abstract phase space networks describing reactive dynamics abstract an abstract network approach is proposed for the description of the dynamics in reactive processes the phase space of the variables concentrations in reactive systems is partitioned into a finite number of segments which constitute the nodes of the abstract network transitions between the nodes are dictated by the dynamics of the reactive process and provide the links between the nodes these are weighted networks since each link weight reflects the transition rate between the corresponding states nodes with this construction the network properties mirror the dynamics of the underlying process and one can investigate the system properties by studying the corresponding abstract network as a working example the lattice limit cycle llc model is used its corresponding abstract network is constructed and the transition matrix elements are computed via kinetic dynamic monte carlo simulations for this model it is shown that the degree distribution follows a power law with exponent 1 while the average clustering coefficient c n scales with the network size number of nodes n as c n n 1 46 the computed exponents classify the llc abstract reactive network into the scale free networks this conclusion corroborates earlier investigations demonstrating the formation of fractal spatial patterns in llc reactive dynamics due to stochasticity and to clustering of homologous species the present construction of abstract networks based on the partition of the phase space is generic and can be implemented with appropriate adjustments in many dynamical systems and in time series analysis

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

scaling and memory in the non poisson process of limit order cancelation abstract the order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order driven markets we investigate the dynamics of order cancelation by studying the statistical properties of inter cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the shenzhen stock exchange of china in year 2003 three types of cancelations are considered including cancelation of any limit orders of buy limit orders and of sell limit orders we find that the distributions of the inter cancelation durations of individual stocks can be well modeled by weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks complex intra day patterns are also unveiled in the inter cancelation durations the detrended fluctuation analysis dfa and the multifractal dfa show that the inter cancelation durations possess long term memory and multifractal nature which are not influenced by the intra day patterns no clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale these findings indicate that the cancelation of limit orders is a non poisson process which has potential worth in the construction of order driven market models

multifractal properties of the indian financial market abstract we investigate the multifractal properties of the logarithmic returns of the indian financial indices bse nse by applying the multifractal detrended fluctuation analysis the results are compared with that of the us s p 500 index numerically we find that q th order generalized hurst exponents h q and q change with the moments q the nonlinear dependence of these scaling exponents and the singularity spectrum f show that the returns possess multifractality by comparing the mf dfa results of the original series to those for the shuffled series we find that the multifractality is due to the contributions of long range correlations as well as the broad probability density function the financial markets studied here are compared with the binomial multifractal model bmfm and have a smaller multifractal strength than the bmfm

lacunarity and multifractal analysis of the large dla mass distribution abstract we show the methodology used to analyze fractal and mass multifractal properties of very large diffusion limited aggregation dla clusters with a maximum of 10 9 particles for 2d aggregates and 10 8 particles for 3d clusters to support our main result the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects in order to estimate lacunarity measures for large dla clusters we develop a variant of the gliding box algorithm which reduces the computer time needed to obtain experimental results we show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters lacunarity analysis shows provided we study small clusters mass distributions data which might be interpreted as two different values of fractal dimensions while the cluster grows however this effect tends to vanish when the cluster size increases further in such a way that monofractality is achieved the outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior vicsek et al 1990 13 detected for dla clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena since the scaling behavior of our dla clusters space corresponds to monofractal objects being this situation remarkably noticeable in the limit of very large clusters

multifractal hurst analysis of crude oil prices abstract daily records of international crude oil prices are studied using multifractal analysis methods rescaled range hurst analysis provides evidence that the crude oil market is a persistent process with long run memory effects on the other hand height height correlation analysis reveals evidence of multifractal structures in the sense that the crude oil dynamics displays mixing of rough hurst exponents the existence of two characteristic time scales in the order of weeks and quarters is discovered and the corresponding prices dynamics are extracted using moving average based filtering these results seem to demonstrate that the crude oil market is consistent with the random walk assumption only at time scales of the order of days to weeks a plausible oil price formation mechanism is discussed in terms of the market dynamics at three different time scales

