer equation in special cases

an impedance boundary condition efie that is low frequency and refinement stable a discretization of the impedance boundary condition electric field integral equation ibc efie is introduced that 1 yields the correct solution at arbitrarily small frequencies and 2 requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases the low frequency stabilization is based on a projector based discrete helmholtz splitting rescaling and recombination that depends on the low frequency behavior of both the efie operator and the surface impedance condition the dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the ibc term

numerical limit of the spinodal point abstract the relation is studied between the phase boundary c pb and the spinodal point c s of the ferromagnetic ising model in the two dimensional triangular lattice using a series of approximations in the cvm cluster variation method hierarchy we keep the magnetization m fixed and extrapolate the temperature difference t pb m n t s m n for n 1 3 5 7 and 9 triangle approximations of the cvm it is found that the limiting value of the difference is practically zero our analysis indicates i the spinodal decomposition is to be treated as a system changing from the quenched initial state and the free energy curve used in the spinodal analysis is not a fixed curve but is changing in time and ii cases can occur in which a quenched system is initially decomposing in the nucleation mode but switches to the spinodal decomposition mode in time

approximations for a frustrated ising model abstract the cluster effective field approximation was proposed as a useful approximation for the study of frustrated ising models in order to examine its usefulness the ising model with frustration on the centred square lattice is studied in the square effective field approximation and the results are compared with those in the pair and in the square approximation and with the exact results the study is made in the framework of the cluster variation method

reentrant transitions in the van hemmen model of a spin glass the van hemmen model of a spin glass which is an ising model with random couplings jij between sites i and j equal to j0 j i j j i where i i are independent identically distributed random variables is studied in the pair approximation of the cluster variation method for the family of probability distributions 12 1 p i a p i 12 1 p i a where p is varied phase diagrams are constructed they are qualitatively different from the mean field phase diagrams and display a competition between tendencies towards spin glass and towards ferromagnetic ordering which results in reentrant transitions it is argued that the observed effects are not accidental but are borne by the competition of bonds of the underlying lattice system

uniform surface integral equation formulation for mixed impedance boundary conditions a numerical approach based on the surface integral equation sie method is developed for the analysis of time harmonic electromagnetic scattering by impenetrable objects equipped with mixed impedance boundary conditions mibcs mibc is an axially anisotropic generalization of the conventional isotropic leontovich impedance boundary condition the developed sie formulation utilizes surface helmholtz decomposition the self dual formulation of yan and jin and loop and star rwg functions a combined field formulation is applied to avoid internal resonances

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

generalized cluster description of multicomponent systems a general formalism for the description of configurational cluster functions in multicomponent systems is developed the approach is based on the description of configurational cluster functions in terms of an orthogonal basis in the multidimensional space of discrete spin variables the formalism is used to characterize the reduced density matrices or cluster probability densities and the free energy functional obtained in the cluster variation method approximation for the particular representation chosen the expectation values of the base functions are the commonly used multisite correlation functions the latter form an independent set of variational parameters for the free energy which in general facilitates the minimization procedure a new interpretation of the cluster variation method as a self consistency relation on the renormalized cluster energies is also presented

global exponential stability for stochastic coupled systems on networks with markovian switching abstract this paper investigates the global exponential stability of stochastic coupled systems on networks with markovian switching scsnms sufficient conditions are established to guarantee p th moment exponential stability and almost surely exponential stability of the scsnms by using concepts from graph theory and m matrix into lyapunov method consequently the upper boundaries of the p th moment lyapunov exponent and the sample lyapunov exponent are given finally to illustrate the capabilities of the stability principle easy verifiable sufficient conditions of global exponential stability for a stochastic coupled oscillator on network with markovian switching are obtained

pair correlations in the cluster variation approximation abstract the cluster variation method is used to obtain approximate free energy functions for a binary system in an inhomogeneous field in order to calculate the fourier transform of the pair correlation functions in the two dimensional square lattice using the nearest neighbors square as the basic cluster the correlation functions are correctly given up to the order 7 in the inverse temperature the effect of second neighbor pairs and many body interactions is investigated

the survival of the large dimensional basic contact process we consider the d dimensional basic contact process obtaining the limit value of the probability of survival when d and showing that the finite dimensional distributions of the upper invariant measure become of the product form as d

convergence of the cluster variation method for a system on a triangular lattice abstract the paper studies the convergence of the cluster variation method to the rigorous result as the cluster size increases the calculation is done on the phase boundary at t 0 between the a 2 b type ordered phase and the disordered phase on a two dimensional triangular lattice with nearest neighbor interaction it is shown that the phase boundary at t 0 is obtained by maximizing the entropy under the constraint that only a limited number of atomic configurations are allowed formulations are developed for clusters of n 3 5 7 9 11 and 13 points when thermodynamic quantities which are calculated using these clusters are plotted against 1 n they approach the known rigorous n results more or less linearly but with a pseudo period of n 6 an exception is the square of the long range order which bends down as 1 n tends to zero

exact variational methods and cluster variation approximations it is shown that for classical d dimensional lattice models with finite range interactions the translation invariant equilibrium states have the property that their mean entropy is completely determined by their restriction to a subset of the lattice that is infinite in d 1 dimensions and has a width equal to the range of the interaction in the dth dimension this property is used to show proper convergence toward the exact result for a hierarchy of approximations of the cluster variation method that uses one dimensionally increasing basis clusters in a two dimensional lattice

