transition to weak turbulence via spatiotemporal intermittency in the taylor dean system the transition to weak turbulence via spatiotemporal intermittency has been studied in the taylor dean system when the inner cylinder is fixed and only the outer cylinder is rotating the spatiotemporal intermittency regime is characterized by the coexistence of laminar domains and turbulent patches for the same value of the control parameter the transition is supercritical but a particular boundary condition induces an imperfection statistical analysis of the spatiotemporal intermittency shows that the distribution of laminar domains by widths follows a power law decay near the onset while it is exponential for higher values of the control parameter the exponential distribution of the laminar domains has a definite threshold near which the correlation lengths and correlation times of laminar and turbulent domains diverge reinforcing the analogy with second order phase transitions the exponents measured near the critical points in this experiment differ from those observed in other systems thus showing that the spatiotemporal intermittency is not universal in character textcopyright 1996 the american physical society

conjugacy classes of g 2 and spectral rigidity the free group 2 is generated by a 1 2 0 1 and b 10 21 and setting x a exp 2 i x b exp 2 i defines a unitary character on 2 for 0 1 a program is devised to compute tr conj class summed over all primitive conjugacy classes of 2 of trace tr combined with a luo sarnak theorem this yields lower bounds for the spectral variance for a large sampling of characters in the range 0 1 the results indicate that the berry conjecture for spectral rigidity does not hold for this set of classically chaotic systems the program is also used to compute x ln n summed over all primitive conjugacy classes of 2 of norm n x the function 0 x is asymptotic to x and the remainder can be written as x x x the values of x are computed for all traces between 3202 and 4802 here x tr 2 2 the s cluster around 0 6 attaining a maximum of 2 3 finally it is proved that the remainder 0 x x has a negative bias by showing that the mean normalized remainder converges to a negative limit

on network coding for sum networks a directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources we call such a network a sum network it is shown that there exists a solvably and linear solvably equivalent sum network for any multiple unicast network and thus for any directed acyclic communication network it is also shown that there exists a linear solvably equivalent multiple unicast network for every sum network it is shown that for any set of polynomials having integer coefficients there exists a sum network which is scalar linear solvable over a finite field f if and only if the polynomials have a common root in f for any finite or cofinite set of prime numbers a network is constructed which has a vector linear solution of any length if and only if the characteristic of the alphabet field is in the given set the insufficiency of linear net work coding and unachievability of the network coding capacity are proved for sum networks by using similar known results for communication networks under fractional vector linear network coding a sum network and its reverse network are shown to be equivalent however under nonlinear coding it is shown that there exists a solvable sum network whose reverse network is not solvable

torsion homology growth and cycle complexity of arithmetic manifolds let m be an arithmetic hyperbolic 3 manifold such as a bianchi manifold we conjecture that there is a basis for the second homology of m where each basis element is represented by a surface of low genus and give evidence for this we explain the relationship between this conjecture and the study of torsion homology growth

phase transitions in coupled map lattices we clarify some aspects related to critical phenomena in 1d coupled map lattices in particular we explain why a model studied by chate and manneville did not seem to be in the same universality class as directed percolation contrary to first expectations we claim that this model is actually in this universality class but that scaling is extremely late we present a slightly modified model which seems to be in this universality class with respect to some properties but not all in contrast to directed percolation and to the model studied by chate and manneville our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1d maps

linearity and solvability in multicast networks it is known that for every solvable multicast network there exists a large enough finite field alphabet such that a scalar linear solution exists we prove i every binary solvable multicast network with at most two messages has a binary scalar linear solution ii for more than two messages not every binary solvable multicast network has a binary scalar linear solution iii a multicast network that has a solution for a given alphabet might not have a solution for all larger alphabets

reversible and irreversible information networks it is shown that there exist information networks where messages can be sent utilizing network coding more easily in one direction than in the opposite direction this is valid even though each channel is assumed to have the same capacity in both directions it is shown that irreversible information networks only have solutions that use nonlinear network coding this correspondence argues that this result is more surprising than it might appear at first sight and that it follows using ideas resembling the path integral in quantum mechanics