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

multifractal behavior of the korean stock market index kospi abstract we investigate multifractality in the korean stock market index kospi the generalized qth order height height correlation function shows multiscaling properties there are two scaling regimes with a crossover time around t c 40 min we consider the original data sets and the modified data sets obtained by removing the daily jumps which occur due to the difference between the closing index and the opening index to clarify the origin of the multifractality we also smooth the data through convolution with a gaussian function after convolution we observe that the multifractality disappears in the short time scaling regime t t c but remains in the long time scaling regime t t c regardless of whether or not the daily jumps are removed we suggest that multifractality in the short time scaling regime is caused by the local fluctuations of the stock index but the multifractality in the long time scaling regime appears to be due to the intrinsic trading properties such as herding behavior information outside the market the long memory of the volatility and the nonlinear dynamics of the stock market

multifractal model of asset returns with leverage effect abstract multifractal processes are a relatively new tool of stock market analysis their power lies in the ability to take multiple orders of autocorrelations into account explicitly in the first part of the paper we discuss the framework of the lux model and refine the underlying phenomenological picture we also give a procedure of fitting all parameters to empirical data we present a new approach to account for the effective length of power law memory in volatility the second part of the paper deals with the consequences of asymmetry in returns we incorporate two related stylized facts skewness and leverage autocorrelations into the model then from monte carlo measurements we show that this asymmetry significantly increases the mean squared error of volatility forecasts based on a filtering method we give evidence on similar behavior in empirical data

phase transitions and spatio temporal fluctuations in stochastic lattice lotka volterra models we study the general properties of stochastic two species models for predator prey competition and coexistence with lotka volterra type interactions defined on a d dimensional lattice introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical deterministic mean field picture already within mean field theory however spatial constraints modeling locally limited resources lead to the emergence of a continuous active to absorbing state phase transition field theoretic arguments supported by monte carlo simulation results indicate that this transition which represents an extinction threshold for the predator population is governed by the directed percolation universality class in the active state where predators and prey coexist the classical center singularities with associated population cycles are replaced by either nodes or foci in the vicinity of the stable nodes the system is characterized by essentially stationary localized clusters of predators in a sea of prey near the stable foci however the stochastic lattice lotka volterra system displays complex correlated spatio temporal patterns of competing activity fronts correspondingly the population densities in our numerical simulations turn out to oscillate irregularly in time with amplitudes that tend to zero in the thermodynamic limit yet in finite systems these oscillatory fluctuations are quite persistent and their features are determined by the intrinsic interaction rates rather than the initial conditions we emphasize the robustness of this scenario with respect to various model perturbations

initial complexes of prime ideals abstract the simplicial complex defined by any initial ideal of a prime ideal is pure and strongly connected this proves a conjecture of kredel and weispfenning 12 p 234

coexistence versus extinction in the stochastic cyclic lotka volterra model cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity see e g b kerr m a riley m w feldman and b j m bohannan nature 418 171 2002 and b kirkup and m a riley nature 428 412 2004 through analytical methods supported by numerical simulations we address this issue by studying the properties of a paradigmatic non spatial three species stochastic system namely the rock paper scissors or cyclic lotka volterra model while the deterministic approach rate equations predicts the coexistence of the species resulting in regular yet neutrally stable oscillations of the population densities we demonstrate that fluctuations arising in the system with a finite number of agents drastically alter this picture and are responsible for extinction after long enough time two of the three species die out as main findings we provide analytic estimates and numerical computation of the extinction probability at a given time we also discuss the implications of our results for a broad class of competing population systems

lower critical dimension for populations of oscillators with randomly distributed frequencies a renormalization group analysis it is argued by way of a renormalization group analysis that the lower critical dimension of macroscopic mutual entrainment in a class of populations of oscillators satisfies a certain inequality which is sensitive to the tail of the distribution of native frequencies this result is supported in part by numerical simulations as well as a proof of the absence of long range order in one dimension

financial multifractality and its subtleties an example of dax abstract detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency deutsche aktienindex data the tail index the renyi exponents based on the box counting algorithm for the graph d q and the generalized hurst exponents h q are computed in parallel for short and daily return times the results indicate a more complicated nature of the stock market dynamics than just consistent multifractal

on superheight conditions for the affineness of open subsets in this paper we consider the open complement u of a hypersurface y v a in an affine scheme x we study the relations between the affineness of u the intersection of y with closed subschemes the property that every closed surface in u is affine the property that every analytic closed surface is stein and the superheight of a defining ideal a

