well quasi orders generated by a word shuffle rewriting given a set i of words the set l i e of all words obtained by the shuffle of copies of words of i is naturally provided with a partial order for u v in l i e u i v if and only if v is the shuffle of u and another word of l i e in f d alessandro s varricchio well quasi orders unavoidable sets and derivation systems in word avoidability complexity and morphisms wacam rairo theoretical informatics and applications 40 3 2006 407 426 special issue the authors have opened the problem of the characterization of the finite sets i such that i is a well quasi order on l i e in this paper we give an answer in the case when i consists of a single word w

dynamics of one and two dimensional fronts in a bistable equation with time delayed global feedback propagation failure and control mechanisms we study the evolution of fronts in a bistable equation with time delayed global feedback in the fast reaction and slow diffusion regime this equation generalizes the hodgkin grafstein and allen cahn equations we derive a nonlinear equation governing the motion of fronts which includes a term with delay in the one dimensional case this equation is linear we study the motion of one and two dimensional fronts finding a much richer dynamics than for the previously studied cases without time delayed global feedback we explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a hopf bifurcation as the delay time increases we show that for certain delay times the prevailing phase is different from that corresponding to the system in the absence of global coupling numerical simulations of the partial differential equation are in agreement with the analytical predictions

representing recursively enumerable languages by iterated deletion a characterization of the recursively enumerable languages in terms of the iterated deletion operation is given this solves two open problems posed by ito and silva on the closure properties and decidability of iterated deletion

identification of market trends with string and d2 brane maps abstract the multidimensional string objects are introduced as a new alternative for an application of string models for time series forecasting in trading on financial markets the objects are represented by open string with 2 endpoints and d2 brane which are continuous enhancement of 1 endpoint open string model we show how new object properties can change the statistics of the predictors which makes them the candidates for modeling a wide range of time series systems string angular momentum is proposed as another tool to analyze the stability of currency rates except the historical volatility to show the reliability of our approach with application of string models for time series forecasting we present the results of real demo simulations for four currency exchange pairs

on language equations with invertible operations the paper studies language equations of the type x l r and l y r where l and r are given languages and is an invertible binary word language operation for most of the considered insertion and deletion operations the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular l and r in case l is a context free language and r is a regular one the existence of a solution is generally undecidable the results can be extended to more complex linear equations systems of linear equations as well as for equations of higher degree

insertion and deletion closure of languages abstract to a given language l we associate the sets ins l resp del l consisting of words with the following property their insertion into deletion from any word of l yields words which also belong to l properties of these sets and of languages which are insertion deletion closed are obtained of special interest is the case when the language is ins closed del closed and finitely generated then the minimal set of generators turns out to be a maximal prefix and suffix code which is regular if l is regular in addition we study the insertion base of a language and languages which have the property that both they and their complements are ins closed

strange attractors in coupled reaction diffusion cells abstract a numerical study of two identical reaction cells with diffusion coupling has shown that the structure of motion in the system in principle agrees with results reported for variety of dynamic systems when the characteristic parameter is varied alternating sub intervals of stable periodic p k and stable aperiodic a l solutions appear the sub intervals are connected by intervals where tangent bifurcations and infinite sequences of subharmonic bifurcations occur feigenbaum relation holds for the studied sequence of subharmonic bifurcations aperiodic chaotic states are characterized by a complete set of one dimensional lyapunov exponents by power spectra and by corresponding poincare maps the spectra of lyapunov exponents are of the type 0 and show that the topological dimension of the chaotic attractor is two the power spectra are of two different types a the spectra with sharp peaks located above the broad band noise showing statistical phase coherence of the attractor b the flat spectra showing only broad band noise corresponding to phase incoherent attractor the phase coherence is present close after every point of accumulation phase incoherence arises when the strange attractors contain unstable periodic orbits with different topology the relations of bifurcated stable and unstable periodic solutions computed by means of continuation techniques to the structure of the strange attractor is discussed and poincare maps are used to illustrate the dependence of the structure of the attractors on the value of the characteristic parameter

time delay effects on coupled limit cycle oscillators at hopf bifurcation abstract we present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at hopf bifurcation for a simple model consisting of just two oscillators with a time delayed coupling the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death phase locked and incoherent regions a novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators similar results are obtained for an array of n oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified some general analytic results for the n thermodynamic limit are also obtained and the implications of the time delay effects for physical applications are discussed

