bandt pompe approach to the classical quantum transition abstract by regarding the celebrated classical quantum transition problem as one pertaining to the domain of dynamic systems theory we present a discussion that exhibits the superiority of the bandt pompe approach to the extraction of a probability distribution from time series values

generalized relative entropies in the classical limit abstract our protagonists are i the cressie read family of divergences characterized by the parameter ii tsallis generalized relative entropies characterized by the q one and as a particular instance of both iii the kullback leibler kl relative entropy in their normalized versions we ascertain the equivalence between i and ii additionally we employ these three entropic quantifiers in order to provide a statistical investigation of the classical limit of a semiclassical model whose properties are well known from a purely dynamic viewpoint this places us in a good position to assess the appropriateness of our statistical quantifiers for describing involved systems we compare the behaviour of i ii and iii as one proceeds towards the classical limit we determine optimal ranges for and or q it is shown the tsallis quantifier is better than kl s for 1 5 q 2 5

chaos in time dependent variational approximations to quantum dynamics dynamical chaos has recently been shown to exist in the gaussian approximation in quan tum mechanics and in the self consistent mean eld approach to studying the dynamics ofquantum elds in this study we rst show that any variationalapproximationto the dynam ics of a quantum system based on the dirac action principle leads to a classical hamiltoniandynamics for the variational parameters since this hamiltonian is generically nonlinearand nonintegrable the dynamics thus generated can be chaotic in distinction to the exactquantum evolution we then restrict attention to a system of two biquadratically coupledquantum oscillators and study two variational schemes the leading order large n fourcanonical variables and hartree six canonical variables approximations the chaos seenin the approximate dynamics is an artifact of the approximations this is demonstrated bythe fact that its onset occurs on the same characteristic time scale as the breakdown of theapproximations when compared to numerical solutions of the time dependent schr odingerequation pacs numbers 05 45 b 03 65 sq 2 30 wd 03 65 w

towards an information geometric characterization classification of complex systems ii critical parameter values from the c d manifold abstract in our previous paper i we derived information geometric objects from the two parameter generalized entropy of hanel and thurner 2011 using the c d parameters as labels of the corresponding manifolds here we follow a completely different approach by considering these parameters as coordinates of a single information manifold this gives a manageable two dimensional manifold amenable to easy manipulations but most importantly it offers a direct characterization of complex systems in terms of the pair of the c d values as a result we obtain certain characteristic values from the scalar curvature which we could conjecture that they represent complex systems with specific behavior it is further observed that the boundary values of the c d parameters which characterize the hanel thurner classification are in some sense singular this asks for a regularization scheme which we try to establish

simple measure for complexity a measure of complexity is proposed based on appropriately defined notions of order and disorder which has a considerable degree of flexibility in its dependence on these concepts the possible functional dependencies which result encompass those of many earlier definitions of complexity the proposed measure is in principle easy to calculate and has the property of an intensive thermodynamic quantity with appropriate choices of parameters it behaves similarly to effective measure complexity for the logistic map it is also a generalization of the normalized complexity of lopez ruiz et al but does not suffer from over universality

intensive entropic non triviality measure abstract we discuss a way of characterizing probability distributions complementing that provided by the celebrated notion of information measure with reference to a measure of complexity that we call a nontriviality measure our starting point is the lmc measure of complexity advanced by lopez ruiz et al phys lett a 209 1995 321 and its analysis by anteneodo and plastino phys lett a 223 1997 348 an improvement of some of their troublesome characteristics is thereby achieved basically we replace the euclidean distance to equilibrium by the jensen shannon divergence the resulting measure turns out to be i an intensive quantity and ii allows one to distinguish between different degrees of periodicity we apply the cured measure to the logistic map so as to clearly exhibit its advantages

