decoding least effort and scaling in signal frequency distributions abstract here assuming a general communication model where objects map to signals a power function for the distribution of signal frequencies is derived the model relies on the satisfaction of the receiver hearer communicative needs when the entropy of the number of objects per signal is maximized evidence of power distributions in a linguistic context some of them with exponents clearly different from the typical 2 of zipf s law is reviewed and expanded we support the view that zipf s law reflects some sort of optimization but following a novel realistic approach where signals e g words are used according to the objects e g meanings they are linked to our results strongly suggest that many systems in nature use non trivial strategies for easing the interpretation of a signal interestingly constraining just the number of interpretations of signals does not lead to scaling

hamiltonian dynamics of preferential attachment prediction and control of network dynamics are grand challenge problems in network science the lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades here we study the dynamics of networks evolving according to preferential attachment pa known to approximate well the large scale growth dynamics of a variety of real networks we show that this dynamics is hamiltonian thus casting the study of complex networks dynamics to the powerful canonical formalism in which the time evolution of a dynamical system is described by hamilton s equations we derive the explicit form of the hamiltonian that governs network growth in pa this hamiltonian turns out to be nearly identical to graph energy in the configuration model which shows that the ensemble of random graphs generated by pa is nearly identical to the ensemble of random graphs with scale free degree distributions in other words pa generates nothing but random graphs with power law degree distribution the extension of the developed canonical formalism for network analysis to richer geometric network models with non degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales

clustering of random scale free networks we derive the finite size dependence of the clustering coefficient of scale free random graphs generated by the configuration model with degree distribution exponent 2l ensuremath gamma l3 degree heterogeneity increases the presence of triangles in the network up to levels that compare to those found in many real networks even for extremely large nets we also find that for values of ensuremath gamma ensuremath approx 2 clustering is virtually size independent and at the same time becomes a de facto non self averaging topological property this implies that a single instance network is not representative of the ensemble even for very large network sizes

understanding scaling through history dependent processes with collapsing sample space history dependent processes are ubiquitous in natural and social systems many such stochastic processes especially those that are associated with complex systems become more constrained as they unfold meaning that their sample space or their set of possible outcomes reduces as they age we demonstrate that these sample space reducing ssr processes necessarily lead to zipf s law in the rank distributions of their outcomes we show that by adding noise to ssr processes the corresponding rank distributions remain exact power laws p x x where the exponent directly corresponds to the mixing ratio of the ssr process and noise this allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its sample space as it unfolds noisy ssr processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from 2 to we discuss several applications showing how ssr processes can be used to understand zipf s law in word frequencies and how they are related to diffusion processes in directed networks or aging processes such as in fragmentation processes ssr processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative preferential or self organized critical processes

tutte polynomial of scale free networks the tutte polynomial of a graph or equivalently the q state potts model partition function is a two variable polynomial graph invariant of considerable importance in both statistical physics and combinatorics the computation of this invariant for a graph is np hard in general in this paper we focus on two iteratively growing scale free networks which are ubiquitous in real life systems based on their self similar structures we mainly obtain recursive formulas for the tutte polynomials of two scale free networks lattices one is fractal and large world while the other is non fractal but possess the small world property furthermore we give some exact analytical expressions of the tutte polynomial for several special points at x y plane such as the number of spanning trees the number of acyclic orientations etc

black scholes schrodinger zipf mandelbrot model framework for improving a study of the coauthor core score abstract the data and findings by miskiewicz 2013 on the relationship between the number j of publications ranked according to their decreasing importance for some scientist with her his coauthors ca i e j 1 r as found in ausloos 2013 when specific types of publications i e proceedings in a generalized sense and peer review journals are considered are reexamined along the zipf mandelbrot law mandelbrot 1977 i e j 1 r the statistics are much improved the exponent and are compared the m a core value i e the core number of cas 1 is unaffected of course a black scholes schrodinger model framework is proposed to describe the findings

nondistributive algebraic structures derived from nonextensive statistical mechanics we propose a two parametric nondistributive algebraic structure that follows from q q logarithm and q q exponential functions properties of generalized q q operators are analyzed we also generalize the proposal into a multiparametric structure generalization of logarithm and exponential functions and the corresponding algebraic operators all n parameter expressions recover n 1 generalization when the corresponding qn 1 nonextensive statistical mechanics has been the source of successive generalizations of entropic forms and mathematical structures in which this work is a consequence

ferromagnetic phase transitions of inhomogeneous systems modelled by square ising models with diamond type bond decorations abstract the two dimensional ising model defined on square lattices with diamond type bond decorations is employed to study the nature of the ferromagnetic phase transitions of inhomogeneous systems the model is studied analytically under the bond renormalization scheme for an n level decorated lattice the long range ordering occurs at the critical temperature given by the fitting function k b t c j n 1 6410 0 6281 exp 0 5857 n and the local ordering inside n level decorated bonds occurs at the temperature given by the fitting function k b t m j n 1 6410 0 8063 exp 0 7144 n the critical amplitude a sin g n of the logarithmic singularity in specific heat characterizes the width of the critical region and it varies with the decoration level n as a sin g n 0 2473 exp 0 3018 n obtained by fitting the numerical results the cross over from a finite decorated system to an infinite decorated system is not a smooth continuation for the case of infinite decorations the critical specific heat becomes a cusp with the height c n 0 639852 the results are compared with those obtained in the cell decorated ising model

