structure generating mechanisms in agent based models abstract the emergence of dynamical structures in multi agent systems is analysed three different mechanisms are identified namely 1 sensitive dependence in the agent dynamics and convex coupling 2 sensitive dependence and extremal dynamics and 3 interaction through a collectively generated field the dynamical origin of the emergent structures is traced back either to a modification by interaction of the lyapunov spectrum or to multistable dynamics

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

fixed point attractor analysis for a class of neurodynamics nearly all models in neural networks start from the assumption that the input output characteristic is a sigmoidal function on parameter space we present a systematic and feasible method for analyzing the whole spectrum of attractors all saturated all but one saturated all but twosaturated and so on of a neurodynamical system with a saturated sigmoidal function as its input output characteristic we present an argument that claims under a mild condition that only all saturated or all but one saturated attractors are observable for the neurodynamics for any given all saturated configuration all but one saturated configuration the article shows how to construct an exact parameter region r such that if and only if the parameters fall within r then is an attractor a fixed point of the dynamics the parameter region for an all saturated fixed point attractor is independent of the specific choice of a saturated sigmoidal function whereas for an all but one saturated fixed point it

biseparating maps between operator algebras we prove that a biseparating map between spaces b e and some other banach algebras is automatically continuous and a multiple of an algebra isomorphism

weakly compact orthogonality preservers on c algebras we establish a complete description of weakly compact orthogonality preserving operators from a c algebra a or a jb algebra to a jb triple e we prove that any such operator is the sum of a series of mutually orthogonal triple homomorphisms from a to a certain peirce 2 subspace of e multiplied by a mutually orthogonal norm null sequence in e which enjoy certain operator commutativity relations

phase transition and critical behavior in a model of organized criticality we study a model of organized criticality where a single avalanche propagates through an a priori static i e organized sandpile configuration the latter is chosen according to an i i d distribution from a borel probability measure on 0 1 the avalanche dynamics is driven by a standard toppling rule however we simplify the geometry by placing the problem on a directed rooted tree as our main result we characterize which are critical in the sense that they do not admit an infinite avalanche but exhibit a power law decay of avalanche sizes our analysis reveals close connections to directed site percolation both in the characterization of criticality and in the values of the critical exponents

the number of synaptic inputs and the synchrony of large sparse neuronal networks the prevalence of coherent oscillations in various frequency ranges in the central nervous system raises the question of the mechanisms that synchronize large populations of neurons we study synchronization in models of large networks of spiking neurons with random sparse connectivity synchrony occurs only when the average number of synapses m that a cell receives is larger than a critical value mc below mc the system is in an asynchronous state in the limit of weak coupling assuming identical neurons we reduce the model to a system of phase oscillators that are coupled via an effective interaction in this framework we develop an approximate theory for sparse networks of identical neurons to estimate mc analytically from the fourier coefficients of our approach relies on the assumption that the dynamics of a neuron depend mainly on the number of cells that are presynaptic to it we apply this theory to compute mc for a model of inhibitory networks of integrate and fire i f neurons as a function of the intrinsic neuronal properties e g the refractory period tr the synaptic time constants and the strength of the external stimulus iext the number mc is found to be nonmonotonous with the strength of iext for tr 0 we estimate the minimum value of mc over all the parameters of the model to be 363 8 above mc the neurons tend to fire in smeared one cluster states at high firing rates and smeared two or more cluster states at low firing rates refractoriness decreases mc at intermediate and high firing rates these results are compared to numerical simulations we show numerically that systems with different sizes n behave in the same way provided the connectivity m is such that 1 meff 1 m 1 n remains constant when n varies this allows extrapolating the large n behavior of a network from numerical simulations of networks of relatively small sizes n 800 in our case we find that our theory predicts with remarkable accuracy the value of mc and the patterns of synchrony above mc provided the synaptic coupling is not too large we also study the strong coupling regime of inhibitory sparse networks all of our simulations demonstrate that increasing the coupling strength reduces the level of synchrony of the neuronal activity above a critical coupling strength the network activity is asynchronous we point out a fundamental limitation for the mechanisms of synchrony relying on inhibition alone if heterogeneities in the intrinsic properties of the neurons and spatial fluctuations in the external input are also taken into account