spatiotemporal chaos in mixed linear nonlinear two dimensional coupled logistic map lattice abstract we investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2dcml here the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices and the former 2dcml system is only a special case in the proposed system in this paper the criteria such kolmogorov sinai entropy density and universality bifurcation diagrams space amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system furthermore we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2dcml system and the mlncml system theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors which is more suitable for cryptography

synchronization and coherence in thermodynamic coupled map lattices with intermediate range coupling in spatially extended systems intermediate range interactions arise naturally in some physical contexts to study them we investigate a model of coupled map lattices cml s with intermediate range coupling and derive analytic conditions for its synchronization we find that in these cml s if the range of coupling is fixed the law of large numbers applies for the mean field the total normalized power in nonzero components of the power spectrum of the mean field goes to zero in the thermodynamic limit we also show that in the same limit the relevant parameter for synchronization and coherence is the fraction of sites coupled and not their number s1063 651x 99 07410 3 pacs number s 05 45 2a the past decade has seen a surge of interest in synchronization and coherence in coupled map lattices cml s 1 10 most work has focused on systems with finite degrees of freedom and short range global or random coupling in this paper we study the synchronization of one and two dimensional 1d and 2d cml s with intermediaterange couplings in the thermodynamic limit this study is related to systems with finite degrees of freedom studied by sinha et al 2 and kozma 10 in these works each site is coupled to a range of neighbors on either side rather than just its nearest neighbors this may be a valid approximation in systems where interaction strength decays slowly with distance just as cml s with nearest neighbor coupling could be considered to be a discretization of partial differential equation cml s with intermediate range coupling could be seen as a discretization of a partial integro differential equation in fact such integro differential equations have often been used in modeling certain physico chemical reactions 11 elimination of rapidly diffusing components in a system of diffusion coupling can also lead to effectively nonlocal coupling in resultant equations 12 cml s in which coupling between two sites separated by distance r decays as power law 1 r a with exponent a have also been considered as models for biological neural networks 6 in the present work we derive the analytic conditions for synchronization in our cml s we find that in the thermodynamic limit the relevant parameter for synchronization is the fraction of sites coupled and not their number we present numerical results which show that for the mean field in the cml s with a fixed range of coupling sites for each site the law of large numbers applies and the total normalized power in nonzero components of the power spectrum goes to zero in the thermodynamic limit this is in sharp contrast with the conjecture of sinha et al 2

spatio temporal intermittency in coupled map lattices abstract the transition to turbulence in a one dimensional array of maps coupled by diffusion is shown to display critical properties resembling those of directed percolation the analogy is supported by the reconstruction of a probabilistic cellular automation with closely similar statistical properties numerical results suggest however that spatio temporal intermittency does not belong to the same universality class as directed percolation

a geometric perspective to multiple unicast network coding the multiple unicast network coding conjecture states that for multiple unicast sessions in an undirected network network coding is equivalent to routing simple and intuitive as it appears the conjecture has remained open since its proposal in 2004 and is now a well known unsolved problem in the field of network coding based on a recently proposed tool of space information flow we present a geometric framework for analyzing the multiple unicast conjecture the framework consists of four major steps in which the conjecture is transformed from its throughput version to cost version from the graph domain to the space domain and then from high dimension to 1 d where it is to be eventually proved we apply the geometric framework to derive unified proofs to known results of the conjecture as well as new results previously unknown a possible proof to the conjecture based on this framework is outlined

achievable rate regions for network coding determining the achievable rate region for networks using routing linear coding or nonlinear coding is thought to be a difficult task in general and few are known we describe the achievable rate regions for four interesting networks completely for three and partially for the fourth in addition to the known matrix computation method for proving outer bounds for linear coding we present a new method that yields actual characteristic dependent linear rank inequalities from which the desired bounds follow immediately

simple geodesics and a series constant over teichmuller space we investigate the birman series set in a neighborhood of a cusp on a punctured surface showing that it is homeomorphic to a cantor set union countably many isolated points cross a line the local topology of the cantor set is shown to be related in a simple way to the global behavior of simple geodesics from this we deduce that a certain series is constant across the teichmuller space