function reconstruction as a classical moment problem a maximum entropy approach we present a systematic study of the reconstruction of non negative functions via maximum entropy approach utilizing the information contained in a finite number of moments of the functions for testing the efficacy of the approach we reconstruct a set of functions using an iterative entropy optimization scheme and study the convergence profile as the number of moments is increased a wide variety of functions are considered that include a distribution with a sharp discontinuity an oscillatory function a distribution with singularities and finally a distribution with several spikes and fine structure the last example is important in the context of the determination of the natural density of the logistic map the convergence of the method is studied by comparing the moments of the approximated functions with the exact ones furthermore by varying the number of moments and iterations we examine to what extent the features of the functions such as the divergence behavior at singular points within the interval is reproduced the proximity of the reconstructed maximum entropy solution to the exact solution is examined via kullback leibler divergence and variation measures for different number of moments

technical allocative and overall efficiency estimation and inference abstract nonparametric data envelopment analysis and free disposal hull estimators are frequently used to estimate cost revenue and profit efficiency as well as the corresponding allocative efficiencies papers in the literature often report sample means of such estimates along with sample standard deviations inviting readers to make inference about means of these efficiencies using classical methods based on the standard lindeberg feller central limit theorem clt a number of papers explicitly make inference using the classical methods however the statistical properties of these estimators are until now unknown this paper establishes rates of convergence and existence of limiting distributions for the various estimators these properties are needed in order to make inference about individual producers using subsampling methods in addition properties of the first two moments of the estimators are derived and these results are subsequently used to establish new clts for the estimators providing formal justification for inference making the results reveal that the classical clts and methods do not provide valid inference when fdh estimators are used and provide valid inference when dea estimators only in a few restrictive special cases

the fuzzy weighted average within a generalized means function the fuzzy weighted average is widely used to solve hierarchical evaluation problems including fuzzy consideration for the operations of scoring weighting and aggregating previous works considered the fuzziness of score and weight and used the additive function to aggregate these weighted scores this study considers the aggregation operator also as a fuzzy variable and uses a generalized means function to fuzzify the aggregation operator within a fuzzy weighted average in practice the proposed model not only considers both the relative important of the criteria and its achieved performance but also conveys the influence of the dm s decision maker s evaluation attitude thus the proposed model can flexibly reflect any dm s evaluation attitude such as open neutral or rigorous thereby the proposed model can make an objective evaluation that approaches a real decision making situation and thus has the potential to be a useful management tool for improved resolution of fuzzy hierarchical evaluation problems

on aggregate farrell efficiencies in this paper we establish the fact that an industry maximal revenue is the sum of its firms maximal revenues this fact enables us to discover conditions for aggregation of farrell efficiencies

formulation of the k w turbulence model revisited this paper presents a reformulated version of the author sk model of turbulence revisions include the addition of just one new closure coefficient and an adjustment to the dependence of eddy viscosity on turbulence properties the result is a significantly improved model that applies to both boundary layers and free shear flows and that has very little sensitivity to finite freestream boundary conditions on turbulence properties the improvements to the k model facilitate a significant expansion of its range of applicability the new model like preceding versions provides accurate solutions for mildly separated flows and simple geometries such as that of a backward facing step the model s improvement over earlier versions lies in its accuracy for even more complicated separated flows this paper demonstrates the enhanced capability for supersonic flow into compression corners and a hypersonic shock wave boundary layer interaction the excellent agreement is achieved without introducing any compressibility modifications to the turbulence model

clausius inequality beyond the weak coupling limit the quantum brownian oscillator we consider a quantum linear oscillator coupled at an arbitrary strength to a bath at an arbitrary temperature we find an exact closed expression for the oscillator density operator this state is noncanonical but can be shown to be equivalent to that of an uncoupled linear oscillator at an effective temperature t eff with an effective mass and an effective spring constant we derive an effective clausius inequality deltaq eff or t eff ds where deltaq eff is the heat exchanged between the effective weakly coupled oscillator and the bath and s represents a thermal entropy of the effective oscillator being identical to the von neumann entropy of the coupled oscillator using this inequality for a cyclic process in terms of a variation of the coupling strength we confirm the validity of the second law for a fixed coupling strength this inequality can also be tested for a process in terms of a variation of either the oscillator mass or its spring constant then it is never violated the properly defined clausius inequality is thus more robust than assumed previously