information entropy and power law distributions for chaotic systems the power law is found for density distributions for the chaotic systems of most different nature physical geophysical biological economical social etc on the basis of the maximum entropy principle for the renyi entropy its exponent q is expressed as a function q of the renyi parameter the difference between the renyi and boltzmann shannon entropies a modified lyapunov functional r for the same power law distribution is negative and as a function of has a well defined minimum at which remains within the narrow range from 1 5 to 3 when varying other characteristic parameters of any concrete systems relevant variations of the exponent q are found within the range 1 3 5 the same range of observable values of q is typical for the various applications where the power law distribution takes place it is known under the following names triangular or trapezoidal in physics and technics gutenberg richter law in geophysics zipf pareto law in economics and the humanities lotka low in science of science etc as the negative r indicates self organisation of the system the negative minimum of r corresponds to the most self organised state thus the comparison between the calculated range of variations of q and observable values of the exponent q testifies that the most self organised states are as a rule realised regardless of the nature of a chaotic system

generalized entropies and the transformation group of superstatistics superstatistics describes statistical systems that behave like superpositions of different inverse temperatures so that the probability distribution is where the kernel f is nonnegative and normalized f d 1 we discuss the relation between this distribution and the generalized entropic form the first three shannon khinchin axioms are assumed to hold it then turns out that for a given distribution there are two different ways to construct the entropy one approach uses escort probabilities and the other does not the question of which to use must be decided empirically the two approaches are related by a duality the thermodynamic properties of the system can be quite different for the two approaches in that connection we present the transformation laws for the superstatistical distributions under macroscopic state changes the transformation group is the euclidean group in one dimension

the primes contain arbitrarily long arithmetic progressions we prove that there are arbitrarily long arithmetic progressions of primes there are three major ingredients the first is szemeredi s theorem which asserts that any subset of the integers of positive density contains progressions of arbitrary length the second which is the main new ingredient of this paper is a certain transference principle this allows us to deduce from szemeredi s theorem that any subset of a suficiently pseudorandom set or measure of positive relative density contains progressions of arbitrary length the third ingredient is a recent result of goldston and yildirim which we reproduce here using this one may place a large fraction of the primes inside a pseudorandom set of almost primes or more precisely a pseudorandom measure concentrated on almost primes with positive relative density

q plane zeros of the potts partition function on diamond hierarchical graphs we report exact results concerning the zeros of the partition function of the potts model in the complex q plane as a function of a temperature like boltzmann variable v for the m th iterate graphs dm of the diamond hierarchical lattice including the limit m in this limit we denote the continuous accumulation locus of zeros in the q planes at fixed v v0 as bq v0 we apply theorems from complex dynamics to establish the properties of bq v0 for v 1 the zero temperature potts antiferromagnet or equivalently chromatic polynomial we prove that bq 1 crosses the real q axis at i a minimal point q 0 ii a maximal point q 3 iii q 32 27 iv a cubic root that we give with the value q q1 1 638 896 9 and v an infinite number of points smaller than q1 converging to 32 27 from above similar results hold for bq v0 for any 1 0 potts ferromagnet we also provide the computer generated plots of bq v0 at various values of v0 in both the antiferromagnetic and ferromagnetic regimes and compare them to the numerically computed zeros of z d4 q v0

statistical ensemble of scale free random graphs a thorough discussion of the statistical ensemble of scale free connected random tree graphs is presented methods borrowed from field theory are used to define the ensemble and to study analytically its properties the ensemble is characterized by two global parameters the fractal and the spectral dimensions which are explicitly calculated it is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified the stability of the scale free regime is also considered when it breaks down either a scale is spontaneously generated or else a singular node appears and the graphs become crumpled a new computer algorithm to generate these random graphs is proposed possible generalizations are also discussed in particular more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary degenerate scale free random graphs

determining the number of samples required to estimate entropy in natural sequences calculating the shannon entropy for symbolic sequences has been widely considered in many fields for descriptive statistical problems such as estimating the n gram entropy of english language text a common approach is to use as much data as possible to obtain progressively more accurate estimates however in some instances only short sequences may be available this gives rise to the question of how many samples are needed to compute entropy in this paper we examine this problem and propose a method for estimating the number of samples required to compute shannon entropy for a set of ranked symbolic natural events the result is developed using a modified zipf mandelbrot law and the dvoretzky kiefer wolfowitz inequality and we propose an approximation which yields an estimate for the minimum number of samples required to obtain an estimate of entropy with a given confidence level and degree of accuracy

first digit law in nonextensive statistics nonextensive statistics characterized by a nonextensive parameter q is a promising and practically useful generalization of the boltzmann statistics to describe power law behaviors from physical and social observations we here explore the unevenness of the first digit distribution of nonextensive statistics analytically and numerically we find that the first digit distribution follows benford s law and fluctuates slightly in a periodical manner with respect to the logarithm of the temperature the fluctuation decreases when q increases and the result converges to benford s law exactly as q approaches 2 the relevant regularities between nonextensive statistics and benford s law are also presented and discussed

information content of turbulence we treat a turbulent velocity field as a message in the same way as a book or a picture all messages can be described by their entropy per symbol h defined as in shannon s theory of communication in a turbulent flow as the reynolds number re increases more correlated degrees of freedom are excited and participate in the turbulent cascade experiments in a turbulent soap film suggest that the spatial entropy density h is a decreasing function of re namely h proportionality logre const in the logistic map also analyzed here increasing the control parameter r increases h a modified logistic map with additional coupling to past iterations suggests the significance of correlations

strategy for investments from zipf law s abstract we have applied the zipf method to extract the exponent for seven financial indices dax ftse djia nasdaq sp hang seng and nikkei 225 after having translated the signals into a text based on two letters we follow considerations based on the signal hurst exponent and the notion of a time dependent zipf law and exponent in order to implement two simple investment strategies for such indices we show the time dependence of the returns

a tsallis statistics based neural network model for novel word learning abstract we invoke the tsallis entropy formalism a nonextensive entropy measure to include some degree of non locality in a neural network that is used for simulation of novel word learning in adults a generalization of the gradient descent dynamics realized via nonextensive cost functions is used as a learning rule in a simple perceptron the model is first investigated for general properties and then tested against the empirical data gathered from simple memorization experiments involving two populations of linguistically different subjects numerical solutions of the model equations corresponded to the measured performance states of human learners in particular we found that the memorization tasks were executed with rather small but population specific amounts of nonextensivity quantified by the entropic index q our findings raise the possibility of using entropic nonextensivity as a means of characterizing the degree of complexity of learning in both natural and artificial systems