research on the fractal structure in the chinese stock market abstract applying fractal theory this paper probes and discusses self similarity and scale invariance of the chinese stock market it analyses three kinds of scale indexes i e autocorrelation index hurst index and the scale index on the basis of detrended fluctuation analysis dfa algorithm and promotes dfa into a recursive algorithm using the three kinds of scale indexes we conduct empirical research on the chinese shanghai and shenzhen stock markets the results indicate that the rate of returns of the two stock markets does not obey the normal distribution a correlation exists between the stock price indexes over time scales the stock price indexes exhibit fractal time series it indicates that the policy guide hidden at the back influences the characteristic of the chinese stock market

simplicial ideals 2 linear ideals and arithmetical rank abstract in the first part of this paper we study scrollers and linearly joined varieties scrollers were introduced in barile and morales 2004 bm4 linearly joined varieties are an extension of scrollers and were defined in eisenbud et al 2005 eghp there they proved that scrollers are defined by homogeneous ideals having a 2 linear resolution a particular class of varieties of important interest in classical geometry are cohen macaulay varieties of minimal degree they were classified geometrically by the successive contribution of del pezzo 1885 dp bertini 1907 b and xambo 1981 x and algebraically in barile and morales 2000 bm2 they appear naturally studying the fiber cone of a codimension two toric ideals morales 1995 m gimenez et al 1993 1999 gms1 gms2 barile and morales 1998 bm1 ha 2006 h ha and morales 2009 hm let s be a polynomial ring and i s a homogeneous ideal defining a sequence of linearly joined varieties we compute depth s i we prove that c v depth s i 1 where c v is the connectedness dimension of the algebraic set defined by i we characterize sets of generators of i and give an effective algorithm to find equations as an application we prove that ara i projdim s i in the case where v is a union of linear spaces in particular this applies to any square free monomial ideal having a 2 linear resolution in the case where v is a union of linear spaces the ideal i can be characterized by a tableau which is an extension of a ferrer or young tableau all these results are new and extend results in barile and morales 2004 bm4 eisenbud et al 2005 eghp

scaling cluster dynamics and complex oscillations in a multispecies lattice lotka volterra model abstract the cluster formation in the cyclic 4 1 lattice lotka volterra model is studied by kinetic monte carlo simulations on a square lattice support at the mean field level this model demonstrates conservative four dimensional oscillations which depending on the parameters can be chaotic or quasi periodic when the system is realized on a square lattice substrate the various species organize in domains clusters with fractal boundaries and this is consistent with dissipative dynamics for small lattice sizes the entire lattice oscillates in phase and the size distribution of the clusters follows a pure power law distribution when the system size is large many independently oscillating regions are formed and as a result the cluster size distribution in addition to the power law acquires a exponential decay dependence this combination of power law and exponential decay of distributions and correlations is indicative in this case of mixing and superposition of regions oscillating asynchronously

multifractality in the stock market price increments versus waiting times abstract by applying the multifractal detrended fluctuation analysis to the high frequency tick by tick data from deutsche borse both in the price and in the time domains we investigate multifractal properties of the time series of logarithmic price increments and inter trade intervals of time we show that both quantities reveal multiscaling and that this result holds across different stocks the origin of the multifractal character of the corresponding dynamics is among others the long range correlations in price increments and in inter trade time intervals as well as the non gaussian distributions of the fluctuations since the transaction to transaction price increments do not strongly depend on or are almost independent of the inter trade waiting times both can be sources of the observed multifractal behaviour of the fixed delay returns and volatility the results presented also allow one to evaluate the applicability of the multifractal model of asset returns in the case of tick by tick data

scaling self similarity and multifractality in fx markets abstract this paper presents an empirical investigation of scaling and multifractal properties of us dollar deutschemark usd dem returns the data set is ten years of 5 min returns the cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space this presents strong evidence that the usd dem returns exhibit power law scaling in the tails to test the multifractal properties of usd dem returns the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns these moments show different slopes for these powers of absolute returns the nonlinearity of the scaling exponent indicates that the returns are multifractal