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

deformed exponentials and logarithms in generalized thermostatistics abstract criteria are given that deformed logarithmic and exponential functions should satisfy with a pair of such functions one can associate another function called the deduced logarithmic function it is shown that generalized thermostatistics can be formulated in terms of deformed exponential functions together with the associated deduced logarithmic functions

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

composite indicators as generalized benefit of the doubt weighted averages abstract composite indicators cis are usually computed as arithmetic weighted averages of often normalized sub indicators several studies criticized this procedure for implying requirements and properties that are often hard to maintain in practical applications recent studies explored the multiplicative aggregation and more specifically the geometric weighted average as aggregator in ci building this paper takes this exploration one step further by considering other members of the family of generalized weighted averages as aggregator in the construction of cis it is argued that the choice for a particular version of the generalized weighted average enables to reflect decision makers attitudes in the evaluation for the human development index results show that the choice for a specific version of the generalized weighted average as aggregator in ci construction impacts country rankings

estimation of returns to scale using data envelopment analysis abstract generalization of the measure of returns to scale from a single number to an interval permits extension of the concept to dea data domains with multiple inputs and multiple outputs the key new approach is a partition of the optimal frontier into three parts corresponding respectively to increasing constant and decreasing returns to scale these parts are characterized in terms of optimal primal solutions and optimal dual solutions for both the original charnes cooper rhodes model 1978 and the later banker charnes cooper model 1984 and relying on concepts developed by r d banker 1984 and r m thrall 1988

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

choosing weights from alternative optimal solutions of dual multiplier models in dea in this paper we propose a two step procedure to be used for the selection of the weights that we obtain from the multiplier model in a dea efficiency analysis it is well known that optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and consequently have alternate optima for the weights different optimal weights may then be obtained depending for instance on the software used the idea behind the procedure we present is to explore the set of alternate optima in order to help make a choice of optimal weights the selection of weights for a given extreme efficient point is connected with the dimension of the efficient facets of the frontier our approach makes it possible to select the weights associated with the facets of higher dimension that this unit generates and in particular it selects those weights associated with a full dimensional efficient facet fdef if any in this sense the weights provided by our procedure will have the maximum support from the production possibility set we also look for weights that maximize the relative value of the inputs and outputs included in the efficiency analysis in a sense to be described in this article

tsallis deformation parameter q quantifies the classical quantum transition abstract we investigate the classical limit of a type of semiclassical evolution the pertinent system representing the interaction between matter and a given field on using tsallis q entropy as a quantifier of the ensuing dynamics we find that it not only appropriately describes the quantum classical transition but that the associated deformation parameter q itself characterizes the different regimes involved in the process detecting the most salient fine details of the changeover

bandt pompe tsallis quantifier and quantum classical transition abstract we concern ourselves with statistical quantifiers of semiclassical time evolutions and their classical limit the system of interest represents the interaction between matter and a given field our tool here is the so called permutation entropy evaluated by recourse to the so called bandt pompe technique within a tsallis scenario we encounter that the most salient details of the quantum classical transition are well described indeed in a better fashion than that of previous approaches

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

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

brain electrical activity analysis using wavelet based informational tools ii tsallis non extensivity and complexity measures the processing of information by the brain is reflected in dynamical changes of the electrical activity in i time ii frequency and iii space therefore the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency the present work complements the efforts described in rosso et al physica a 313 2002 587 devoted to non extensive information measures a la tsallis here we show that the notion of complexity using 1 appropriate information theory tools adapted to a non extensive scenario and 2 scalp eeg data provides one with valuable insights into the dynamics of neural activity in particular using different complexity measures we detect the presence of states characterized by both order and maximal complexity

