radial distribution function within the framework of the tsallis statistical mechanics abstract this study is conducted to obtain the radial distribution function rdf within the tsallis statistical mechanics to this end probability distribution functions are applied in the first and fourth versions of the tsallis statistics moreover a closed formula is proposed for rdf the power nature of the probability distribution in the tsallis statistics makes it difficult to separate kinetic energy and configurational potential parts by using the taylor expansion around q 1 of the power distribution it is possible to show the independency of momenta and coordinates through integrating over the phase space variables in addition at low densities numerical calculations have been performed for the rdf our results show that the correlation increases as q values increase

a systolic design for connectivity problems in this paper we present a design suited to vlsi implementation for a one dimensional array to solve graph connectivity problems the computational model is relatively primitive in that only the two end cells of the array can interact with the external environment and only adjacent cells in the array are allowed to communicate however we show that an array of n 1 cells can be used for a graph with n vertices to find the connected components a spanning tree or when used in conjunction with a systolic priority queue a minimum spanning tree the area time and i o requirements compare favorably with other models proposed for this problem in the case of sparse graphs

rigorous properties and uncertainty like relationships on product complexity measures application to atomic systems most of research on complexities and the corresponding conclusions have been obtained by numerically quantifying their values and little attention has been paid to their theoretical properties and the exact meaning within an statistical framework valid for any arbitrary n dimensional distribution in the present work different product complexities constructed as a product of two relevant information quantities associated to the concepts of uncertainty and localization are investigated different results on product complexities such as rigorous bounds uncertainty like inequalities relationships among themselves and also statistical interpretations are given for the sake of completeness some of these analytical results on product complexities are numerically checked for the one particle densities of atomic systems in both conjugated spaces

tsallis information dimension of complex networks abstract the fractal and self similarity properties are revealed in many complex networks the information dimension is a useful method to describe the fractal and self similarity properties of the complex networks in order to show the influence of different parts in the complex networks to the information dimension we have proposed a new information dimension based on the tsallis entropy namely the tsallis information dimension the proposed information dimension is changed according to the scale which is described by the nonextensivity parameter q and it is inverse with the nonextensivity parameter q the existing information dimension is a special case of the tsallis information dimension when q 1 the tsallis information dimension is a generalized information dimension of the complex networks

a general approach to the systematic derivation of so 3 shift operator relations i theory a new technique is established for the construction of relations between products consisting of two three or more so 3 shift operators within the framework of the lie algebras of so 3 tensor operators constructed out of an underlying single boson structure

shift operator techniques for the classification of multipole phonon states xi properties of mixed type quadratic product operators in r 7 expressions connecting r 3 scalar and nonscalar product operators of the type p jl kokl and okl jp jl are constructed within the group r 7

measure the structure similarity of nodes in complex networks based on relative entropy abstract similarity of nodes is a basic structure quantification in complex networks lots of methods in research on complex networks are based on nodes similarity such as node s classification network s community structure detection network s link prediction and so on therefore how to measure nodes similarity is an important problem in complex networks in this paper a new method is proposed to measure nodes structure similarity based on relative entropy and each node s local structure in the new method each node s structure feature can be quantified as a special kind of information the quantification of similarity between different pair of nodes can be replaced as the quantification of similarity in structural information then relative entropy is used to measure the difference between each pair of nodes structural information at last the value of relative entropy between each pair of nodes is used to measure nodes structure similarity in complex networks comparing with existing methods the new method is more accuracy to measure nodes structure similarity

shift operator techniques for the classification of multipole phonon states xii o0l eigenstate and eigenvalue determination in r 7 on account of previously derived relations between quadratic shift operator products in the group g2 part of the eigenvalue spectrum of the scalar shift operator p0l is derived in closed form the corresponding eigenstates which are closely related to the octupole phonon states are defined in terms of angular momentum lowering shift operator actions upon the maximum angular momentum state

