the mean field approximation model of company s income growth abstract we introduce a mean field type approximation for description of company s income statistics utilizing huge company data we show that a discrete version of langevin equation with additive and multiplicative noises can appropriately describe the time evolution of a company s income fluctuation in statistical sense the zipf s law of income distribution is shown to be held in a steady sate widely and country dependence of income distribution can also be nicely implemented in our numerical simulation

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

sources of exponents abstract examples are given of scaling relationships governed by fractional exponents additional examples are presented with heavy tail probability distributions governed by a fractional exponent this includes the analysis of the boltzmann gibbs entropy subject to an appropriate constraint to generate long tailed probability distributions the stretched exponential distribution is employed to derive a time scale for the glass transition that contains an essential singularity at a critical temperature these examples demonstrate that there are many routes to producing fractional exponents in physical systems

growth and fluctuations of personal income pareto s law states that the distribution of personal income obeys a power law in high income range many researchers have proposed models over a century since its discovery but the dynamical understanding of hie phenomenon necessitates empirical study on growth of individual income here we uncovered several properties in the fluctuations of individual income growth derived from income tax data including all taxpayers more than 80 000 with high income iii japan for two consecutive years 1997 and 1998 in a relatively stable period of economics in this work 8 we show i that the dynamics has approximate time reversal symmetry in the period ii that the distribution of growth rate is independent of income tax in the past yearm and iii that the pareto s law breaks down in bubble collapse of japanese economy in 1990 it is shown in 3 how these phenomenological facts are consistent with pareto law these findings provide first direct observation of dynamical process of ruuirey flow in an economic network and its relation to risky assets price fluctuations of lands and stocks

the κ generalized distribution a new descriptive model for the size distribution of incomes this paper proposes the generalized distribution as a model for describing the distribution and dispersion of income within a population formulas for the shape moments and standard tools for inequality measurement such as the lorenz curve and the gini coefficient are given a method for parameter estimation is also discussed the model is shown to fit extremely well the data on personal income distribution in australia and in the united states c 2008 elsevier b v all rights reserved

shape of growth rate distribution determines the type of non gibrat s property abstract in this study the authors examine exhaustive business data on japanese firms which cover nearly all companies in the mid and large scale ranges in terms of firm size to reach several key findings on profits sales distribution and business growth trends here profits denote net profits first detailed balance is observed not only in profits data but also in sales data furthermore the growth rate distribution of sales has wider tails than the linear growth rate distribution of profits in log log scale on the one hand in the mid scale range of profits the probability of positive growth decreases and the probability of negative growth increases symmetrically as the initial value increases this is called non gibrat s first property on the other hand in the mid scale range of sales the probability of positive growth decreases as the initial value increases while the probability of negative growth hardly changes this is called non gibrat s second property under detailed balance non gibrat s first and second properties are analytically derived from the linear and quadratic growth rate distributions in log log scale respectively in both cases the log normal distribution is inferred from non gibrat s properties and detailed balance these analytic results are verified by empirical data consequently this clarifies the notion that the difference in shapes between growth rate distributions of sales and profits is closely related to the difference between the two non gibrat s properties in the mid scale range

lorenzian analysis of infinite poissonian populations and the phenomena of paretian ubiquity abstract the lorenz curve is a universally calibrated statistical tool measuring quantitatively the distribution of wealth within human populations we consider infinite random populations modeled by inhomogeneous poisson processes defined on the positive half line the randomly scattered process points representing the wealth of the population members or any other positive valued measure of interest such as size mass energy etc for these populations the notion of macroscopic lorenz curve is defined and analyzed and the notion of lorenzian fractality is defined and characterized we show that the only non degenerate macroscopically observable lorenz curves are power laws manifesting paretian statistics thus providing a universal lorenzian explanation to the ubiquitous appearance of paretian probability laws in nature