an empirical non parametric likelihood family of data based benford like distributions abstract a mathematical expression known as benford s law provides an example of an unexpected relationship among randomly selected sequences of first significant digits fsds newcomb note on the frequency of use of the different digits in natural numbers am j math 4 1881 39 40 and later benford the law of anomalous numbers proc am philos soc 78 4 1938 551 572 conjectured that fsds would exhibit a weakly monotonic decreasing distribution and proposed a frequency proportional to the logarithmic rule unfortunately the benford fsd function does not hold for a wide range of scale invariant multiplicative data to confront this problem we use information theoretic methods to develop a data based family of alternative benford like exponential distributions that provide null hypotheses for testing purposes two data sets are used to illustrate the performance of generalized benford like distributions

additive rank one preservers on block triangular matrix spaces in this note we address a description of the general form of additive rank one preservers on block triangular matrix spaces over an arbitrary field as an application we characterize additive mappings preserving rank additivity on block triangular matrix algebras

measuring information based energy and temperature of literary texts abstract we apply a statistical method information based energy to quantify informative symbolic sequences to apply this method to literary texts it is assumed that different words with different occurrence frequencies are at different energy levels and that the energy occurrence frequency distribution obeys a boltzmann distribution the temperature within the boltzmann distribution can be an indicator for the author s writing capacity as the repertory of thoughts the relative temperature of a text is obtained by comparing the energy occurrence frequency distributions of words collected from one text versus from all texts of the same author combining the relative temperature with the shannon entropy as the text complexity the information based energy of the text is defined and can be viewed as a quantitative evaluation of an author s writing performance we demonstrate the method by analyzing two authors shakespeare in english and jin yong in chinese and find that their well known works are associated with higher information based energies this method can be used to measure the creativity level of a writer s work in linguistics and can also quantify symbolic sequences in different systems

explaining the uneven distribution of numbers in nature the laws of benford and zipf abstract the distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of benford s law we analyze in detail this property for different data sets and give a general explanation for the origin of the benford s law in terms of multiplicative processes we show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity finally we derive a relation between the generalized benford s law and the popular zipf s law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics

scale free brain functional networks functional magnetic resonance imaging is used to extract functional networks connecting correlated human brain sites analysis of the resulting networks in different tasks shows that a the distribution of functional connections and the probability of finding a link versus distance are both scale free b the characteristic path length is small and comparable with those of equivalent random networks and c the clustering coefficient is orders of magnitude larger than those of equivalent random networks all these properties typical of scale free small world networks reflect important functional information about brain states

benford s law and first letter of words a universal first letter law fll is derived and described it predicts the percentages of first letters for words in novels the fll is akin to benford s law bl of first digits which predicts

the significant digit law in statistical physics abstract the occurrence of the nonzero leftmost digit i e 1 2 9 of numbers from many real world sources is not uniformly distributed as one might naively expect but instead the nature favors smaller ones according to a logarithmic distribution named benford s law we investigate three kinds of widely used physical statistics i e the boltzmann gibbs bg distribution the fermi dirac fd distribution and the bose einstein be distribution and find that the bg and fd distributions both fluctuate slightly in a periodic manner around benford s distribution with respect to the temperature of the system while the be distribution conforms to it exactly whatever the temperature is thus benford s law seems to present a general pattern for physical statistics and might be even more fundamental and profound in nature furthermore various elegant properties of benford s law especially the mantissa distribution of data sets are discussed

uniform random sampling not recommended for large graph size estimation abstract the norm of data size estimation is to use uniform random samples whenever possible there have been tremendous efforts in obtaining uniform random samples using methods such as metropolis hasting random walk or importance sampling 2 this paper shows that on the contrary to the common practice uniform random sampling should be avoided when pps probability proportional to size sampling is available for large data to develop intuition of the sampling process we discuss the sampling and estimation problem in the context of graph the size is the number of nodes in the graph uniform random sampling corresponds to uniform random node rn sampling and pps sampling is approximated by random edge re sampling in this setting we show that for large graphs re sampling outperforms rn sampling with a ratio proportional to the normalized graph degree variance this result is particularly important in the era of big data when data are typically large and scale free 3 resulting in large degree variance we derive the result by giving the variances of rn and re estimators each step of the derivation is supported and demonstrated by simulation studies assuming power law distributions then we use 18 real world networks to verify the result furthermore we show that the performance of random walk rw sampling is data dependent and can be significantly worse than rn and re more specifically rw can estimate online social networks but not web graphs due to the difference of the graph conductance

applications of the first digit law to measure correlations the quasiempirical benford law predicts that the distribution of the first significant digit of random numbers obtained from mixed probability distributions is surprisingly meaningful and reveals some universal behavior we generalize this finding to examine the joint first digit probability of a pair of two random numbers and show that undetectable correlations by means of the usual covariance based measure can be identified in the statistics of the corresponding first digits we illustrate this new measure by analyzing the correlations and anticorrelations of the positions of two interacting particles in their quantum mechanical ground state this suggests that by using this measure the presence or absence of correlations can be determined even if only the first digit of noisy experimental data can be measured accurately

tutte polynomials of two self similar network models the tutte polynomial t g x y of a graph g or equivalently the q state potts model partition function is a two variable polynomial graph invariant of considerable importance in combinatorics and statistical physics graph operations have been extensively applied to model complex networks recently in this paper we study the tutte polynomials of the diamond hierarchical lattices and a class of self similar fractal models which can be constructed through graph operations firstly we find out the behavior of the tutte polynomial under k inflation and k subdivision which are two graph operations secondly we compute and gain the tutte polynomials of this two self similar fractal models by using their structure characteristic moreover as an application of the obtained results some evaluations of their tutte polynomials are derived such as the number of spanning trees and the number of spanning forests