potts model partition functions on two families of fractal lattices abstract the partition function of q state potts model or equivalently the tutte polynomial is computationally intractable for regular lattices the purpose of this paper is to compute partition functions of q state potts model on two families of fractal lattices based on their self similar structures and by applying the subgraph decomposition method we divide their tutte polynomials into two summands and for each summand we obtain a recursive formula involving the other summand as a result the number of spanning trees and their asymptotic growth constants and a lower bound of the number of connected spanning subgraphs or acyclic root connected orientations for each of such two lattices are obtained

mechanisms of avalanche dynamics and forms of scaling in sandpiles abstract the probability distributions of several avalanche quantities of the bak tang wiesenfeld sandpile in two dimensions display multifractal scaling this explains why this prototype model remained extremely problematic and controversial for such a long time after its introduction other models like the manna model obey instead standard finite size scaling and fall in different universality classes an analysis of time series for the waves into which avalanches can be decomposed shows that the different forms of scaling can be ascribed to the respective autocorrelation functions the intermittency of the bak tang wiesenfeld sandpile is due to this autocorrelation being long range in time unlike in the manna case a coarse graining of the wave time series elucidates these differences and the mechanism leading to multifractality

dynamics and entropy in the zhang model of self organized criticality we give a detailed study of dynamical properties of the zhang model including evaluation of topological entropy and estimates for the lyapunov exponents and the dimension of the attractor in the thermodynamic limit the entropy goes to zero and the lyapunov spectrum collapses

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

on mappings preserving the sharp and star orders abstract the present paper is devoted to the study of linear maps preserving certain relations such as the sharp partial order and the star partial order in semisimple banach algebras and c algebras

asymptotic behavior and synchronizability characteristics of a class of recurrent neural networks we propose an approach to the analysis of the influence of the topology of a neural network on its synchronizability in the sense of equal output activity rates given by a particular neural network model the model we introduce is a variation of the zhang model we investigate the time asymptotic behavior of the corresponding dynamical system in particular the conditions for the existence of an invariant compact asymptotic set and apply the results of the synchronizability analysis on a class of random scale free networks and to the classical random networks with poisson connectivity distribution

renormalization group study of sandpile on the triangular lattice abstract we apply the renormalization group approach to the sandpile on the triangular lattice the only attractive fixed point is found the obtained fixed point height probabilities are compared with numerical simulations the value of critical exponent of avalanche size distribution is found to be 1 36 the probabilities of the sand transition are compared with the branching probabilities of the spanning trees on the triangular lattice which are also evaluated

nonscalar matrix polynomial representation of some scalar polynomials abstract we show how a class of scalar polynomials can be expressed as nonscalar matrix polynomials to which matrix methods can be applied that yield improvements over scalar results and generate new ones to demonstrate the advantages of this approach we use it to compute bounds for the zeros of those polynomials

threshold state and a conjecture of poghosyan poghosyan priezzhev and ruelle we prove a precise relationship between the threshold state of the fixed energy sandpile and the stationary state of dhar s abelian sandpile in the limit as the initial condition s0 tends to infty the former is obtained by size biasing the latter according to burst size an avalanche statistic the question of whether and how these two states are related has been a subject of some controversy since 2000

large scale simulations of the zhang sandpile model we consider the non abelian sandpile model introduced by y c zhang on a two dimensional square lattice the static and dynamical properties of the model are investigated and compared to the abelian sandpile model of bak tang and wiesenfeld a detailed analysis which takes the finite size effects into account yields that the exponents of the avalanche probability distribution are the same as in the abelian model

properties and applications of laplacian spectra for koch networks for a network knowledge of its laplacian eigenvalues is central to understanding its structure and dynamics in this paper we study the laplacian spectra of a family of koch networks with scale free and small world properties we derive some recursive relations between the laplacian characteristic polynomials of koch networks and their subgraphs at different iterations based on the obtained recurrence relations we determine explicitly the product of all nonzero laplacian eigenvalues as well as the sum of the reciprocals of these eigenvalues then using these results we further evaluate the number of spanning trees kirchhoff index global mean first passage time and average path length of the family of koch networks finally we determine the number of spanning forests under certain conditions we expect that our method can be adapted to other types of self similar networks

self organization and anomalous diffusion abstract the self organizing process is investigated in the continuum limit of the cellular automaton model introduced by bak tang and wiesenfeld an anomalous diffusion equation is proposed for the description of this process and an analytical method for the solutionis presented in one dimension based on an adiabatic approximation