average is over abstract the popular perception of statistical distributions is depicted by the iconic bell curve which comprises of a massive bulk of middle class values and two thin tails one of small left wing values and one of large right wing values the shape of the bell curve is unimodal and its peak represents both the mode and the mean thomas friedman the famous new york times columnist recently asserted that we have entered a human era in which average is over in this paper we present mathematical models for the phenomenon that friedman highlighted while the models are derived via different modeling approaches they share a common foundation inherent tipping points cause the models to phase shift from a normal bell shape statistical behavior to an anomalous statistical behavior the unimodal shape changes to an unbounded monotone shape the mode vanishes and the mean diverges hence i there is an explosion of small values ii large values become super large iii middle class values are wiped out leaving an infinite rift between the small and the super large values and iv average is over indeed

power law behavior in social and economical phenomena abstract we have already found power law behavior in various phenomena such as high tax payer population distribution name distribution passenger number at stations student number in a university from high schools and so on we can explain why these phenomena show such interesting behaviors by doing simulations based on adequate models we have come to the conclusion that there are fractal structures underlying those phenomena

derivation of the distribution from extended gibrat s law abstract employing profits data of japanese companies in 2002 and 2003 we identify the non gibrat s law which holds in the middle profits region from the law of detailed balance in all regions gibrat s law in the high region and the non gibrat s law in the middle region we kinematically derive the profits distribution function in the high and middle range uniformly the distribution function accurately fits with empirical data without any fitting parameter

random matrix ensembles from nonextensive entropy the classical gaussian ensembles of random matrices can be constructed by maximizing boltzmann gibbs shannon s entropy s text bgs ensuremath ensuremath int d mathbf h p mathbf h mathrm ln p mathbf h with suitable constraints here we construct and analyze random matrix ensembles arising from the generalized entropy s q 1 ensuremath ensuremath int d mathbf h p mathbf h q q ensuremath 1 thus s 1 s text bgs the resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form making q ensuremath rightarrow 1 recovers the gaussian ensembles if q ensuremath ne 1 the joint probability distributions p mathbf h cannot be factorized i e the matrix elements of mathbf h are correlated in the limit of large matrices two different regimes are observed when ql1 p mathbf h has compact support and the fluctuations tend asymptotically to those of the gaussian ensembles anomalies appear for qg1 both p mathbf h and the marginal distributions p h ij show power law tails numerical analyses reveal that the nearest neighbor spacing distribution is also long tailed not wigner dyson and after proper scaling very close to the result for the 2 ifmmode times else texttimes fi 2 case char22 a generalization of wigner s surmise we discuss connections of these nonextensive ensembles with other non gaussian ones such as the so called l evy ensembles and those arising from soft confinement

maximum entropy and stability of a random process with a 1 f power spectrum under deterministic action abstract the principle of maximum entropy has been used to analyze the stability of the resulting process observed during the interaction of a random process with a 1 f spectrum and a deterministic action in lumped and distributed systems of nonlinear stochastic differential equations describing the coupled nonequilibrium phase transitions under the action of a harmonic force the stable resulting process is divided into two branches depending on the amplitude of the harmonic force under the action of exponential relaxation in a lumped system with an increase in the dumping coefficient the power spectrum of the resulting process becomes a spectrum of the lorentz type

on 1 f noise and other distributions with long tails abstract it is shown following shockley shockley w 1957 proc ire 45 279 290 that when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks the distribution function for successes in the primary task is log normal it is also shown that when the dispersion of the log normal distribution is large the distribution is mimicked by a 1 x distribution over a wide range of x this argument provides a generic set of processes that yields the much observed 1 x distribution and will also lead to a 1 f noise spectrum it is commonly found that distributions that seem to be log normal over a broad range say to the 95th percentile of a population change to an inverse fractional power pareto distribution for the last few percentile annual income distributions are examples with this structure the very wealthy generally achieve their superwealth through amplification processes that are not available to most we have introduced a simple amplification model to characterize the transition from a log normal distribution to an inverse power pareto tail