derivation of power law distributions within standard statistical mechanics abstract we show that within classical statistical mechanics it is possible to naturally derive power law distributions which are of tsallis type the only assumption is that microcanonical distributions have to be separable from of the total system energy which is reasonable for any sensible measurement we demonstrate that all separable distributions are parametrized by a separation constant q which is one to one related to the q parameter in tsallis distributions the power laws obtained are formally equivalent to those obtained by maximizing the tsallis entropy under q constraints we further ask why nature fixes the separation constant q to 1 in so many cases leading to standard thermodynamics we answer this with an explicit example where it is possible to relate q to system size and interaction parameters characterizing the physical system we argue that these results might be helpful to explain the ubiquity of tsallis distributions in nature

the denominator rule for share weighting aggregation abstract in this paper we prove that the denominator rule namely that weighting shares should be defined in term of the denominator variable of the relevant index is a necessary and sufficient condition for consistent arithmetic aggregation of any ratio type performance measures including efficiency indices we then illustrate the applicability of the denominator rule in the aggregation of scale efficiency measures of the effect of input congestion and of capacity utilization indices

dynamical approach study of spurious steady state numerical solutions of nonlinear differential equations i the dynamics of time discretization and its implications for algorithm development in computational fluid dynamics abstract the goal of this paper is to utilize the theory of nonlinear dynamics approach to investigate the possible sources of errors and slow convergence and nonconvergence of steady state numerical solutions when using the time dependent approach for nonlinear hyperbolic and parabolic partial differential equations terms this interdisciplinary research belongs to a subset of a new field of study in numerical analysis sometimes referred to as the dynamics of numerics and the numerics of dynamics at the present time this new interdisciplinary topic is still the property of an isolated discipline with all too little effort spent in pointing out an underlying generality that could make it adaptable to diverse fields of applications this is the first of a series of research papers under the same topic our hope is to reach researchers in the fields of computational fluid dynamics cfd and in particular hypersonic and combustion related cfd by simple examples in which the exact solutions of the governing equations are known the application of the apparently straightforward numerical technique to genuinely nonlinear problems can be shown to lead to incorrect or misleading results one striking phenomenon is that with the same initial data the continuum and its discretized counterpart can asymptotically approach different stable solutions this behavior is especially important for employing a time dependent approach to the steady state since the initial data are usually not known and a freestream condition or an intelligent guess for the initial conditions is often used with the unique property of the different dependence of the solution on initial data for the partial differential equation and the discretized counterpart it is not easy to delineate the true physics from numerical artifacts when numerical methods are the sole source of solution procedure for the continuum part i concentrates on the dynamical behavior of time discretization for scalar nonlinear ordinary differential equations in order to motivate this new yet unconventional approach to algorithm development in cfd and to serve as an introduction for parts 11 and iii of the same series of research papers

polynomial convergence of primal dual algorithms for the second order cone program based on the mz family of directions in this paper we study primal dual path following algorithms for the second order cone programming socp based on a family of directions that is a natural extension of the monteiro zhang mz family for semidefinite programming we show that the polynomial iteration complexity bounds of two well known algorithms for linear programming namely the short step path following algorithm of kojima et al and monteiro and adler and the predictor corrector algorithm of mizuno et al carry over to the context of socp that is they have an o loge 1 iteration complexity to reduce the duality gap by a factor of e where n is the number of second order cones since the mz type family studied in this paper includes an analogue of the alizadeh haeberly and overton pure newton direction we establish for the first time the polynomial convergence of primal dual algorithms for socp based on this search direction

improving finite sample approximation by central limit theorems for estimates from data envelopment analysis abstract we propose an improvement of the finite sample approximation of the central limit theorems clts that were recently derived for statistics involving production efficiency scores estimated via data envelopment analysis dea or free disposal hull fdh approaches the improvement is very easy to implement since it involves a simple correction of the variance estimator with an estimate of the bias of the already employed statistics without any additional computational burden and reserves the original asymptotic results such as consistency and asymptotic normality the proposed approach persistently showed improvement in all the scenarios that we tried in various monte carlo experiments especially for relatively small samples or relatively large dimensions measured by total number of inputs and outputs of the underlying production model this approach therefore is expected to produce more accurate estimates of confidence intervals of aggregates of individual efficiency scores in empirical research using dea or fdh approaches and so must be valuable for practitioners we also illustrate this method using a popular real data set to confirm that the difference in the estimated confidence intervals can be substantial a step by step implementation algorithm of the proposed approach is included in the appendix