scaling and memory in the return intervals of realized volatility abstract we perform return interval analysis of 1 min realized volatility defined by the sum of absolute high frequency intraday returns for the shanghai stock exchange composite index ssec and 22 constituent stocks of ssec the scaling behavior and memory effect of the return intervals between successive realized volatilities above a certain threshold q are carefully investigated in comparison with the volatility defined by the closest tick prices to the minute marks the return interval distribution for the realized volatility shows a better scaling behavior since 20 stocks out of 22 stocks and the ssec pass the kolmogorov smirnov ks test and exhibit scaling behaviors among which the scaling function for 8 stocks could be approximated well by a stretched exponential distribution revealed by the ks goodness of fit test under the significance level of 5 the improved scaling behavior is further confirmed by the relation between the fitted exponent and the threshold q in addition the similarity of the return interval distributions for different stocks is also observed for the realized volatility the investigation of the conditional probability distribution and the detrended fluctuation analysis dfa show that both short term and long term memory exists in the return intervals of realized volatility

multifactor analysis of multiscaling in volatility return intervals we study the volatility time series of 1137 most traded stocks in the u s stock markets for the two year period 2001 2002 and analyze their return intervals which are time intervals between volatilities above a given threshold q we explore the probability density function of pq assuming a stretched exponential function pqe we find that the exponent depends on the threshold in the range between q 1 and 6 standard deviations of the volatility this finding supports the multiscaling nature of the return interval distribution to better understand the multiscaling origin we study how depends on four essential factors capitalization risk number of trades and return we show that depends on the capitalization risk and return but almost does not depend on the number of trades this suggests that relates to the portfolio selection but not on the market activity to further characterize the multiscaling of individual stocks we fit the moments of m s m 1 m in the range of 10 100 by a power law m the exponent is found also to depend on the capitalization risk and return but not on the number of trades and its tendency is opposite to that of moreover we show that decreases with increasing approximately by a linear relation the return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization

synchronization and desynchronization in a network of locally coupled wilson cowan oscillators a network of wilson cowan wc oscillators is constructed and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis the network is a 2d matrix where each oscillator is coupled only to its neighbors we show analytically that a chain of locally coupled oscillators the piecewise linear approximation to the wc oscillator synchronizes and we present a technique to rapidly entrain finite numbers of oscillators the coupling strengths change on a fast time scale based on a hebbian rule a global separator is introduced which receives input from and sends feedback to each oscillator in the matrix the global separator is used to desynchronize different oscillator groups unlike many other models the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding gestalt principles of feature grouping the ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure ground segregation based on oscillatory correlation

phase locked patterns and amplitude death in a ring of delay coupled limit cycle oscillators we study the existence and stability of phase locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical hopf bifurcation the coupling is limited to nearest neighbors and is linear we analyze a model set of discrete dynamical equations using the method of plane waves the resultant dispersion relation which is valid for any arbitrary number of oscillators displays important differences from similar relations obtained from continuum models we discuss the general characteristics of the equilibrium states including their dependencies on various system parameters we next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay time delay is found to expand the range of possible phase locked patterns and to contribute favorably toward their stability the amplitude death state is studied in the parameter space of time delay and coupling strength it is shown that death island regions can exist for any number of oscillators n in the presence of finite time delay a particularly interesting result is that the size of an island is independent of n when n is even but is a decreasing function of n when n is odd

monadic thue systems abstract certain infinite thue systems over a finite alphabet are studied in particular systems s e such that for each a e the set u u a s is a context freelanguage the syntactic structure of sets of ancestors and sets of descendants is considered as well as that of unions of congruence classes taken over infinite context free languages or regular sets the common descendant problem is shown to be tractable while the common ancestor problem is shown to be undecidable even for finite systems the word problem for confluent systems of this type is shown to be tractable the question of whether an infinite system of this type is confluent is shown to be undecidable as is the question of whether the congruence generated by such a system has a confluent presentation

nonlinear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb abstract a mathematical model of the process of pattern recognition in the first olfactory sensory cortex of the rabbit is presented it explains the formation and alteration of spatial patterns in neural activity observed experimentally during classical pavlovian conditioning on each inspiration of the animal a surge of receptor input enters the olfactory bulb eeg activity recorded at the surface of the bulb undergoes a transition from a low amplitude background state of temporal disorder to coherent oscillation there is a distinctive spatial pattern of rms amplitude in this oscillation which changes reliably to a second pattern during each successful recognition by the animal of a conditioned stimulus odor when a new odor is paired as conditioned stimulus these patterns are replaced by new patterns that stabilize as the animal adapts to the new environment i will argue that a unification of the theories of pattern formation and associative memory is required to account for these observations this is achieved in a model of the bulb as a discrete excitable medium with spatially inhomogeneous coupling expressed by a connection matrix the theory of multiple hopf bifurcations is employed to find coupled equations for the amplitudes of competing unstable oscillatory modes these may be created in the system by proper coupling and selectively evoked by specific classes of inputs this allows a view of limit cycle attractors as stored fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory

a top bottom price approach to understanding financial fluctuations abstract the presence of sequences of top and bottom tb events in financial series is investigated for the purpose of characterizing such switching points they clearly mark a change in the trend of rising or falling prices of assets to the opposite tendency are of crucial importance for the players decision and also for the market stability previous attempts to characterize switching points have been based on the behavior of the volatility and on the definition of microtrends the approach used herein is based on the smoothing of the original data with a gaussian kernel the events are identified by the magnitude of the difference of the extreme prices by the time lag between the corresponding events waiting time and by the time interval between events with a minimal magnitude return time results from the analysis of the inter day dow jones industrial average index djia from 1928 to 2011 are discussed q gaussian functions with power law tails are found to provide a very accurate description of a class of measures obtained from the series statistics

scaling properties and universality of first passage time probabilities in financial markets financial markets provide an ideal frame for the study of crossing or first passage time events of non gaussian correlated dynamics mainly because large data sets are available tick by tick data of six futures markets are herein considered resulting in fat tailed first passage time probabilities the scaling of the return with its standard deviation collapses the probabilities of all markets examined and also for different time horizons into single curves suggesting that first passage statistics is market independent at least for high frequency data on the other hand a very closely related quantity the survival probability shows away from the center and tails of the distribution a hyperbolic t ensuremath 1 2 decay typical of a markovian dynamics albeit the existence of memory in markets modifications of the weibull and student distributions are good candidates for the phenomenological description of first passage time properties under certain regimes the scaling strategies shown may be useful for risk control and algorithmic trading

synchronization rates in classes of relaxation oscillators relaxation oscillators arise frequently in physics electronics mathematics and biology their mathematical definitions possess a high degree of flexibility in the sense that through appropriate parameter choices relaxation oscillators can be made to exhibit qualitatively different kinds of oscillations we study numerically four different classes of relaxation oscillators through their synchronization rates in one dimensional chains with a heaviside step function interaction and obtain the following results relaxation oscillators in the sinusoidal and relaxation regime both exhibit an average time to synchrony spl sim n where n is the chain length relaxation oscillators in the singular limit exhibit spl sim n sup p where p is a numerically obtained value less than 0 5 relaxation oscillators in the singular limit with parameters modified so that they resemble spike oscillations exhibit spl sim log n in chains and spl sim log l in two dimensional square networks of length l finally using a sigmoid interaction results in spl sim n sup 2 for relaxation oscillators in the sinusoidal and relaxation regimes indicating that the form of the coupling is a controlling factor in the synchronization rate

multifractals embedded in short time series an unbiased estimation of probability moment an exact estimation of probability moments is the base for several essential concepts such as the multifractals the tsallis entropy and the transfer entropy by means of approximation theory we propose a new method called factorial moment based estimation of probability moments theoretical prediction and computational results show that it can provide us an unbiased estimation of the probability moments of continuous order calculations on probability redistribution model verify that it can extract exactly multifractal behaviors from several hundred recordings its powerfulness in monitoring evolution of scaling behaviors is exemplified by two empirical cases i e the gait time series for fast normal and slow trials of a healthy volunteer and the closing price series for shanghai stock market by using short time series with several hundred lengths a comparison with the well established tools displays significant advantages of its performance over the other methods the factorial moment based estimation can evaluate correctly the scaling behaviors in a scale range about three generations wider than the multifractal detrended fluctuation analysis and the basic estimation the estimation of partition function given by the wavelet transform modulus maxima has unacceptable fluctuations besides the scaling invariance focused in the present paper the proposed factorial moment of continuous order can find its various uses such as finding nonextensive behaviors of a complex system and reconstructing the causality relationship network between elements of a complex system

locally excitatory globally inhibitory oscillator networks a novel class of locally excitatory globally inhibitory oscillator networks legion is proposed and investigated the model of each oscillator corresponds to a standard relaxation oscillator with two time scales in the network an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern while preventing other oscillators from jumping up computer simulations demonstrate that the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks this model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure ground segregation in real time

limit cycle oscillators subject to a delayed feedback the coexistence of two stable limit cycles exhibiting different periods is examined for a nonlinear oscillator subject to a delayed feedback for the case of a weakly nonlinear oscillator we discuss the validity of a previously determined phase equation for the case of a strongly nonlinear oscillator we derive a phase equation and analyze its bifurcation diagram our analysis is motivated by previous experimental studies of chemical oscillators controlled by a delayed feedback