random walks with self similar clusters abstract we construct a random walk on a lattice having a hierarchy of self similar clusters built into the distribution function of allowed jumps the random walk is a discrete analog of a levy flight and coincides with the levy flight in the continum limit the fourier transform of the jump distribution function is the continuous nondifferentiable function of weierstrass we show that for cluster formation it is necessary that the mean squared displacement per jump be infinite and that the random walk be transient we interpret our random walk as having an effective dimension higher than the spatial dimension available to the walker the difference in dimensions is related to the fractal hausdorff besicovitch dimension of the self similar clusters

a generalized kolmogorov sinai like entropy under markov shifts in symbolic dynamics abstract in this paper a generalized kolmogorov sinai like entropy ks q entropy in the sense of tsallis is proposed with a nonextensive parameter q under markov shifts which contains the classical kolmogorov sinai ks entropy and the renyi entropy as well as bernoulli shifts as special cases to verify the formula of this ks q entropy a one dimensional iterative system is chosen as an example of markov shifts and its ks q entropy is evaluated by a new refinement method of symbolic dynamics called symbolic refinement which differs from the conventional numerical method the numerical results show that this ks q entropy is monotonically decreasing as q increases

statistical properties and uses of the wavelet variance estimator for the scale analysis of time series abstract many physical processes are an amalgam of components operating on different scales and scientific questions about observed data are often inherently linked to understanding the behavior at different scales we explore time scale properties of time series through the variance at different scales derived using wavelet methods the great advantage of wavelet methods over ad hoc modifications of existing techniques is that wavelets provide exact scale based decomposition results we consider processes that are stationary nonstationary but with stationary dth order differences and nonstationary but with local stationarity we study an estimator of the wavelet variance based on the maximal overlap undecimated discrete wavelet transform the asymptotic distribution of this wavelet variance estimator is derived for a wide class of stochastic processes not necessarily gaussian or linear the variance of this distribution is estimated using spectral methods simulations confirm the theoretical result

income distribution boltzmann analysis and its extension abstract the paper aims at describing income distribution in moderate income regions starting with dividing income behaviors into the two parts random and deterministic and by introducing instantaneous model for theoretical derivations and cumulative model for positive tests this paper applies the equilibrium approach of statistical mechanics in the study of nonconserved individual income course the random income follows a stationary distribution similar to the maxwell boltzmann distribution in the instantaneous model combining this result with marginal analysis the probability distribution of individual income process that is composed of the random and deterministic income courses approximately obeys a distribution law mixing exponential function with a logarithmic prefactor using the census or income survey data of usa uk japan and new zealand the distribution law has been tested the results show that it agrees very well with most of the empirical data the discussion suggests that there might be essentially different income processes to happen in moderate and high income regions

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

principal component analysis with external information on both subjects and variables a method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis in this method the original data are first decomposed into several components according to external information the components are then subjected to principal component analysis to explore structures within the components it is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices the numerical method based on the qr decomposition is described which simplifies the computation considerably the proposed method includes a number of interesting special cases whose relations to existing methods are discussed examples are given to demonstrate practical uses of the method

stable equilibrium based on levy statistics a linear boltzmann equation approach to obtain further insight on possible power law generalizations of boltzmann equilibrium concepts we consider stochastic collision models the models are a generalization of the rayleigh collision model for a heavy one dimensional particle m interacting with ideal gas particles with a mass m m similar to previous approaches we assume elastic uncorrelated and impulsive collisions we let the bath particle velocity distribution function to be of general form namely we do not postulate a specific form of power law equilibrium we show under certain conditions that the velocity distribution function of the heavy particle is levy stable the maxwellian distribution being a special case we demonstrate our results with numerical examples the relation of the power law equilibrium obtained here to thermodynamics is discussed in particular we compare between two models a thermodynamic and an energy scaling approaches these models yield insight into questions like the meaning of temperature for power law equilibrium and into the issue of the universality of the equilibrium i e is the width of the generalized maxwellian distribution functions obtained here independent of coupling constant to the bath

