generating labeled planar graphs uniformly at random we present a deterministic polynomial time algorithm to sample a labeled planar graph uniformly at random our approach uses recursive formulae for the exact number of labeled planar graphs with n vertices and m edges based on a decomposition into 1 2 and 3 connected components we can then use known sampling algorithms and counting formulae for 3 connected planar graphs

on the robustness of interconnections in random graphs a symbolic approach graphs are models of communication networks this paper applies symbolic combinatorial techniques in order to characterize the interplay between two parameters of a random graph namely its density the number of edges in the graph and its robustness to link failures here robustness means multiple connectivity by short disjoint paths a triple g s t where g is a graph and s t are designated vertices is called l robust if s and t are connected via at least two edge disjoint paths of length at most l we determine the expected number of ways to get from s to t via two edge disjoint paths of length l in the classical random graph model gn p by means of symbolic combinatorial methods we then derive bounds on related threshold probabilities as functions of l and n

synchronization in lattices of coupled oscillators with various boundary conditions where index i is the ordered pair given by i i1 i2 for 1 i1 i2 n i i are constants with i i 0 x y are two vectors in rn2 with components xi and yi respectively fi is a c2 function with fi 0 0 0 gi t is a periodic function of t c1 c2 denote the coupling coe7cients l is a diagonalizable operator on rn2 with max i 0 0 for all i l the spectrum of l lx i and ly i denote the ith components of lx and ly respectively if c1 c2 0 then system 1 1 represents the motion of the ith oscillator in an n n uncoupled squared lattice the individual dynamics for the ith node in the lattice is

routes to complete synchronization via phase synchronization in coupled nonidentical chaotic oscillators we study the transition route to complete synchronization through phase synchonization in generic coupled nonidentical chaotic oscillators through numerical studies two routes are found i e one via lag synchronization the other via the intermittent chaotic burst state without lag synchronization we claim that these two routes are universal as evidence we analyze several examples on the basis of the conventional theory of intermittency in the presence of noise

the lorenz fermi pasta ulam experiment we consider a chain of lorenz 63 systems connected through a local nearest neighbour coupling we refer to the resulting system as the lorenz fermi pasta ulamlattice because of its similarity to the celebrated experiment conducted by fermi pasta and ulam at large coupling strengths the systems synchronize to a global chaotic orbit of the lorenz attractor for smaller coupling the synchronized state loses stability instead steady spatially structured equilibrium states are observed these steady states are related to the heteroclinic orbits of the system describing stationary solutions to the partial differential equation that emerges on taking the continuum limit of the lattice notably these orbits connect saddle foci suggesting the existence of a multitude of such equilibria in relatively wide systems on lowering the coupling strength yet further the steady states lose stability in what appear to be always subcritical hopf bifurcations this can lead to a variety of time dependent states with fixed time averaged spatial structure such solutions can be limit cycles tori or possibly chaotic attractors cluster states can also occur though with less regularity consisting of lattices in which the elements are partitioned into families of synchronized subsystems ultimately for very weak coupling the lattice loses its time averaged spatial structure at this stage the properties of the lattice are probably chaotic and approximately scale with the lattice size suggesting that the system is essentially an ensemble of elements that evolve largely independent of one another the weak interaction however is sufficient to induce widespread coherent phases these are ephemeral states in which the dynamics of one or more subsystems takes a more regular form we present measures of the complexity of these incoherent lattices and discuss the concept of a dynamical horizon that is the distance along the lattice that one subsystem can effectively influence another and error propagation how the introduction of a disturbance in one subsystem becomes spread throughout the lattice 2000 elsevier science b v all rights reserved

an asymptotic theory for recurrence relations based on minimization and maximization we derive asymptotic approximations for the sequence f n defined recursively by f n min1 j

mean phase coherence as a measure for phase synchronization and its application to the eeg of epilepsy patients abstract we apply the concept of phase synchronization of chaotic and or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms eegs recorded from patients with temporal lobe epilepsy using the mean phase coherence as a statistical measure for phase synchronization we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity in particular we observe distinct differences in the degree of synchronization between recordings from seizure free intervals and those before an impending seizure indicating an altered state of brain dynamics prior to seizure activity

synchronized chaos and other coherent states for two coupled neurons abstract the parametrized time discrete dynamics of two recurrently coupled chaotic neurons is investigated basic dynamical features of this system are demonstrated for symmetric couplings of identical neurons periodic as well as chaotic orbits constrained to a manifold m of synchronized states are observed parameter domains for locally stable synchronization manifolds m are determined by numerical simulations in addition to the synchronized dynamics there often co exist periodic quasiperiodic and even chaotic attractors representing different kinds of non synchronous coherent dynamics simulation results for selected sets of parameters are presented and synchronization conditions for systems with non identical neurons are derived also these more general systems inherit the above mentioned dynamical properties

minimal spanning forests minimal spanning forests on infinite graphs are weak limits of minimal spanning trees from finite subgraphs these limits can be taken with free or wired boundary conditions and are denoted fmsf free minimal spanning forest and wmsf wired minimal spanning forest respectively the wmsf is also the union of the trees that arise from invasion percolation started at all vertices we show that on any cayley graph where critical percolation has no infinite clusters all the component trees in the wmsf have one end a s in z d this was proved by alexander ann probab 23 1995 87 104 but a different method is needed for the nonamenable case we also prove that the wmsf components are thin in a different sense namely on any graph each component tree in the wmsf has p c 1 a s where p c denotes the critical probability for having an infinite cluster in bernoulli percolation on the other hand the fmsf is shown to be thick on any connected graph the union of the fmsf and independent bernoulli percolation with arbitrarily small parameter is a s connected in conjunction with a recent result of gaboriau this implies that in any cayley graph the expected degree of the fmsf is at least the expected degree of the fsf the weak limit of uniform spanning trees we also show that the number of infinite clusters for bernoulli p u percolation is at most the number of components of the fmsf where p u denotes the critical probability for having a unique infinite cluster finally an example is given to show that the minimal spanning tree measure does not have negative associations

