memory function versus binary correlator in additive markov chains abstract we study properties of the additive binary markov chain with short and long range correlations a new approach is suggested that allows one to express global statistical properties of a binary chain in terms of the so called memory function the latter is directly connected with the pair correlator of a chain via the integral equation that is analyzed in great detail to elucidate the relation between the memory function and pair correlator some specific cases were considered that may have important applications in different fields

memory functions of the additive markov chains applications to complex dynamic systems abstract a new approach to describing correlation properties of complex dynamic systems with long range memory based on a concept of additive markov chains phys rev e 68 2003 061107 is developed an equation connecting the memory and correlation function of the system under study is presented this equation allows reconstructing a memory function using a correlation function of the system effectiveness and robustness of the proposed method is demonstrated by simple model examples memory functions of concrete coarse grained literary texts are found and their universal power law behavior at long distances is revealed

binary n step markov chains and long range correlated systems a theory of systems with long range correlations based on the consideration of binary n step markov chains is developed in our model the conditional probability that the i th symbol in the chain equals zero or unity is a linear function of the number of unities among the preceding n symbols the correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length l are obtained analytically and numerically if the persistent correlations are not extremely strong the variance is shown to be nonlinearly dependent on l a self similarity of the studied stochastic process is revealed the applicability of the developed theory to the coarse grained written and dna texts is discussed

application of a quantum ensemble model to linguistic analysis abstract a new set of parameters to describe the behavior of word frequencies in texts is proposed an analogy between the word frequency distribution and the bose distribution is suggested and the notion of temperature is introduced for this case the calculations are made for english ukrainian and the guinean maninka languages a correlation between the language structure the level of analyticity and the defined parameters is shown to exist

a growth model that generates an n tuple zipf law abstract the n tuple zipf law widely exists in real symbol sequences such as dna and language based on the n tuple zipf analysis on a vast amount of empirical data we propose a model that can generate sequences with n tuple zipf features in simple words it is an iterative copy and paste process repeatedly select a random subsequence from the current sequence and attach it to the end numerical results of our model show that the n tuple zipf law exists in our model generated data we give detailed analytical derivations of our model and get two estimation equations the zipf exponent and the minimal length of n tuple for zipf law to appear our model can also reproduce the symmetry breaking process of atgc number differences in dna data

equivariant cohomology of k contact manifolds we investigate the equivariant cohomology of the natural torus action on a k contact manifold and its relation to the topology of the reeb flow using the contact moment map we show that the equivariant cohomology of this action is cohen macaulay the natural substitute of equivariant formality for torus actions without fixed points as a consequence generic components of the contact moment map are perfect morse bott functions for the basic cohomology of the orbit foliation mathcal f of the reeb flow assuming that the closed reeb orbits are isolated we show that the basic cohomology of mathcal f vanishes in odd degrees and that its dimension equals the number of closed reeb orbits we characterize k contact manifolds with minimal number of closed reeb orbits as real cohomology spheres we also prove a gkm type theorem for k contact manifolds which allows to calculate the equivariant cohomology algebra under the nonisolated gkm condition

bunches of random cross correlated sequences the statistical properties of random cross correlated sequences constructed by the convolution method likewise referred to as the rice or the inverse fourier transformation are examined we clarify the meaning of the filtering function the kernel of the convolution operator and show that it is the value of the cross correlation function which describes correlations between the initial white noise and constructed correlated sequences the matrix generalization of this method for constructing a bunch of n cross correlated sequences is presented algorithms for their generation are reduced to solving the problem of decomposition of the fourier transform of the correlation matrix into a product of two mutually conjugate matrices different decompositions are considered the limits of weak and strong correlations for the one point probability and pair correlation functions of sequences generated by the method under consideration are studied special cases of heavy tailed distributions of the generated sequences are analyzed we show that if the filtering function is rather smooth the distribution function of generated variables has the gaussian or levy form depending on the analytical properties of the distribution or characteristic functions of the initial white noise anisotropic properties of statistically homogeneous random sequences related to the asymmetry of a filtering function are revealed and studied these asymmetry properties are expressed in terms of the third or fourth order correlation functions several examples of the construction of correlated chains with a predefined correlation matrix are given