chaotic dynamics markovian coarse graining and information abstract the conditions for mapping chaotic dynamics into a markov chain through finite coarse graining are derived a chapman kolmmogorov equation giving rise to an h theorem is deduced in which the transition probability matrix is expressed entirely in terms of the properties of the underlying deterministic dynamics and of the phase space partition the validity of the conditions ensuring the mapping is verified on simple models of dissipative as well as conservative dynamical systems the implications of the results in the problem of irreversibility and the relation between deterministic chaos information and complexity are discussed

chaotic dynamics markov partitions and zipf s law a chaotic dynamics model creating markovian strings of symbols as well as sequences of words is presented and its possible relevance to zipf s law is discussed

stable equilibrium based on levy statistics stochastic collision models approach we investigate equilibrium properties of two very different stochastic collision models i the rayleigh particle and ii the driven maxwell gas for both models the equilibrium velocity distribution is a levy distribution the maxwell distribution being a special case we show how these models are related to fractional kinetic equations our work demonstrates that a stable power law equilibrium which is independent of details of the underlying models is a natural generalization of maxwell s velocity distribution

generalized distribution functions and an alternative approach to generalized planck radiation law abstract in this study recently introduced generalized distribution functions are summarized and by using one of these distribution functions namely generalized planck distribution an alternative approach to the generalized planck law for the blackbody radiation has been tackled the expression obtained is compared with the expression given by c tsallis et al phys rev e 52 1995 1447 and it is found that this approximate scheme provides bounds to the exact result depending on the values of q index

reshape scale method a novel multi scale entropic analysis approach abstract the reshape scale rs method was introduced in this article as a novel approach to perform multi scale transition of sample entropy this method was able to quantify the orderliness in the signal by determining the distance over which the subsequent data points can remain affiliated to one another entropic half life enhl was introduced to characterize such an affiliation the method was tested for 1 f processes for different values furthermore the dependency of the multi scale entropy analysis developed by costa et al 2002 6 to the probability density function and the standard deviation of autoregressive signals was studied and discussed

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

tail universalities in rank distributions as an algebraic problem the beta like function abstract although power laws of the zipf type have been used by many workers to fit rank distributions in different fields like in economy geophysics genetics soft matter networks etc these fits usually fail at the tail some distributions have been proposed to solve the problem but unfortunately they do not fit at the same time the body and the tail of the distribution we show that many different data in rank laws like in granular materials codons author impact in scientific journal etc can be very well fitted by the integrand of a beta function that we call beta like function then we propose that such universality can be due to the fact that systems made from many subsystems or choices present stretched exponential frequency rank functions which qualitatively and quantitatively are well fitted with the beta like function distribution in the limit of many random variables we give a plausibility argument for this observation by transforming the problem into an algebraic one finding the rank of successive products of numbers which is basically a multinomial process from a physical point of view the observed behavior at the tail seems to be related with the onset of different mechanisms that are dominant at different scales providing crossovers and finite size effects

irreversible thermodynamics in the framework of tsallis entropy abstract the symmetry of the kinetic onsager coefficients is proved in the context of tsallis generalization of boltzmann gibbs statistics a generalized nyquist theorem is also introduced the analysis of the noise spectrum of the thermodynamics fluctuation is presented in the framework of tsallis entropy a comment about the spectrum 1 in connection with non gaussian statistics is also discussed

