diagonal plane sections of trivariate copulas we introduce the notion of diagonal plane section of a trivariate copula as an additional tool to describe its tail dependence behavior this notion extends the concept of diagonal section of a bivariate copula we provide existence results for trivariate copulas with a given diagonal plane function related results are discussed especially about extensions to a higher dimensional setting

family optimal investment strategy for a random household expenditure under the cev model abstract the family optimal investment strategy for a random household expenditure is investigated assume that the family is allowed to invest in a financial market consisting of one risk free asset and one risky asset whose price process satisfies the constant elasticity of variance cev model the target is to maximize the expected exponential utility of the family terminal wealth and obtain the optimal investment strategy employing techniques of stochastic control theory and the dual theory we derive the hamilton jacobi bellman hjb equation and obtain an approximate expression for the optimal investment strategy in the slow fluctuating regime numerical examples are presented to illustrate the effects of parameters on the optimal strategies

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

explicit solution of a general consumption investment problem this paper solves a general consumption and investment decision problem in closed form an investor seeks to maximize total expected discounted utility of consumption there are n distinct risky investments modelled by dependent geometric brownian motion processes and one riskless deterministic investment the analysis allows for a general utility function and general rates of return the model and analysis take into consideration the inherent nonnegativity of consumption and consider bankruptcy so this paper generalizes many of the results of lehoczky sethi and shreve lehoczky j s sethi s shreva 1983 optimal consumption and investment policies allowing consumption constraints and bankruptcy math oper res 8 613 636 the value function is determined explicitly as are the optimal consumption and investment policies the analysis is extended to consider more general risky investments under certain conditions the value functions derived for geometric brownian motion are shown to provide upper and lower bounds on the value functions in the more general context

the non markovian property of q gaussian process abstract in this paper the q gaussian process based on the non extensive theory is discussed from a mathematical point of view which has been widely applied to many anomalous diffusion systems in physics and finance firstly the discussion of non markovian property of q gaussian process provides a numerical support for the future theoretical research secondly the martingale and self similarity of this process are obtained by tsallis distributions thirdly the long dependence is analyzed by simulations and hurst exponents are compared with those of fractional brownian motion at last the european call option price formula driven by this process is simulated by which we find that this process can better match anomalous diffusion and the volatility smile

relative information of type s csiszar s f divergence and information inequalities during past years dragomir has contributed a lot of work providing different kinds of bounds on the distance information and divergence measures in this paper we have unified some of his results using the relative information of type s and relating it with the csiszar s f divergence

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

nonextensive triangle equality and other properties of tsallis relative entropy minimization kullback leibler relative entropy has unique properties in cases involving distributions resulting from relative entropy minimization tsallis relative entropy is a one parameter generalization of kullback leibier relative entropy in the nonextensive thermostatistics in this paper we present the properties of tsallis relative entropy minimization and present some differences with the classical case in the representation of such a minimum relative entropy distribution we highlight the use of the q product an operator that has been recently introduced to derive the mathematical structure behind the tsallis statistics one of our main results is the generalization of triangle equality of relative entropy minimization to the nonextensive case

gamma function to beck cohen superstatistics abstract in this paper we show a mathematical construction of beck cohen superstatistics in the bayesian point of view with the help of the two representations of a gamma function furthermore it is shown how some results for superstatistics are related to each other

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

portfolio selection problem with value at risk constraints under non extensive statistical mechanics the optimal portfolio selection problem is a major issue in the financial field in which the process of asset prices is usually modeled by a wiener process that is the return distribution of the asset is normal however several empirical results have shown that the return distribution of the asset has the characteristics of fat tails and aiguilles and is not normal in this work we propose an optimal portfolio selection model with a value at risk var constraint in which the process of asset prices is modeled by the non extensive statistical mechanics instead of the classical wiener process the model can describe the characteristics of fat tails and aiguilles of returns using the dynamic programming principle we derive a hamilton jacobi bellman hjb equation then employing the lagrange multiplier method we obtain closed form solutions for the case of logarithmic utility moreover the empirical results show that the price process can more accurately fit the empirical distribution of returns than the familiar wiener process in addition as the time increases the constraint becomes binding that is to control the risk the agent reduces the proportion of the wealth invested in the risky asset furthermore at the same confidence level the agent reduces the proportion of the wealth invested in the risky asset more quickly under our model than under the model based on the wiener process this can give investors a good decision making reference

dynamic mean variance portfolio selection with no shorting constraints this paper is concerned with mean variance portfolio selection problems in continuous time under the constraint that short selling of stocks is prohibited the problem is formulated as a stochastic optimal linear quadratic lq control problem however this lq problem is not a conventional one in that the control portfolio is constrained to take nonnegative values due to the no shorting restriction and thereby the usual riccati equation approach involving a completion of squares does not apply directly in addition the corresponding hamilton jacobi bellman hjb equation inherently has no smooth solution to tackle these difficulties a continuous function is constructed via two riccati equations and then it is shown that this function is a viscosity solution to the hjb equation solving these riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original mean variance problem an example illustrating these results is also presented