on computing the coefficients of bivariate holonomic formal series in this work we study the problem of computing the coefficients of holonomic formal series in two commuting variables given a formal series x y n k 0 cnkxnyk specified by a holonomic system j 0d1 pj x y xj 0 and j 0d2qj x y yj 0 with a suitable finite set of intial conditions xayb x y we show that the coefficient xiyj x y can be computed in time o i j under the uniform cost criterion

object grammars and bijections a new systematic approach for the specification of bijections between sets of combinatorial objects is presented it is based on the notion of object grammars object grammars give recursive descriptions of objects and generalize context free grammars the study of a particular substitution in these object grammars confirms once more the key role of dyck words in the domain of enumerative and bijective combinatorics

generic behavior of master stability functions in coupled nonlinear dynamical systems master stability functions msfs are fundamental to the study of synchronization in complex dynamical systems for example for a coupled oscillator network a necessary condition for synchronization to occur is that the msf at the corresponding normalized coupling parameters be negative to understand the typical behaviors of the msf for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators we address this issue by examining systematically msfs for known chaotic oscillators our computations and analysis indicate that it is generic for msfs being negative in a finite interval of a normalized coupling parameter a general scheme is proposed to classify the typical behaviors of msfs into four categories these results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators

synchronicity in coupled sine circle maps some numerical results abstract we study the spatially synchronised and temporally periodic orbits of a 1 d lattice of coupled sine circle maps a numerical study of the synchronised solutions reveals synchronisation over large regions of parameter space the entire devil s staircase of periodic orbits as seen for the single circle map is observed for the synchronised coupled sine circle map lattice the parameter regions for which the synchronised solution is obtained are investigated for different types of initial conditions these reveal interesting structures in the parameter space and appear to be symmetric about 0 5

uniform random generation of words of rational languages the problem of generating uniformly at random words of a given language has been the subject of extensive study in the last few years an important part of that work is devoted to the generation of words of context free languages see e g 6 8 9 12 for a given integer n 0 the words of length n 0 of any unambiguous context free language can be generated uniformly at random by using algorithms derived from the general method which was introduced by wilf 14 15 and systematized by flajolet et al 7 clearly this can be applied to the set of rational languages which constitute an important special case of context free languages most authors use the uniform measure of complexity see 1 in order to compute the complexity of the algorithms of generation this measure is based on the following hypotheses any simple arithmetic operation addition multiplication has time cost 0 1 and a constant amount of memory space is taken by any number thus we know that words of any rational language can be generated by using an algorithm which with respect to the uniform measure of complexity runs in linear time in terms of the length of the words and constant space 9 this measure is realistic only if there is a reasonable bound on the numbers involved in the operations however the classical random generation algorithms involve operations on numbers which grow exponentially in terms of the length of the words to be generated moreover the programs which make use of these algorithms are generally used to generate very large words for example for the purpose of studying the asymptotic behavior of some parameters therefore the uniform measure does not reflect the real behavior of such programs it turns out that the logarithmic measure of complexity is much more realistic one assumes that the space taken by a number k is o log k and that any simple arithmetic operation can be done in time o log k it is with respect to this measure that we will evaluate the performance of algorithms in this paper our goal is to design efficient algorithms in terms of logarithmic complexity to generate uniformly at random words from certain classes of rational languages we consider rational languages defined by their minimal finite deterministic automata when computing complexity neither the size of the automaton nor the cardinality of the alphabet are taken in account in section 2 we present some background on rational languages and their generating series we describe briefly the classical method for generating words of such languages and we study its logarithmic complexity we show that it is at best quadratic for most languages this is due mainly to computations on numbers which grow exponentially with the length of the words to be generated in order to improve significantly the efficiency of the algorithms we must avoid handling of large numbers or at least decrease substantially the frequency of computations on such numbers another alternative briefly discussed in 7 and 12 is to compute with floating point numbers instead of integers in this case the logarithmic complexity is time linear however using floating point numbers leads inevitably to approximations which prevent the exact uniformity of the generation in sections 3 and 4 we show that in some cases we can avoid computations on large numbers entirely or almost entirely while keeping the exact uniformity of the generation we determine two classes of rational languages for which this is the case section 3 concerns languages whose associated generating series have a unique singularity we present a simple version of the classical algorithm which totally avoids handling of large numbers the logarithmic complexity of the method is o n log n in time and o log n in memory space section 4 focuses on languages whose associated generating series have the following property there exists a unique singularity of minimum modulus and this singularity is simple for such languages we give a probabilistic version of the classical algorithm which generates words randomly while avoiding most computations on large numbers this method needs a preprocessing stage which can be done in polynomial time and linear space in terms of the length n of the words following preprocessing any word of length n can be generated in average linear time and space

chaotic synchronization in lattice of partial state coupled lorenz equations abstract in this paper we study chaotic synchronization in lattices of coupled lorenz equations with neumann or periodic boundary condition three different coupling configurations in the single x i y i or z i component are considered synchronization is affected by coupling rules we prove that synchronization occurs for either x i or y i component coupling provided the coupling coefficient is sufficiently large moreover we determine the dependence of coupling coefficients on the lattice size for the case of the z i component coupling we demonstrate by numerical experience that the synchronization cannot occur

deco polyominoes permutations and random generation abstract in this paper we introduce a class of polyominoes called deco polyominoes in bijection with the set of permutations of the first k integers we evaluate some typical parameters for this class of polyominoes and define a linear algorithm for randomly generating them moreover we define the polyominoes corresponding to the directed animals on the hexagonal and triangular lattices and examine these polyominoes deco class as far as deco polyominoes corresponding to animals on the hexagonal lattice are concerned we find a bijection with a class of permutations finally we give linear algorithms for randomly generating both hexagonal and triangular deco polyominoes