characteristic functional approach to multiplicative fractal noise with application to environmental fluctuations in nonlinear chemical systems far from equilibrium a temporal analog of anderson localization abstract we compute the characteristic functional of a nonlinear transformation of a set of random variables the equation is applied to the study of fractal stochastic processes with multiplicative noise for illustration we investigate two types of chemical systems subjected to environmental fluctuations we analyze the interaction between the intrinsic chemical fluctuations and environmental noise and evaluate the stochastic properties of the system in the presence of multiplicative noise for an autocatalytic reaction subjected to external noise and with gaussian and generally non markovian multiplicative external noise the averaged joint probability density of concentrations displays long tails of the negative power law type which are independent of the detailed properties of the noise we also study the influence of multiplicative noise on a nonlinear chemical system with a stable limit cycle in the presence of multiplicative noise the limit cycle collapses and the average trajectory in the composition space becomes a spiral this effect is a temporal analog of anderson localization we evaluate the damping factors and localization times for different types of noise ranging from noise with infinite memory static disorder and noise with long memory dynamic disorder with fractal noise to markovian noise dynamic disorder with short memory

dynamics of layered interfaces arising from phase boundaries the dynamics of a material in two phases is studied in the context of phase field models based on a landau ginzburg free energy functional they consist of a system of two nonlinear diffusion equat

heavy tailed targets and ab normal asymptotics in diffusive motion abstract we show that under suitable confinement conditions the ordinary fokker planck equation may generate non gaussian heavy tailed probability density functions pdfs like for example cauchy or more general levy stable distributions in its long time asymptotics in fact all heavy tailed pdfs known in the literature can be obtained this way for the underlying diffusion type processes our main focus is on their transient regimes and specifically the crossover features when an initially infinite number of pdf moments decreases to a few or none at all the time dependence of the variance if in existence t with 0 2 may in principle be interpreted as a signature of subdiffusive normal diffusive or superdiffusive behavior under confining conditions the exponent is generically well defined in substantial periods of time however there is no indication of any universal time rate hierarchy due to a proper choice of the driver and or external potential

entropic basis of the pareto law based on the assumption that certain economies achieve quasi equilibrium an appropriate economic statistical thermodynamics is formulated in which entropy emerges naturally under the assumption that the small group of high income agents whose income distribution satisfies pareto s law does not much interact with the larger group of lower income agents the corresponding statistical thermodynamic relations are applied in order to derive the pareto law the derivation requires the assumption that the sum of logarithms of the incomes of the individual agents or the product of incomes in this group is conserved a strong plausibility argument for this assumption is presented it also turns out in accordance with intuition that in order to increase the average income of an agent more risk in the form of greater entropy production must be assumed other consequences are discussed and an experimental demonstration of the uniformity of economic temperature in a system at economic equilibrium is presented

crossover from weak to strong disorder regime in the duration of epidemics abstract we study the susceptible infected recovered sir model in complex networks considering that not all individuals in the population interact in the same way this heterogeneity between contacts is modeled by a continuous disorder in our model the disorder represents the contact time or the closeness between individuals we find that the duration time of an epidemic has a crossover with the system size from a power law regime to a logarithmic regime depending on the transmissibility related to the strength of the disorder using percolation theory we find that the duration of the epidemic scales as the average length of the branches of the infection our theoretical findings supported by simulations explains the crossover between the two regimes

rates of convergence of non extensive statistical distributions to levy distributions in full and half spaces the levy type distributions are derived using the principle of maximum tsallis non extensive entropy both in the full and half spaces the rates of convergence to the exact levy stable distributions are determined by taking the n fold convolutions of these distributions the marked difference between the problems in the full and half spaces is elucidated analytically it is found that the rates of convergence depend on the ranges of the levy indices an important result emerging from the present analysis is deduced if interpreted in terms of random walks implying the dependence of the asymptotic long time behaviours of the walks on the ranges of the levy indices if n is identified with the total time of the walks

beyond lognormal inequality the lorenz flow structure abstract observed from a socioeconomic perspective the intrinsic inequality of the lognormal law happens to manifest a flow generated by an underlying ordinary differential equation in this paper we extend this feature of the lognormal law to a general lorenz flow structure of lorenz curves objects that quantify socioeconomic inequality the lorenz flow structure establishes a general framework of size distributions that span continuous spectra of socioeconomic states ranging from the pure communism extreme to the absolute monarchy extreme this study introduces and explores the lorenz flow structure analyzes its statistical properties and its inequality properties unveils the unique role of the lognormal law within this general structure and presents various examples of this general structure beyond the lognormal law the examples include the inverse pareto and pareto laws which often govern the tails of composite size distributions