a comment on solving the puzzles of structural efficiency abstract in a recent paper by li and cheng li s k cheng y s 2007 solving the puzzles of structural efficiency european journal of operational research 180 2 713 722 they developed the shadow price model to solve the existing puzzles of structural efficiency theoretically however we observe that the optimal shadow price vector in the shadow price model by li and cheng 2007 is not always unique as a result the decomposition of the structural efficiency is arbitrarily generated depending on the shadow price vector we choose finally an example with multiple inputs and outputs is used to illustrate the phenomenon

dynamical complexity detection in pre seismic emissions using nonadditive tsallis entropy abstract we investigate within the framework of nonextensive tsallis entropy particular aspects of the relation between signal analysis and signals originating in a very special nonlinear system the focal area of an impending earthquake the tsallis like time dependent entropy is shown to be a rather powerful tool for providing a novel quantitative strategy for monitoring the focal area states just before the earthquake occurrence

modeling stochastic frontier based on vine copulas abstract this article models a production function and analyzes the technical efficiency of listed companies in the united states germany and england between 2005 and 2012 based on the vine copula approach traditional estimates of the stochastic frontier assume that data is multivariate normally distributed and there is no source of asymmetry the proposed method based on vine copulas allow us to explore different types of asymmetry and multivariate distribution using data on product capital and labor we measure the relative efficiency of the vine production function and estimate the coefficient used in the stochastic frontier literature for comparison purposes this production vine copula predicts the value added by firms with given capital and labor in a probabilistic way it thereby stands in sharp contrast to the production function where the output of firms is completely deterministic the results show that on average s p500 companies are more efficient than companies listed in england and germany which presented similar average efficiency coefficients for comparative purposes the traditional stochastic frontier was estimated and the results showed discrepancies between the coefficients obtained by the application of the two methods traditional and frontier vine opening new paths of non linear research

generalized boltzmann factors and the maximum entropy principle entropies for complex systems abstract we generalize the usual exponential boltzmann factor to any reasonable and potentially observable distribution function b e by defining generalized logarithms as inverses of these distribution functions we are led to a generalization of the classical boltzmann gibbs entropy s bg d e e b e ln b e to the expression s d e e 0 b e d x x which contains the classical entropy as a special case we show that this is the unique modification of entropy which is compatible with the maximum entropy principle for arbitrary non exponential distribution functions we demonstrate that this entropy has two important features first it describes the correct thermodynamic relations of the system and second the observed distributions are straightforward solutions to the jaynes maximum entropy principle with the ordinary not escort constraints tsallis entropy is recovered as a further special case

thermodynamics with generalized ensembles the class of dual orthodes abstract we address the problem of the foundation of generalized ensembles in statistical physics the approach is based on boltzmann s concept of orthodes these are the statistical ensembles that satisfy the heat theorem according to which the heat exchanged divided by the temperature is an exact differential this approach can be seen as a mechanical approach alternative to the well established information theoretic one based on the maximization of generalized information entropy our starting point are the tsallis escort ensembles which have been previously proved to be orthodes and have been proved to interpolate between canonical and microcanonical ensembles here we shall see that the tsallis escort ensembles belong to a wider class of orthodes that include the most diverse types of ensembles all such ensembles admit both a microcanonical like parametrization via the energy and a canonical like one via the parameter for this reason we name them dual one central result used to build the theory is a generalized equipartition theorem the theory is illustrated with a few examples and the equivalence of all the dual orthodes is discussed

