non logarithmic jensen shannon divergence abstract the jensen shannon divergence is a symmetrized and smoothed version of the kullback leibler divergence recently it has been widely applied to the analysis and characterization of symbolic sequences in this paper we investigate a generalization of the jensen shannon divergence this generalization is done in the framework of the non extensive tsallis statistics we study its basic properties and we investigate its applicability as a tool for segmentating symbolic sequences

on the structure of graded leibniz triple systems abstract we study the structure of a leibniz triple system e graded by an arbitrary abelian group g which is considered of arbitrary dimension and over an arbitrary base field k we show that e is of the form e u j 1 i j with u a linear subspace of the 1 homogeneous component e 1 and any ideal i j of e satisfying i j e i k i j i k e e i j i k 0 if j k where the relation in 1 g g 1 l g 0 defined by g h if and only if g is connected to h

lie algebras with a set grading abstract consider g a lie algebra graded by an arbitrary set i set grading we show that g decomposes as the sum of well described graded ideals plus maybe a certain linear subspace under mild conditions the simplicity of g is characterized and it is shown that the above decomposition is actually the direct sum of the family of its minimal graded ideals each one being a simple set graded lie algebra

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

physical complexity of variable length symbolic sequences abstract a measure called physical complexity is established and calculated for a population of sequences based on statistical physics automata theory and information theory it is a measure of the quantity of information in an organism s genome it is based on shannon s entropy measuring the information in a population evolved in its environment by using entropy to estimate the randomness in the genome it is calculated from the difference between the maximal entropy of the population and the actual entropy of the population when in its environment estimated by counting the number of fixed loci in the sequences of a population up until now physical complexity has only been formulated for populations of sequences with the same length here we investigate an extension to support variable length populations we then build upon this to construct a measure for the efficiency of information storage which we later use in understanding clustering within populations finally we investigate our extended physical complexity through simulations showing it to be consistent with the original

jensen tsallis divergence and atomic dissimilarity for ionized systems in conjugated spaces abstract a generalization of the original jensen shannon divergence jsd is presented in this work which gives rise to a non extensive one parameter divergence providing a powerful dissimilarity measure between electronic distributions the analysis performed in this study employs the jtd measure to compare one particle densities of neutral and ionized atomic systems that generalizes and improves some previous results based on other measures of divergence such an improvement mainly arises from the capability of jtd to modify by means of its order parameter the relative contribution of specific relevant regions of the atomic densities under comparison in both position and momentum spaces relevant information of the ionization processes attending to structural pattern and periodicity is found as well as the strong correlation between extremal values of the neutral cation jtd and those of the atomic ionization potential similar conclusions are obtained from processes involving an anion the analysis includes a study of the dependence of jtd on its order for fixed atomic couples

compositional segmentation and long range fractal correlations in dna sequences a segmentation algorithm based on the jensen shannon entropic divergence is used to decompose long range correlated dna sequences into statistically significant compositionally homogeneous patches by adequately setting the significance level for segmenting the sequence the underlying power law distribution of patch lengths can be revealed some of the identified dna domains were uncorrelated but most of them continued to display long range correlations even after several steps of recursive segmentation thus indicating a complex multi length scaled structure for the sequence on the other hand by separately shuffling each segment or by randomly rearranging the order in which the different segments occur in the sequence shuffled sequences preserving the original statistical distribution of patch lengths were generated both types of random sequences displayed the same correlation scaling exponents as the original dna sequence thus demonstrating that neither the internal structure of patches nor the order in which these are arranged in the sequence is critical therefore long range correlations in nucleotide sequences seem to rely only on the power law distribution of patch lengths textcopyright 1996 the american physical society

a monoparametric family of metrics for statistical mechanics abstract in a recent paper we have studied a generalization of the jensen shannon divergence jsd physica a 329 2003 81 this generalization was made in the context of tsallis statistical mechanics the present work is devoted to an investigation of the metric character of the jsd generalization

generalized divergences from generalized entropies abstract several quantifiers of information also known as entropies have been introduced in different contexts and from different motivations for almost each one of these entropies a measure of the loss or gain of information has been introduced in this work we introduce generalized weighted divergences associated with an arbitrary entropy the resulting measures are closely related to bregman divergences we study the main formal properties of the resulting divergences we extend them to weighted probability distributions and we apply some of them to the analysis of simulated and real time series