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

fractional levy motions and related processes this paper investigates some properties of a class of random motions called fractional levy motions flms and their fractal time extension flm identifies with fractional brownian motion fbm sampled in fractal levy time this two parameter class of processes borrows hyperbolic temporal dependence to fbm and heavy tailedness to levy flights or motions lm it is shown that there exists a family of flms which shares with standard brownian motion bm the strict diffusivity property that the dispersion measured in terms of quantiles grows as time raised to the power processes from this class are critical in that they separate both sub superdiffusive flms and finite infinite variance motions related ornstein uhlenbeck and multiplicative processes are also briefly investigated flms are self similar but not levy stable in sharp contrast to brownian whether fractional or not and standard or fractional stable in the taqqu wolpert sense levy motions fsms stable processes are self similar as a result of levy stability however the converse is false there are motions with stationary increments which are self similar but not stable the fractional levy motion is one of them in the pure jump process class it turns out that all processes discussed so far bm fbm lm flm fsm are self similar with stationary increments we finally introduce a natural one parameter family of fractional processes for which a weaker notion of self similarity seems to hold i e self similarity of the unidimensional distributions it is fractal time brownian motion ft bm such a process is obtained as a weak limit of fractal time random walk models with 0 1 the tail exponent of the waiting times ft bm identifies with brownian motion now sampled in fractal inverse levy time this construction extends to fbm lm and flm we therefore introduce and study ft fbm ft lm and ft flm which are the fractal time extensions of fbm lm and flm these processes are not strongly self similar nor stable nor do they have stationary increments

universal poisson process limits for general random walks abstract this paper considers ensembles of general independent and identically distributed random walks taking the ensemble size to grow infinitely large and also taking the running time of the random walks to grow infinitely large universal poisson process limits are obtained specifically it is established that the positions of general linear random walks converge universally to poisson processes over the real line with uniform and exponential intensities and it is established that the positions of general geometric random walks converge universally to poisson processes over the positive half line with harmonic and power intensities corollaries to these universal convergence results yield the extreme value statistics of gumbel weibull and frechet

shlesinger hughes stochastic renormalization iterated logarithmic tails and multiple hierarchical fractal aggregation abstract the multiple hierarchical fractal aggregation is used as an illustration for a new type of asymptotic behavior of fractal random processes defined in terms of a multiple shlesinger hughes renormalization procedure the joint probability distributions of aggregate sizes for a multiple association process are analyzed based on the following set of assumptions a the system contains basic units of different types however each aggregate is made up of a single type of units b the size of a single aggregate obeys a geometrical distribution of the flory type c the aggregation process occurs in a hierarchical way i e each aggregate of a given type triggers the generation of a complex of another type a chain of joint size probability distributions is introduced we show that these probability distributions depend on the probabilities that a unit from a given aggregate is active that is that it may trigger the aggregation process of basic units of another type these probabilities generate a chain of fractal exponents which characterize the asymptotic behavior of the size probability distributions the probability distribution attached to a succession of q 2 aggregation processes has a very long tail with a logarithmic shape it is an inverse power of the q th iterate logarithm of size n ln ln ln n this decay law is much slower than the inverse power laws characteristic for the usual statistical fractals

the renormalization group and optimization of entropy we illustrate the possible connection that exists between the extremal properties of entropy expressions and the renormalization group rg approach when applied to systems with scaling symmetry we consider three examples 1 gaussian fixed point criticality in a fluid or in the capillary wave model of an interface 2 levy like random walks with self similar cluster formation and 3 long ranged bond percolation in all cases we find a decreasing entropy function that becomes minimum under an appropriate constraint at the fixed point we use an equivalence between random walk distributions and order parameter pair correlations in a simple fluid or magnet to study how the dimensional anomaly at criticality relates to walks with long tailed distributions