colored noise induced chaotic array synchronization the effect of a time correlated gaussian noise on one dimensional arrays consisting of diffusively coupled chaotic cells is analyzed a resonance effect between the time scale of the chaotic attractor and the colored gaussian noise has been found as well depending on the number of cells coupling and noise strength an improvement of the synchronization or a poor synchronization between cells within the array can occur for some values of the time correlation these nonlinear cooperative effects are studied in terms of a linear stability analysis around the uniform synchronized behavior

controlled non uniform random generation of decomposable structures consider a class of decomposable combinatorial structures using different types of atoms z z 1 z z we address the random generation of such structures with respect to a size n and a targeted distribution in k of its distinguished atoms we consider two variations on this problem in the first alternative the targeted distribution is given by k real numbers m 1 m k such that 0 0 is the number of undistinguished atoms the structures must be generated uniformly among the set of structures of size n that contain exactlyn i atoms z i email protected email protected k we give a o r email protected i 1 kn i 2 mnklogn algorithm for generating m structures which simplifies into a o email protected i 1 kn i mn for regular specifications

percolation like scaling exponents for minimal paths and trees in the stochastic mean field model author s aldous dj abstract in the mean field or random link model there are n points and inter point distances are independent random variables for 0 l l l and in the n limit let l 1 n times the maximum number of steps in a path whose average step length is l the function l is analogous to the percolation function in percolation theory there is a critical value l e 1 at which becomes non zero and presumably a scaling exponent in the sense l equivalent to sign l l recently developed probabilistic methodology in some sense a rephrasing of the cavity method developed in the 1980s by mezard and parisi provides a simple albeit non rigorous way of writing down such functions in terms of solutions of fixed point equations for probability distributions solving numerically gives convincing evidence that 3 a parallel study with trees and connected edge sets in place of paths gives scaling exponent 2 while the analogue for classical percolation has scaling exponent 1 the new exponents coincide with those recently found in a different context comparing optimal and near optimal solutions of the mean field travelling salesman problem tsp and the minimum spanning tree mst problem and reinforce the suggestion that scaling exponents determine universality classes for optimization problems on random points 2005 the royal society

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

an analytical calculation of neighbourhood order probabilities for high dimensional poissonian processes and mean field models consider that the coordinates of n points are randomly generated along the edges of a d dimensional hypercube random point problem the probability p d n m n that an arbitrary point is the mth nearest neighbour to its own nth nearest neighbour cox probabilities plays an important role in spatial statistics also it has been useful in the description of physical processes in disordered media here we propose a simpler derivation of cox probabilities where we stress the role played by the system dimensionality d in the limit d the distances between pair of points become independent random link model and closed analytical forms for the neighbourhood probabilities are obtained both for the thermodynamic limit and finite size system breaking the distance symmetry constraint drives us to the random map model for which the cox probabilities are obtained for two cases whether a point is its own nearest neighbour or not

animals and skew trees resume les animaux diriges sont mis en bijection avec une famille d arbres asymetriques les arbres guingois cette bijection conduit a un codage simple des animaux et permet leur enumeration elle correspond aussi a une representation des animaux comme empilements de dominos

chemins de schroder et hierarchies aleatoires abstract un chemin de schroder est un chemin positif du plan z 2 commencant et terminant sur l axe des abscisses en effectuant des pas nord est sud est ou deux pas est consecutifs nous donnons dans cet article un algorithme de complexite moyenne o n en espace et en temps qui engendre de facon aleatoire et uniforme un chemin de schroder de longueur 2n si l on considere uniquement les chemins de schroder n ayant aucun pas horizontal sur l axe des abscisses on obtient un ensemble de chemins enumeres par les petits nombre de schroder nous donnons une bijection entre ces chemins et des arbres ordonnes enracines appeles arbres de schroder ou hierarchies ordonnees dont les noeuds internes ont au moins deux fils nous deduisons de cette bijection un algorithme lineaire de generation aleatoire et uniforme de hierarchies ordonnees selon le nombre de feuilles

synchronization analysis of linearly coupled systems described by differential equations with a coupling delay when a transmission delay occurs in the interconnection of linearly coupled systems described by ordinary differential equations lcodes both synchronization and the final synchronized state will vary in this paper mathematical analysis is presented on the synchronization phenomena of lcodes with a single coupling delay criteria are derived for both local and global synchronization it is known that in addition to the dynamical behaviors of the underlying uncoupled system and the coupling configuration the coupling strength and the coupling delay also play key roles on the stability of synchronization both theoretical and numerical analysis indicate that under some conditions if the coupling strength is large enough the coupled system can be completely synchronized for any coupling delay on the other hand in some cases the coupled system can be synchronized if the coupling delay is small enough

brief paper oscillation analysis of linearly coupled piecewise affine systems application to spatio temporal neuron dynamics this paper discusses oscillation analysis of a large number of linearly coupled piecewise affine pwa systems motivated by various kinds of reaction diffusion systems including cell signaling dynamics and neural dynamics we derive a sufficient condition under which the system shows an oscillatory behavior called y oscillation it is known that the analysis of pwa systems is difficult due to their switching nature an important feature of the result obtained is that under the assumption that every subsystem has a specific property in common the criteria can be rewritten in terms of coupling topology in an easily checkable way so it is applicable to large scale systems the results obtained are applied to theoretical investigation of the cardiac action potential generation propagation represented by spatio temporal fitzhugh nagumo equations

generating random binary trees a survey this paper surveys algorithms for generating unbiased random binary trees there exist several linear time algorithms the best algorithms use only integers of size o n to generate binary trees on n nodes