mathematical modelling of surface vibration with volume constraint and its analysis abstract a hyperbolic problem with volume constraint is investigated by means of a minimizing method called the discrete morse flow a weak solution is introduced in a constructive way and results of numerical computations are shown

decomposition of dna sequence complexity profiles of sequence compositional complexity provide a view of the spatial heterogeneity of symbolic sequences at different levels of detail sequence compositional complexity profiles are here decomposed into partial profiles using the branching property of the shannon entropy this decomposition shows the complexity contributed by each individual symbol or group of symbols in particular we apply this method to the mapping rules symbol groupings commonly used in dna sequence analysis we find that strong weak bindings are remarkable homogeneously distributed as compared to purine pyrimidine and that a and t are the most heterogeneous distributed bases

nonextensive information theoretic kernels on measures positive definite kernels on probability measures have been recently applied to classification problems involving text images and other types of structured data some of these kernels are related to classic information theoretic quantities such as shannon s mutual information and the jensen shannon js divergence meanwhile there have been recent advances in nonextensive generalizations of shannon s information theory this paper bridges these two trends by introducing nonextensive information theoretic kernels on probability measures based on new js type divergences these new divergences result from extending the the two building blocks of the classical js divergence convexity and shannon s entropy the notion of convexity is extended to the wider concept of q convexity for which we prove a jensen q inequality based on this inequality we introduce jensen tsallis jt q differences a nonextensive generalization of the js divergence and define a k th order jt q difference between stochastic processes we then define a new family of nonextensive mutual information kernels which allow weights to be assigned to their arguments and which includes the boolean js and linear kernels as particular cases nonextensive string kernels are also defined that generalize the p spectrum kernel we illustrate the performance of these kernels on text categorization tasks in which documents are modeled both as bags of words and as sequences of characters

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

decompositions of linear spaces induced by bilinear maps abstract let v be an arbitrary linear space and f v v v a bilinear map we show that for any choice of basis b of v the bilinear map f induces on v a decomposition v j j v j as a direct sum of linear subspaces which is f orthogonal in the sense f v j v k 0 when j k and in such a way that any v j is strongly f invariant in the sense f v j v f v v j v j we also characterize the f simplicity of any v j finally an application to the structure theory of arbitrary algebras is also provided

monoparametric family of metrics derived from classical jensen shannon divergence abstract jensen shannon divergence is a well known multi purpose measure of dissimilarity between probability distributions it has been proven that the square root of this quantity is a true metric in the sense that in addition to the basic properties of a distance it also satisfies the triangle inequality in this work we extend this last result to prove that in fact it is possible to derive a monoparametric family of metrics from the classical jensen shannon divergence motivated by our results an application into the field of symbolic sequences segmentation is explored additionally we analyze the possibility to extend this result into the quantum realm

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 variational scheme for hyperbolic obstacle problems abstract we consider an obstacle problem for possibly non local wave equations and we prove existence of weak solutions through a convex minimization approach based on a time discrete approximation scheme we provide the corresponding numerical implementation and raise some open questions

a variational approach to a constrained hyperbolic free boundary problem abstract this paper concerns the construction of a weak solution to a constrained hyperbolic equation in one space dimension the problem includes a nonlocal term corresponding to a volume constraint and the presence of a free boundary we approach our problem by means of a variational method known as the discrete morse flow

jensen shannon divergence in conjugate spaces the entropy excess of atomic systems and sets with respect to their constituents abstract the disorder of a composite system or of a set of different systems is always higher than the mere sum of the internal disorder of its constituents one of the most widely used functionals employed for measuring the randomness of a single distribution is the shannon entropy from which the increase of disorder within the composite system with respect to those of the constituents is quantified by means of the jensen shannon divergence jsd in this work two different applications of the jsd in the study of the information content of atomic electron densities are carried out i finding the contribution for a given atom of its composing subshells to the total atomic information ii and similarly for selected sets of atoms such as periods and groups throughout the periodic table as well as isoelectronic series in both cases the analysis is performed in the two conjugate position and momentum spaces and the results are interpreted according to physically relevant quantities such as the ionization potential

tsallis entropy and cortical dynamics the analysis of eeg signals abstract we undertake the study of eeg signals by recourse to a wavelet based multiresolution analysis as adapted to an information measure scenario different information measures are employed it is shown that non extensive ones seem to be of particular usefulness