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

application of combined field integral equation for electromagnetic scattering by dielectric and composite objects combined field integral equation cfie is applied for computing electromagnetic scattering by arbitrarily shaped three dimensional dielectric and composite objects the objectives of this paper are as follows first to present a cfie formulation which can be used in the analysis of piecewise dielectric and composite metallic and dielectric objects with junctions second to show that properly choosing the coupling coefficients of the equations the conditioning of the discretized matrix equation can be essentially improved and rapidly converging iterative solutions can be obtained even without preconditioning

the two dimensional annni model in the cvm approximation the phase diagram of the two dimensional annni model is investigated by the cluster variation method cvm we confirm the stability of the disordered phase down tot 0 and the absence of a lifshitz point at finite temperature fork 1 2 wherek the ratio of the second to the first neighbor pair interactions two different modulation regimes for the correlation functions of the disordered phase are separated by a disorder line along which theq vector of the susceptibility maximum undergoes a lock in transition the study in reciprocal space of the stability of the disordered phase allows us to define a critical line in the phase diagram along which theq vector characterizing the instability is incommensurate finally we show the existence of another lifshitz point fork tending to infinity

multivariable harmonic balance for central pattern generators the central pattern generator cpg is a nonlinear oscillator formed by a group of neurons providing a fundamental control mechanism underlying rhythmic movements in animal locomotion we consider a class of cpgs modeled by a set of interconnected identical neurons based on the idea of multivariable harmonic balance we show how the oscillation profile is related to the connectivity matrix that specifies the architecture and strengths of the interconnections specifically the frequency amplitudes and phases are essentially encoded in terms of a pair of eigenvalue and eigenvector this basic principle is used to estimate the oscillation profile of a given cpg model moreover a systematic method is proposed for designing a cpg based nonlinear oscillator that achieves a prescribed oscillation profile

matrix perturbation analysis for weakly coupled oscillators the central pattern generator for controlling animal locomotion is generally not a single oscillator but a group of interconnected oscillators although the whole group can be analyzed as a bulky single oscillator it is difficult with such an approach to reveal the essential mechanism of phase coordination among oscillators in this paper a new approach based on the multivariable harmonic balance is used to analyze a group of identical oscillators that are weakly coupled to each other specifically a lower dimensional matrix representing the coupling structure is abstracted from the overall neuronal connectivity matrix of large dimension so that the coupling matrix captures the essential mechanism for phase coordination of the oscillators moreover this framework provides an effective way to design the neuronal interconnections to achieve prescribed coordination among the oscillators

a simplified cluster variation method abstract a variational calculation is given of an approximation scheme which is far easier to apply than the cluster variation method in the higher approximations the curie temperature of the ising model in the square approximation in the present scheme is obtained as 2 6253 and 4 7611 respectively for the system on the square and the sc lattice these values are nearly equal to the mean values of those in the pair bethe and the square kikuchi approximation the phase diagram in the square approximation of the present scheme is compared with other approximations and the exact result for a frustrated ising model on the centred square lattice

mixed impedance boundary conditions a novel set of isotropic electromagnetic boundary conditions generalizing some of the recently introduced boundary conditions is introduced for a planar boundary it is required that the boundary appears as an impedance boundary for the te and tm components of the field with different surface impedances in the general case thus such conditions can be dubbed as mixed impedance boundary conditions it is shown that the conditions can be alternatively expressed in terms of normal components of the fields at the boundary and in this form they can be defined for non planar boundaries as well the conditions generalize those of the isotropic impedance boundary and the more recently considered db and d b boundaries as a numerical example scattering from a mixed impedance sphere is considered and it is found that the sphere could be useful as a cloaking device

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

tiling problems and undecidability in the cluster variation method in cluster approximations for lattice systems the thermodynamic behavior of the infinite system is inferred from that of a relatively small finite subsystem cluster approximations being made for the influence of the surrounding system in this context we study for translation invariant classical lattice systems the conditions under which a state for a cluster admits an extension to a global translation invariant state this extension problem is related to undecidable tiling problems the implication is that restrictions of global translation invariant states cannot be characterized purely locally in general this means that there is an unavoidable element of uncertainty in the application of a cluster approximation