distributions of triplets in genetic sequences abstract distributions of triplets in some genetic sequences are examined and found to be well described by a two parameter markov process with a sparse transition matrix the standard deviations of all the relevant parameters are not large indicating that most sequences gather in a small region in the parameter space different sequences have very similar values of the entropy calculated directly from the data and the two parameters characterizing the markov process fitting the sequence no relevance with taxonomy or coding noncoding is clearly observed

simultaneous reconstruction of material and transient source parameters using the invariant imbedding method this paper extends the time domain wave splitting and invariant imbedding method to an inhomogeneous wave equation with a source term uxx utt a x ux 2d x i t the direct scattering and inverse source problems of this equation are studied operators j that map the source function into the scattered waves at the edges of the slab are defined a system of coupled nonlinear integrodifferential equations for these scattering operator kernels is obtained the direct scattering problem is to obtain the scattering operator kernels j and r when parameters a and d are given the inverse problem is to simultaneously reconstruct a x and d x from the scattering operator kernels r 0 t 0 t 2 and j 0 t 0 t 1 both numerical inversion algorithms and the small time approximate reconstruction method are presented a green s function technique is used to derive green s operator kernel equations for the calculation of the internal field it provides an alternative effective and fast way to compute the scatterin

fitting chinese syllable to character mapping spectrum by the beta rank function abstract we define the syllable to character mapping spectrum in chinese as the normalized number of characters per syllable ranked from high to low this spectrum provides a statistical characterization of the relationship between spoken and written chinese we have shown that two functions the logarithmic function and the beta rank function fit the syllable to character mapping spectrum well the beta rank function is even better than the logarithmic function judged by two measures of data fitting performance the sum of square errors and akaike information criterion we comment on why the beta rank function is a good fitting function for many range limited ranking data whereas for range open data it may be out performed by other functions such as a power law function in the case of zipf s law

can analysis of word frequency distinguish between writings of different authors abstract various literature writings are compared by the rank distance d between two word frequency zipf plots introduced by s havlin physica a 216 1995 148 we studied 22 books written by six authors for this ensemble of books we find that the mean distance between books written by the same authors d 15 2 2 6 is considerably smaller than that between books written by different authors d 21 8 3 2 in good agreement with earlier results on a smaller sample of books our results suggest that the distribution of the rank difference of the same words in different books decays exponentially

method for generating long range correlations for large systems we propose a new method to generate a sequence of random numbers with long range power law correlations that overcomes known difficulties associated with large systems the new method presents an improvement on the commonly used methods we apply the algorithm to generate enhanced diffusion isotropic and anisotropic self affine surfaces and isotropic and anisotropic correlated percolation

multi directed eulerian growing networks abstract we introduce and analyze a model of a multi directed eulerian network that is a directed and weighted network where a path exists that passes through all the edges of the network once and only once networks of this type can be used to describe information networks such as human language or dna chains we are able to calculate the strength and degree distribution in this network and find that they both exhibit a power law with an exponent between 2 and 3 we then analyze the behavior of the accelerated version of the model and find that the strength distribution has a double slope power law behavior finally we introduce a non eulerian version of the model and find that the statistical topological properties remain unchanged our analytical results are compared with numerical simulations

cyclization of a polymer first passage problem for a non markovian process we discuss a closure of a polymer chain released from a state with given end to end distance considering the situation as a first passage problem for a non markovian process we express the survival probability through the three time distribution of the end to end distance and evaluate it numerically by solving a volterra equation we also show how the wilemski fixmann approximation emerges within this scheme and discuss its geometrical nature