automatic continuity of orthogonality preservers on a non commutative lp τ space abstract elements a and b of a non commutative l p space associated to a von neumann algebra n equipped with a normal semifinite faithful trace are called orthogonal if l a l b r a r b 0 where l x and r x denote the left and right support projections of x a linear map t from l p n to a normed space y is said to be orthogonality to p orthogonality preserving if t a t b p a p b p whenever a and b are orthogonal in this paper we prove that an orthogonality to p orthogonality preserving linear bijection from l p n 1 p p 2 to a banach space x is automatically continuous whenever n is a separably acting von neumann algebra if n is a semifinite factor not of type i 2 we establish that every orthogonality to p orthogonality preserving linear mapping t l p n x is continuous and invertible whenever t 0 furthermore there exists a positive constant c p 1 p p 2 so that t t 1 c p 2 for every non zero orthogonality to p orthogonality preserving linear mapping t l p n x for p 1 this inequality holds with c p 1 that is t is a multiple of an isometry

tutte polynomials of two self similar network models the tutte polynomial t g x y of a graph g or equivalently the q state potts model partition function is a two variable polynomial graph invariant of considerable importance in combinatorics and statistical physics graph operations have been extensively applied to model complex networks recently in this paper we study the tutte polynomials of the diamond hierarchical lattices and a class of self similar fractal models which can be constructed through graph operations firstly we find out the behavior of the tutte polynomial under k inflation and k subdivision which are two graph operations secondly we compute and gain the tutte polynomials of this two self similar fractal models by using their structure characteristic moreover as an application of the obtained results some evaluations of their tutte polynomials are derived such as the number of spanning trees and the number of spanning forests

toppling distributions in one dimensional abelian sandpiles we consider toppling distributions for the abelian sandpile model in one dimension we study the avalanche mass and duration distributions in the thermodynamic limit we also investigate their dependence on the seeding distribution which describes how sand is dropped none of the models shows criticality

sandpile models and random walkers on finite lattices abelian sandpile models both deterministic such as the bak tang wiesenfeld btw model p bak c tang and k wiesenfeld phys rev lett 59 381 1987 and stochastic such as the manna model s s manna j phys a 24 l363 1991 are studied on finite square lattices with open boundaries the avalanche size distribution p l n is calculated for a range of system sizes l the first few moments of this distribution are evaluated numerically and their dependence on the system size is examined the sandpile models are conservative in the sense that grains are conserved in the bulk and can leave the system only through the boundaries it is shown that the conservation law provides an interesting connection between the sandpile models and random walk models using this connection it is shown that the average avalanche sizes l for the btw and manna models are equal to each other and both are equal to the average path length of a random walker starting from a random initial site on the same lattice of size l this is in spite of the fact that the sandpile models with deterministic btw and stochastic manna toppling rules exhibit different critical exponents indicating that they belong to different universality classes

lyapunov exponents and transport in the zhang model of self organized criticality we discuss the role played by lyapunov exponents in the dynamics of zhang s model of self organized criticality we show that a large part of the spectrum the slowest modes is associated with energy transport in the lattice in particular we give bounds on the first negative lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time we then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites we use a finite size scaling ansatz for the lyapunov spectrum and relate the scaling exponent to the scaling of quantities such as avalanche size duration density of active sites etc

linear disjointness preservers of w algebras in this paper we give a complete description of the structure of zero product and orthogonality preserving linear maps between w algebras in particular two w algebras are isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions it is also the case when they have equivalent linear and left right ideal structures

orthogonality and disjointness preserving linear maps between fourier and fourier stieltjes algebras of locally compact groups this paper is devoted to the study of orthogonality and disjointness preserving linear maps between fourier and fourier stieltjes algebras of locally compact groups we show that a linear bijection a g1 a g2 resp b g1 b g2 between two fourier algebras resp fourier stieltjes algebras of locally compact groups will induce a topological group isomorphism between g1 and g2 provided that preserves both disjointness and some kind of orthogonality this improves earlier results of j j font and m s monfared where amenability of the groups or continuity of the linear maps are assumed we also study the structure of bounded and unbounded disjointness preserving linear functionals of fourier algebras in the development general results about disjointness and orthogonality preserving linear maps between c algebras w algebras and their preduals are obtained

generalization and variations of pellet s theorem for matrix polynomials abstract we derive a generalized matrix version of pellet s theorem itself based on a generalized rouche theorem for matrix valued functions to generate upper lower and internal bounds on the eigenvalues of matrix polynomials variations of the theorem are suggested to try and overcome situations where pellet s theorem cannot be applied