a trade investment model for distribution of wealth econophysics provides a strategy for understanding the potential mechanisms underlying the anomalous distribution of wealth found in real societies we present a computational nonlinear stochastic model for the distribution of wealth that depends upon three parameters and two mechanisms trade and investment to avoid economic paradoxes the trade mechanism is assumed to be related to the poorer trader s wealth and to statistically advantage the poorer of the two traders the two mechanisms together are shown to generate a distribution that reproduces the full range of the empirical wealth distribution and not only the inverse power law tail that pareto found in western societies at the end of the 19th century

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

maximum entropy in a nonlinear system with a 1 f power spectrum abstract an analysis of master slave hierarchy has been made in a system of nonlinear stochastic equations describing fluctuations with a 1 f spectrum at coupled nonequilibrium phase transitions it is shown that for a system of stochastic equations there exist different probability distribution functions with power law non gaussian and gaussian tails the governing equation of a system has a probability distribution function with gaussian tails therefore distribution functions for governing equations may be used for finding the gibbs shannon entropy the local maximum of this entropy has been found it corresponds to the tuning of the parameters of the equations to criticality and points to the stability of fluctuations with a 1 f spectrum the tsallis entropy and the renyi entropy for the probability distribution functions with power law tails have been calculated the parameter q which is included in the determination of these entropies has been found from the condition that the coordinates of the maximum gibbs shannon entropy coincide with the maxima of the tsallis and renyi entropies

maximum entropy approach to stretched exponential probability distributions we introduce a nonextensive entropy functionals whose optimization under simple constraints mean values of some standard quantities yields stretched exponential probability distributions which occur in many complex systems the new entropy functional is characterized by a parameter the stretching exponent such that for d 1 the standard logarithmic entropy is recovered we study its mathematical properties showing that the basic requirements for a well behaved entropy functional are verified i e s possesses the usual properties of positivity equiprobability concavity and irreversibility and verifies khinchin axioms except the one related to additivity since s is nonextensive the entropys is shown to be superadditive for 1

a statistical study of temporally smoothed wavelet coherence the use of the wavelet coherence of two series in hypothesis testing relies on some sort of smoothing being carried out in order that the coherence estimator is not simply unity a previous study considered averaging via the use of multiple morse wavelets here we consider time domain smoothing and use of a single morlet wavelet since the morlet wavelet is complex valued we derive analytic results for the case of wavelet coherence calculated from complex valued jointly stationary and gaussian time series the temporally smoothed wavelet coherence can be written in terms of welch s overlapping segment averaging wosa spectrum estimators and by using multitaper equivalent representations for the wosa estimators we show that goodman s distribution is appropriate asymptotically and readily derive the appropriate degrees of freedom the theoretical results are verified via simulations and illustrated using solar physics data

from entropy maximization to equality maximization gauss laplace pareto and subbotin abstract the entropy maximization paradigm of statistical physics is well known to generate the omnipresent gauss law in this paper we establish an analogous socioeconomic model which maximizes social equality rather than physical disorder in the context of the distributions of income and wealth in human societies we show that on a logarithmic scale the laplace law is the socioeconomic equality maximizing counterpart of the physical entropy maximizing gauss law and that this law manifests an optimized balance between two opposing forces i the rich and powerful striving to amass ever more wealth and thus to increase social inequality and ii the masses struggling to form more egalitarian societies and thus to increase social equality our results lead from log gauss statistics to log laplace statistics yield paretian power law tails of income and wealth distributions and show how the emergence of a middle class depends on the underlying levels of socioeconomic inequality and variability also in the context of asset prices with laplace distributed returns our results imply that financial markets generate an optimized balance between risk and predictability