long range memory and non markov statistical effects in human sensorimotor coordination in this paper the non markov statistical processes and long range memory e ects in human sensorimotor coordination are investigated the theoretical basis of this study is the statistical theory of non stationary discrete non markov processes in complex systems phys rev e 62 6178 2000 the human sensorimotor coordination was experimentally studied by means of standard dynamical tappingtest on the g roup of 32 youngpeoples with tap numbers up to 400 this test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere the numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function the memory functions of low orders and the 7rst three points of the statistical spectrum of non markovity parameter our observations demonstrate that with the regard to results of the standard dynamic tapping test it is possible to divide all examinees into 7ve di erent dynamic types we have introduced the con ict coe cient to estimate quantitatively the order disorder e ects underlying life systems the last one re ects the existence of disbalance between the nervous and the motor human coordination the suggested classi7cation of the neurophysiological activity represents the dynamic generalization of the well known neuropsychological types and provides the new approach in a modern neuropsychology c

correlation properties of the random linear high order markov chains abstract the aim of this paper is to study the correlation properties of random sequences with additive linear conditional probability distribution function cpdf and elaborate a reliable tool for their generation it is supposed that the state space of the sequence under examination belongs to a finite set of real numbers the cpdf is assumed to be additive and linear with respect to the values of the random variable we derive the equations that relate the correlation functions of the sequence to the memory function coefficients which determine the cpdf the obtained analytical solutions for the equations connecting the memory and correlation functions are compared with the results of numerical simulation examples of possible correlation scenarios in the high order additive linear chains are given

computation of generalized equivariant cohomologies of kac moody flag varieties abstract in 1998 goresky kottwitz and macpherson showed that for certain projective varieties x equipped with an algebraic action of a complex torus t the equivariant cohomology ring h t x can be described by combinatorial data obtained from its orbit decomposition in this paper we generalize their theorem in three different ways first our group g need not be a torus second our space x is an equivariant stratified space along with some additional hypotheses on the attaching maps third and most important we allow for generalized equivariant cohomology theories e g instead of h t for these spaces we give a combinatorial description of e g x as a subring of e g f i where the f i are certain invariant subspaces of x our main examples are the flag varieties g p of kac moody groups g with the action of the torus of g in this context the f i are the t fixed points and e g is a t equivariant complex oriented cohomology theory such as h t k t or mu t we detail several explicit examples

an electromagnetic inverse problem for dispersive media the dispersion of transient electromagnetic waves in a homogeneous medium can be characterized by expressing either the complex permittivity as a function of frequency or the susceptibility kernel as a function of time in this paper a time domain technique is used to derive a nonlinear integrodifferential equation which relates the susceptibility kernel for a one dimensional homogeneous slab to the reflection operator for the medium thus the susceptibility kernel which is a function of time can be determined from reflection data a numerical implementation of this technique is shown the more general case of a medium consisting of a stack of homogeneous dispersive layers is also addressed

continuous stochastic processes with nonlocal memory we study the non markovian random continuous processes described by the mori zwanzig equation as a starting point we use the markovian gaussian ornstein uhlenbeck process and introduce an integral memory term depending on the past of the process into an expression for the higher order transition probability function and the stochastic differential equation we show that the proposed processes can be considered as continuous time interpolations of discrete time higher order autoregressive sequences an equation connecting the memory function the kernel of integral term and the two point correlation function is obtained a condition for stationarity of the process is established we suggest a method to generate stationary continuous stochastic processes with a prescribed pair correlation function as an illustration some examples of numerical simulation of the processes with nonlocal memory are presented

isotropy properties of the multi step markov symbolic sequences abstract a new object of the probability theory the two sided chain of symbols introduced in ref arxiv physics 0306170 is used to study isotropy properties of binary multi step markov chains with the long range correlations established statistical correspondence between the markov chains and certain two sided sequences allows us to prove the isotropy properties of three classes of the markov chains one of them is the important class of weakly correlated additive markov chains which turned out to be equivalent to the additive two sided sequences

exact moments in a continuous time random walk with complete memory of its history we present a continuous time generalization of a random walk with complete memory of its history phys rev e 70 045101 r 2004 and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is poisson distributed we analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion these transitions which are also present in the discrete time case arise from the memory of the process and are not reproduced by fokker planck approximations to the evolution equation of this random walk