on the spectra of so 3 scalars in the enveloping algebra of su 3 formulas are given that make it possible to calculate the eigenvalues of the two independent so 3 scalars o0l and q0l in the su 3 enveloping algebra

stock market and motion of a variable mass spring we establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock market dynamics within an economic model based on simple temporal demand and supply functions e canessa j phys a 33 2000 3637 the total system energy et is shown to be proportional to a decreasing time dependent spring constant kt this model allows to derive log periodicity cos log t tc on commodity prices and oscillations surplus and shortages in the level of stocks we also made an attempt to connect these results to the tsallis statistics parameter q based on a possible force entropy correlation e canessa physica a 341 2004 165 and find that the tsallis second entropic term i 1wpiq q 1 relates to the square of the demand or supply function

pinning synchronization of delayed complex dynamical networks with nonlinear coupling abstract in this paper we find that complex networks with the watts strogatz or scale free ba random topological architecture can be synchronized more easily by pin controlling fewer nodes than regular systems theoretical analysis is included by means of lyapunov functions and linear matrix inequalities lmi to make all nodes reach complete synchronization numerical examples are also provided to illustrate the importance of our theoretical analysis which implies that there exists a gap between the theoretical prediction and numerical results about the minimum number of pinning controlled nodes

on the axiomatic requirement of range to measure uncertainty abstract how to measure uncertainty is still an open issue probability theory is a primary tool to express the aleatoric uncertainty the shannon s information entropy is an effective measure for the uncertainty in probability theory dempster shafer theory an extension of probability theory has the ability to express the aleatoric and epistemic uncertainty simultaneously with respect to such uncertainties in dempster shafer theory a justifiable uncertainty measure is required to satisfy five axiomatic requirements based on previous studies in this paper we show that one of the axiomatic requirements the requirement of range is questionable the correct range of uncertainty should be 0 log 2 2 x rather than 0 log 2 x according to the concept of entropy

a new look at q exponential distributions via excess statistics q exponential distributions play an important role in nonextensive statistics they appear as the canonical distributions i e the maximum generalized q entropy distributions under mean constraint their relevance is also independently justified by their appearance in the theory of superstatistics introduced by beck and cohen in this paper we provide a third and independent rationale for these distributions we indicate that q exponentials are stable by a statistical normalization operation and that pickands extreme values theorem plays the role of a clt like theorem in this context this suggests that q exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold moreover we give an asymptotic connection between excess distributions and maximum q entropy we also highlight the role of generalized pareto distributions in many applications and present several methods for the practical estimation of q exponential parameters

thermodynamics from first principles correlations and nonextensivity the standard formulation of thermostatistics being based on the boltzmann gibbs distribution and logarithmic shannon entropy describes idealized uncorrelated systems with extensive energies and short range interactions in this rapid communication we use the fundamental principles of ergodicity via liouville s theorem the self similarity of correlations and the existence of the thermodynamic limit to derive generalized forms of the equilibrium distribution for long range interacting systems significantly our formalism provides a justification for the well studied nonextensive thermostatistics characterized by the tsallis distribution which it includes as a special case we also give the complementary maximum entropy derivation of the same distributions by constrained maximization of the gibbs shannon entropy the consistency between the ergodic and maximum entropy approaches clarifies the use of the latter in the study of correlations and nonextensive thermodynamics

a generalized statistical complexity measure applications to quantum systems a two parameter family of complexity measures c based on the renyi entropies is introduced and characterized by a detailed study of its mathematical properties this family is the generalization of a continuous version of the lopez ruiz mancini calbet complexity which is recovered for 1 and 2 these complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system when one of the parameters or goes to infinity one of the global factors becomes a local factor for this special case the complexity is calculated on different quantum systems h atom harmonic oscillator and square well