electromagnetic boundary and its realization with anisotropic metamaterial a set of boundary conditions requiring vanishing of the normal components of the d and b vectors at the boundary surface is introduced and labeled as that of db boundary basic properties of the db boundary are studied in this paper reflection of an arbitrary plane wave incident with a complex propagation vector is analyzed for the planar db boundary it is shown that waves polarized transverse electric te and transverse magnetic tm with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes the basic problem of current source above the planar db boundary is solved by applying te and tm decomposition for the source realization of the db boundary in terms of an interface of uniaxially anisotropic metamaterial half space with zero axial medium parameters is considered it is also shown that such a medium with small axial parameters acts as a spatial filter for waves incident at the interface which could be used for narrowing the beam of a directive antenna application of db boundary as an isotropic soft surface with low interaction between antenna apertures also appears possible

solving ibc cfie with dual basis functions the surface integral equation method is applied to solve electromagnetic scattering by arbitrarily shaped three dimensional imperfectly conducting objects modeled with the leontovitch impedance boundary condition ibc dual basis functions are used to remove previously reported difficulties associated with the solution of the combined field integral equation for objects with the ibc by expanding the magnetic current with quasi curl conforming dual functions and the electric current with divergence conforming primary rwg functions leads to a stable discretization procedure for the rotation n operator required by the ibc

cluster variation method in statistical physics and probabilistic graphical models the cluster variation method cvm is a hierarchy of approximate variational techniques for discrete ising like models in equilibrium statistical mechanics improving on the mean field approximation and the bethe peierls approximation which can be regarded as the lowest level of the cvm in recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models the foundations of the cvm are briefly reviewed and the relations with similar techniques are discussed the main properties of the method are considered with emphasis on its exactness for particular models and on its asymptotic properties the problem of the minimization of the variational free energy which arises in the cvm is also addressed and recent results about both provably convergent and message passing algorithms are discussed

computation of scattering by db objects with surface integral equation method electromagnetic scattering by objects with a db boundary condition normal components of the electric and magnetic flux densities d and b vanish at the boundary surface is investigated scattering of arbitrary shaped three dimensional objects is analyzed with the surface integral equation method a significant difference compared to the more conventional boundary conditions is that the uniqueness of the solution to the scattering problem with db boundary depends on the connectivity of the object for a simply connected object the solution is unique but for a multiply connected object some additional conditions are required it appears that these additional conditions are satisfied if divergence free basis functions are used to expand the unknown surface current densities the developed method is applied to calculate polarizabilities scattering efficiencies and radar cross sections rcs of the db sphere and cube and the results are compared with those of the pec cube and sphere

towards the classification of all boolean cellular automata abstract a classification scheme for all boolean cellular automata models involving an arbitrary number of inputs is proposed the scheme is based upon counting the number of stable points for a given rule i e points whose time development is stable with respect to small perturbations when applied to all cellular automata with 2 3 4 or 5 boolean inputs the latter involving more than 4000 million cases it yields in each case a nontrivial classification i e there is no single class in which nearly all the rules lie in addition it is shown how rules satisfying a given boolean differential equation can easily be obtained

breaking of periodicity at positive temperatures we discuss a classical lattice gas model without periodic or quasiperiodic ground states the only ground state configurations of our model are nonperiodic thue morse sequences we show that low temperature phases of such models can be ordered in fact we prove the existence of an ordered nonmixing low temperature translation invariant equilibrium state which has nonperiodic gibbs states in its extremal decomposition

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

more really is different abstract in 1972 p w anderson suggested that more is different meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents we strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems the infinite periodic ising lattice cannot in general be derived from a microscopic description this provides evidence that emergent behavior occurs in such systems and indicates that even if a theory of everything governing all microscopic interactions were discovered the understanding of macroscopic order is likely to require additional insights

complexity of two dimensional patterns in dynamical systems such as cellular automata and iterated maps it is often useful to look at a language or set of symbol sequences produced by the system there are well established classification schemes such as the chomsky hierarchy with which we can measure the complexity of these sets of sequences and thus the complexity of the systems which produce them in this paper we look at the first few levels of a hierarchy of complexity for two or more dimensional patterns we show that several definitions of regular language or local rule that are equivalent in d 1 lead to distinct classes in d 2 we explore the closure properties and computational complexity of these classes including undecidability and l nl and np completeness results we apply these classes to cellular automata in particular to their sets of fixed and periodic points finite time images and limit sets we show that it is undecidable whether a ca in d 2 has a periodic point of a given period and that certain local lattice languages are not finite time images or limit sets of any ca we also show that the entropy of a d dimensional ca s finite time image cannot decrease faster than t d unless it maps every initial condition to a single homogeneous state

a gauss newton method for the synthesis of periodic outputs with central pattern generators it is assumed that a central pattern generator possesses an exponentially stable limit cycle which originates a periodic output signal we propose a method based on a gauss newton iteration to determine the values of the neural coupling parameters that allows to approximate a given reference output signal we present two applications the first is a ring network of morris lecar neurons where the output of the system is the sum of the membrane potential of all neurons the second is a network of six neural cells for the generation of the leg movements of a hexapod

two dimensional translation invariant probability distributions approximations characterizations and no go theorems we study the properties of the set of marginal distributions of infinite translation invariant systems in the two dimensional square lattice in cases where the local variables can only take a smal