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

phase transition in random walks with long range correlations motivated by recent results in the theory of correlated sequences we analyze the dynamics of random walks with long term memory binary chains with long range correlations in our model the probability for a unit bit in a binary string depends on the fraction of unities preceding it we show that the system undergoes a dynamical phase transition from normal diffusion in which the variance d l scales as the string s length l into a superdiffusion phase d l approximately lalpha alpha 1 when the correlation strength exceeds a critical value we demonstrate the generality of our results with respect to alternative models and discuss their applicability to various data such as coarse grained dna sequences written texts and financial data

memory functions and correlations in additive binary markov chains a theory of additive markov chains with a long range memory proposed earlier in usatenko et al 2003 phys rev e 68 061107 is developed and used to describe statistical properties of long range correlated systems the convenient characteristics of such systems memory functions and their relation to the correlation properties of the systems are examined various methods for finding the memory function via the correlation function are proposed the inverse problem calculation of the correlation function by means of the prescribed memory function is also solved this is demonstrated for the analytically solvable model of the system with a step wise memory function

competition between two kinds of correlations in literary texts a theory of additive markov chains with long range memory is used to describe the correlation properties of coarse grained literary texts the complex structure of the correlations in the texts is revealed anti persistent correlations at small distances l approximately 300 define this non trivial structure for some concrete examples of literary texts the memory functions are obtained and their power law behavior at long distances is disclosed this property is shown to be a cause of self similarity of texts with respect to the decimation procedure

probability distribution of intersymbol distances in random symbolic sequences applications to improving detection of keywords in texts and of amino acid clustering in proteins symbolic sequences have been extensively investigated in the past few years within the framework of statistical physics paradigmatic examples of such sequences are written texts and deoxyribonucleic acid dna and protein sequences in these examples the spatial distribution of a given symbol a word a dna motif an amino acid is a key property usually related to the symbol importance in the sequence the more uneven and far from random the symbol distribution the higher the relevance of the symbol to the sequence thus many techniques of analysis measure in some way the deviation of the symbol spatial distribution with respect to the random expectation the problem is then to know the spatial distribution corresponding to randomness which is typically considered to be either the geometric or the exponential distribution however these distributions are only valid for very large symbolic sequences and for many occurrences of the analyzed symbol here we obtain analytically the exact randomly expected spatial distribution valid for any sequence length and any symbol frequency and we study its main properties the knowledge of the distribution allows us to define a measure able to properly quantify the deviation from randomness of the symbol distribution especially for short sequences and low symbol frequency we apply the measure to the problem of keyword detection in written texts and to study amino acid clustering in protein sequences in texts we show how the results improve with respect to previous methods when short texts are analyzed in proteins which are typically short we show how the measure quantifies unambiguously the amino acid clustering and characterize its spatial distribution

non abelian gkm theory we describe a generalization of gkm theory for actions of arbitrary compact connected lie groups to an action satisfying the non abelian gkm conditions we attach a graph encoding the structure of the non abelian 1 skeleton i e the subspace of points with isotopy rank at most one less than the rank of the acting group we show that the algebra structure of the equivariant cohomology can be read off from this graph in comparison with ordinary abelian gkm theory there are some special features due to the more complicated structure of the non abelian 1 skeleton

correlation function inadequacy in random sequence entropy measures considering symbolic and numerical random sequences in the framework of the additive markov chain approach we establish a relation between their correlation functions and conditional entropies we express the entropy by means of the two point probability distribution functions and then evaluate the entropy for the numerical random chain in terms of the correlation function we show that such approximation gives a satisfactory result only for special types of random sequences in general case the conditional entropy of numerical sequences obtained in the two point distribution function approach is lower we derive the conditional entropy of the additive markov chain as a sum of the kullback leibler mutual information and give an example of random sequence with the exactly zero correlation function and the nonzero correlations