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

sublattice synchronization of chaotic networks with delayed couplings synchronization of chaotic units coupled by their time delayed variables is investigated analytically a type of cooperative behavior is found sublattice synchronization although the units of one sublattice are not directly coupled to each other they completely synchronize without time delay the chaotic trajectories of different sublattices are only weakly correlated but not related by generalized synchronization nevertheless the trajectory of one sublattice is predictable from the complete trajectory of the other one the spectra of lyapunov exponents are calculated analytically in the limit of infinite delay times and phase diagrams are derived for different topologies

synchrony and desynchrony in integrate and fire oscillators due to many experimental reports of synchronous neural activity in the brain there is much interest in understanding synchronization in networks of neural oscillators and its potential for computing perceptual organization contrary to hopfield and herz 1995 we find that networks of locally coupled integrate and fire oscillators can quickly synchronize furthermore we examine the time needed to synchronize such networks we observe that these networks synchronize at times proportional to the logarithm of their size and we give the parameters used to control the rate of synchronization inspired by locally excitatory globally inhibitory oscillator network legion dynamics with relaxation oscillators terman wang 1995 we find that global inhibition can play a similar role of desynchronization in a network of integrate and fire oscillators we illustrate that a legion architecture with integrate and fire oscillators can be similarly used to address image analysis

contextual insertions deletions and computability we investigate two generalizations of insertion and deletion of words that have recently become of interest in the context of molecular computing given a pair of words x y called a context the x y contextual insertion of a wordvinto a worduis performed as follows for each occurrence ofxyas a subword inu we include in the result of the contextual insertion the words obtained by insertingvintou betweenxandy the x y contextual deletion operation is defined in a similar way we study closure properties of the chomsky families under the defined operations contextual ins closed and del closed languages and decidability of existence of solutions to equations involving these operations moreover we prove that every turing machine can be simulated by a system based entirely on contextual insertions and deletions

the level crossing and inverse statistic analysis of german stock market index dax and daily oil price time series a b s t r a c t the level crossing and inverse statistics analysis of dax and oil price time series are given we determine the average frequency of positive slope crossings where t 1 is the average waiting time for observing the level again we estimate the probability p k which provides us the probability of observing k times of the level with positive slope in time scale t for analyzed time series we found that maximum k is about 6 we show that by using the level crossing analysis one can estimate how the dax and oil time series will develop we carry out the same analysis for the increments of dax and oil price log returns which is known as inverse statistics and provide the distribution of waiting times to observe some level for the increments 2011 elsevier b v all rights reserved stochastic processes occur in many natural and man made phenomena ranging from various indicators of economic activities in the stock market velocity fluctuations in turbulent flows and heartbeat dynamics etc 1 the level crossing analysis of stochastic processes has been introduced by rice 1944 1945 2 26 and used to describe the turbulence 16 rough surfaces 27 stock markets 28 burgers turbulence and kardar parisi zhang equation 29 30 the level crossing analysis of the data set has the advantage that it gives important global properties of the time series and do not need the scaling feature the almost of the methods in time series analysis are using the scaling features of time series and their applications are restricted to the time series with scaling properties our goal with the level crossing analysis is to characterize the statistical properties of the data set with the hope to better understand the underlying stochastic dynamics and provide a possible tool to estimate its dynamics the level crossing and inverse statistics analysis can be viewed as the complementary method to the other well known methods such as detrended fluctuation analysis dfa 31 detrended moving average dma 32 wavelet transform modulus maxima wtmm 33 rescaled range analysis r s 34 scaled windowed variance swv 35 langevin dynamics 36 detrended cross correlation analysis 37 multifactor analysis of

equations over finite sets of words and equivalence problems in automata theory abstract several observations concerning equations over monoids of finite sets of words are made monoids considered are the monoid of finite prefix codes the monoid of all finite sets and the monoid of all finite multisets as well as some others as an application some known decidability results in automata theory are extended finally several open questions are raised

on the state complexity of closures and interiors of regular languages with subwords and superwords the downward and upward closures of a regular language l are obtained by collecting all the subwords and superwords of its elements respectively the downward and upward interiors of l are obtained dually by collecting words having all their subwords and superwords in l respectively we provide lower and upper bounds on the size of the smallest automata recognizing these closures and interiors we also consider the computational complexity of decision problems for closures of regular languages

augmented moment method for stochastic ensembles with delayed couplings ii fitzhugh nagumo model dynamics of fitzhugh nagumo fn neuron ensembles with time delayed couplings subject to white noises has been studied by using both direct simulations and a semianalytical augmented moment method amm which has been proposed in a preceding paper h hasegawa phys rev e 70 021911 2004 for n unit fn neuron ensembles amm transforms original 2n dimensional stochastic delay differential equations sddes to infinite dimensional deterministic des for means and correlation functions of local and global variables infinite order recursive des are terminated at the finite level m in the level m amm mathrm amm m yielding 8 m 1 dimensional deterministic des when a single spike is applied the oscillation may be induced if parameters of coupling strength delay noise intensity and or ensemble size are appropriate effects of these parameters on the emergence of the oscillation and on the synchronization in fn neuron ensembles have been studied the synchronization shows the fluctuation induced enhancement at the transition between nonoscillating and oscillating states results calculated by amm5 are in fairly good agreement with those obtained by direct simulations