relations between a typical scale and averages in the breaking of fractal distribution abstract we study distributions which have both fractal and non fractal scale regions by introducing a typical scale into a scale invariant system as one of models in which distributions follow power law in the large scale region and deviate further from the power law in the smaller scale region we employ 2 dim quantum gravity modified by the r 2 term as examples of distributions in the real world which have similar property to this model we consider those of personal income in japan over latest twenty fiscal years we find relations between the typical scale and several kinds of averages in this model and observe that these relations are also valid in recent personal income distributions in japan with sufficient accuracy we show the existence of the fiscal years so called bubble term in which the gap has arisen in power law by observing that the data are away from one of these relations we confirm therefore that the distribution of this model has close similarity to those of personal income in addition we can estimate the value of pareto index and whether a big gap exists in power law by using only these relations as a result we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions

on the evolution of domain walls in hard ferromagnets we propose a sharp interface theory for the dynamics of domain walls in highly anisotropic hard ferromagnetic bodies starting from the gilbert equation we consider the asymptotic regime when the hardness parameter goes to infinity and we use the technique of matched expansions to derive a system of two evolution equations for the domain wall regarded as a smooth surface the first equation apart for a nonlocal forcing term has the standard form for a surface set in motion according to its mean curvature the second relates the normal velocity to the internal structure of the domain wall

a renormalization approach to a class of exponential random processes with application to the bronchial tree abstract a new stochastic renormalization approach for multi step decay phenomena is developed a simple physical interpretation of the renormalization method is suggested it consists in grouping successions of variable numbers of decay events into blocks the law of probability multiplication leads to an exponential random process y yx1 x2 0 where both the exponents x1 x2 and the basis y0 are random variables the physically consistent solution of the model corresponds to a super strong renormalization regime the dependence of the moments of the decay parameter on the number of decay steps q can be exactly determined it consists in a linear superposition of inverse power laws in q modulated by periodic functions in in q having different periods the theory is applied to the renormalization of the bronchial tree our computation shows that the lung structure is very tolerant to fluctuations this result supports the mechanism of morphogenesis of fractal biological organs suggested by west ann biomed eng 18 1990 135 the possibilities of application to the scattering phenomena in one dimensional disordered media are also investigated

annual change of pareto index dynamically deduced from the law of detailed quasi balance abstract employing data on the assessed value of land in 1983 2005 japan we investigate the dynamical behavior in the high scale region of non equilibrium systems from the detailed quasi balance and gibrat s law we derive a relation between the change of pareto index and a symmetry in the detailed quasi balance the relation is confirmed in the empirical data nicely

maximum information entropy approach to non markovian random jump processes with long memory application to surprisal analysis in molecular dynamics abstract it is shown that non markovian random jump processes in continuous time and with discrete state variables can be expressed in terms of a variational principle for the information entropy provided that the constraints describe the correlations among a set of dynamic variables at any moment in the past the approach encompasses a broad class of stochastic processes ranging from independent processes through markovian and semi markovian processes to random processes with complete connections two different levels of description are introduced a a microscopic one defined in terms of a set of microscopic state variables and b a mesoscopic one which gives the stochastic properties of the dynamic variables in terms of which the constrains are defined a stochastic description of both levels is given in terms of two different characteristic functionals which completely characterize the fluctuations of micro and mesovariables at the mesoscopic level a statistic thermodynamic description is also possible in terms of a partition functional the stochastic and thermodynamic descriptions of the mesoscopic level are equivalent and the comparison between these two approaches leads to a generalized fluctuation dissipation relation a comparison is performed between the maximum entropy and the master equation approaches to non markovian processes a system of generalized age dependent master equations is derived which provides a description of stochastic processes with long memory the general approach is applied to the problem of surprisal analysis in molecular dynamics it is shown that the usual markovian master equation description is compatible with the information entropy approach provided that the constraints give the evolution of the first two moments of the dynamic variables at any time in the past