nonreversibility and equivalent constructions of multiple unicast networks we prove that for any finite directed acyclic network there exists a corresponding multiple unicast network such that for every alphabet each network is solvable if and only if the other is solvable and for every finite field alphabet each network is linearly solvable if and only if the other is linearly solvable the proof is constructive and creates an extension of the original network by adding exactly s 5m r 1 new nodes where in the original network m is the number of messages r is the average number of receiver nodes demanding each source message and s is the number of messages emitted by more than one source the construction is then used to create a solvable multiple unicast network which becomes unsolvable over every alphabet size if all of its edge directions are reversed and if the roles of source receiver pairs are reversed

disturbance propagation in chaotic extended systems with long range coupling propagation of initially localized perturbations is investigated in chaotic coupled map lattices with long range couplings decaying as a power of the distance the initial perturbation propagates exponentially fast along the lattice with a rate given by the ratio of the maximal lyapunov exponent and the power of the coupling a complementary description in terms of a suitable comoving lyapunov exponent is also given

linear network codes and systems of polynomial equations if beta and gamma are nonnegative integers and f is a field then a polynomial collection p1 hellip pbeta sube z alpha1 hellip alphagamma is said to be solvable over f if there exist omega1hellip omegagamma isin f such that for all i 1 hellip beta we have pi omega1hellip omegagamma 0 we say that a network and a polynomial collection are solvably equivalent if for each field f the network has a scalar linear solution over f if and only if the polynomial collection is solvable over f koetter and medard s work implies that for any directed acyclic network there exists a solvably equivalent polynomial collection we provide the converse result namely that for any polynomial collection there exists a solvably equivalent directed acyclic network hence the problems of network scalar linear solvability and polynomial collection solvability have the same complexity the construction of the network is modeled on a matroid construction using finite projective planes due to maclane in 1936 a set psi of prime numbers is a set of characteristics of a network if for every q isin psi the network has a scalar linear solution over some finite field with characteristic q and does not have a scalar linear solution over any finite field whose characteristic lies outside of psi we show that a collection of primes is a set of characteristics of some network if and only if the collection is finite or co finite two networks n and n are is equivalent if for any finite field f n is scalar linearly solvable over f if and only if n is scalar linearly solvable over f we further show that every network is ls equivalent to a multiple unicast matroidal network

associative memory based on parametrically coupled chaotic elements abstract in this paper we propose an associative memory system based on parametrically coupled chaotic elements the proposed system is obtained by adding a new parameter control to our previously proposed system a chaotic activity in an early association stage makes an efficient association over the memories that are stored by means of autocorrelational learning when the system successfully recalls the target memory the system s motion is dominated by a spatially coherent oscillation while unstable motions remain when the system fails to make the association in addition the system has a large memory capacity a comparison between the proposed system and an approach with a nonmonotonic transfer function is also shown

networks matroids and non shannon information inequalities we define a class of networks called matroidal networks which includes as special cases all scalar linearly solvable networks and in particular solvable multicast networks we then present a method for constructing matroidal networks from known matroids we specifically construct networks that play an important role in proving results in the literature such as the insufficiency of linear network coding and the unachievability of network coding capacity we also construct a new network from the vamos matroid which we call the vamos network and use it to prove that shannon type information inequalities are in general not sufficient for computing network coding capacities to accomplish this we obtain a capacity upper bound for the vamos network using a non shannon type information inequality discovered in 1998 by zhang and yeung and then show that it is smaller than any such bound derived from shannon type information inequalities this is the first application of a non shannon type inequality to network coding we also compute the exact routing capacity and linear coding capacity of the vamos network finally using a variation of the vamos network we prove that shannon type information inequalities are insufficient even for computing network coding capacities of multiple unicast networks

conversion of local transient chaos into global laminar states in coupled map lattices with long range interactions abstract spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales characterized by repeated conversions from spatially localized transient chaos into global laminar patterns a simple model yet retaining some features of more complex systems consists of a lattice of a class of tent maps with an escaping region the coupling prescription we adopt in this work considers the interaction of a site with all its neighbors the corresponding strength decaying with the lattice distance as a power law this makes possible to pass continuously from a local nearest neighbor to a global kind of coupling we investigate statistical properties of both the chaotic transient bursts and the periodic laminar states with respect to the coupling parameters