the mathematical relationship between zipf s law and the hierarchical scaling law abstract the empirical studies of city size distribution show that zipf s law and the hierarchical scaling law are linked in many ways the rank size scaling and hierarchical scaling seem to be two different sides of the same coin but their relationship has never been revealed by strict mathematical proof in this paper the zipf s distribution of cities is abstracted as a q sequence based on this sequence a self similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence an exponential distribution of the average size of cities is derived from the hierarchy thus we have two exponential functions from which follows a hierarchical scaling equation the results can be statistically verified by simple mathematical experiments and observational data of cities a theoretical foundation is then laid for the conversion from zipf s law to the hierarchical scaling law and the latter can show more information about city development than the former moreover the self similar hierarchy provides a new perspective for studying networks of cities as complex systems a series of mathematical rules applied to cities such as the allometric growth law the 2 n principle and pareto s law can be associated with one another by the hierarchical organization

rank distributions of words in correlated symbolic systems and the zipf law the binary many step markov chain with the step like memory function is considered as a model for the analysis of rank distributions of words in correlated stochastic symbolic systems we prove that this distribution obeys the power law with the exponent of the order of unity in the case of rather strong persistent correlations the zipf law is shown to be valid for the rank distribution of words with lengths about and shorter than the correlation length in the markov sequence a self similarity in the rank distribution with respect to the decimation procedure is observed

entropy of high order markov chains beyond the pair correlations abstract the main goal of this paper is to develop an estimate for the entropy of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet we present here the detailed analytical study of the entropy for the high order markov chain in the bilinear approximation in the limit of weak correlations we present analytically the entropy of sequence by means of correlation functions of the second and third orders the appendix contains a short comprehensive introduction into the subject of study

fisher information and the thermodynamics of scale invariant systems abstract we present a thermodynamic formulation for scale invariant systems based on the minimization with constraints of the fisher information measure in such a way a clear analogy between these systems thermal properties and those of gases and fluids is seen to emerge in a natural fashion we focus our attention on the non interacting scenario speaking thus of scale free ideal gases sfigs and present some empirical evidences regarding such disparate systems as electoral results city populations and total citations in physics journals that seem to indicate that sfigs do exist we also illustrate the way in which zipf s law can be understood in a thermodynamical context as the surface of a finite system finally we derive an equivalent microscopic description of our systems which totally agrees with previous numerical simulations found in the literature

a formalism for studying long range correlations in many alphabets sequences abstract we formulate a mean field like theory of long range correlated l alphabets sequences which are actually systems with l 1 independent parameters depending on the values of these parameters the variance on the average number of any given symbol in the sequence shows a linear or a superlinear dependence on the total length of the sequence we present exact solution to the four alphabets and three alphabets sequences we also demonstrate that a mapping of the given sequence into a smaller alphabets sequence namely a coarse graining process does not necessarily imply that long range correlations found in the latter would correspond to those of the former

equilibrium and dynamic methods when comparing an english text and its esperanto translation abstract a comparison of two english texts written by lewis carroll one alice in wonderland also translated into esperanto the other through the looking glass are discussed in order to observe whether natural and artificial languages significantly differ from each other one dimensional time series like signals are constructed using only word frequencies fts or word lengths lts the data is studied through i a zipf method for sorting out correlations in the fts and ii a grassberger procaccia gp technique based method for finding correlations in lts the methods correspond to an equilibrium and a dynamic approach respectively to human texts features there are quantitative statistical differences between the original english text and its esperanto translation but the qualitative differences are very minutes however different power laws are observed with characteristic exponents for the ranking properties and the phase space attractor dimensionality the zipf exponent can take values much less than unity 0 50 or 0 30 depending on how a sentence is defined this variety in exponents can be conjectured to be an intrinsic measure of the book style or purpose rather than the language or author vocabulary richness since a similar exponent is obtained whatever the text moreover the attractor dimension r is a simple function of the so called phase space dimension n i e r n with 0 79 such an exponent could also be conjectured to be a measure of the author style versatility here well preserved in the translation