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

vortices and strings in a model ecosystem we study the spatial pattern formation in a model ecosystem by the position fixed reaction method this ecosystem contains three biospecies whose competing powers are cyclic it is well known that this system is self organized into a quasistationary state and that the mean field approximation mfa never predicts such a pattern formation recently several authors applied the pair approximation pa and obtained considerable improvements however applying pa to our ecosystem fails to yield such an improvement as revealed by computer simulations the failures of mfa and pa may be attributed to the fact that both approximations neglect a long range correlation thus we introduce the concept of topological defects such as vortices or strings and demonstrate that the dynamics of these defects can at least qualitatively account for the observed pattern formation dynamics

scale invariance and universality of economic fluctuations in recent years physicists have begun to apply concepts and methods of statistical physics to study economic problems and the neologism econophysics is increasingly used to refer to this work much recent work is focused on understanding the statistical properties of time series one reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist and it is possible that economic time series viewed from a dierent perspective might yield new results this manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the eld of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on economics we shall see that while scale invariance has been tested for many years universality is relatively less frequently discussed this article reviews the results of two recent studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier in size by as much as eight orders of magnitude ii quantifying business rm uctuations we analyze the computstat database comprising all publicly traded united states manufacturing companies within the years 1974 1993 we nd that the distributions of growth rates is dierent for dierent bins of rm size with a width that varies inversely with a power of rm size similar variation is found for other complex organizations including country size university research budget size and size of species of bird populations c 2000 elsevier science b v all rights reserved

topology of correlation based minimal spanning trees in real and model markets we compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the new york stock exchange during a 12 year trading period with the one obtained from surrogated data simulated by using simple market models we find that the empirical tree has features of a complex network that cannot be reproduced even as a first approximation by a random market model and by the widespread one factor model

power law of quiet time distribution in the korean stock market abstract we report the quiet time probability distribution of the absolute return in the korean stock market index we define the quiet time as a time interval during the absolute return of the stock index that are above a threshold r c through an exponential bin plot we observe that the quiet time distribution qtd shows power law behavior p f t t for a range of threshold values the quiet time distribution has two scaling regimes separated by the crossover time t c 200 min the power law exponents of the quiet time distribution decrease when the return time t increases in the late time regime t t c the power law exponents are independent of the threshold within the error bars for the fixed return time the scaled qtd is characterized by a scaling function such as p f t 1 t f t t where the scaling function f x x 2 and t is the average quiet time the scaling exponents 2 depend on the return time t and are independent of the threshold r c the average quiet time follows the power law such as t r c where the exponents depend on the return time t

four state rock paper scissors games in constrained newman watts networks we study the cyclic dominance of three species in two dimensional constrained newman watts networks with a four state variant of the rock paper scissors game by limiting the maximal connection distance r max in newman watts networks with the long range connection probability p we depict more realistically the stochastic interactions among species within ecosystems when we fix mobility and vary the value of p or r max the monte carlo simulations show that the spiral waves grow in size and the system becomes unstable and biodiversity is lost with increasing p or r max these results are similar to recent results of reichenbach et al nature london 448 1046 2007 in which they increase the mobility only without including long range interactions we compared extinctions with or without long range connections and computed spatial correlation functions and correlation length we conclude that long range connections could improve the mobility of species drastically changing their crossover to extinction and making the system more unstable

stochastic resonance noise enhanced phase coherence we study stochastic resonance in periodically driven stochastic bistable systems in terms of phase synchronization by introduction of an instantaneous phase for the output we show explicitly the effect of phase locking between the input and output the stochastic dynamics of the phase difference between input and output appears to be similar to that of synchronized classical self sustained oscillators the degree of phase coherence is estimated by employing the effective diffusion constant for the phase difference this coherence becomes maximal for optimal noise intensities however phase synchronization effects can only be observed for sufficiently large magnitude of the periodic inputting signal