evidence for directed percolation universality at the onset of spatiotemporal intermittency in coupled circle maps we consider a lattice of coupled circle maps a popular model for the study of mode locked phenomena we find that the onset of spatiotemporal intermittency sti in this system is analogous to directed percolation dp with the transition being to a unique absorbing state for low nonlinearities and to weakly chaotic absorbing states for high nonlinearities we find that the complete set of static exponents and spreading exponents at all critical points match those of dp very convincingly further hyperscaling relations are fulfilled leading to independent controls and consistency checks of the values of all the critical exponents these results provide an example in support of the conjecture that the onset of sti in deterministic models belongs to the dp universality class nonuniversal spreading exponents are seen only for the cases where the initial state is homogeneous with symmetrically placed seeds leading to strictly symmetric spreading however very small departures from homogeneity are sufficient to restore the dp exponents

closure solvability for network coding and secret sharing network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive given a network the network coding solvability problem decides whether all the packets requested by the destinations can be transmitted in this paper we introduce a new approach to this problem we define a closure operator on a digraph closely related to the network coding instance and we show that the constraints for network coding can all be expressed according to that closure operator thus a solution for the network coding problem is equivalent to a so called solution of the closure operator we can then define the closure solvability problem in general which surprisingly reduces to finding secret sharing matroids when the closure operator is a matroid based on this reformulation we can easily prove that any multiple unicast where each node receives at least as many arcs as there are sources solvable by linear functions we also give an alternative proof that any nontrivial multiple unicast with two source receiver pairs is always solvable over all sufficiently large alphabets based on singular properties of the closure operator we are able to generalize the way in which networks can be split into two distinct parts we also provide a new way of identifying and removing useless nodes in a network we also introduce the concept of network sharing where one solvable network can be used to accommodate another solvable network coding instance finally the guessing graph approach to network coding solvability is generalized to any closure operator which yields bounds on the amount of information that can be transmitted through a network

statistics of energy levels without time reversal symmetry aharonov bohm chaotic billiards a planar domain d contains a single line of magnetic flux phi switching on phi breaks time reversal symmetry t for quantal particles with charge q moving in d whilst preserving the geometry of classical billiard trajectories bouncing off the boundary delta d if delta d is such that these classical trajectories are chaotic the authors predict that t breaking will cause the local statistics of quantal energy levels to change their universality class from that of the gaussian orthogonal ensemble goe of random matrix theory to that of the gaussian unitary ensemble gue in the semiclassical limit this transition is abrupt for statistics involving the first n levels gue behaviour requires that the quantum flux alpha identical to q phi h 0 13n 14 the special flux alpha 1 2 corresponds to false t breaking and for this case goe statistics are predicted these predictions are confirmed by numerical computation of spectral statistics for a classically chaotic billiard without symmetry for which delta d is a cubic conformal image of the unit disc

graph theoretical constructions for graph entropy and network coding based communications the guessing number of a directed graph digraph equivalent to the entropy of that digraph was introduced as a direct criterion on the solvability of a network coding instance this paper makes two contributions on the guessing number first we introduce an undirected graph on all possible configurations of the digraph referred to as the guessing graph which encapsulates the essence of dependence amongst configurations we prove that the guessing number of a digraph is equal to the logarithm of the independence number of its guessing graph therefore network coding solvability is no more a problem on the operations made by each node but is simplified into a problem on the messages that can transit through the network by studying the guessing graph of a given digraph and how to combine digraphs or alphabets we are thus able to derive bounds on the guessing number of digraphs second we construct specific digraphs with high guessing numbers yielding network coding instances where a large amount of information can transit we first propose a construction of digraphs with finite parameters based on cyclic codes with guessing number equal to the degree of the generator polynomial we then construct an infinite class of digraphs with arbitrary girth for which the ratio between the linear guessing number and the number of vertices tends to one despite these digraphs being arbitrarily sparse these constructions yield solvable network coding instances with a relatively small number of intermediate nodes for which the node operations are known and linear although these instances are sparse and the sources are arbitrarily far from their corresponding sinks