a general approach to the systematic derivation of so 3 shift operator relations ii applications the technique reported on in the preceding paper is applied to construct shift operator relations in the su 3 and so 5 lie algebras comments are made concerning the integrity basis for so 3 scalar operators appearing in their respective enveloping algebras

empirical regularities of opening call auction in chinese stock market abstract we study the statistical regularities of an opening call auction using the ultra high frequency data of 22 liquid stocks traded on the shenzhen stock exchange in 2003 the distribution of the relative price defined as the relative difference between the order price in the opening call auction and the closing price on the last trading day is asymmetric and that the distribution displays a sharp peak at the zero relative price and a relatively wide peak at the negative relative price the detrended fluctuation analysis dfa method is adopted to investigate the long term memory of relative order prices we further study the statistical regularities of order sizes in the opening call auction and observe a phenomenon of number preference known as order size clustering the probability density function pdf of order sizes could be well fitted by a q gamma function and the long term memory also exists in order sizes in addition both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit order book lob established immediately after the opening call auction and a price clustering phenomenon is observed

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

generalized quantum entropy the generalized quantum entropies are introduced in this paper some important properties such as nonnegativity continuity and concavity are proved but different from the von neumann entropy the subadditivity and additivity fail for the quantum unified r s entropy in general

graph problems on a mesh connected processor array on donne des algorithmes fonctionnant par etapes de o n pour resoudre un certain nombre de problemes de graphes sur un reseau n n de processeurs le probleme considere comprend la recherche des ponts et points d articulation d un graphe non oriente la recherche de la longueur du cycle le plus court la recherche d un arbre maximal minimal et d autres problemes

a new class of entropic information measures formal group theory and information geometry in this work we study generalized entropies and information geometry in a group theoretical framework we explore the conditions that ensure the existence of some natural properties and at the same time of a group theoretical structure for a large class of entropies in addition a method for defining new entropies using previously known ones with some desired group theoretical properties is proposed in the second part of this work the information geometrical counterpart of the previous construction is examined and a general class of divergences are proposed and studied finally a method of constructing new divergences from known ones is discussed in particular some results concerning the riemannian structure associated with the class of divergences under investigation are formulated

vlsi algorithms for the connected component problem this paper presents algorithms for the connected component problem that are suitable for vlsi implementation and use o n 2 area two vlsi models which differ in the number of input output ports allowed to be placed on the boundary of the chip are considered it is shown how to achieve a continuous area time tradeoff of at 2 o n 4 in the range omega n a o n 2 this tradeoff is optimal for one model and for the other model continuous tradeoffs of the form at o n 5 2 in the range omega n a o n 5 4 and at 3 o n 5 in the range omega n 5 4 a o n 2 are exhibited

monotonically equivalent entropies and solution of additivity equation generalized entropies are studied as lyapunov functions for the master equation markov chains three basic properties of these lyapunov functions are taken into consideration universality independence of the kinetic coefficients trace form the form of sum over the states and additivity for composition of independent subsystems all the entropies which have all three properties simultaneously and are defined for positive probabilities are found they form a one parametric family we consider also pairs of entropies s1 s2 which are connected by the monotonous transformation s2 f s1 equivalent entropies all classes of pairs of universal equivalent entropies one of which has a trace form and another is additive these entropies can be different one from another were found these classes consist of two one parametric families the family of entropies which are equivalent to the additive trace form entropies and the family of renyi tsallis entropies

entropy and complexity analysis of dirac delta like quantum potentials abstract the dirac delta like quantum mechanical potentials are frequently used to describe and interpret numerous phenomena in many scientific fields including atomic and molecular physics condensed matter and quantum computation the entropy and complexity properties of potentials with one and two dirac delta functions are here analytically calculated and numerically discussed in both position and momentum spaces we have studied the information theoretic lengths of fisher renyi and shannon types as well as the cramer rao fisher shannon and lmc shape complexities of the lowest lying stationary states of one delta and twin delta they allow us to grasp and quantify different facets of the spreading of the charge and momentum of the system far beyond the celebrated standard deviation