solution of a divide and conquer maximin recurrence the solution of the divide and conquer recurrence m n mathop max limits 1 leqq k n m k m n k min f k f n k is found for a variety of functions f asymptotic bounds on m n are found for arbitrary nondecreasing f and the exact form of m n is determined for f nondecreasing and weakly concave as a corollary to the asymptotic bounds it is shown that m n remains linear even when f is almost linear among the exact forms determined for f x lfloor lg x rfloor the solution is m n m 1 1 n lfloor lg n rfloor nu n where nu n is the number of 1 bits in the binary representation of n for f x lfloor lg x rfloor the solution is m n m 1 1 n lceil lg n rceil 1 while for f x lceil lg x 1 rceil thesolution is m n m 1 2 n lfloor lg n rfloor nu n 1

boltzmann samplers for v balanced cycles this paper is devoted to the random generation of a new operator which we call v balanced colored cycle a cycle of which the components are assigned different colors with frequencies restricted by a vector v we propose an efficient approximate size sampler of linear expected time complexity following the boltzmann model introduced by duchon et al 2004 9 one of our motivations is to show that the absence of a decomposable specification which form the basis of the boltzmann model can be circumvented by mixing boltzmann samplers with other methods of random generation

scaling and universality in continuous length combinatorial optimization we consider combinatorial optimization problems defined over random ensembles and study how solution cost increases when the optimal solution undergoes a small perturbation delta for the minimum spanning tree the increase in cost scales as delta2 for the minimum matching and traveling salesman problems in dimension d 2 the increase scales as delta3 this is observed in monte carlo simulations in d 2 3 4 and in theoretical analysis of a mean field model we speculate that the scaling exponent could serve to classify combinatorial optimization problems of this general kind into a small number of distinct categories similar to universality classes in statistical physics

une theorie combinatoire des series formelles abstract this paper presents a combinatorial theory of formal power series the combinatorial interpretation of formal power series is based on the concept of species of structures a categorical approach is used to formulate it a new proof of cayley s formula for the number of labelled trees is given as well as a new combinatorial proof due to g labelle of lagrange s inversion formula polya s enumeration theory of isomorphism classes of structures is entirely renewed recursive methods for computing cycle index polynomials are described a combinatorial version of the implicit function theorem is stated and proved the paper ends with general considerations on the use of coalgebras in combinatorics

a new dichotomic algorithm for the uniform random generation of words in regular languages we present a new algorithm for generating uniformly at random words of any regular language l when using floating point arithmetics its bit complexity is o qlg 2n in space and o qnlg 2n in time where n stands for the length of the word and q stands for the number of states of a finite deterministic automaton of l we implemented the algorithm and compared its behavior to the state of the art algorithms on a set of large automata from the vlts benchmark suite both theoretical and experimental results show that our algorithm offers an excellent compromise in terms of space and time requirements compared to the known best alternatives in particular it is the only method that can generate long paths in large automata

efficient random sampling of binary and unary binary trees via holonomic equations abstract we present a new uniform random sampler for binary trees with n internal nodes consuming 2 n log n 2 random bits on average this makes it quasi optimal and out performs the classical remy algorithm we also present a sampler for unary binary trees with n nodes taking n random bits on average both are the first linear time algorithms to be optimal up to a constant

invariant manifolds and collective coordinates we introduce suitable coordinate systems for interacting many body systems with invariant manifolds these are cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold in this sense these coordinates are collective we make a connection to zickendraht s collective coordinates and present certain configurations of few body systems where rotations and vibrations decouple from single particle motion these configurations do not depend on details of the interaction

the relevant prefixes of coloured motzkin walks an average case analysis in this paper we study some relevant prefixes of coloured motzkin walks otherwise called coloured motzkin words in these walks the three kinds of step can have a b and c colours respectively in particular when a b c 1 we have the classical motzkin walks while for a c 1 and b 0 we find the well known dyck walks by using the concept of riordan arrays and probability generating functions we find the average length of the relevant prefix in a walk of length n and the corresponding variance in terms of a b and c this result is interesting from a combinatorial point of view and also provides an average case analysis of algorithms related to the problem of ranking and generating uniformly at random the coloured motzkin words

enhanced synchronizability by structural perturbations in this brief report we investigate the collective synchronization of a system of coupled oscillators on a barab asi albert scale free network we propose an approach of structural perturbations aiming at those nodes with maximal betweenness this method can markedly enhance the network synchronizability and is easy to realize the simulation results show that the eigenratio will sharply decrease by one half when only 0 6 of those hub nodes occur under three division processes when the network size n 2000 in addition the present study also provides numerical evidence that the maximal betweenness plays a major role in network synchronization

inertia effects on periodic synchronization in a system of coupled oscillators we study analytically the synchronization phenomena in a set of globally coupled oscillators under external periodic driving with emphasis on the effects of small inertia we examine in detail both the integer and fractional mode locking present in the system with inertia and derive the self consistency equation for the order parameter which reveals variation of the magnitude of the order parameter according to the external periodic driving in particular it is found that the inertia induces discontinuous transitions between the coherent and incoherent states

the random generation of directed animals abstract in this paper we propose an algorithm to randomly generate a directed animal directed animals are well known combinatorial objects and have been widely used for modelling the physical phenomenon of percolation the algorithm consists of three steps and we prove that each of them is performed in linear time finally we report the results of our experiments made by means of appropriate computer programs in order to give empirical evidence that our algorithm really works

automatic average case analysis of algorithms abstract many probabilistic properties of elementary discrete combinatorial structures of interest for the average case analysis of algorithms prove to be decidable this paper presents a general framework in which such decision procedures can be developed it is based on a combination of generating function techniques for counting and complex analysis techniques for asymptotic estimations we expose here the theory of exact analysis in terms of generating functions for four different domains the iterative recursive and unlabelled labelled data type domains we then present some major components of the associated asymptotic theory and exhibit a class of naturally arising functions that can be automatically analyzed a fair fragment of this theory is also incorporated into a system called lambda upsilon omega in this way using computer algebra one can produce automatically non trivial average case analyses of algorithms operating over a variety of decomposable combinatorial structures at a fundamental level this paper is part of a global attempt at understanding why so many elementary combinatorial problems tend to have elementary asymptotic solutions in several cases it proves possible to relate entire classes of elementary combinatorial problems whose structure is well defined with classes of elementary special functions and classes of asymptotic forms relative to counting probabilities or average case complexity