stochastic nature of series of waiting times although fluctuations in the waiting time series have been studied for a long time some important issues such as its long range memory and its stochastic features in the presence of nonstationarity have so far remained unstudied here we find that the waiting times series for a given increment level have long range correlations with hurst exponents belonging to the interval 1 2lhl1 we also study positive negative level asymmetry of the waiting time distribution we find that the logarithmic difference of waiting times series has a short range correlation and then we study its stochastic nature using the markovian method and determine the corresponding kramers moyal coefficients as an example we analyze the velocity fluctuations in high reynolds number turbulence and determine the level dependence of markov time scales as well as the drift and diffusion coefficients we show that the waiting time distributions exhibit power law tails and we were able to model the distribution with a continuous time random walk

modelling volatility recurrence intervals in the chinese commodity futures market abstract the law of extreme event occurrence attracts much research the volatility recurrence intervals of chinese commodity futures market prices are studied the results show that the probability distributions of the scaled volatility recurrence intervals have a uniform scaling curve for different thresholds q so we can deduce the probability distribution of extreme events from normal events the tail of a scaling curve can be well fitted by a weibull form which is significance tested by ks measures both short term and long term memories are present in the recurrence intervals with different thresholds q which denotes that the recurrence intervals can be predicted in addition similar to volatility volatility recurrence intervals also have clustering features through monte carlo simulation we artificially synthesise arma garch class sequences similar to the original data and find out the reason behind the clustering the larger the parameter d of the figarch model the stronger the clustering effect is finally we use the fractionally integrated autoregressive conditional duration model fiacd to analyse the recurrence interval characteristics the results indicated that the fiacd model may provide a method to analyse volatility recurrence intervals

relaxation oscillators with time delay coupling abstract we study networks of relaxation oscillators coupled with time delays synapses a pair of oscillators is analyzed and shown to attain loosely synchronous solutions for a wide range of initial conditions and time delays simulations of one and two dimensional oscillator networks indicate that locally coupled oscillators are also loosely synchronous desynchronous solutions are possible when system parameters are varied to characterize lossely synchronous networks we introduce a measure of synchrony the maximum time difference between any two oscillators in locally excitatory globally inhibitory oscillator networks with time delays we find that desynchronous solutions for different groups of oscillators are maintained and the number of groups that can be segregated is related to the maximum time difference within each group to examine the maximum time difference we display its histograms for oscillator networks in one and two dimensions also a range of initial conditions is given so that the maximum time difference is contained as the system evolves

pattern segmentation in associative memory the goal of this paper is to show how to modify associative memory such that it can discriminate several stored patterns in a composite input and represent them simultaneously segmention of patterns takes place in the temporal domain components of one pattern becoming temporally correlated with each other and anticorrelated with the components of all other patterns correlations are created naturally by the usual associative connections in our simulations temporal patterns take the form of oscillatory bursts of activity model oscillators consist of pairs of local cell populations connected appropriately transition of activity from one pattern to another is induced by delayed self inhibition or simply by noise

spatiotemporal structures in a model with delay and diffusion pattern formation described by differential difference equations with diffusion is investigated it is shown that an arbitrarily small diffusion induces space time turbulence just at the instability threshold of the homogeneous stationary solution we prove this property by deriving a complex ginzburg landau equation on the basis of normal form analysis well above threshold such turbulent structures give way to synchronized states ordered by spirals and targets this secondary instability can be understood with an asymptotic method representing the system as a cellular automaton network

deletion along trajectories we describe a new way to model deletion operations on formal languages called deletion along trajectories we examine its closure properties which differ from those of shuffle on trajectories previously introduced by mateescu et al in particular we define classes of nonregular sets of trajectories such that the associated deletion operation preserves regularity our results give uniform proofs of closure properties of the regular languages for several deletion operations we also show that deletion along trajectories serves as an inverse to shuffle on trajectories this leads to results on the decidability of certain language equations including those of the form ltx r where l r are regular languages and x is unknown

collective dynamics in heterogeneous networks of neuronal cellular automata abstract we examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata each automaton has b active states a single silent state and r b 1 refractory states and can show spiking or bursting behavior depending on the values of b we show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of erdos renyi graphs as a function of edge probability different forms of heterogeneity allow distinct structural phase transitions to become relevant we also show that the dynamics on the network can be described by a semi annealed process and as a result can be related to the boolean lyapunov exponent