nonscalar extension of shift operator techniques for su 3 in an o 3 basis iii shift operators of second degree in the tensor components shift operators qkl 2 k 2 of second degree in the tensor components q 2 2 are constructed relations connecting quadratic shift operator products of the type ojl k qkl or qkl j ojl and of the type qjl k qkl are derived the usefulness of these relations is demonstrated by the example of the ool and qol eigenvalue calculation for various irreducible respresentations p q of su 3

the shift operator technique for so 7 in an su 2 3 basis i theory shift operators for the chain of lie groups so 7 su 2 3 are constructed and several properties are examined quite a number of relations connecting quadratic products of shift operators are built up finally the connection between matrix elements of the shift operators and reduced matrix elements of the tensor operator which forms part of the so 7 generator basis is explained

a new information dimension of complex network based on renyi entropy abstract with the development of high technology and artificial intelligence it evolves into an open issue to calculate the dimension of the complex network in this paper a new dimension renyi dimension combined with renyi entropy and information dimension is proposed a modified box covering algorithm is introduced to calculate the minimum number and the length of the boxes needed to cover the whole network additionally the self weight factor swf and the positive weight factor pwf are defined to illustrate the change of the dimension value based on the perspective of both topology structure and dynamic property the concept of attractors is proposed to illuminate the physical meaning of the weighted parameter in the formula of renyi entropy pwf and swf finally to demonstrate the efficiency of our method it is applied to calculate the dimension of sierpinski weighted fractal network ba networks and many real world networks the results show that attractors exist in the network researched and can access the attractiveness of attractors as a criterion the swf quantifies the total attractiveness of attractors the comparison results with tsallis dimension indicate the stability of the renyi dimension

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

su 2 su 2 shift operators and representations of so 5 su 2 su 2 shift operators analogous to the su 2 shift operators developed and used by the author for the classification and analysis of representations of lie algebras in an su 2 or so 3 basis are obtained for the su 2 su 2 lie algebra in the case where one has an additional set of operators forming an irreducible four dimensional tensor representation of su 2 su 2 the shift operators obtained are used to treat the representations of so 5 in an su 2 su 2 basis

fractal surfaces from simple arithmetic operations fractal surfaces patchwork quilts are shown to arise under most general circumstances involving simple bitwise operations between real numbers a theory is presented for all deterministic bitwise operations on a finite alphabet it is shown that these models give rise to a roughness exponent h that shapes the resulting spatial patterns larger values of the exponent leading to coarser surfaces

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

disequilibrium complexity the schottky effect and q entropies in paramagnetism abstract we investigate connections between statistical quantifiers and paramagnetism more concretely we apply the notions of i disequilibrium and ii statistical complexity to a paramagnetic system of non coupled dipoles interesting insights are thereby obtained in particular we encounter a kind of criticality not associated to the temperature but to the disequilibrium

nonscalar extension of shift operator techniques for su 3 in an o 3 basis ii applications in a preceding paper relations have been derived which connect nonscalar quadratic shift operator products here the extreme usefulness of these relations is demonstrated by the example of the o0l eigenvalue calculation for the cases l p i i 0 1 2 3 and 4 where p q is any su 3 representation for the first time a case of threefold l degeneracy is completely solved in a pure analytical way

on the stability of generalized entropies by the use of a probabilistic coupling technique and generalizing a recent result of zhang 2007 lett math phys 80 171 we derive several sharp inequalities concerning the uniform continuity of some generalized entropies these inequalities capture certain aspects of the interplay between the entropies and the uniform distance variational distance and establish the stability of the involved entropies

on a comparative study between dependence scales determined by linear and non linear measures in this manuscript we present a comparative study about the determination of the relaxation i e independence time scales obtained from the correlation function the mutual information and a criterion based on the evaluation of a nonextensive generalisation of mutual entropy our results show that for systems with a small degree of complexity standard mutual information and the criterion based on its nonextensive generalisation provide the same scale whereas for systems with a higher complex dynamics the standard mutual information presents a time scale consistently smaller