number variance for arithmetic hyperbolic surfaces we prove that the number variance for the spectrum of an arithmetic surface is highly nonrigid in part of the universal range in fact it is close to having a poisson behavior this fact was discovered numerically by schmit bogomolny georgeot and giannoni it has its origin in the high degeneracy of the length spectrum first observed by selberg

extremals of determinants of laplacians on etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte

insufficiency of linear coding in network information flow it is known that every solvable multicast network has a scalar linear solution over a sufficiently large finite field alphabet it is also known that this result does not generalize to arbitrary networks there are several examples in the literature of solvable networks with no scalar linear solution over any finite field however each example has a linear solution for some vector dimension greater than one it has been conjectured that every solvable network has a linear solution over some finite field alphabet and some vector dimension we provide a counterexample to this conjecture we also show that if a network has no linear solution over any finite field then it has no linear solution over any finite commutative ring with identity our counterexample network has no linear solution even in the more general algebraic context of modules which includes as special cases all finite rings and abelian groups furthermore we show that the network coding capacity of this network is strictly greater than the maximum linear coding capacity over any finite field exactly 10 greater so the network is not even asymptotically linearly solvable it follows that even for more general versions of linearity such as convolutional coding filter bank coding or linear time sharing the network has no linear solution

perturbative series and the moduli space of riemann surfaces on utilise des techniques de la theorie quantique des champs pour calculer des quantites reliees aux groupes de symetrie de paires f g ou f est une surface et g une epine de f

energy level statistics of model quantum systems universality and scaling in a lattice point problem we investigate the statistics of the numbern r s of lattice pointsn z 2 in an annular domain r w r w a ra wherer w 0 herea is a fixed convex set with smooth boundary andw is chosen so that the area of r w iss the statistics comes fromr being taken as random with a smooth density in some interval c 1 t c 2 t c 2 c 1 0 we find that in the limitt the variance and distribution of n n r s s depend strongly on hows grows witht there is a saturation regimes t ast in which the fluctuations in n coming from the two boundaries of are independent then there is a scaling regime s t z 0 z in which the distribution depends onz in an almost periodic way going to a gaussian asz 0 the variance in this limit approachesz for generic a but can be larger for degenerate cases the former behavior is what one would expect from the poisson limit of a distribution for annuli of finite area

the linear guessing number of undirected graphs abstract this paper investigates linear guessing number introduced by riis in connection with the network coding theory this paper establishes properties of linear guessing number on undirected graphs in particular lower and upper bounds for linear guessing number are established finally linear guessing numbers of product graphs are investigated

chaotic bursting at the onset of unstable dimension variability dynamical systems possessing symmetries have invariant manifolds according to the transversal stability properties of this invariant manifold nearby trajectories may spend long stretches of time in its vicinity before being repelled from it as a chaotic burst after which the trajectories return to their original laminar behavior the onset of chaotic bursting is determined by the loss of transversal stability of low period periodic orbits embedded in the invariant manifold in such a way that the shadowability of chaotic orbits is broken due to unstable dimension variability characterized by finite time lyapunov exponents fluctuating about zero we use a two dimensional map with an invariant subspace to estimate shadowing distances and times from the statistical properties of the bursts in the transversal direction a stochastic model biased random walk with reflecting barrier is used to relate the shadowability properties to the distribution of the finite time lyapunov exponents

eigenvalue spacings for quantized cat maps according to one of the basic conjectures in quantum chaos the eigenvalues of a quantized chaotic hamiltonian behave like the spectrum of the typical member of the appropriate ensemble of random matrices we study one of the simplest examples of this phenomenon in the context of ergodic actions of groups generated by several linear toral automorphisms cat maps our numerical experiments indicate that for generic choices of cat maps the unfolded consecutive spacing distribution in the irreducible components of the nth quantization given by the n dimensional weil representation approaches the goe gse law of random matrix theory for certain special arithmetic transformations related to the ramanujan graphs of lubotzky phillips and sarnak the experiments indicate that the unfolded consecutive spacing distribution follows poisson statistics we provide a sharp estimate in that direction

examples of infinite covolume subgroups of rm psl 2 mathbb r r with big limit sets we provide examples of finitely generated infinite covolume subgroups of rm psl 2 mathbb r r with a big limit set e g that contains an open subset of the geometric boundary they are given by the so called semi arithmetic fuchsian groups admitting modular embeddings