block insertion and deletion on trajectories in this paper we introduce block insertion and deletion on trajectories which provide us with a new framework to study properties of language operations with the parallel syntactical constraint provided by trajectories these operations properly generalize several sequential as well as parallel binary language operations such as catenation sequential insertion k insertion parallel insertion quotient sequential deletion k deletion etc we establish some relationships between the new operations and shuffle and deletion on trajectories and obtain several closure properties of the families of regular and context free languages under the new operations moreover we obtain several decidability results of three types of language equation problems which involve the new operations the first one is to answer given languages l 1 l 2 l 3 and a trajectory set t whether the result of an operation between l 1 and l 2 on the trajectory set t is equal to l 3 the second one is to answer for three given languages l 1 l 2 l 3 whether there exists a set of trajectories such that the block insertion or deletion between l 1 and l 2 on this trajectory set is equal to l 3 the third problem is similar to the second one but the language l 1 is unknown while languages l 2 l 3 as well as a trajectory set t are given

state complexity of unique rational operations for each basic language operation we define its unique counterpart as being the operation that results in a language whose words can be obtained uniquely through the given operation these unique operations can arguably be viewed as combined basic operations placing this work in the popular area of state complexity of combined operations on regular languages we study the state complexity of unique rational operations and we provide upper bounds and empirical results meant to cast light into this matter equally important we hope to have provided a generic methodology for estimating their state complexity

multispikes and synchronization in a large neural network with temporal delays coherent rhythms in the gamma frequency range are ubiquitous in the nervous system and thought to be important in a variety of cognitive activities such rhythms are known to be able to synchronize with millisecond precision across distances with significant conduction delay it is mysterious how this can operate in a setting in which cells receive many inputs over a range of time here we analyze a version of mechanism previously proposed that the synchronization in the ca1 region of the hippocampus depends on the firing of doublets by the interneurons using a network of local circuits that are arranged in a possibly disordered lattice we determine the conditions on parameters for existence and stability of synchronous solutions in which the inhibitory interneurons fire single spikes doublets or triplets per cycle we show that the synchronous solution is only marginally stable if the interneurons fire singlets if they fire doublets the synchronous state is asymptotically stable in a larger subset of parameter space than if they fire triplets an unexpected finding is that a small amount of disorder in the lattice structure enlarges the parameter regime in which the doublet solution is stable synaptic noise reduces the regime in which the doublet configuration is stable but only weakly

extending regular expressions with iterated shuffle it is shown that every finite expression which uses the operations union product kleene star and iterated shuffle in any order starting with finite sets defines a language which can be recognized non deterministically by some multicounter machine in quasirealtime it is known that this family is in general not closed with respect to iterated shuffle as a consequence of the characterization each such language is in nspace log n and thus in p however if p np then also neither p nor nspace log n are closed under iterated shuffle the proof uses the new concept of so called shuffle schemes and a number of results on algebraic language theory

on codes defined by bio operations we consider the classes of codes and codes which are superclasses of outfix and hyper codes respectively these restrictions are based on the synchronized insertion operation which serves as a model for the gene rearrangement function in certain unicellular organisms we investigate the classes of codes and codes from a theoretical perspective examine their relationships with traditional code classes and consider related decidability problems

generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena the integrate and fire if neuron model and the piecewise linear version of fitzhugh nagumo pl neuron model with a time scale parameter mu are frequently being used in the study of synchronization phenomena although the two models are regarded to be different type we show a certain equivalence between them by deriving the coupled if model of an improved version with a firing duration from the recovery variable coupled system of the pl model under taking the limit of mu 0 without a loss of any coupling properties in the coupled if model with the duration time the synchronization behavior of a pair of neurons with excitatory or inhibitory synaptic coupling can be systematically explored in terms of three parameters in the model synaptic strength decaying relaxation rate of the synaptic coupling and the parameter exhibiting the firing duration we find some irregularly synchronous behavior with or without constant firing order alternations we show that the duration of an impulse plays an important role in synchronization phenomena

scaling behavior in probabilistic neuronal cellular automata we study a neural network model of interacting stochastic discrete two state cellular automata on a regular lattice the system is externally tuned to a critical point which varies with the degree of stochasticity or the effective temperature there are avalanches of neuronal activity namely spatially and temporally contiguous sites of activity a detailed numerical study of these activity avalanches is presented and single joint and marginal probability distributions are computed at the critical point we find that the scaling exponents for the variables are in good agreement with a mean field theory

new types of automata to solve fixed point problems the aim of this article is to find the supremum of x ax x b and x k where a b and k are three fixed rational languages this problem and its solution are formally inspired by retroaction in control theory to get the solution we introduce a new type of automata whose acceptance condition is a positive boolean formula the time complexity of our algorithm depends linearly on the size of a quadratically on the size of k and exponentially on the size of b where the size is measured by the number of states of the minimal automaton