additive preservers of rank on alternate matrix spaces over fields and applications abstract suppose f is any field and n is an integer with n 4 let k n f be the set of all n n alternate matrices over f and let k n f be the non associative ring formed by k n f under the usual addition and the multiplication defined by x y xyx for all x y k n f a pair of n n matrices a b is said to be rank additive if rank a b rank a rank b and rank subtractive if rank a b rank a rank b we say that an operator k n f k n f is additive if x y x y for any x y k n f a preserver of rank additivity respectively rank subtractivity on k n f if it preserves the set of all rank additive respectively rank subtractive pairs a preserver of rank on k n f if rank x rank x for every x k n f and a ring endomorphism of k n f if it is additive and satisfies x y x y for any x y k n f we determine the general form of all additive preservers of rank respectively rank additivity and rank subtractivity on k n f and characterize all ring endomorphisms of k n f

the law of the leading digits and the world religions abstract benford s law states that the occurrence of significant digits in many data sets is not uniform but tends to follow a logarithmic distribution such that the smaller digits appear as first significant digits more frequently than the larger ones we investigate here numerical data on the country wise adherent distribution of seven major world religions i e christianity islam buddhism hinduism sikhism judaism and baha ism to see if the proportion of the leading digits occurring in the distribution conforms to benford s law we find that the adherent data of all the religions except christianity excellently does conform to benford s law furthermore unlike the adherent data on christianity the significant digit distribution of the three major christian denominations i e catholicism protestantism and orthodoxy obeys the law thus in spite of their complexity general laws can be established for the evolution of religious groups

entropy distribution and condensation in random networks with a given degree distribution the entropy of network ensembles characterizes the amount of information encoded in the network structure and can be used to quantify network complexity and the relevance of given structural properties observed in real network datasets with respect to a random hypothesis in many real networks the degrees of individual nodes are not fixed but change in time while their statistical properties such as the degree distribution are preserved here we characterize the distribution of entropy of random networks with given degree sequences where each degree sequence is drawn randomly from a given degree distribution we show that the leading term of the entropy of scale free network ensembles depends only on the network size and average degree and that entropy is self averaging meaning that its relative variance vanishes in the thermodynamic limit we also characterize large fluctuations of entropy that are fully determined by the average degree in the network finally above a certain threshold large fluctuations of the average degree in the ensemble can lead to condensation meaning that a single node in a network of size n can attract o n links

the first digit frequencies of prime numbers and riemann zeta zeros prime numbers seem to be distributed among the natural numbers with no law other than that of chance however their global distribution presents a quite remarkable smoothness such interplay between randomness and regularity has motivated scientists across the ages to search for local and global patterns in this distribution that could eventually shed light on the ultimate nature of primes in this paper we show that a generalization of the well known first digit benford s law which addresses the rate of appearance of a given leading digit d in datasets describes with astonishing precision the statistical distribution of leading digits in the prime number sequence moreover a reciprocal version of this pattern also takes place in the sequence of the non trivial riemann zeta zeros we prove that the prime number theorem is in the final analysis responsible for these patterns

q exponential weibull and q weibull distributions an empirical analysis abstract in a comparative study the q exponential and weibull distributions are employed to investigate frequency distributions of basketball baskets cyclone victims brand name drugs by retail sales and highway length in order to analyze the intermediate cases a distribution the q weibull one which interpolates the q exponential and weibull ones is introduced it is verified that the basketball baskets distribution is well described by a q exponential whereas the cyclone victims and brand name drugs by retail sales ones are better adjusted by a weibull distribution on the other hand for highway length the q exponential and weibull distributions do not give satisfactory adjustment being necessary to employ the q weibull distribution furthermore the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law q exponential with q 1 controversy

criticality of the potts ferromagnet in migdal kadanoff like hierarchical lattices within the real space renormalisation group framework the authors discuss the critical point and exponent nu of the potts ferromagnet in b sized migdal kadanoff like hierarchical lattices both b to infinity and b to 1 limits are exhibited the important discrepancies that might exist between the exact results for d dimensional hierarchical lattices and d dimensional bravais lattices are illustrated

random texts exhibit zipf s law like word frequency distribution it is shown that the distribution of word frequencies for randomly generated texts is very similar to zipf s law observed in natural languages such as english the facts that the frequency of occurrence of a word is almost an inverse power law function of its rank and the exponent of this inverse power law is very close to 1 are largely due to the transformation from the word s length to its rank which stretches an exponential function to a power law function

linear additive preservers of ranks 2 and 4 on alternate matrix spaces over fields abstract let kn f be the linear space of all n n alternate matrices over a field f an operator f kn f kn f is said to be additive if f a b f a f b for any a b kn f linear if f is additive and f aa af a for every a f and a kn f and a preserver of ranks 2 and 4 on kn f if rank f x rank x for every x kn f with rank x 2 or 4 when n 4 we characterize all linear respectively additive preservers of ranks 2 and 4 on kn f over any field respectively any field that is not isomorphic to a proper subfield of itself furthermore it is also shown that the condition f is not isomorphic to a proper subfield of itself is necessary for the obtained conclusion on additive preservers of ranks 2 and 4 on kn f

scale free characteristics of random networks the topology of the world wide web the world wide web forms a large directed graph whose vertices are documents and edges are links pointing from one document to another here we demonstrate that despite its apparent random character the topology of this graph has a number of universal scale free characteristics we introduce a model that leads to a scale free network capturing in a minimal fashion the self organization processes governing the world wide web c 2000 elsevier science b v all rights reserved pacs 84 35 i 64 60 fr 87 23 ge