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

efficient iteration in admissible combinatorial classes the exhaustive generation of combinatorial objects has a vast range of practical applications and is a common theme in the combinatorial research field but most previous works in this area concentrate in the efficient generation of particular families of combinatorial objects the novel approach of the work presented here is to provide efficient generic algorithms where the input is not just the size n of the objects to be generated but a finite specification of the combinatorial class whose objects we want to list since the algorithms are generic they do not exploit any particular feature of the class to be generated nevertheless they work in constant amortized time per generated object that is they generate all n objects of a given size in n time these algorithms are useful for both rapid prototyping and for inclusion into general purposes libraries because of their flexibility with only a relatively modest penalty on efficiency furthermore the framework presented in this paper nicely combines with the framework developed by flajolet et al for the enumeration and random generation of combinatorial objects and with the framework developed by the authors for the unranking of combinatorial objects

synchronization in stochastic coupled systems theoretical results the stability of synchronized states including equilibrium point periodic orbit or chaotic attractor in stochastic coupled dynamical systems ordinary differential equations is considered a general approach is presented based on the master stability function gershg orin disc theory and the extreme value theory in statistics to yield constraints on the distribution of coupling to ensure the stability of synchronized dynamics three types of different behaviour global stable exponential stable and power stable are found depending on the nature of the distribution of the interactions between units systems with specific coupling schemes are used as examples to illustrate our general method

pseudo riddling in chaotic systems abstract previous investigations of riddling have focused in the case where the dynamical invariant set in the symmetric invariant subspace of the system is a chaotic attractor a situation expected to arise commonly in dynamical systems however is that the dynamics in the invariant subspace is in a periodic window in such a case there are both a stable periodic attractor and a coexisting non attracting chaotic saddle in the invariant subspace we show that riddling can still occur in a generalized sense in particular we argue that the basin of the periodic attractor in the invariant subspace contains both an open set and a set of measure zero with riddled holes that belong to the basin of another attractor we call such basin pseudo riddled and we argue that pseudo riddling can be more pervasive than riddling of chaotic attractors because it can occur regardless of whether the chaotic saddle in the invariant subspace is transversely stable or unstable we construct an analyzable model derive a scaling law for pseudo riddling and provide numerical support we also show that the chaotic saddle in the invariant subspace can undergo an enlargement into the full phase space when it becomes transversely unstable

spatial recurrence plots we propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time we introduce spatial recurrence plots srps as a graphical representation of the pointwise correlation matrix in terms of a two dimensional spatial return plot this technique is applied to the study of complex patterns generated by coupled map lattices which are characterized by measures of complexity based on srps we show that the complexity measures we propose for srps provide a systematic way of investigating the distribution of spatially coherent structures such as synchronization domains in lattice profiles this approach has potential for many more applications e g in surface roughness analyzes

synchronization and amplitude death in hypernetworks we study dynamical systems on a hypernetwork namely by coupling them through several variables for the case when the coupling s are all linear a comprehensive analysis of the master stability function msf for synchronized dynamics is presented and through application to a number of paradigmatic examples the typical forms of the msf are discussed the msf formalism for hypernetworks also provides a framework to study synchronization in systems that are diffusively coupled through dissimilar variables char22 the so called conjugate coupling that can lead to amplitude or oscillation death

chaotic synchronization by the intermittent feedback method this paper studies the synchronization of chaotic systems by the intermittent feedback method which is efficient a sufficient synchronization criterion for a general intermittent linear state error feedback control is obtained by using a lyapunov function and differential inequalities numerical simulations for the chaotic chua oscillator are presented to illustrate the theoretical results

uniform random generation of strings in a context free language let s be the set of all strings of length n generated by a given context free grammar a uniform random generator is one which produces strings from s with equal probability in generating these strings care must be taken in choosing the disjuncts that form the right hand side of a grammar rule so that the produced string will have the specified length uniform random generators have applications in studying the complexity of parsers in estimating the average efficiency of theorem provers for the propositional calculus in establishing a measure of ambiguity of a grammar etc two methods are presented for generating uniform random strings in an unambiguous context free language the first method will generate a random string of length n in linear time but must use a precomputed table of size o n r 1 where r is the number of nonterminals in the grammar used to specify the language the second method precomputes part of the table and calculates the other entries as they are called for it requi

random generation of q convex sets the problem of randomly generating q convex sets is considered we present two generators the first one uses the q convex hull of a set of random points in order to generate a q convex set included in the square 0 n 2 this generator is very simple but is not uniform and its performance is quadratic in n the second one exploits a coding of the salient points which generalizes the coding of a border of polyominoes it is uniform and is based on the method by rejection experimentally this algorithm works in linear time in the length of the word coding the salient points besides concerning the enumeration problem we determine an asymptotic formula for the number of q convex sets according to the size of the word coding the salient points in a special case and in general only an experimental estimation

simulating size constrained galton watson trees we discuss various methods for generating random galton watson trees conditional on their sizes being equal to n a linear expected time algorithm is proposed

synchronization and symmetry breaking bifurcations in constructive networks of coupled chaotic oscillators the spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest neighbor couplings is studied by using master stability equations and numerical simulations the generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row sum the symmetry breaking oscillation patterns that resulted from the hopf bifurcation from synchronous states are analyzed by the symmetry group theory