alternating and synchronous rhythms in reciprocally inhibitory model neurons we study pacemaker rhythms generated by two nonoscillatory model cells that are coupled by inhibitory synapses a minimal ionic model that exhibits postinhibitory rebound pir is presented when the post synaptic conductance depends instantaneously on presynaptic potential the classical alternating rhythm is obtained using phase plane analysis we identify two underlying mechanisms release and escape for the out of phase oscillation when the postsynaptic conductance is not instantaneous but decays slowly the two cells can oscillate synchronously with no phase difference in each case different stable activity patterns can coexist over a substantial parameter range

on properties of bond free dna languages the input data for dna computing must be encoded into the form of single or double dna strands as complementary parts of single strands can bind together forming a double stranded dna sequence one has to impose restrictions on these sets of dna words languages to prevent them from interacting in undesirable ways we recall a list of known properties of dna languages which are free of certain types of undesirable bonds then we introduce a general framework in which we can characterize each of these properties by a solution of a uniform formal language inequation this characterization allows us among others to construct i a uniform algorithm deciding in polynomial time whether a given dna language possesses any of the studied properties and ii in many cases also an algorithm deciding whether a given dna language is maximal with respect to the desired property

patterns of chaos synchronization small networks of chaotic units which are coupled by their time delayed variables are investigated in spite of the time delay the units can synchronize isochronally i e without time shift moreover networks cannot only synchronize completely but can also split into different synchronized sublattices these synchronization patterns are stable attractors of the network dynamics different networks with their associated behaviors and synchronization patterns are presented in particular we investigate sublattice synchronization symmetry breaking spreading chaotic motifs synchronization by restoring symmetry and cooperative pairwise synchronization of a bipartite tree

aspects of shuffle and deletion on trajectories word and language operations on trajectories provide a general framework for the study of properties of sequential insertion and deletion operations a trajectory gives a syntactical constraint on the scattered insertion deletion of a word into from another one with an intuitive geometrical interpretation moreover deletion on trajectories is an inverse of the shuffle on trajectories these operations are a natural generalization of many binary word operations like catenation quotient insertion deletion shuffle etc besides they were shown to be useful e g in concurrent processes modelling and recently in biocomputing area we begin with the study of algebraic properties of the deletion on trajectories then we focus on three standard decision problems concerning linear language equations with one variable involving the above mentioned operations we generalize previous results and obtain a sequence of new ones particularly we characterize the class of binary word operations for which the validity of such a language equation is un decidable for regular and context free operands

the role of weight normalization in competitive learning the effect of different kinds of weight normalization on the outcome of a simple competitive learning rule is analyzed it is shown that there are important differences in the representation formed depending on whether the constraint is enforced by dividing each weight by the same amount divisive enforcement or subtracting a fixed amount from each weight subtractive enforcement for the divisive cases weight vectors spread out over the space so as to evenly represent typical inputs whereas for the subtractive cases the weight vectors tend to the axes of the space so as to represent extreme inputs the consequences of these differences are examined

synchronization in relaxation oscillator networks with conduction delays we study locally coupled networks of relaxation oscillators with excitatory connections and conduction delays and propose a mechanism for achieving zero phase lag synchrony our mechanism is based on the observation that different rates of motion along different nullclines of the system can lead to synchrony in the presence of conduction delays we analyze the system of two coupled oscillators and derive phase compression rates this analysis indicates how to choose nullclines for individual relaxation oscillators in order to induce rapid synchrony the numerical simulations demonstrate that our analytical results extend to locally coupled networks with conduction delays and that these networks can attain rapid synchrony with appropriately chosen nullclines and initial conditions the robustness of the proposed mechanism is verified with respect to different nullclines variations in parameter values and initial conditions

variable diffusion in stock market fluctuations abstract we analyze intraday fluctuations in several stock indices to investigate the underlying stochastic processes using techniques appropriate for processes with nonstationary increments the five most actively traded stocks each contains two time intervals during the day where the variance of increments can be fit by power law scaling in time the fluctuations in return within these intervals follow asymptotic bi exponential distributions the autocorrelation function for increments vanishes rapidly but decays slowly for absolute and squared increments based on these results we propose an intraday stochastic model with linear variable diffusion coefficient as a lowest order approximation to the real dynamics of financial markets and to test the effects of time averaging techniques typically used for financial time series analysis we find that our model replicates major stylized facts associated with empirical financial time series we also find that ensemble averaging techniques can be used to identify the underlying dynamics correctly whereas time averages fail in this task our work indicates that ensemble average approaches will yield new insight into the study of financial markets dynamics our proposed model also provides new insight into the modeling of financial markets dynamics in microscopic time scales