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

on the nature of benford s law we study multiplicative and a ne sequences of real numbers de1ned by n j 1 j n j j where j and j are sequences of positive real numbers in the multiplicative case j 0 for all j we investigate the conditions under which the leading digits k of n j have the following probability distribution known as benford s law p k log10 k 1 k we present two main results first we show that contrary to the usual assumption in the literature j does not necessarily need to come from a chaotic or independent random process for benford s law to hold the multiplicative driving force may be a deterministic quasiperiodic or even periodic forcing second we give conditions under which the distribution of the 1rst digits of an a ne process displays benford s law our proofs use techniques from ergodic theory c 2002 elsevier science b v all rights reserved

complex networks created by aggregation we study aggregation as a mechanism for the creation of complex networks in this evolution process vertices merge together which increases a number of highly connected hubs we study a range of complex network architectures produced by the aggregation fat tailed in particular scale free distributions of connections are obtained for both networks with a finite number of vertices and growing networks we observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges finally we demonstrate the importance of structural correlations in these networks

statistical mechanical approach to human language abstract we use the formulation of equilibrium statistical mechanics in order to study some important characteristics of language using a simple expression for the hamiltonian of a language system which is directly implied by the zipf law we are able to explain several characteristic features of human language that seem completely unrelated such as the universality of the zipf exponent the vocabulary size of children the reduced communication abilities of people suffering from schizophrenia etc while several explanations are necessarily only qualitative at this stage we have nevertheless been able to derive a formula for the vocabulary size of children as a function of age which agrees rather well with experimental data

hyperbolic geometry of complex networks we develop a geometric framework to study the structure and function of complex networks we assume that hyperbolic geometry underlies these networks and we show that with this assumption heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry conversely we show that if a network has some metric structure and if the network degree distribution is heterogeneous then the network has an effective hyperbolic geometry underneath we then establish a mapping between our geometric framework and statistical mechanics of complex networks this mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes while the auxiliary fields coupled to edges are linear functions of these energies or distances the geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures finally we show that targeted transport processes without global topology knowledge made possible by our geometric framework are maximally efficient according to all efficiency measures in networks with strongest heterogeneity and clustering and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

potts model on sierpinski carpets and their relation to hypercubic lattices of non integer dimensionality the authors study the critical frontiers and the high and low temperature asymptotic behavior of the potts model two site correlation function for several sierpinski carpets with fractal dimension lying between one and two they simulate the sierpinski carpets by means of appropriate hierarchical lattices obtaining from their basic cells the two graphs among others that arise from the anisotropic bond moving schemes they correspond to the asymptotic high and low temperature dominant terms for the hierarchical lattice two site correlation function exact result by taking the infinite limit size of the basic cell these asymptotic behaviors tends to those of the sierpinski carpets it is then possible to compare them with similar results obtained from analytical extension to d 2 of the hypercubic lattice their results indicate that these asymptotic behaviors do not always coincide suggesting that possibly they may not identify the sierpinski carpets exhibited by gefen et al 1984 as a correct implementation of the analytical extension of hypercubic lattices

benford s law a poisson perspective abstract benford s law is a counterintuitive statistical law asserting that the distribution of leading digits taken from a large ensemble of positive numerical values that range over many orders of scale is logarithmic rather than uniform as intuition suggests in this paper we explore benford s law from a poisson perspective considering ensembles of positive numerical values governed by poisson process statistics we show that this poisson setting naturally accommodates benford s law and i establish a poisson characterization and a poisson multidigit extension of benford s law ii study a system invariant leading digit distribution which generalizes benford s law and establish a poisson characterization and a poisson multidigit extension of this distribution iii explore the universal emergence of the system invariant leading digit distribution couple this universal emergence to the universal emergence of the weibull and frechet extreme value distributions and distinguish the special role of benford s law in this universal emergence iv study the continued fractions counterpart of the system invariant leading digit distribution and establish a poisson characterization of this distribution and v unveil the elemental connection between the system invariant leading digit distribution and its continued fractions counterpart this paper presents a panoramic poisson approach to benford s law to its system invariant generalization and to its continued fractions counterpart

maximum entropy formalism fractals scaling phenomena and 1 f noise a tale of tails in this report on examples of distribution functions with long tails we a show that the derivation of distributions with inverse power tails from a maximum entropy formalism would be a consequence only of an unconventional auxilliary condition that involves the specification of the average value of a complicated logarithmic function b review several models that yield log normal distributions c show that log normal distributions may mimic 1 f noise over a certain range and d present an amplification model to show how log normal personal income distributions are transformed into inverse power pareto distributions in the high income range

critical properties of the s4 model on diamond type hierarchial lattices we study the critical properties of the s 4 model on diamond type hierarchical lattices in the presence of an external magnetic field it is assumed that for this type of inhomogenous fractal lattice the gaussian distribution constant the four spins interaction parameter and the external magnetic field in the s4 model depend on the coordination number of the site on the fractal lattices by combining the real space renormalization group scheme with the cumulative expansion method we obtain the critical points and further calculate critical exponents according to the scaling theory the results show that on diamond type hierarchical lattices with branches m 4 of 2 bonds the critical point of the s4 model is just the gaussian fixed point and therefore critical exponents are in full agreement with those of the gaussian model and that on those with m 4 the wilson fisher fixed point as well as the gaussian fixed point is obtained the wilson fisher fixed point has a decisive influence on the critical behavior of the system and critical exponents are related to the fractal dimensionality we found that the s4 model on the fractal lattices and that on the translation symmetric lattices show similar behaviors in the dependence of the critical properties on the dimensionality c 2005 elsevier b v all rights reserved