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

towards an information geometric characterization classification of complex systems i use of generalized entropies abstract using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the information geometry based on these entropies our aim at this stage is to construct first some fundamental geometric objects which will be used in the development of our geometrical framework we first establish the existence of a two parameter family of probability distributions then using this family we derive the associated metric and we state a generalized cramer rao inequality this gives a first two parameter classification of complex systems finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes our analysis is based on the two parameter family of generalized entropies of hanel and thurner 2011

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

extending fare and zelenyuk 2003 abstract in our recent work fare and zelenyuk 2003 on aggregate farrell efficiency scores european journal of operational research 146 3 615 620 we have proposed a way of aggregating farrell type efficiency scores with weights and aggregation function derived from economic type optimization behaviour in this comment we correct a mathematical error present in that work as well as generalize the price independent weights we have proposed earlier

an attractor in a solar time series a time series analysis of observed solar radio pulsations suggests that there must be a low dimensional attractor the power spectrum cannot be interpreted as a superposition of periodic components estimates of the maximum lyapunov exponent and of the kolmogorov entropy give some indications for a deterministic chaos in order to study the limitations inherent in small data samples we include data from the lorenz model and an artificial noise record consequences for the physical modelling of the pulsation event are discussed

the tsallis complexity of a semiclassical time evolution abstract an investigation is undertaken of semiclassical time evolutions and their classical limit with the intent of getting insights into the classical quantum frontier we deal with a system that represents the interaction between matter and a given field and our main research tool is the so called q complexity quantifier for which two different versions are considered the probability distribution associated with the time evolution process is determined by recourse to the bandt pompe symbolic technique c bandt b pompe permutation entropy a natural complexity measure for time series phys rev lett 88 2002 174102 1 174102 4 the most salient details of the quantum classical transition turn out to be described not only well but also in a better fashion than that of previous literature

aggregation of scale efficiency abstract in this article we generalize the aggregation theory in efficiency and productivity analysis by deriving solutions to the problem of aggregation of individual scale efficiency measures primal and dual into aggregate primal and dual scale efficiency measures of a group e g industry the new aggregation result is coherent with aggregation framework and solutions that were earlier derived for other related efficiency measures and can be used in practice for estimation of scale efficiency of an industry or other groups of firms within it

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

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

numerical evidence of multiple solutions for the reynolds averaged navier stokes equations in this paper evidence is presented for the existence of multiple solutions of reynolds averaged navier stokes equations with the one equation spalart allmaras and two equation wilcox k turbulence models on fixed grids in three dimensions and how they were obtained is described the two major configurations considered are an academic extruded two dimensional airfoil geometry and the trap wing test case the observed appearance of the multiple solutions seems to be closely related to smooth body separation sometimes massive routinely observed in flows over high lift configurations especially near stall angles of attack the results are obtained and cross verified with two stabilized finite element codes streamwise upwind petrov galerkin which provide residual converged results for complex flows with second order discretizations in the paper the ways multiple solutions have been obtained are described including such obvious ones as providing a different initial guess to the steady state solver

generalized entropies from first principles a derivation of power law canonical distributions from first principle statistical mechanics including the exponential distribution as a particular case is presented it is shown that these distributions arise naturally and that the heat capacity of the heat bath is the condition that determines its type as a consequence a physical interpretation for the parameter q of the generalized entropy is given

asymptotically scale invariant occupancy of phase space makes the entropy sq extensive phase space can be constructed for n equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated if they are locally correlated we expect the boltzmann gibbs entropy s bg k i p i ln p i to be extensive i e s bg n n for n in particular if they are independent s bg is strictly additive i e s bg n ns bg 1 n however if the subsystems are globally correlated we expect for a vast class of systems the entropy s q k 1 i p q i q 1 with s 1 s bg for some special value of q 1 to be the one which is extensive i e s q n n for n another concept which is relevant is strict or asymptotic scale freedom or scale invariance defined as the situation for which all marginal probabilities of the n system coincide or asymptotically approach for n the joint probabilities of the n 1 system if each subsystem is a binary one scale freedom is guaranteed by what we hereafter refer to as the leibnitz rule i e the sum of two successive joint probabilities of the n system coincides or asymptotically approaches the corresponding joint probability of the n 1 system the kinds of interplay of these various concepts are illustrated in several examples one of them justifies the title of this paper we conjecture that these mechanisms are deeply related to the very frequent emergence in natural and artificial complex systems of scale free structures and to their connections with nonextensive statistical mechanics summarizing we have shown that for asymptotically scale invariant systems it is s q with q 1 and not s bg the entropy which matches standard clausius like prescriptions of classical thermodynamics