factors that predict better synchronizability on complex networks while shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network the suppressing tendency of the heterogeneity of the degree distribution even for shorter characteristic path length has also been reported to see this we investigate the effects of various factors such as the degree characteristic path length heterogeneity and betweenness centrality on synchronization and find a consistent trend between the synchronization and the betweenness centrality the betweenness centrality is thus proposed as a good indicator for synchronizability

loss of synchronization in coupled rossler systems this paper considers the loss of synchronization for a system of two coupled rossler oscillators bifurcation curves for the transverse destabilization of low periodic orbits embedded in the synchronized chaotic state are obtained and we show that desynchronization for a pair of symmetrically coupled identical rossler systems is associated with different orbits undergoing transverse pitchfork or period doubling bifurcations the transverse destabilization of the period 1 orbit is examined in detail and we follow the sequence of bifurcations that the asynchronous periodic cycles undergo in the presence of an asymmetry in the coupling the transverse period doubling bifurcation remains essentially the same the transverse pitchfork bifurcation on the other hand is transformed into a transcritical riddling bifurcation if the interacting rossler oscillators have different parameter values the non generic character of the pitchfork bifurcation leads it to be replaced by a saddle node bifurcation occurring off the symmetric sub space finally we show how the transverse stability properties of the equilibrium point can be used to obtain approximative analytical results for the transverse stability of the coupled chaotic oscillators 2001 elsevier science b v all rights reserved

stability analysis of dynamical regimes in nonlinear systems with discrete symmetries we present a theorem that allows one to simplify the linear stability analysis of periodic and quasiperiodic nonlinear regimes in n particle mechanical systems with different kinds of discrete symmetry this theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than the dimension of the full system as an example of such a simplification we discuss the stability of bushes of modes invariant manifolds for the fermi pasta ulam chains and prove another theorem about the maximal dimension of the above mentioned subsystems

global mu synchronization of linearly coupled unbounded time varying delayed neural networks with unbounded delayed coupling in this brief we study the global synchronization of linearly coupled neural networks with delayed couplings where the intrinsic systems are recurrently connected neural networks with unbounded time varying delays and the couplings include instant couplings and unbounded delayed couplings the concept of mu synchronization is introduced some sufficient conditions are derived for the global mu synchronization for the underlined coupled systems

dynamics and synchronization of numerical solutions of the burgers equation for chebyshev spectral solutions of the forced burgers equation with low values of the viscosity coefficient several bifurcations and stable attractors can be observed periodic orbits quasiperiodic and strange ones may arise bistability can also be observed necessary conditions for these attractors to appear are discussed and justification for the non emerging of bistability for an example of a system symmetry break is presented as an application for the dynamical behavior of spectral solutions of burgers equation the dynamics and synchronization of unidirectionally coupling of chebyshev spectral solutions of burgers equations by means of a linear coupling are described and discussed also a nonlinear coupling is proposed and discussed

boundedness and synchronization of y coupled lorenz systems with or without controllers abstract the purpose of this paper is to investigate the boundedness and synchronization of y coupled lorenz systems when the coupling term is only added to the second variable we call them y coupled lorenz systems in this paper we first prove the boundedness of y coupled lorenz systems which ensures the existence and uniqueness of the solution when t based on the boundedness we prove that for y coupled lorenz systems quad condition is satisfied it should be pointed out that quad condition plays an essential role in the discussion of synchronization based on the boundedness and quad condition we prove that if the coupling is strong enough the y coupled lorenz systems can achieve the complete synchronization globally and exponentially

forbidden subgraphs in connected graphs given a set h1 h2 of connected non acyclic graphs a free graph is one which does not contain any member of as copy define the excess of a graph as the difference between its number of edges and its number of vertices let wk be the exponential generating function egf for brief of connected free graphs of excess equal to k k 1 for each fixed a fundamental differential recurrence satisfied by the egfs wk is derived we give methods on how to solve this nonlinear recurrence for the first few values of k by means of graph surgery we also show that for any finite collection of non acyclic graphs the egfs wk are always rational functions of the generating function t of cayley s rooted non planar labelled trees from this we prove that almost all connected graphs with n nodes and n k edges are free whenever k o n1 3 and by means of wright s inequalities and saddle point method limiting distributions are derived for sparse connected free components that are present when a random graph on n nodes has approximately n 2 edges in particular the probability distribution that it consists of trees unicyclic components q 1 cyclic components all free is derived similar results are also obtained for multigraphs which are graphs where self loops and multiple edges are allowed

asymptotic synchronization in n dimensional second order dissipative lattices of coupled oscillators abstract by introducing a new norm which is equivalent to the usual norm in the phase space we prove that for n dimensional second order dissipative lattices of coupled oscillators with external periodic forces under dirichlet neumann and periodic boundary conditions if the system is bounded dissipative and the coupled coefficients are both large enough the asymptotic synchronization will occur and we give a concrete bounded dissipative second order lattices system our results show that the bounds of the difference between the components of any solution are directly proportional to m n 2 and inversely proportional to the coupled coefficients where m is the mesh size and n is the space dimension of lattice points

a proof of parisi s conjecture on the random assignment problem an assignment problem is the optimization problem of finding in an m by n matrix of nonnegative real numbers k entries no two in the same row or column such that their sum is minimal such an optimization problem is called a random assignment problem if the matrix entries are random variables we give a formula for the expected value of the optimal k assignment in a matrix where some of the entries are zero and all other entries are independent exponentially distributed random variables with mean 1 thereby we prove the formula 1 1 4 1 9 1 k2 conjectured by g parisi for the case k m n and the generalized conjecture of d coppersmith and g b sorkin for arbitrary k m and n