theory of analogous force on number sets abstract a general statistical thermodynamic theory that considers given sequences of x integers to play the role of particles of known type in an isolated elastic system is proposed by also considering some explicit discrete probability distributions px for natural numbers we claim that they lead to a better understanding of probabilistic laws associated with number theory sequences of numbers are treated as the size measure of finite sets by considering px to describe complex phenomena the theory leads to derive a distinct analogous force fx on number sets proportional to px x t at an analogous system temperature t in particular this leads to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits the theory also allows to establish recursion relations to predict sequences of fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the benford s law in fibonacci numbers a possible relevance to prime numbers is also analyzed

universality in the tail of musical note rank distribution abstract although power laws have been used to fit rank distributions in many different contexts they usually fail at the tails languages as sequences of symbols have been a popular subject for ranking distributions and for this purpose music can be treated as such here we show that more than 1800 musical compositions are very well fitted by the first kind two parameter beta distribution which arises in the ranking of multiplicative stochastic processes the parameters a and b are obtained for classical jazz and rock music revealing interesting features specially we have obtained a clear trend in the values of the parameters for major and minor tonal modes finally we discuss the distribution of notes for each octave and its connection with the ranking of the notes

covid 19 flattening the curve and benford s law for many countries attempting to control the fast rising number of coronavirus cases and deaths the race is on to flatten the curve since the spread of coronavirus disease 2019 covid 19 has taken on pandemic proportions in the absence of significant control interventions the curve could be steep with the number of covid 19 cases growing exponentially in fact this level of proliferation may already be happening since the number of patients infected in italy closely follows an exponential trend thus we propose a test when the numbers are taken from an exponential distribution it has been demonstrated that they automatically follow benford s law bl as a result if the current control interventions are successful and we flatten the curve i e we slow the rate below an exponential growth rate then the number of infections or deaths will not obey bl for this reason bl may be useful for assessing the effects of the current control interventions and may be able to answer the question how flat is flat enough in this study we used an epidemic growth model in the presence of interventions to describe the potential for a flattened curve and then investigated whether the epidemic growth model followed bl for ten selected countries with a relatively high mortality rate among these countries south korea showed a particularly high degree of control intervention although all of the countries have aggressively fought the epidemic our analysis shows that all countries except for japan satisfied bl indicating the growth rates of covid 19 were close to an exponential trend based on the simulation table in this study bl test shows that the data from japan is incorrect

empirical likelihood as a goodness of fit measure summary the method of empirical likelihood can be viewed as one of allocating probabilities to an n cell contingency table so as to minimise a goodness of fit criterion it is shown that when the cressie read power divergence statistic is used as the criterion confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the cressie read parameter including 1 maximum entropy 0 empirical likelihood and 1 pearson s z2 it is noted that in the power divergence family empirical likelihood is the only member which is bartlettcorrectable however simulation results suggest that for the mean using a scaled f distribution yields more accurate coverage levels for moderate sample sizes

the riemann zeros and eigenvalue asymptotics comparison between formulae for the counting functions of the heights tn of the riemann zeros and of semiclassical quantum eigenvalues en suggests that the tn are eigenvalues of an unknown hermitean operator h obtained by quantizing a classical dynamical system with hamiltonian hcl many features of hcl are provided by the analogy for example the riemann dynamics should be chaotic and have periodic orbits whose periods are multiples of logarithms of prime numbers statistics of the tn have a similar structure to those of the semiclassical en in particular they display random matrix universality at short range and nonuniversal behaviour over longer ranges very refined features of the statistics of the tn can be computed accurately from formulae with quantum analogues the riemann siegel formula for the zeta function is described in detail its interpretation as a relation between long and short periodic orbits gives further insights into the quantum spectral fluctuations we speculate that the riemann dynamics is related to the trajectories generated by the classical hamiltonian hcl xp

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

scale free networks with exponent one a majority of studied models for scale free networks have degree distributions with exponents greater than two real networks however can demonstrate essentially more heavy tailed degree distributions we explore two models of scale free equilibrium networks that have the degree distribution exponent ensuremath gamma 1 p q ensuremath sim q ensuremath ensuremath gamma such degree distributions can be identified in empirical data only if the mean degree of a network is sufficiently high our models exploit a rewiring mechanism they are local in the sense that no knowledge of the network structure apart from the immediate neighborhood of the vertices is required these models generate uncorrelated networks in the infinite size limit where they are solved explicitly we investigate finite size effects by the use of simulations we find that both models exhibit disassortative degree degree correlations for finite network sizes in addition we observe a markedly degree dependent clustering in the finite networks we indicate a real world network with a similar degree distribution

additive preservers of rank additivity on the spaces of symmetric and alternate matrices denote the set of n n symmetric matrices resp alternate matrices over a field f by sn f resp kn f we characterize the bijective additive preservers of rank additivity on sn f and kn f the set sn f resp kn f forms a non associative ring with respect to the addition a b a b and the multiplication a b a b aba where a b sn f resp kn f the forms of any automorphism of the two non associative rings are also given

a mechanism to derive multi power law functions an application in the econophysics framework abstract it is generally recognized that economical systems and more in general complex systems are characterized by power law distributions sometime these distributions show a changing of the slope in the tail so that more appropriately they show a multi power law behavior we present a method to derive analytically a two power law distribution starting from a single power law function recently obtained in the frameworks of the generalized statistical mechanics based on the sharma taneja mittal information measure in order to test the method we fit the cumulative distribution of personal income and gross domestic production of several countries obtaining a good agreement for a wide range of data

revisiting the benford law when the benford like distribution of leading digits in sets of numerical data is expectable abstract the benford law states that the frequencies of decimal digits at the first place of numbers corresponding to various kinds of statistical or experimental data are not equal changing from 0 3 for 1 to 0 04 for 9 the corresponding frequencies distribution is described by the logarithmic function as is shown in the present article the benford distribution is a particular case of a more general mathematical statement namely if a function describing the dependence between two measurable quantities has a positive second derivative then the mentioned above frequencies decrease for digits from 1 to 9 the exact benford distribution is valid for the exponential function only explicit expressions for frequencies of leading digits are obtained and specified for the power logarithmic and tangent functions as examples the kinematic experiment was performed to illustrate the above results also the tabulated data on thermal conductivities of liquids confirm the proposed formula for frequencies distribution