empirical fractal geometry analysis of some speculative financial bubbles abstract empirical evidence of a multifractal signature during increasing of a financial bubble leading to a crash is presented the april 2000 crash in the nasdaq composite index and a time series from the discrete chakrabarti stinchcombe model for earthquakes are analyzed using a geometric approach and some common patterns are identified these patterns can be related the geometry of the rising period of a financial bubbles with the non concave entropy problem

indices for testing neural codes one of the most critical challenges in systems neuroscience is determining the neural code a principled framework for addressing this can be found in information theory with this approach one can determine whether a proposed code can account for the stimulus response relationship specifically one can compare the transmitted information between the stimulus and the hypothesized neural code with the transmitted information between the stimulus and the behavioral response if the former is smaller than the latter i e if the code cannot account for the behavior the code can be ruled out the information theoretic index most widely used in this context is shannon s mutual information the shannon test however is not ideal for this purpose while the codes it will rule out are truly nonviable there will be some nonviable codes that it will fail to rule out here we describe a wide range of alternative indices that can be used for ruling codes out the range includes a continuum from shannon information to measures of the performance of a bayesian decoder we analyze the relationship of these indices to each other and their complementary strengths and weaknesses for addressing this problem

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

a pair of commuting scalars for g 2 su 2 su 2 g 2 su 2 su 2 is a two missing labels problem and therefore in order to give a complete and orthogonal specification of states of irreducible representations of g 2 in an su 2 su 2 basis one needs to find a pair of commuting hermitian operators which are scalar with respect to the su 2 su 2 subalgebra a theorem due to peccia and sharp states that there are apart from the lie algebra invariants twice as many functionally independent scalars as missing labels here two commuting su 2 su 2 scalars are obtained both of sixth order in the g 2 basis elements they are in fact combinations of five scalars of different tensorial types indicating that the functionally independent ones are in general insufficient to provide the lowest order commuting scalars an expression for the sixth order invariant of g 2 is also obtained

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

parallel computation of cluster properties application to 2d percolation the authors discuss various parallel algorithms for the enumeration of two dimensional cluster properties in such problems as percolation and the ising model as an application in a monte carlo simulation performed on the icl distributed array processor dap they re examine the numerical evidence for a recent conjecture by jug 1986 concerning percolation singularities in two dimensions

diffusion on fractal phase spaces and entropy production abstract complex systems may show strongly non exponential relaxation the origins of these behavior seem to be related to the fractal structure of the phase space in this article we consider the diffusion on a dilute hypercube this stochastic process is a coarse grained model for the time evolution of a glassy system where both the dynamics and the structure of the phase space was considered as simple as possible we characterize this process using two quantities a memory function and the tsallis entropy the first one is a measure of mixing while the second is related to non extensivity we characterize quantitatively their relationship finally we discuss the implications for other glassy and complex systems

student s t and r distributions unified derivation from an entropic variational principle abstract the optimization of the recently generalized entropy of the form s q 1 dx p x q q 1 with the constraints dx p x 1 and x 2 q dx x 2 p x q 1 yields the student s t distribution for q 1 and the r distribution for q

classical and fractal analysis of vehicle demand on the ferry boat system abstract transportation problems are important complex systems because of the increased number of vehicles in cities in this paper we study time series of vehicle demand by using the ferry boat system between salvador city and itaparica island in bahia brazil we compare the traditional demand analysis arima method with the self affine ones the scaling exponent and the density of crossing points in addition taking into account the inherent self affine behavior we study the stationary states of this dynamic process by using a nonlinear fokker planck equation the present findings indicate that the scaling exponent describes some properties of flux of vehicles using the ferry boat system the behavior of gives an alternative explanation about demand analysis and the nonlinear fokker planck equation presents a solution close to the stationary behavior of this complex dynamical analysis