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

scaling and correlation in financial time series we discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of nancial time series i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to very drastic events such as the crash of 19 october 1987 sometimes referred to as black monday the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as 8 orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by 3 orders of magnitude from 1 min up to approximately 10 days ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law persisting for several months iii volatility and trading activity we quantify the relation between trading activity measured by the number of transactions nt and the price change gt for a given stock over a time interval t t t we nd that nt displays long range power law correlations in time which leads to the interpretation that the long range correlations previously found for jgtj are connected to those of nt c 2000 elsevier science b v all rights reserved

probability distribution function and multiscaling properties in the korean stock market abstract we consider the probability distribution function pdf and the multiscaling properties of the index and the traded volume in the korean stock market we observed the power law of the pdf at the fat tail region for the return volatility the traded volume and changes of the traded volume we also investigate the multifractality in the korean stock market we consider the multifractality by the detrended fluctuation analysis mfdfa we observed the multiscaling behaviors for index return traded volume and the changes of the traded volume we apply mfdfa method for the randomly shuffled time series to observe the effects of the autocorrelations the multifractality is strongly originated from the long time correlations of the time series

power law and multiscaling properties of the chinese stock market abstract we investigate the cumulative probability density function pdf and the multiscaling properties of the returns in the chinese stock market by using returns data adjusted for thin trading we find that the distribution has power law tails at shorter microscopic timescales or lags however the distribution follows an exponential law for longer timescales furthermore we investigate the long range correlation and multifractality of the returns in the chinese stock market by the dfa and mfdfa methods we find that all the scaling exponents are between 0 5 and 1 by dfa method which exhibits the long range power law correlations in the chinese stock market moreover we find by mfdfa method that the generalized hurst exponents h q are not constants which shows the multifractality in the chinese stock market we also find that the correlation of shenzhen stock market is stronger than that of shanghai stock market

on the multifractal effects generated by monofractal signals we study quantitatively the level of false multifractal signal one may encounter while ana lyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis mf dfa the investigated effect appears as a result of finite length of used data series and is additionally amplified by the long term memory the data eventually may contain we pro vide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized hurst exponent valuesh or a threshold in the width of multifractal spectrum below which multifractal properties of the system are only apparent i e do not exist despite 6 0 orh 6 0 we find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent its strength decays according to power law with respect to the length of time series the influ ence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated this provides additional set of semi analytical results the obtained formulas are significant in any interdisciplinary application of multifractality including physics financial data analysis or physiology because they allow to separate the true multifractal phenomena from the apparent artificial multifractal effects they should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

markov processes hurst exponents and nonlinear diffusion equations with application to finance abstract we show by explicit closed form calculations that a hurst exponent h 1 2 does not necessarily imply long time correlations like those found in fractional brownian motion fbm we construct a large set of scaling solutions of fokker planck partial differential equations pdes where h 1 2 thus markov processes which by construction have no long time correlations can have h 1 2 if a markov process scales with hurst exponent h 1 2 then it simply means that the process has nonstationary increments for the scaling solutions we show how to reduce the calculation of the probability density to a single integration once the diffusion coefficient d x t is specified as an example we generate a class of student t like densities from the class of quadratic diffusion coefficients notably the tsallis density is one member of that large class the tsallis density is usually thought to result from a nonlinear diffusion equation but instead we explicitly show that it follows from a markov process generated by a linear fokker planck equation and therefore from a corresponding langevin equation having a tsallis density with h 1 2 therefore does not imply dynamics with correlated signals e g like those of fbm a short review of the requirements for fbm is given for clarity and we explain why the usual simple argument that h 1 2 implies correlations fails for markov processes with scaling solutions finally we discuss the question of scaling of the full green function g x t x t of the fokker planck pdes

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

synchronization of stochastic oscillations due to long range diffusion we investigate the effect of long range diffusive mixing on stochastic processes taking place on low dimensional catalytic supports as a working example the cyclic lattice lotka volterra llv model is used which is conservative at the mean field level and demonstrates fractal patterns and local oscillations when realized on low dimensional lattice supports we show that the local oscillations are synchronized when a weak long range diffusive process is added to llv and global oscillations of limit cycle type emerge this phenomenon is demonstrated as a nonequilibrium phase transition and takes place when the mixing to reaction rate p order parameter is above a critical point p c the value of the critical point is shown to depend on the kinetic parameters the global oscillations in this case emerge as a result of phase synchronization between local oscillations on sublattices