asymmetric abeiian sandpile models in the abelian sandpile models introduced by dhar long time behavior is determined by an invariant measure supported uniformly on a set of implicitly defined recurrent configurations of the system dhar proposed a simple procedure theburning algorithm as a possible test of whether a configuration is recurrent and later with majumdar verified the correctness of this test when the toppling rules of the sandpile are symmetric we observe that the test is not valid in general and give a new algorithm which yields a test correct for all sandpiles we also obtain necessary and sufficient conditions for the validity of the original test the results are applied to a family of deterministic one dimensional sandpile models originally studied by lee liang and tzeng

what can one learn about self organized criticality from dynamical systems theory we develop a dynamical system approach for the zhang model of self organized criticality for which the dynamics can be described either in terms of iterated function systems or as a piecewise hyperbolic dynamical system of skew product type in this setting we describe the soc attractor and discuss its fractal structure we show how the lyapunov exponents the haussdorf dimensions and the system size are related to the probability distribution of the avalanche size via the ledrappier young formula

bounds for eigenvalues of matrix polynomials upper and lower bounds are derived for the absolute values of the eigenvalues of a matrix polynomial or matrix the bounds are based on norms of the coefficient matrices and involve the inverses of the leading and trailing coefficient matrices they generalize various existing bounds for scalar polynomials and single matrices a variety of tools are used in the derivations including block companion matrices gershgorin s theorem the numerical radius and associated scalar polynomials numerical experiments show that the bounds can be surprisingly sharp on practical problems

synchronization in networks of excitatory and inhibitory neurons with sparse random connectivity in model networks of e cells and i cells excitatory and inhibitory neurons respectively synchronous rhythmic spiking often comes about from the interplay between the two cell groups the e cells synchronize the i cells and vice versa under ideal conditions homogeneity in relevant network parameters and all to all connectivity for instance this mechanism can yield perfect synchronization we find that approximate imperfect synchronization is possible even with very sparse random connectivity the crucial quantity is the expected number of inputs per cell as long as it is large enough more precisely as long as the variance of the total number of synaptic inputs per cell is small enough tight synchronization is possible the desynchronizing effect of random connectivity can be reduced by strengthening the e i synapses more surprising it cannot be reduced by strengthening the i e synapses however the decay time constant of inhibition plays an important role faster decay yields tighter synchrony in particular in models in which the inhibitory synapses are assumed to be instantaneous the effects of sparse random connectivity cannot be seen

orthogonality preserving linear maps on c algebras with non zero socles abstract we study orthogonality preserving surjective linear maps from a unital c algebra with non zero socle a to a c algebra in particular we prove that when a has essential socle every biorthogonality preserving surjective linear map t a b is automatically bounded and a jordan isomorphism multiplied by an invertible element

automatic continuity of biorthogonality preservers between compact c algebras and von neumann algebras abstract we prove that every biorthogonality preserving linear surjection between two dual or compact c algebras or between two von neumann algebras is automatically continuous

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

automatic continuity of m norms on c algebras abstract elements a and b of a c algebra are called orthogonal a b if a b a b 0 we say that vectors x and y in a banach space x are semi m orthogonal x sm y if x y max x y we prove that every linear bijection t a x where x is a banach space a is either a von neumann algebra or a compact c algebra and t a sm t b whenever a b must be continuous consequently every complete semi m norm on a von neumann algebra or on a compact c algebra is automatically continuous

a finite difference approximation of a two layer system for growing sandpiles we study from a numerical point of view a system of partial differential equations recently proposed in k p hadeler and c kuttler granular matter 2 1999 pp 9 18 to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded table in such a system an eikonal equation for the standing layer of the pile is coupled to an advection equation for the rolling layer we analyze a suitable explicit finite difference scheme in one dimension and discuss its properties a comparison is made with respect to the variational approach of l prigozhin european j appl math 7 1996 pp 225 235 particularly in terms of steady state solutions since the effective equilibrium configuration reached by the growing process is not completely clear for this model we show experiments in one and two dimensions which characterize the steady state solutions for different source terms