beyond the zipf mandelbrot law in quantitative linguistics abstract in this paper the zipf mandelbrot law is revisited in the context of linguistics despite its widespread popularity the zipf mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of words contained in some given corpus in particular we focus our attention on the important deviations that become statistically relevant as larger corpora are considered and that ultimately could be understood as salient features of the underlying complex process of language generation finally it is shown that all the different observed regimes can be accurately encompassed within a single mathematical framework recently introduced by c tsallis

critical behaviour of the bond diluted potts model on sierpinski carpets a four parameter bond moving renormalisation is used to study the critical properties of the bond diluted q state potts model on sierpinski carpets fixed points critical exponents and a phase diagram are obtained in the authors results there is a borderline value q qt for q qt there is crossover to a new diluted fixed point this behaviour is similar to that of the diluted system on a regular lattice with translational invariance they give some values of qt for carpets with different b l where b and l are structure parameters of carpets

some general techniques on linear preserver problems abstract several general techniques on linear preserver problems are described the first one is based on a transfer principle in model theoretic algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0 the second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied the third one is about solving linear preserver problems on more general operator algebras by reducing the problems to idempotent preservers numerous examples will be given to demonstrate the proposed techniques

uncorrelated random networks we define a statistical ensemble of nondegenerate graphs i e graphs without multiple connections and self connections between nodes the node degree distribution is arbitrary but the nodes are assumed to be uncorrelated this completes our earlier publication phys rev 64 046118 2001 where trees and degenerate graphs were considered an efficient algorithm generating nondegenerate graphs is constructed the corresponding computer code is available on request finite size effects in scale free graphs i e those where the tail of the degree distribution falls like n beta are carefully studied we find that in the absence of dynamical internode correlations the degree distribution is cut at a degree value scaling like n gamma with gamma min 1 2 1 beta 1 where n is the total number of nodes the consequence is that independently of any specific model the internode correlations seem to be a necessary ingredient of the physics of scale free networks observed in nature

correlation measure to detect time series distances whence economy globalization abstract an instantaneous time series distance is defined through the equal time correlation coefficient the idea is applied to the gross domestic product gdp yearly increments of 21 rich countries between 1950 and 2005 in order to test the process of economic globalisation some data discussion is first presented to decide what eks gk or derived gdp series should be studied distances are then calculated from the correlation coefficient values between pairs of series the role of time averaging of the distances over finite size windows is discussed three network structures are next constructed based on the hierarchy of distances it is shown that the mean distance between the most developed countries on several networks actually decreases in time which we consider as a proof of globalization an empirical law is found for the evolution after 1990 similar to that found in flux creep the optimal observation time window size is found 15 years

approximate tolerance limits for zipf mandelbrot distributions abstract zipf mandelbrot distributions are commonly used to model natural phenomena where the frequency of an event s occurrence is inversely proportional to its rank based on that frequency of occurrence this discrete distribution typically exhibits a large number of rare events however it may be of interest to obtain reasonable limits that bound the majority of the number of different events we propose the use of statistical tolerance limits as a way to quantify such a bound the tolerance limits are constructed using wald confidence limits for the zipf mandelbrot parameters and are shown through a simulation study to have coverage probabilities near the nominal levels we also calculate zipf mandelbrot tolerance limits for two real datasets and discuss the associated computer code developed for the r programming language

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

gini characterization of extreme value statistics abstract this paper presents a profound connection between gini s index and extreme value statistics gini s index is a quantitative gauge for the evenness of probability laws defined on the positive half line and is the common measure of societal egalitarianism applied in economics and in the social sciences extreme value statistics namely the gumbel frechet and weibull probability laws are the only possible asymptotic statistics emerging from the extremes of large ensembles of independent and identically distributed random variables extreme value statistics play a major role all across science and engineering in the analysis of rare and extreme events introducing generalizations of gini s index and exploring an elemental poissonian structure underlying the extreme value statistics we establish in this paper a gini based characterization of extreme value statistics

the first digit frequencies in data of turbulent flows abstract considering the first significant digits noted d in data sets of dissipation for turbulent flows the probability to find a given number d 1 or 2 or 9 would be 1 9 for a uniform distribution instead the probability closely follows newcomb benford s law namely p d log 1 1 d the discrepancies between newcomb benford s law and first digits frequencies in turbulent data are analysed through shannon s entropy the data sets are obtained with direct numerical simulations for two types of fluid flow an isotropic case initialized with a taylor green vortex and a channel flow results are in agreement with newcomb benford s law in nearly homogeneous cases and the discrepancies are related to intermittent events thus the scale invariance for the first significant digits which supports newcomb benford s law seems to be related to an equilibrium turbulent state namely with a significant inertial range a matlab octave program provided in appendix is such that part of the presented results can easily be replicated

rank one preserving r linear maps on spaces of self adjoint operators on complex hilbert spaces abstract let h be a complex hilbert space and let s a h be the space of all self adjoint operators on h let denote the subset of s a h consisting of all rank one operators a map l from s a h to itself is called a rank one preserver on s a h if l and is said to be r linear if l a b l a l b and l ka kl a for any k r and a b s a h where r is the field of real numbers we give a complete classification of all r linear and weakly continuous rank one preservers on s a h moreover we also determine the general form of all r linear and weakly continuous rank preservers respectively rank one idempotence preservers on s a h

multiplicative processes and power laws takayasu sato and takayasu phys rev lett 79 966 1997 revisited the question of stochastic processes with multiplicative noise which have been studied in several different contexts over the past decades we focus on the regime found for a generic set of control parameters in which stochastic processes with multiplicative noise produce intermittency of a special kind characterized by a power law probability density distribution we briefly explain the physical mechanism leading to a power law probability distribution function and provide a list of references for these results dating back from a quarter of century we explain how the formulation in terms of the characteristic function developed by takayasu sato and takayasu can be extended to exponents ensuremath mu g2 which explains the reason for the lucky coincidence the multidimensional generalization of the results of takayasu sato and takayasu and the present status of the problem are briefly summarized the discovery of stretched exponential tails in the presence of the cutoff introduced by takayasu sato and takayasu is explained theoretically we end by briefly listing applications