solution of fractional kinetic equation by a class of integral transform of pathway type solutions of fractional kinetic equations are obtained through an integral transform named p transform introduced in this paper the p transform is a binomial type transform containing many class of transforms including the well known laplace transform the paper is motivated by the idea of pathway model introduced by mathai linear algebra appl 396 317 328 2005 10 1016 j laa 2004 09 022 the composition of the transform with differential and integral operators are proved along with convolution theorem as an illustration of applications to the general theory of differential equations a simple differential equation is solved by the new transform being a new transform the p transform of some elementary functions as well as some generalized special functions such as h function g function wright generalized hypergeometric function generalized hypergeometric function and mittag leffler function are also obtained the results for the classical laplace transform is retrieved by letting 1

zeroth law compatibility of nonadditive thermodynamics nonextensive thermodynamics is criticized by the statement that the zeroth law cannot be satisfied with nonadditive composition rules corrected in this paper we determine the general functional form of those nonadditive composition rules that are compatible with the zeroth law of thermodynamics we find that this general form is additive for the formal logarithms of the original quantities and the familiar relations of thermodynamics apply to these our result offers a possible solution to the long standing questions about equilibrium between extensive and nonextensive systems or systems with different nonextensivity parameters

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

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

multiwavelet packet entropy and its application in transmission line fault recognition and classification multiwavelets possess better properties than traditional wavelets multiwavelet packet transformation has more high frequency information spectral entropy can be applied as an analysis index to the complexity or uncertainty of a signal this paper tries to define four multiwavelet packet entropies to extract the features of different transmission line faults and uses a radial basis function rbf neural network to recognize and classify 10 fault types of power transmission lines first the preprocessing and postprocessing problems of multiwavelets are presented shannon entropy and tsallis entropy are introduced and their difference is discussed second multiwavelet packet energy entropy time entropy shannon singular entropy and tsallis singular entropy are defined as the feature extraction methods of transmission line fault signals third the plan of transmission line fault recognition using multiwavelet packet entropies and an rbf neural network is proposed finally the experimental results show that the plan with the four multiwavelet packet energy entropies defined in this paper achieves better performance in fault recognition the performance with sa4 symmetric antisymmetric multiwavelet packet tsallis singular entropy is the best among the combinations of different multiwavelet packets and the four multiwavelet packet entropies

limit behaviour and scaling relations of two kinds of noisy logistic map in the vicinity of chaos threshold and their robustness abstract in this paper we numerically investigate the distribution of the sums of the iterates of the logistic map and the relationships among the important properties of the nonlinear dynamics in the vicinity of the chaos threshold by adding two kinds of contributions with different densities the first one is the well known white noise whereas the second is a newly defined one named as quartic term which makes contributions from the own structure of the map as the chaos threshold is approached the iterates of the standard logistic map i e noise free have strong correlations and the standard central limit theorem is not valid anymore in a recent work tirnakli 2009 it has been shown that the limit distribution seems to converge to q gaussian distribution which maximizes the nonadditive entropy s q 1 i p i q q 1 under appropriate conditions in this work we investigate the effect of these contributions i e white noise and quartic term on the limit distribution and on the range of the obtained q gaussian distribution as a result of these findings under the existence of white noise and also the quartic term we analyse the validity of the scaling relations among correlation fractality the lyapunov divergence and q gaussian distributions which have recently been observed in afsar 2014 the results obtained here strengthen the argument that the central limit behaviour is given by a q gaussian as the chaos threshold is approached and indicate that the scaling relations obtained for the standard logistic map among the range of the q gaussian the correlation dimension the correlation length the lyapunov exponent fractality and the distance from the chaos threshold are robust under the existence of white noise and the quartic term