closure and decidability properties of some language classes with respect to ciliate bio operations the process of gene unscrambling in ciliates a type of unicellular protozoa which accomplishes the difficult task of re arranging gene segments in the correct order and deleting non coding sequences from an encrypted version of a dna strand has been modeled and studied so far from the point of view of the computational power of the dna bio operations involved here we concentrate on a different aspect of the process by considering only the linear version of the bio operations that do not involve thus any circular strands and by studying the resulting formal operations from a purely language theoretic point of view we investigate closure properties of language families under the mentioned bio operations and study language equations involving them we also study the decidability of the existence of solutions to equations of the form l y r x l r where l and r are given languages x and y are unknowns and signifies one of the defined bio operations

on the complexity and decidability of some problems involving shuffle abstract the complexity and decidability of various decision problems involving the shuffle operation denoted by are studied the following three problems are all shown to be np complete given a nondeterministic finite automaton nfa m and two words u and v is l m u v is u v l m and is l m u v it is also shown that there is a polynomial time algorithm to determine for nfa s m 1 m 2 and a deterministic pushdown automaton m 3 whether l m 1 l m 2 l m 3 the same is true when m 1 m 2 m 3 are one way nondeterministic l reversal bounded k counter machines with m 3 being deterministic other decidability and complexity results are presented for testing whether given languages l 1 l 2 and r from various languages families satisfy l 1 l 2 r and r l 1 l 2 several closure results on shuffle are also shown

increase of coherence in excitable systems by delayed feedback the control of coherence and spectral properties of noise induced oscillations by time delayed feedback is studied in a fitzhugh nagumo system which serves as a paradigmatic model of excitable systems a semianalytical approach based on a discrete model with waiting time densities is developed which allows one to predict quantitatively the increase of coherence measured by the correlation time and the modulation of the main frequencies of the stochastic dynamics in dependence on the delay time the analytical mean field approximation is in good agreement with numerical results for the full nonlinear model

global competition and local cooperation in a network of neural oscillators abstract an architecture of locally excitatory globally inhibitory oscillator networks is proposed and investigated both analytically and by computer simulation the model for each oscillator corresponds to a standard relaxation oscillator with two time scales oscillators are locally coupled by a scheme that resembles excitatory synaptic coupling and each oscillator also inhibits other oscillators through a common inhibitor oscillators are driven to be oscillatory by external stimulation the network exhibits a mechanism of selective gating whereby an oscillator jumping up to its active phase rapidly recruits the oscillators stimulated by the same pattern while preventing the other oscillators from jumping up we show analytically that with the selective gating mechanism the network rapidly achieves both synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks computer simulations demonstrate the model s promising ability for segmenting multiple input patterns in real time this model lays a physical foundation for the oscillatory correlation theory of feature binding and may provide an effective computational framework for scene segmentation and figure ground segregation

computing with arrays of coupled oscillators an application to preattentive texture discrimination recent experimental findings gray et al 1989 eckhorn et al 1988 seem to indicate that rapid oscillations and phase lockings of different populations of cortical neurons play an important role in neural computations in particular global stimulus properties could be reflected in the correlated firing of spatially distant cells here we describe how simple coupled oscillator networks can be used to model the data and to investigate whether useful tasks can be performed by oscillator architectures a specific demonstration is given for the problem of preattentive texture discrimination texture images are convolved with different sets of gabor filters feeding into several corresponding arrays of coupled oscillators after a brief transient the dynamic evolution in the arrays leads to a separation of the textures by a phase labeling mechanism the importance of noise and of long range connections is briefly discussed

population dynamics of spiking neurons fast transients asynchronous states and locking an integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate and fire type is discussed it is analytically shown that transients from a state of incoherent firing can be immediate the stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived the response of a population of noisy integrate and fire neurons to an input current of small amplitude is calculated and characterized by a linear filter l the stability of perfectly synchronized locked solutions is analyzed

shuffle and scattered deletion closure of languages we introduce and study the notion of shue residual of a language l the set containing the words whose shue with l is completely included in l several properties and a characterization of the shue residual of a language are obtained the shue closure of a language l the smallest language that is shue closed and contains l is investigated moreover conditions for the existence of maximal languages whose shue residual equals a given language are obtained the paper also considers an operation dual to shue namely scattered deletion the scattered deletion of a word w from u consists of the words obtained by sparsely deleting from u the letters of w in the order in which they appear in w the scattered deletion residual and scattered deletion closure of a language are dened and studied finally relationships and interdependencies between shue scattered deletion and other insertion and deletion operations are obtained c 2000 elsevier science b v all rights reserved