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

stochastic multiplicative processes with reset events we study a stochastic multiplicative process with reset events it is shown that the model develops a stationary power law probability distribution for the relevant variable whose exponent depends on the model parameters two qualitatively different regimes are observed corresponding to intermittent and regular behavior in the boundary between them the mean value of the relevant variable is time independent and the exponent of the stationary distribution equals ensuremath 2 the addition of diffusion to the system modifies in a nontrivial way the profile of the stationary distribution numerical and analytical results are presented

benford s law and the fsd distribution of economic behavioral micro data abstract in this paper we focus on the first significant digit fsd distribution of european micro income data and use information theoretic entropy based methods to investigate the degree to which benford s fsd law is consistent with the nature of these economic behavioral systems we demonstrate that benford s law is not an empirical phenomenon that occurs only in important distributions in physical statistics but that it also arises in self organizing dynamic economic behavioral systems the empirical likelihood member of the minimum divergence entropy family is used to recover country based income fsd probability density functions and to demonstrate the implications of using a benford prior reference distribution in economic behavioral system information recovery

incidence of q statistics in rank distributions we show that size rank distributions with power law decay often only over a limited extent observed in a vast number of instances in a widespread family of systems obey tsallis statistics the theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the lyapunov exponent is negligible or vanishes the relevant statistical mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints and the resulting duality of entropy indexes is seen to portray physically relevant information whereas the value of the index fixes the distribution s power law exponent that for the dual index 2 ensures the extensivity of the deformed entropy

benford s law and complex atomic spectra we found that in transition arrays of complex atomic spectra the strengths of electric dipolar lines obey benford s law which means that their significant digits follow a logarithmic distribution favoring the smallest values this indicates that atomic processes result from the superposition of uncorrelated probability laws and that the occurrence of digits reflects the constraints induced by the selection rules furthermore benford law can be a useful test of theoretical spectroscopic models its applicability to the statistics of electric dipolar lines can be understood in the framework of random matrix theory and is consistent with the porter thomas law

on the validation of the newcomb benford law and the weibull distribution in neuromuscular transmission abstract the neuromuscular junction represents a relevant substrate for revealing important biophysical mechanisms of synaptic transmission in this context calcium ions are important in the synapse machinery providing the nerve impulse transmission to the muscle fiber in this work we carefully investigated whether intervals of spontaneous electrical activity recorded in seven different calcium concentrations conform to the newcomb benford law our analysis revealed that electrical discharge of neuromuscular junction yields the expected values for newcomb benford law for first and second digits for different calcium concentrations on the other hand first two digits archived conformity especially for concentrations much above the physiological level we next examined previous theoretical studies establishing a relation between the law and lognormal and weibull distributions we showed that the weibull distribution is more appropriate to fit the intervals as compared to the lognormal distribution altogether the present findings strongly suggest that the electrical discharge dynamics is characterized by base invariance and scale invariance being the time intervals also well described by weibull statistics

the dependence of frequency distributions on multiple meanings of words codes and signs the dependence of the frequency distributions due to multiple meanings of words in a text is investigated by deleting letters by coding the words with fewer letters the number of meanings per code

network properties of written human language we investigate the nature of written human language within the framework of complex network theory in particular we analyze the topology of orwell s 1984 focusing on the local properties of the network such as the properties of the nearest neighbors and the clustering coefficient we find a composite power law behavior for both the average nearest neighbor s degree and average clustering coefficient as a function of the vertex degree this implies the existence of different functional classes of vertices furthermore we find that the second order vertex correlations are an essential component of the network architecture to model our empirical results we extend a previously introduced model for language due to dorogovtsev and mendes we propose an accelerated growing network model that contains three growth mechanisms linear preferential attachment local preferential attachment and the random growth of a predetermined small finite subset of initial vertices we find that with these elementary stochastic rules we are able to produce a network showing syntacticlike structures

one dimensional dynamical systems and benford s law one dimensional projections of at least almost all orbits of many multi dimensional dynamical systems are shown to follow benford s law i e their base b mantissa distribution is asymptotically logarithmic typically for all bases b as a generalization and uniflcation of known results it is proved that under a generic non resonance condition on a 2c d d for every z 2c d real and imaginary part of each non trivial component of a n z n2n0 and e at z t 0 follow benford s law also benford behavior is found to be ubiquitous for several classes of non linear maps and difierential equations in particular emergence of the logarithmic mantissa distribution turns out to be generic for complex analytic maps t with t 0 0 jt0 0 j 1 the results signiflcantly extend known facts obtained by other e g number theoretical methods and also generalize recent flndings for one dimensional systems

punctuation effects in english and esperanto texts abstract a statistical physics study of punctuation effects on sentence lengths is presented for written texts alice in wonderland and through a looking glass the translation of the first text into esperanto is also considered as a test for the role of punctuation in defining a style and for contrasting natural and artificial but written languages several log log plots of the sentence length rank relationship are presented for the major punctuation marks different power laws are observed with characteristic exponents the exponent can take a value much less than unity c a 0 50 or 0 30 depending on how a sentence is defined the texts are also mapped into time series based on the word frequencies the quantitative differences between the original and translated texts are very minutes at the exponent level it is argued that sentences seem to be more reliable than word distributions in discussing an author style