irreversibility entropy and incomplete information abstract the open system has been proved to be a system with perfect accessibility represented as a probability space in which is defined a p a measure but the p a measure is not yet known consequently it is difficult to develop the statistical thermodynamics for an irreversible system here its integral expression is obtained in order to its use in the statistical thermodynamic analysis of the complex and irreversible systems

tsallis like information measures and the analysis of complex signals abstract a tsallis like information measure that elaborates upon those of the tsallis type is shown to be a rather powerful tool for the analysis of complex non stationary signals as exemplified by the henon map and eegs the ensuing results could be of importance concerning the automatic detection of epileptic spikes

nonscalar extension of shift operator techniques for su 3 in an o 3 basis i theory a set of relations is set up which connect quadratic products of the shift operators okl k 0 1 2 which are nonscalar with respect to the o 3 subgroup of su 3 the usefulness of these relations is illustrated by the calculation of the eigenvalues of the scalar shift operator o0l for various irreducible representations p q of su 3

totally symmetric irreducible representations of the group so 6 in the principal so 3 subgroup basis explicit matrix elements are found for the generators of the group so 6 in an arbitrary totally symmetric irreducible representation using the physical principal so 3 subgroup in the chain so 6 so 5 so 3 the internal one missing label problem is solved through the definition of intrinsic states associated to the su 2 su 2 subgroup in the chain so 6 so 5 su 2 su 2 and out of which is projected a complete set of states in the physical basis by integrations over the physical rotation group manifold the matrix elements of the so 6 generators in the su 2 su 2 basis are themselves obtained by the intermediate use of an su 2 su 2 u 1 basis the latter group being a subgroup of so 6 but not of so 5

on the derivation of power law distributions within classical statistical mechanics far from the thermodynamic limit we show that within classical statistical mechanics without taking the thermodynamic limit the most general boltzmann factor for the canonical ensemble is a q exponential function the only assumption here is that microcanonical distributions have to be separated from the total system energy which is the prerequisite for any sensible measurement we derive that all separable distributions are parametrized by a mathematical separation constant q which can be related to the non extensivity q parameter in tsallis distributions we further demonstrate that nature fixes the separation constant q to 1 for large dimensionality of gibbs phase space our results will be relevant for systems with a low dimensional space for example nanosystems comprised of a small number of particles or for systems with a dimensionally collapsed phase space which might be the case for a large class of complex systems

age innovations and time operator of networks abstract we extend the time operator and age to network evolution models internal age formulas and the distribution of innovations are computed for erd s renyi random networks for markov networks and barabasi albert preferential attachment networks the innovation probabilities are found to be proportional to the quadratic entropy which coincides with the tsallis entropy for entropic index q 2 in all markov networks as well as in the linear growth mechanism the distribution of innovations in the barabasi albert model is a new probability distribution of the logarithmic type

roundoff induced attractors and reversibility in conservative two dimensional maps we numerically study two conservative two dimensional maps namely the baker map whose lyapunov exponent is known to be positive and a typical one exhibiting a vanishing lyapunov exponent chosen from the generalized shift family of maps introduced by c moore phys rev lett 64 1990 2354 in the context of undecidability we calculate the time evolution of the entropy sq 1 i 1wpiq q 1 s1 sbg i 1wpilnpi we exhibit the dramatic effect introduced by numerical precision indeed in spite of being area preserving maps they present well after the initially concentrated ensemble has spread virtually all over the phase space unexpected pseudo attractors fixed point like for the baker map and more complex structures for the moore map these pseudo attractors and the apparent time partial reversibility they provoke gradually disappear for increasingly large precision in the case of the moore map they are related to zero lebesgue measure effects associated with the frontiers existing in the definition of the map in addition to the above and consistent with the results by v latora and m baranger phys rev lett 82 1999 520 we find that the rate of the far from equilibrium entropy production of baker map numerically coincides with the standard kolmogorov sinai entropy of this strongly chaotic system

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