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

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

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

on the denominator rule and a theorem by janos aczel abstract in this note we compare and contrast arithmetic and geometric share weighting aggregations of ratio expressions i e relative scores and we provide conditions under which they result in approximately the same value of the aggregate measure we also provide some comparative empirical results about the differences among the suggested alternative aggregate measures

a nonextensive modification of the gutenberg richter law q stretched exponential form abstract we study the cumulative distribution for the magnitude of earthquakes in the context of nonextensive statistical mechanics a new modification of the gutenberg richter gr law is introduced we use seismic data sets which were recorded in two different regions iran and california to compute the cumulative distribution of the magnitudes the empirical data are fitted extremely well by our suggested expression for the modified gr law over the whole range of magnitudes

generalized statistical complexity measures geometrical and analytical properties abstract we discuss bounds on the values adopted by the generalized statistical complexity measures m t martin et al phys lett a 311 2003 126 p w lamberti et al physica a 334 2004 119 introduced by lopez ruiz et al phys lett a 209 1995 321 and shiner et al phys rev e 59 1999 1459 several new theorems are proved and illustrated with reference to the celebrated logistic map

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

geometric mean quantity index numbers with benefit of the doubt weights abstract geometric mean index numbers are a multiplicative aggregation of price or quantity ratios with their importance exponents weights derived from one or more observed budget shares in the specific context of composite indicator construction we propose to use the budget shares as naturally generated by the linear benefit of the doubt model this approach is directly inspired by the literature on index number theory our basic model is easily extended to provide transitive composite indicator orderings in a multilateral setting also a multi factor decomposition is proposed to explain the intertemporal evolution of a single entity we illustrate our results with social inclusion data for the eu countries

determining merged relative scores the starting point in this paper is the following type of situation performances of people or technologies are measured by their scores with respect to different benchmarks relative to those of some base performance in order to arrive at a decision one wants to merge average aggregate the scores of each individual or technology into a single number which can then be compared with that of another individual or technology the situation is similar at least technically to price indices where present prices of different products are considered relative to prices of these products in a base year and we again want to merge these into one number in this paper one solves most of these problems one also states a few problems which are still open

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

an occurrence of multiple projections in dea based measurement of technical efficiency theoretical comparison among dea models from desirable properties this study discusses nine desirable properties that a measure of technical efficiency te needs to satisfy from the perspective of production economics and optimization seven data envelopment analysis dea models are theoretically compared from a viewpoint of nine te criteria all the seven dea models suffer from a problem of multiple projections even though a unique projection for efficiency comparison is one of the nine desirable properties furthermore all the dea models violate the property on aggregation of inputs and outputs thus the seven dea models do not satisfy all desirable te properties in addition the comparison provides us with the following guidelines a the additive model violates all desirable te properties b russell measure and sbm ergm perform as well as ram as a non radial measure if we are interested in strict monotonicity the two models outperform the other dea models including ram in contrast if we are interested in translation invariance ram is better than russell measure and sbm ergm c the radial measures ccr and bcc have the property of linear homogeneity d the ccr model is useful for measuring a frontier shift among different periods e if a data set contains a negative value ram becomes a dea model to handle the negative value because it has the property of translation invariance after examining the desirable te properties this study proposes a new approach to deal with an occurrence of multiple projections the proposed approach includes a test to examine an occurrence of multiple projections a mathematical expression of a projection set and a selection process of a unique reference set as the largest one covering all the possible reference sets