a calculus for the random generation of labelled combinatorial structures a systematic approach to the random generation of labelled combinatorial objects is presented it applies to structures that are decomposable i e formally specifiable by grammars involving set sequence and cycle constructions a general strategy is developed for solving the random generation problem with two closely related types of methods for structures of size n the boustrophedonic algorithms exhibit a worst case behaviour of the form o n log n the sequential algorithms have worst case o n2 while offering good potential for optimizations in the average case the complexity model is in terms of arithmetic operations and both methods appeal to precomputed numerical table of linear size that can be computed in time o n2 a companion calculus permits systematically to compute the average case cost of the sequential generation algorithm associated to a given specification using optimizations dictated by the cost calculus several random generation algorithms of the sequential type are developed most of them have expected complexity 1 2n log n and are thus only slightly superlinear the approach is exemplified by the random generation of a number of classical combinatorial structures including cayley trees hierarchies the cycle decomposition of permutations binary trees functional graphs surjections and set partitions

synchronization in lattices of coupled oscillators abstract we consider coupled nonlinear oscillators with external periodic forces and the dirichlet boundary conditions we prove that synchronization occurs provided that the coupling is dissipative and the coupling coefficients are sufficiently large the synchronization here is of an obvious type the size of an attractor is comparable to the difference of the subsystems

the mean field traveling salesman and related problems the edges of a complete graph on n vertices are assigned i i d random costs from a distribution for which the interval 0 t has probability asymptotic to t as t 0 through positive values in this so called pseudo dimension 1 mean field model we study several optimization problems of which the traveling salesman is the best known we prove that as n the cost of the minimum traveling salesman tour converges in probability to a certain number approximately 2 0415 which is characterized analytically

discriminating differing types of synchrony in neural systems abstract we apply our previously established measure m ochowski and r dzakpasu condtional entropies phase synchronization and changes in the directionality of information flow in neural systems j phys a 37 2004 3823 to a pair of coupled non identical hindmarsh rose models of thalamo cortical neurons and demonstrate that the measure is able to detect causal interdependencies between the activity of the neurons which may remain undetected when using other methods the discrimination between the states when these interdependencies are pronounced or abolished may be important as they may underlie different physiological states we show the robustness of the discrimination of the measure in the presence of noise

a framework for generating some discrete sets with disjoint components by using uniform distributions discrete tomography deals with the reconstruction of discrete sets from few projections assuming that the set to be reconstructed belongs to a certain class of discrete sets with some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem the average performance of reconstruction algorithms are often tested on such classes by choosing elements of a given class from uniform random distributions this paper presents a general framework for generating discrete sets with disjoint connected components using uniform distributions especially the uniform random generation of hv convex discrete sets and q convex discrete sets according to the size of the minimal bounding rectangle are discussed

from object grammars to eco systems in this paper we make a comparison between two methods for the enumeration of combinatorial objects namely the eco method and object grammars both based on a recursive description for the examined class of objects in particular we study the problem of passing from an object grammar to an equivalent eco system first we solve this problem for any unidimensional unambiguous and complete object grammar with any linear parameter then we treat the more complex cases of q linear parameters and of multidimensional object grammars giving some explanatory examples in particular we determine a new eco system for the class of directed convex polyominoes

random generation of trees and other combinatorial objects abstract in this paper we present a general method for the random generation of some classes of combinatorial objects our basic idea is to translate eco method enumerating combinatorial objects from a method for the enumeration of combinatorial objects into a random generation method the algorithms we illustrate are based on the concepts of succession rule and generating tree the former is a law that predicts the combinatorial object class growth according to a given parameter the generating tree related to a given succession rule is a particular labelled plane tree that represents the rule in an extensive way each node of a generating tree can also be seen as a particular combinatorial object and so a random path in the generating tree coincides with the random generation of that combinatorial object the generation is uniform if we take the probability of each branch to be selected into account when the path is generated we also give the formulae evaluating complexity finally we take the class of m ary trees into consideration in order to illustrate our general method in this case the average time complexity of the generating algorithm can be estimated as o mn

cost volume relationship for flows through a disordered network in a network where the cost of flow across an edge is nonlinear in the volume of flow and where sources and destinations are uniform one can consider the relationship between total volume of flow through the network and the minimum cost of any flow with given volume under a simple probability model locally tree like directed network independent cost volume functions for different edges we show how to compute the minimum cost in the infinite size limit the argument uses a probabilistic reformulation of the cavity method from statistical physics and is not rigorous as presented here the methodology seems potentially useful for many problems concerning flows on this class of random networks making arguments rigorous is a challenging open problem

a parallel algorithm for the generation of a permutation and applications abstract a parallel algorithm is presented for generating a permutation of size n the algorithm uses o n processors and runs in o log 2 n time we show also that this algorithm permits the generation of a dyck word the same techniques work for motzkin words left factors of dyck or motzkin words and words which are in bijection with trees split into patterns as defined by dershowitz and zaks 1989 see alonso 1992

uniform generation of a motzkin word abstract we present a simple and efficient algorithm which builds randomly and uniformly a motzkin word of size n the average complexity of this algorithm is o n the basic idea is to choose a slightly enlarged probability space where uniformity can be achieved and then to filter out the desired words without destorying uniformity

uniform random generation of decomposable structures using floating point arithmetic the em recursive method formalized by nijenhuis and wilf cite niwi78 and systematized by flajolet van cutsem and zimmermann cite flziva94 is extended here to floating point arithmetic the resulting adz method enables one to generate decomposable data structures both labelled or unlabelled uniformly at random in expected o n 1 epsilon time and space after a preprocessing phase of o n 2 epsilon time which reduces to o n 1 epsilon for context free grammars