scaling in the norwegian stock market the main objective of this paper is to investigate the validity of the much used assumptions that stock market returns follow a random walk and are normally distributed for this purpose the concepts of chaos theory and fractals are applied two independent models are used to examine price variations in the norwegian and us stock markets the first model used is the range over standard deviation or r s statistic which tests for persistence or antipersistence in the time series both the norwegian and us stock markets show significant persistence caused by long run memory components in the series in addition an average non periodic cycle of four years is found for the us stock market these results are not consistent with the random walk assumption the second model investigates the distributional scaling behaviour of the high frequency price variations in the norwegian stock market the results show a remarkable constant scaling behaviour between different time intervals this means that there is no intrinsic time scale for the dynamics of stock price variations the relationship can be expressed through a scaling exponent describing the development of the distributions as the time scale changes this description may be important when constructing or improving pricing models such that they coincide more closely with the observed market behaviour the empirical distributions of high frequency price variations for the norwegian stock market is then compared to the levy stable distribution with the relevant scaling exponent found by using the r s and distributional scaling analysis good agreement is found between the levy profile and the empirical distribution for price variations less than 6 standard deviations covering almost three orders of magnitude in the data for probabilities larger than 6 standard deviations there seem to be an exponential fall off from the levy profile in the tails which indicates that the second moment may be finite

fixation in a cyclic lotka volterra model we study a cyclic lotka volterra model of n interacting species populating a d dimensional lattice in the realm of a kirkwood approximation a critical number of species nc d above which the system fixates is determined analytically we find nc d 5 14 23 in dimensionsdd 1 2 3 in remarkably good agreement with simulation results in two dimensions a cyclic variant of the lotka volterra model of interacting populations originally introduced by vito volterra for the description of the struggle for existence among species 1 2 has then appeared in a number of apparently unrelated fields ranging from plasma physics 3 to integrable systems 4 5 recently the cyclic lotka volterra model also known as the cyclic voter model has attracted considerable interest as it was realized that introduction of the spatial structure drastically enriches the dynamics 6 11 namely if species live on a one dimensional 1d lattice a homogeneous initial state evolves into a coarsening mosaic of interacting species this heterogeneous spatial structure spontaneously develops when the number of species is sufficiently small n nc fixation occurs i e the system approaches a frozen state little is known in higher dimensions not even the existence of nc has yet been established theoretically or numerically in simulations on two dimensional 2d lattices with n 6 10 species no sign of fixation has been found and instead a reactive steady state has been observed 6 11 in this letter we investigate the cyclic lotka volterra model in the framework of a kirkwood like approximation this approach predicts a finite nc in all spatial dimensions in the following we shall use the language of the voter model 12 consider the cyclic voter model with n possible opinions each site of a d dimensional cubic lattice is occupied by a voter which has an opinion labelled by with d 1 n voters can change their opinions in a cyclic manner 1 modulo n according to the opinions of their neighbourhood specifically the following sequential dynamics is implemented i we randomly choose a site of opinion say and one of its 2d nearest neighbours of opinion ii if d 1 then the chosen site changes its opinion from to d 1 and iii otherwise opinion does not change we set the timescale so that in unit time each site of the lattice is chosen once on average when nd 2 the cyclic voter model is

effects of disorder on synchronization of discrete phase coupled oscillators we study synchronization in populations of phase coupled stochastic three state oscillators characterized by a distribution of transition rates we present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of n types of oscillators n 2 3 4 by exploring the linear stability of the nonsynchronous fixed point we also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution of finite width even in the presence of transition rate disorder numerical and analytical results point to a single phase transition to macroscopic synchrony at a critical value of the coupling strength numerical simulations make possible further characterization of the synchronized arrays

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

three state model and chemical reactions a three state model is formulated in terms of raising and lowering operators as an application cyclic chemical reactions with three different species in the solid state are studied the evolution equations for the densities and for the correlation functions can be derived starting from a master equation in a generalized fock space representation on a lattice such a description guarantees the consideration of the excluded volume effect in contrast to the classical kinetic behaviour the system offers stable and unstable regimes depending on the averaged composition ratio