a stochastic calculus model of continuous trading optimal portfolios the problem of choosing a portfolio of securities so as to maximize the expected utility of wealth at a terminal planning horizon is solved via stochastic calculus and convex analysis this problem is decomposed into two subproblems with security prices modeled as semimartingales and trading strategies modeled as predictable processes the set of terminal wealths is identified as a subspace in a space of integrable random variables the first subproblem is to find the terminal wealth that maximizes expected utility convex analysis is used to derive necessary and sufficient conditions for optimality and an existence result the second subproblem of finding the admissible trading strategy that generates the optimal terminal wealth is a martingale representation problem the primary advantage of this approach is that explicit formulas can readily be derived for the optimal terminal wealth and the corresponding expected utility as is shown for the case of an exponential utility function and a risky security modeled as geometric brownian motion

copulas based time series combined forecasters time series combined forecasters have been superior to the respective single models in statistical terms in this way the linear combination functions e g the simple average sa and the minimal variance mv approaches have been the main alternatives for aggregation in the literature in this work it is presented a copulas based method for combining biased single models copulas are multivariate functions that operate on marginal probability distributions and have the specific advantage of generalizing mv by flexibly modelling the forecasters residuals and then the dependence among them a typical divide and conquer framework that can result in superior combined forecasters the usefulness of the copulas based combination method is highlighted by means of a comparison with sa and mv models based on a number of simulated cases and a real world time series

information divergence and risk for binary experiments we unify f divergences bregman divergences surrogate regret bounds proper scoring rules cost curves roc curves and statistical information we do this by systematically studying integral and variational representations of these objects and in so doing identify their representation primitives which all are related to cost sensitive binary classification as well as developing relationships between generative and discriminative views of learning the new machinery leads to tight and more general surrogate regret bounds and generalised pinsker inequalities relating f divergences to variational divergence the new viewpoint also illuminates existing algorithms it provides a new derivation of support vector machines in terms of divergences and relates maximum mean discrepancy to fisher linear discriminants

new constructions of diagonal patchwork copulas we present a method for constructing symmetric copulas which generalizes the diagonal patchwork construction of copulas procedure we also show how it is related to a new construction of a generalized farlie gumbel morgenstern distribution and to the copula transforms

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

quasi copulas with a given sub diagonal section abstract as is well known the frechet hoeffding bounds are the best possible for both copulas and quasi copulas for every quasi copula q max x y 1 0 q x y min x y for all x y 0 1 sharper bounds hold when the quasi copulas take prescribed values e g along their diagonal or horizontal resp vertical sections here we pursue two goals first we investigate construction methods for quasi copulas with a given sub diagonal section i e with prescribed values along the straight line segment joining the points x 0 0 and 1 1 x 0 for x 0 0 1 then we determine the best possible bounds for sets of quasi copulas with a given sub diagonal section

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

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

copulas diagonals and tail dependence we present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence moreover we present the tail concentration function which depends on the diagonal section of a copula as a tool to give a description of tail dependence at finite scale the tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space moreover it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior

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

steering in spin tomographic probability representation abstract the steering property known for two qubit state in terms of specific inequalities for the correlation function is translated for the state of qudit with the spin j 3 2 since most steering detection inequalities are based on the correlation functions we introduce analogs of such functions for the single qudit systems the tomographic probability representation for the qudit states is applied the connection between the correlation function in the two qubit system and the single qudit is presented in an integral form with an intertwining kernel calculated explicitly in tomographic probability terms

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

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

independence results for multivariate tail dependence coefficients in this paper we study some properties of multivariate lower and upper tail dependence coefficients and analyze the relationship between pairwise tail independence mutual tail independence and extremal independence

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

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

a symmetric information divergence measure of the csiszar s f divergence class and its bounds a symmetric measure of information divergence is proposed this measure belongs to the class of csiszar s f divergences its properties are studied and bounds in terms of well known divergence measures obtained a numerical illustration is carried out to compare this measure with some known divergence measures

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

new parametric measures of information in this paper methods are presented for obtaining parametric measures of information from the non parametric ones and from information matrices the properties of these measures are examined the one dimensional parametric measures which are derived from the non parametric are superior to fisher s information measure because they are free from regularity conditions but if we impose the regularity conditions of the fisherian theory of information these measures become linear functions of fisher s measure

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

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

optimal investment problem under non extensive statistical mechanics abstract the optimal investment problem in which the asset price process is modeled by the non extensive statistical mechanics is studied in this paper by the methods of deterministic control and the dynamic programming we obtain the optimal strategy with logarithmic utility function power utility function and quadratic utility function respectively moreover the numerical results indicate that the optimal investment strategy is affected by the non extensive parameter the proportion invested in the risky asset decreases as the wealth increases under quadratic utility function but it remains unchanged under power utility and logarithmic utility function

on the refinement of jensen s inequality the main purpose of this work is to present the extension of the recent results given by dragomir s s dragomir a new refinement of jensen s inequality in linear spaces with applications math comput model 52 2010 1497 1505 where new refinement of jensen s inequality is presented and given applications in the information theory our work improves the basic result of dragomir through a stronger refinement of jensen s inequality which is then applied to the information theory and obtained stronger lower bounds for the mean f deviation and f divergences