energy level statistics of the hadamard gutzwiller ensemble abstract the statistical properties of the quantal energy levels of the hadamard gutzwiller ensemble whose classical members belong to the class of systems with hard chaos are investigated based on a sample of 4500 energy levels it is shown that the short range statistics as nearest neighbour spacing distributions are governed by the goe predictions of random matrix theory which was first surmised by wigner and by landau and smorodinsky for nuclear level statistics this result strengthens the hypothesis that quantum systems with chaotic classical counterpart display level repulsion as predicted by random matrix theory however the level statistics describing correlations over greater level distances deviate from the goe predictions which is explained as a simple consequrnce of the fact that the spectral rigidity 3 l introduced by dyson and mehta saturates non universally at a finite value for l in complete agreement with the semiclassical theory developed by berry

correlations for pairs of closed geodesics in this article we consider natural counting problems for closed geodesics on negatively curved surfaces we present asymptotic estimates for pairs of closed geodesics the differences of whose lengths lie in a prescribed family of shrinking intervals related pair correlation problems have been studied in both quantum chaos and number theory

directed percolation universality in asynchronous evolution of spatiotemporal intermittency we present strong evidence that a coupled map lattice model for spatiotemporal intermittency belongs to the universality class of directed percolation when the updating rules are asynchronous i e when only one randomly chosen site is evolved at each time step in contrast when the system is subjected to parallel updating available numerical evidence suggest that it does not belong to this universality class and that it is not even universal we argue that in the absence of periodic external forcing the asynchronous rule is the more physical

reduction and fixed points of boolean networks and linear network coding solvability linear network coding transmits data through networks by letting the intermediate nodes combine the messages they receive and forward the combinations toward their destinations the solvability problem asks whether the demands of all the destinations can be simultaneously satisfied by using linear network coding the guessing number approach converts this problem into determining the number of fixed points of coding functions f a n to a n over a finite alphabet a usually referred to as boolean networks if a 0 1 with a given interaction graph that describes which local functions depend on which variables in this paper we generalize the so called reduction of coding functions in order to eliminate variables we then determine the maximum number of fixed points of a fully reduced coding function whose interaction graph has a loop on every vertex since the reduction preserves the number of fixed points we then apply these ideas and results to obtain four main results on the linear network coding solvability problem first we prove that non decreasing coding functions cannot solve any more instances than routing already does second we show that the triangle free undirected graphs are linearly solvable if and only if they are solvable by routing this is the first classification result for the linear network coding solvability problem third we exhibit a new class of non linearly solvable graphs fourth we determine large classes of strictly linearly solvable graphs

on the index coding problem and its relation to network coding and matroid theory the index coding problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks an instance of the index coding problem includes a sender that holds a set of information messages x x1 xk and a set of receivers r each receiver x h in r needs to obtain a message x x and has prior side information consisting of a subset h of x the sender uses a noiseless communication channel to broadcast encoding of messages in x to all clients the objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers in this paper we analyze the relation between the index coding problem the more general network coding problem and the problem of finding a linear representation of a matroid in particular we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem specifically we show that vector linear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

a geometric characterization of arithmetic fuchsian groups the trace set of a fuchsian group encodes the set of lengths of closed geodesics in the surface h luo and sarnak showed that the trace set of a cofinite arithmetic fuchsian group satisfies the bounded clustering property sarnak then conjectured that the b c property actually characterizes arithmetic fuchsian groups schmutz stated the even stronger conjecture that a cofinite fuchsian group is arithmetic if its trace set has linear growth he proposed a proof of this conjecture in the case when the group contains at least one parabolic element but unfortunately this proof contains a gap in the present paper we point out this gap and we prove sarnak s conjecture under the assumption that the fuchsian group contains parabolic elements

the behaviour of eigenstates of arithmetic hyperbolic manifolds in this paper we study some problems arising from the theory of quantum chaos in the context of arithmetic hyperbolic manifolds we show that there is no strong localization scarring onto totally geodesic submanifolds arithmetic examples are given which show that the random wave model for eigenstates does not apply universally in 3 degrees of freedom