grobner deformations connectedness and cohomological dimension abstract in this paper we will compare the connectivity dimension c p i of an ideal i in a polynomial ring p with that of any initial ideal of i generalizing a theorem of kalkbrener and sturmfels m kalkbrener b sturmfels initial complex of prime ideals adv math 116 1995 365 376 we prove that c p lt i min c p i dim p i 1 for each monomial order as a corollary we have that every initial complex of a cohen macaulay ideal is strongly connected our approach is based on the study of the cohomological dimension of an ideal a in a noetherian ring r and its relation with the connectivity dimension of r a in particular we prove a generalized version of a theorem of grothendieck a grothendieck cohomologie locale des faisceaux coherents et theoremes de lefschetz locaux et globaux sga 2 in seminaire de geometrie algebrique du bois marie 1962 as consequence of these results we obtain some necessary conditions for an open subscheme of a projective scheme to be affine

fractal properties of the lattice lotka volterra model the lattice lotka volterra llv model is studied using mean field analysis and monte carlo simulations while the mean field phase portrait consists of a center surrounded by an infinity of closed trajectories when the process is restricted to a two dimensional 2d square lattice local inhomogeneities fluctuations appear spontaneous local clustering is observed on lattice and homogeneous initial distributions turn into clustered structures reactions take place only at the interfaces between different species and the borders adopt locally fractal structure intercluster surface reactions are responsible for the formation of local fluctuations of the species concentrations the box counting fractal dimension of the llv dynamics on a 2d support is found to depend on the reaction constants while the upper bound of fractality determines the size of the local oscillators lacunarity analysis is used to determine the degree of clustering of homologous species besides the spontaneous clustering that takes place on a regular 2d lattice the effects of fractal supports on the dynamics of the llv are studied for supports of dimensionality d s 2 the lattice can for certain domains of the reaction constants adopt a poisoned state where only one of the species survives by appropriately selecting the fractal dimension of the substrate it is possible to direct the system into a poisoned or oscillatory steady state at will

study of interacting particle systems the transition to the oscillatory behavior of a prey predator model abstract a prey predator system with intelligent pursuit and evasion is studied by means of computer simulations it is found that the model exhibits a coexistence state between prey and predators in this state and depending on the parameters the system may evolve toward two different regimes characterized by the behavior of the prey predator population whitin the oscillatory fixed point regime the specie s density changes periodically remains constant respectively the transition between such regimes is rationalized in terms of a dynamic percolation process

long term correlations and multifractal nature in the intertrade durations of a liquid chinese stock and its warrant abstract the intertrade duration of equities is an important financial measure characterizing trading activities it is defined as the waiting time between successive trades of an equity using the ultrahigh frequency data of a liquid chinese stock and its associated warrant we perform a comparative investigation of the statistical properties of their intertrade duration time series the distributions of the two equities can be better described by the shifted power law form than the weibull form and their scaled distributions do not collapse onto a single curve although the intertrade durations of the two equities have very different magnitude their intraday patterns exhibit very similar shapes both detrended fluctuation analysis dfa and detrending moving average analysis dma show that the 1 min intertrade duration time series of the two equities are strongly correlated in addition both multifractal detrended fluctuation analysis mfdfa and multifractal detrending moving average analysis mfdma unveil that the 1 min intertrade durations possess multifractal nature however the difference between the two singularity spectra of the two equities obtained from the mfdma is much smaller than that from the mfdfa

phase transitions for rock scissors paper game on different networks monte carlo simulations and dynamical mean field approximations are performed to study the phase transitions in the rock scissors paper game on different host networks these graphs are originated from lattices by introducing quenched and annealed randomness simultaneously in the resulting phase diagrams three different stationary states are identified for all structures the comparison of results on different networks suggests that the value of the clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase the critical behavior of phase transitions seems to be universal and can be described by the same exponents

monomial and toric ideals associated to ferrers graphs each partition a 1 2 an determines a so called ferrers tableau or equivalently a ferrers bipartite graph its edge ideal dubbed a ferrers ideal is a squarefree monomial ideal that is generated by quadrics we show that such an ideal has a 2 linear minimal free resolution i e it defines a small subscheme in fact we prove that this property characterizes ferrers graphs among bipartite graphs furthermore using a method of bayer and sturmfels we provide an explicit description of the maps in its minimal free resolution this is obtained by associating a suitable polyhedral cell complex to the ideal graph along the way we also determine the irredundant primary decomposition of any ferrers ideal we conclude our analysis by studying several features of toric rings of ferrers graphs in particular we recover establish formulae for the hilbert series the castelnuovo mumford regularity and the multiplicity of these rings while most of the previous works in this highly investigated area of research involve path counting arguments we offer here a new and self contained approach based on results from gorenstein liaison theory