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

positivity preservation and adaptive solution for the k model of turbulence a simple change of dependent variables that guarantees positivity of turbulence variables in numerical simulation codes is presented the approach consists of solving for the natural logarithm of the turbulence variables which are known to be strictly positive the approach is valid for any numerical scheme be it finite difference a finite volume or a finite element method the work focuses on the advantages of the proposed change of dependent variables within the framework of an adaptive finite element method the turbulence equations in logarithmic variables are presented for the standard e model error estimation and mesh adaptation procedures are described the formulation is validated on a shear layer case for which an analytical solution is available this provides a framework for rigorous comparison of the proposed approach with the standard solution technique which makes use of k and e as dependent variables the approach is then applied to solve turbulent flow over a naca0012 airfoil for which experimental measurements are available the proposed procedure results in a robust adaptive algorithm improved predictions of turbulence variables are obtained using the proposed formulation

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

computational strategy for russell measure in dea second order cone programming abstract in aggregation for data envelopment analysis dea a jointly measured efficiency score among inputs and outputs is desirable in performance analysis a separate treatment between output oriented efficiency and input oriented efficiency is often needed in the conventional radial dea models such radial measures usually need to measure both that a current performance attains an efficiency frontier and that all the slacks are zero on optimality in the analytical framework of the radial measure russell measure is proposed to deal with such a difficulty a major difficulty associated with the russell measure is that it is modeled by a nonlinear programming formulation hence a conventional linear programming algorithm usually applied for dea cannot solve the russell measure this study newly proposes a reformulation of the russell measure by a second order cone programming socp model and applies the primal dual interior point algorithm to solve the russell measure

on some methods for performance ranking and correspondence analysis in the dea context two novel methods named performance baseline and performance correspondence matrices are proposed to evaluate the performance of decision making units dmus based on the techniques of singular value decomposition svd the performance baseline matrix can be used to rank all the dmus because it provides a common basis for performance comparison the performance correspondence matrix can be used to conduct performance cluster analysis with which to explore the structure of input output variables that are associated with dmus the analysis can reveal the performance difference of the dmus and the key input output variables determining the efficiency of a certain dmu and provides valuable quantitative information for adjusting variables to improve efficiency of the dmu three case studies are presented to demonstrate that the proposed methods in this work are effective and easy to use and can provide insights into proper selection of input output variables for performance comparison to avoid over manipulating dea models in practice

duality and profit efficiency for the hyperbolic measure model abstract the hyperbolic measure hm model is a radial non oriented model that is often used in data envelopment analysis dea it is formulated as a non linear programming problem and hence the conventional linear programming methods customarily used in dea cannot be applied to it in general in this paper we reformulate the hyperbolic measure model in a semidefinite programming framework which opens the way to solving the hm model by reliable and efficient interior point algorithms and allows us to benefit from simple primal dual correspondence in semidefinite programming we derive the dual of the hm model and so for the first time establish its multiplier form we also offer an economic interpretation of the dual hm model via a comparison with the multiplier form of the directional distance model and relate the hm score to the so called nerlovian profit efficiency

information gain within nonextensive thermostatistics we discuss the information theoretical foundations of the kullback information gain recently generalized within a nonextensive thermostatistical formalism general properties are studied and in particular a consistent test for measuring the degree of correlation between random variables is proposed in addition minimum entropy distributions are discussed and the h theorem is proved within the generalized context

merging relative scores abstract this paper considers the problem of scoring alternative technologies based on their performance on different benchmarks normalizing the scores relative to those of a base technology and then finding a merged or combined score based on the normalized or relative scores similar problems occur if we score alternative job candidates or students on the basis of different tests or criteria and seek to merge relative scores after normalization they also occur when we obtain index numbers such as price indices here we measure different items at different times normalize relative to some base time and merge the relative measures of the different items obtained at a fixed time we attempt to identify merging methods which will guarantee that certain types of conclusions based on them will be invariant if the base technology job candidate student or time is changed

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

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100