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

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

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

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

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

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

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

troublesome aspects of the renyi maxent treatment we study in great detail the possible existence of a renyi associated thermodynamics with negative results in particular we uncover a hidden relation in renyi s variational problem maxent this relation connects the two associated lagrange multipliers canonical ensemble with the mean energy u and the renyi parameter as a consequence of such relation we obtain anomalous renyi maxent thermodynamic results

on copulas and their diagonals we formulate the necessary and sufficient conditions for a function d 0 1 0 1 to be the diagonal section of a multivariate absolutely continuous copula moreover we provide some simple analytic formulas for copulas having given diagonal section or given distribution functions of order statistics

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

absolutely continuous copulas with given sub diagonal section abstract recently durante and jaworski 2008 6 have proved that the class of absolutely continuous copulas with a given diagonal section is non empty in case that the diagonal function is such that the set of points where this coincides with the identity function has null measure in this paper we show that if we consider sub diagonals or super diagonals then the framework changes concretely for each sub diagonal function there exists an absolutely continuous copula having this function as sub diagonal section

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

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

connections of generalized divergence measures with fisher information matrix abstract in this paper parametric measures of information for the multiparameter case are obtained using csiszar s nonparametric measure of information as well as continuous and differentiable functions thereof the same idea is applied to some of the unified r s divergence measures presented in taneja relationships of the new parametric measures with fisher s information matrix are derived and their connections with the cramer rao inequality is established this work generalizes the results of kagan aggarwal and ferentinos and papioannou

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

third law of thermodynamics as a key test of generalized entropies the laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level the third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium conversely the entropy can vanish only at absolute zero temperature here we ask whether or not generalized entropies satisfy this fundamental property we propose a direct analytical procedure to test if a generalized entropy satisfies the third law assuming only very general assumptions for the entropy s and energy u of an arbitrary n level classical system mathematically the method relies on exact calculation of ds du in terms of the microstate probabilities pi to illustrate this approach we present exact results for the two best known generalizations of statistical mechanics specifically we study the kaniadakis entropy s which is additive and the tsallis entropy sq which is nonadditive we show that the kaniadakis entropy correctly satisfies the third law only for 1 1 thereby shedding light on why is conventionally restricted to this interval surprisingly however the tsallis entropy violates the third law for q 1 finally we give a concrete example of the power of our proposed method by applying it to a paradigmatic system the one dimensional ferromagnetic ising model with nearest neighbor interactions

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

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

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

doubly stochastic measures topology and latticework hairpins abstract we investigate topologies which can be put on the set of doubly stochastic measures on the unit square and show equivalence of all the standard ones and others considered here this topology has a very nice characterization in terms of copulas in terms of this topology we establish a simple relationship between a metric distance between two doubly stochastic measures concentrated on hairpins and the sup norm distance between their mass spreaders show the denseness of polygonal hairpins in the set of hairpins and show the nowhere denseness of latticework hairpins in the set of hairpins

extremal lipschitz continuous aggregation functions with a given diagonal section abstract in this paper we study the smallest and the greatest m lipschitz continuous n ary aggregation functions with a given diagonal section we show that several properties that were studied for the smallest and the greatest 1 lipschitz continuous binary aggregation functions with a given diagonal section extend naturally to higher dimensions while considering different lipschitz constants just as in the binary case we show that the smallest n quasi copula with a given diagonal section coincides with the smallest 1 lipschitz n ary aggregation function with that diagonal section additionally we show that the smallest n quasi copula with a given diagonal section called the bertino n quasi copula is supermodular for any n 2

on the convexity of some divergence measures based on entropy functions three measures of divergence between vectors in a convex set of a n dimensional real vector space are defined in terms of certain types of entropy functions and their convexity property is studied among other results a classification of the entropies of degree alpha is obtained by the convexity of these measures these results have applications in information theory and biological studies

hamilton jacobi bellman quasi variational inequality arising in an environmental problem and its numerical discretization abstract a hamilton jacobi bellman quasi variational inequality hjbqvi for a river environmental restoration problem with wise use of sediment is formulated and its mathematical properties are analyzed a finite difference scheme with a penalization technique is then established for solving the hjbqvi the scheme is free from any iterative solvers and is unconditionally stable and convergent in the viscosity sense under certain conditions a demonstrative application example of the hjbqvi is finally presented

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

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

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 note on reverse pinsker inequalities a simple method is shown to provide optimal variational bounds on f divergences with possible constraints on relative information extremums the known results are refined or proved to be optimal as particular cases

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

on a family of multivariate copulas for aggregation processes we introduce a family of multivariate copulas a special type of n ary aggregation operations depending on a univariate function this family is used in the construction of a special aggregation operation that satisfies a lipschitz condition several examples are provided and some statistical properties are studied