quantitative approach to multifractality induced by correlations and broad distribution of data abstract we analyze quantitatively the effect of spurious multifractality induced by the presence of fat tailed symmetric and asymmetric probability distributions of fluctuations in time series in the presented approach different kinds of symmetric and asymmetric broad probability distributions of synthetic data are examined starting from levy regime up to those with finite variance we use nonextensive tsallis statistics to construct all considered data in order to have good analytical description of frequencies of fluctuations in the whole range of their magnitude and simultaneously the full control over exponent of power law decay for tails of probability distribution the semi analytical compact formulas are then provided to express the level of spurious multifractality generated by the presence of fat tails in terms of tsallis parameter q and the scaling exponent of the asymptotic decay of cumulated probability density function cdf the results are presented in hurst and holder languages more often used in study of multifractal phenomena according to the provided semi analytical relations it is argued how one can make a clear quantitative distinction for any real data between true multifractality caused by the presence of nonlinear correlations spurious multifractality generated by fat tailed shape of distributions eventually with their asymmetry and the correction due to linear autocorrelations in analyzed time series of finite length in particular the spurious multifractal effect of fat tails is found basic for proper quantitative estimation of all spurious multifractal effects examples from stock market data are presented to support these findings

phase diagrams for three strategy evolutionary prisoner s dilemma games on regular graphs evolutionary prisoner s dilemma games are studied with players located on square lattice and random regular graph defining four neighbors for each one the players follow one of the three strategies tit for tat unconditional cooperation and defection the simplified payoff matrix is characterized by two parameters the temptation b to choose defection and the cost c of inspection reducing the income of tit for tat the strategy imitation from one of the neighbors is controlled by pairwise comparison at a fixed level of noise using monte carlo simulations and the extended versions of pair approximation we have evaluated the b c phase diagrams indicating a rich plethora of phase transitions between stationary coexistence absorbing and oscillatory states including continuous and discontinuous phase transitions by reasonable costs the tit for tat strategy prevents extinction of cooperators across the whole span of b determining the prisoner s dilemma game irrespective of the connectivity structure we also demonstrate that the system can exhibit a repetitive succession of oscillatory and stationary states upon changing a single payoff value which highlights the remarkable sensitivity of cyclical interactions on the parameters that define the strength of dominance

rock scissors paper game on regular small world networks the spatial rock scissors paper game or cyclic lotka volterra system is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours degree at each site on the square lattice this system exhibits a self organizing pattern with equal concentration of the competing strategies species if the quenched background is constructed by substituting random links for the nearest neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value this transition can also be observed if the standard link is replaced temporarily by a random one with a probability p at each step of iteration above a second threshold value of p the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous absorbing states in this case the results of monte carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one two four and six site clusters

statistical properties of share volume traded in financial markets we quantitatively investigate the ideas behind the often expressed adage it takes volume to move stock prices and study the statistical properties of the number of shares traded q deltat for a given stock in a fixed time interval deltat we analyze transaction data for the largest 1000 stocks for the two year period 1994 95 using a database that records every transaction for all securities in three major us stock markets we find that the distribution p q deltat displays a power law decay and that the time correlations in q deltat display long range persistence further we investigate the relation between q deltat and the number of transactions n deltat in a time interval deltat and find that the long range correlations in q deltat are largely due to those of n deltat our results are consistent with the interpretation that the large equal time correlation previously found between q deltat and the absolute value of price change g deltat related to volatility are largely due to n deltat

multifractal geometry in stock market time series it has been recently noticed that time series of returns in stock markets are of multifractal multiscaling character in that context multifractality has been always evidenced by its statistical signature i e the scaling exponents associated to a related variable however a direct geometrical framework much more revealing about the underlying dynamics is possible in this paper we present the techniques allowing the multifractal decomposition we will show that there exists a particular fractal component the most singular manifold msm which contains the relevant information about the dynamics of the series it is possible to reconstruct the series at a given precision from the msm we analyze the dynamics of the msm which shows revealing features about the evolution of this type of series