antipersistent binary time series completely antipersistent binary time series are sequences in which every time that an n bit string appears the sequence is continued with a different bit than that after the last occurrence of this dynamics is phrased in terms of a walk on a debruijn graph and properties of transients and cycles are studied the predictability of the generated time series for an observer who sees a longer or shorter time window is investigated also for sequences that are not completely antipersistent

phase transition and information cascade in a voting model in this paper we introduce a voting model that is similar to a keynesian beauty contest and analyse it from a mathematical point of view there are two types of voters copycat and independent and two candidates our voting model is a binomial distribution independent voters doped in a beta binomial distribution copycat voters we find that the phase transition in this system is at the upper limit of t where t is the time or the number of the votes our model contains three phases if copycats constitute a majority or even half of the total voters the voting rate converges more slowly than it would in a binomial distribution if independents constitute the majority of voters the voting rate converges at the same rate as it would in a binomial distribution we also study why it is difficult to estimate the conclusion of a keynesian beauty contest when there is an information cascade

reconstruction of source and medium parameters via wave splitting and green function equations this paper applies the time domain wave splitting and the green function concepts to study two inverse problems involving an internal transient source embedded in a nondispersive inhomogeneous medium these two inverse problems are 1 given the physical one way travel time green operator kernel bar g 0 t and the source space distribution function reconstruct the wave speed profile c z of the medium 2 given the same kernel bar g 0 t and the medium wave speed function recover the source space distribution profile p z both numerical inversion algorithms and approximate reconstruction formulas are presented several computational examples are given

spectral analysis and synthesis of 1d dichotomous long range correlated systems from diffraction gratings to quantum wires spectral properties of 1d systems with long range correlated disorder and their response to an applied field are examined an algorithm based on the additive multi step markov chains is used to ana

symbolic stochastic dynamical systems viewed as binary n step markov chains a theory of systems with long range correlations based on the consideration of binary n step markov chains is developed in the model the conditional probability that the ith symbol in the chain equals zero or unity is a linear function of the number of unities among the preceding n symbols the correlation and distribution functions as well as the variance of the number of symbols in the words of arbitrary length l are obtained analytically and numerically a self similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented the diffusion fokker planck equation governing the distribution function of the l words is explored if the persistent correlations are not extremely strong the distribution function is shown to be the gaussian with the variance being nonlinearly dependent on l the applicability of the developed theory to the coarse grained written and dna texts is discussed

survival probabilities of history dependent random walks we analyze the dynamics of random walks with long term memory binary chains with long range correlations in the presence of an absorbing boundary an analytically solvable model is presented in which a dynamical phase transition occurs when the correlation strength parameter ensuremath mu reaches a critical value ensuremath mu c for strong positive correlations ensuremath mu g ensuremath mu c the survival probability is asymptotically finite whereas for ensuremath mu l ensuremath mu c it decays as a power law in time chain length

equivariant cohomology of quaternionic flag manifolds abstract the main result of the paper is a borel type description of the sp 1 n equivariant cohomology ring of the manifold fl n h of all complete flags in h n to prove this we obtain a goresky kottwitz macpherson type description of that ring

randomness versus specifics for word frequency distributions the text length dependence of real word frequency distributions can be connected to the general properties of a random book it is pointed out that this finding has strong implications when decidi

direct and inverse scattering in the time domain via invariant imbedding equations this paper examines the implementation of a new approach to direct and inverse scattering problems in the time domain which is applied here to the case of a one dimensional lossless medium the method is based on an integro differential equation which is satisfied by the reflection kernel and has been derived elsewhere using invariant imbedding techniques an example of an exact solution to this equation is given numerical schemes for solving the direct and inverse problems are derived by discretizing this equation the behavior of the resulting algorithms is then tested on several examples the results suggest that the inversion method is stable in the presence of additive noise