spectral equivalence of matrix polynomials and the index sum theorem abstract the concept of linearization is fundamental for theory applications and spectral computations related to matrix polynomials however recent research on several important classes of structured matrix polynomials arising in applications has revealed that the strategy of using linearizations to develop structure preserving numerical algorithms that compute the eigenvalues of structured matrix polynomials can be too restrictive because some structured polynomials do not have any linearization with the same structure this phenomenon strongly suggests that linearizations should sometimes be replaced by other low degree matrix polynomials in applied numerical computations motivated by this fact we introduce equivalence relations that allow the possibility of matrix polynomials with coefficients in an arbitrary field to be equivalent with the same spectral structure but have different sizes and degrees these equivalence relations are directly modeled on the notion of linearization and consequently inherit the simplicity applicability and most relevant properties of linearizations simultaneously though they are much more flexible in the possible degrees of equivalent polynomials this flexibility allows us to define in a unified way the notions of quadratification and l ification to introduce the concept of companion form of arbitrary degree and to provide concrete and simple examples of these notions that generalize in a natural and smooth way the classical first and second frobenius companion forms the properties of l ifications are studied in depth in this process a fundamental result on matrix polynomials the index sum theorem is recovered and extended to arbitrary fields although this result is known in the systems theory literature for real matrix polynomials it has remained unnoticed by many researchers it establishes that the sum of the finite and infinite partial multiplicities together with the left and right minimal indices of any matrix polynomial is equal to the rank times the degree of the polynomial the index sum theorem turns out to be a key tool for obtaining a number of significant results on the possible sizes and degrees of l ifications and companion forms on the minimal index preservation properties of companion forms of arbitrary degree as well as on obstructions to the existence of structured companion forms for structured matrix polynomials of even degree this paper presents many new results blended together with results already known in the literature but extended here to the most general setting of matrix polynomials of arbitrary sizes and degrees over arbitrary fields therefore we have written the paper in an expository and self contained style that makes it accessible to a wide variety of readers

a dynamical system approach to soc models of zhang s type we discuss zhang s model of soc in the framework of hyperbolic dynamical systems with singularities the fractal structure of the invariant energy distribution correlation decay like phenomena and symbolic coding are discussed

self organized criticality and thermodynamic formalism we develop a thermodynamic formalism for a dissipative version of the zhang model of self organized criticality where a parameter allows us to tune the local energy dissipation by constructing a suitable markov partition we define gibbs measures in the sense of sinai ruelle and bowen partition functions and topological pressure allowing the analysis of probability distributions of avalanches we discuss the infinite size limit in this setting in particular we show that a lee yang phenomenon occurs in the conservative case this suggests new connections to classical critical phenomena

introduction to the sandpile model abstract this article is based on a talk given by one of us evi at the conference statphys taipei 1997 it overviews the exact results in the theory of the sandpile model and discusses briefly the yet unsolved problem of calculation of avalanche distribution exponents the key ingredients include the analogy with the critical reaction diffusion system the spanning tree representation of height configurations and the decomposition of the avalanche process into waves of topplings

algebraic aspects of abelian sandpile models the abelian sandpile models feature a finite abelian group g generated by the operators corresponding to particle addition at various sites we study the canonical decomposition of g as a product of cyclic groups g z d1 z d2 z d3 z dg where g is the least number of generators of g and di is a multiple of di 1 the structure of g is determined in terms of the toppling matrix delta we construct scalar functions linear in the height variables of the pile that are invariant under toppling at any site these invariants provide convenient coordinates to label the recurrent configurations of the sandpile for an l l square lattice we show that g l in this case we observe that the system has non trivial symmetries transcending the obvious symmetries of the square namely those coming from the action of the cyclotomic galois group gall of the 2 l 1 th roots of unity which operates on the set of eigenvalues of h these eigenvalues are algebraic integers the product of which is the order mod g mod with the help of gall we are able to group the eigenvalues into certain subsets the products of which are separately integers and thus obtain an explicit factorization of mod g mod we also use gall to define other simpler sets of toppling invariants

dynamical properties of the zhang model of self organized criticality critical exponents of the infinitely slowly driven zhang model of self organized criticality are computed for d52 and 3 with particular emphasis devoted to the various roughening exponents besides confirming recent estimates of some exponents new quantities are monitored and their critical exponents computed among other results it is shown that the three dimensional exponents do not coincide with the bak tang wiesenfeld phys rev lett 59 381 1987 phys rev a 38 364 1988 abelian model and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide as is usually implicitly assumed an explanation for this is provided the possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed s1063 651x 98 06107 8 pacs number s 64 60 lx

disjointness preservers of aw algebras abstract in this paper we study bijective linear maps a b between a w algebras preserving either zero products or range orthogonality such a map is automatically continuous and provides an algebra or a algebra isomorphism 1 1 from a onto b our results extend previous works for the case of w algebras and also cover such maps between c algebras satisfying an extra assumption on preserving abelian c subalgebras