cross correlation of instantaneous phase increments in pressure flow fluctuations applications to cerebral autoregulation we investigate the relationship between the blood flow velocities bfv in the middle cerebral arteries and beat to beat blood pressure bp recorded from a finger in healthy and post stroke subjects during the quasisteady state after perturbation for four different physiologic conditions supine rest head up tilt hyperventilation and co2 rebreathing in upright position to evaluate whether instantaneous bp changes in the steady state are coupled with instantaneous changes in the bfv we compare dynamical patterns in the instantaneous phases of these signals obtained from the hilbert transform as a function of time we find that in post stroke subjects the instantaneous phase increments of bp and bfv exhibit well pronounced patterns that remain stable in time for all four physiologic conditions while in healthy subjects these patterns are different less pronounced and more variable we propose an approach based on the cross correlation of the instantaneous phase increments to quantify the coupling between bp and bfv signals we find that the maximum correlation strength is different for the two groups and for the different conditions for healthy subjects the amplitude of the cross correlation between the instantaneous phase increments of bp and bfv is small and attenuates within 3 5 heartbeats in contrast for post stroke subjects this amplitude is significantly larger and cross correlations persist up to 20 heartbeats further we show that the instantaneous phase increments of bp and bfv are cross correlated even within a single heartbeat cycle we compare the results of our approach with three complementary methods direct bp bfv cross correlation transfer function analysis and phase synchronization analysis our findings provide insight into the mechanism of cerebral vascular control in healthy subjects suggesting that this control mechanism may involve rapid adjustments within a heartbeat of the cerebral vessels so that bfv remains steady in response to changes in peripheral bp

enumerative encoding of correlation immune boolean functions le bars and viola have recently proposed an innovative recursive decomposition of the first order correlation immune boolean functions based on their work this paper presents the design of an enumerative encoding of these boolean functions this is the first enumerative encoding of a class of boolean functions defined by a cryptographic property in this paper we study three major milestones to do this encoding the conceptual computational tree the use of normal classes and signed permutations and a dynamic selection of the decomposition our enumerative encoding algorithm is practicable up to 8 variables which is the best result we may expect due to the combinatorial explosion of the numbers of classes

enumeration and random generation of accessible automata we present a bijection between the set a n of deterministic and accessible automata with n states on a k letters alphabet and some diagrams which can themselves be represented as partitions of a set of kn 1 elements into n non empty subsets this combinatorial construction shows that the asymptotic order of the cardinality of a n is related to the stirling number knn our bijective approach also yields an efficient random sampler for the uniform distribution of automata with n states its complexity is o n 3 2 using the framework of boltzmann samplers

synchronization analysis of linearly coupled networks of discrete time systems abstract in this paper we present a framework for analysis of synchronization of linearly coupled map lattices lcmls the dynamics at each node of the coupled map lattices is described by a general difference equation which can be of chaotic or others as for coupling configuration of the linearly coupled map lattices it is not assumed that the coupling matrix is symmetric and irreducible criteria are obtained for both local and global synchronization these criteria reveal that two factors influence synchronization dynamical behaviors at each node and coupling configuration by these criteria one can verify whether the lcml is synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration a scale d is presented to measure the synchronization capability of a linearly coupled map lattice as we show d can be regarded as a function of the smallest and the largest eigenvalues of the coupling matrix various kinds of coupling schemes including complex networks such as small world sw lattice and scale free network are studied the quantity d is carefully analyzed and calculated for each case

asynchronous states in networks of pulse coupled oscillators we use a mean field approach to analyze the stability of the asynchronous state in a population of all to all pulse coupled nonlinear oscillators we determine the conditions that must be satisfied by the time constants and phase dependence characterizing the coupling between the oscillators in order for the asynchronous state to be stable we also consider the effects of noise this work complements results on synchronous states in similar models and allows us to study the validity of firing rate models commonly used for neural networks

sampling different kinds of acyclic automata using markov chains we propose algorithms that use markov chain techniques to generate acyclic automata uniformly at random we first consider deterministic accessible and acyclic automata then focus on the class of minimal acyclic automata in each case we explain how to define random local transformations that describe an ergodic and symmetric markov chain the distribution of the automaton obtained after t random steps in this markov chain tends to the uniform distribution as t tends to infinity

basic analytic combinatorics of directed lattice paths this paper develops a unified enumerative and asymptotic theory of directed two dimensional lattice paths in half planes and quarter planes the lattice paths are specified by a finite set of rules that are both time and space homogeneous and have a privileged direction of increase they are then essentially one dimensional objects the theory relies on a specific kernel method that provides an important decomposition of the algebraic generating functions involved as well as on a generic study of singularities of an associated algebraic curve consequences are precise computable estimates for the number of lattice paths of a given length under various constraints bridges excursions meanders as well as a characterization of the limit laws associated to several basic parameters of paths

unstable dimension variability in coupled chaotic systems systems of coupled chaotic maps and flows arise in many situations of physical and biological interest the aim of this paper is to analyze and to present numerical evidence for a common type of nonhyperbolic behavior in these systems unstable dimension variability we show that unstable periodic orbits embedded in the dynamical invariant set of such a system can typically have different numbers of unstable directions the consequence of this may be severe the system cannot be modeled deterministically in the sense that no trajectory of the model can be realized by the natural chaotic system that the model is supposed to describe and quantify we argue that unstable dimension variability can arise for small values of the coupling parameter severe modeling difficulties nonetheless occur only for reasonable coupling when the unstable dimension variability is appreciable we speculate about the possible physical consequences in this case

interaction of chaotic rotating waves in coupled rings of chaotic cells abstract the interaction of two chaotic rotating waves of the type recently reported by matias et al europhys lett 37 1997 379 is studied experimentally with arrays of non linear electronic circuits arranged in ring geometries unidirectional coupling is assumed for the cell to cell coupling within the same ring but between rings cells are coupled diffusively depending on the relative sense of driving competition between a rotating chaotic wave and a global synchronized state has been observed the results are rationalized by means of a linear stability analysis around the uniform synchronized behavior where the circulant symmetry of the system allows to express the problem as a superposition of a series of fourier modes