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

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

geometrical aspects of a generalized statistical mechanics abstract we discuss here the use of generalized forms of entropy taken as information measures to characterize phase transitions and critical behavior in thermodynamic systems our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics models the thermodynamics of the system is the focus of attention in this geometric context

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

can complexity decrease in congestive heart failure abstract the complexity of a signal can be measured by the recurrence period density entropy rpde from the reconstructed phase space we have chosen a window based rpde method for the classification of signals as rpde is an average entropic measure of the whole phase space we have observed the changes in the complexity in cardiac signals of normal healthy person nhp and congestive heart failure patients chfp the results show that the cardiac dynamics of a healthy subject is more complex and random compare to the same for a heart failure patient whose dynamics is more deterministic we have constructed a general threshold to distinguish the border line between a healthy and a congestive heart failure dynamics the results may be useful for wide range for physiological and biomedical analysis

fisher like atomic divergences mathematical grounds and physical applications abstract two different local divergence measures the fisher fd and the jensen fisher jfd ones are compared in this work by applying them to atomic one particle densities in position and momentum spaces they are defined in terms of the absolute and the relative fisher information functionals the analysis here afforded includes not only neutral atoms but also singly charged cations the results are interpreted and justified according to i shell filling patterns ii short and long range behaviors of the atomic densities and iii the value of the atomic ionization potential the strengths of the fd measure as compared to the jfd one are emphasized

variational approach to evolutionary free boundary problems abstract the analysis of evolutionary nonlocal problems represented by volume constrained motion is discussed in the physical sense these problems can describe the motion of droplets on a solid plane the variational approach called the discrete morse flow combined with a fluid dynamics model appears to be a suitable tool

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

divergence measures based on the shannon entropy a novel class of information theoretic divergence measures based on the shannon entropy is introduced unlike the well known kullback divergences the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved more importantly their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds these bounds are crucial in many applications of divergence measures the measures are also well characterized by the properties of nonnegativity finiteness semiboundedness and boundedness

estimating and improving the signal to noise ratio of time series by symbolic dynamics we investigate the effect of symbolic encoding applied to times series consisting of some deterministic signal and additive noise as well as time series given by a deterministic signal with randomly distributed initial conditions as a model of event related brain potentials we introduce an estimator of the signal to noise ratio snr of the system by means of time averages of running complexity measures such as shannon and r enyi entropies and prove its asymptotical equivalence with the linear snr in the case of shannon entropies of symbol distributions a snr improvement factor is defined exhibiting a maximum for intermediate values of noise amplitude in analogy to stochastic resonance phenomena we demonstrate that the maximum of the snr improvement factor can be shifted toward smaller noise amplitudes by using higher order r enyi entropies instead of the shannon entropy for a further improvement of the snr a half wave encoding of noisy time series is introduced finally we discuss the effect of noisy phases on the linear snr as well as on the snr defined by symbolic dynamics it is shown that longer symbol sequences yield an improvement of the latter

on split leibniz algebras abstract in order to begin an approach to the structure of arbitrary leibniz algebras with no restrictions neither on the dimension nor on the base field we introduce the class of split leibniz algebras as the natural extension of the class of split lie algebras by developing techniques of connections of roots for this kind of algebras we show that any of such algebras l is of the form l u j i j with u a subspace of the abelian subalgebra h in the sense h h 0 and any i j a well described ideal of l satisfying i j i k 0 if j k in the case of l being of maximal length we characterize the simplicity of the algebra in terms of connections of roots

analysis of symbolic sequences using the jensen shannon divergence we study statistical properties of the jensen shannon divergence d which quantifies the difference between probability distributions and which has been widely applied to analyses of symbolic sequences we present three interpretations of d in the framework of statistical physics information theory and mathematical statistics and obtain approximations of the mean the variance and the probability distribution of d in random uncorrelated sequences we present a segmentation method based on d that is able to segment a nonstationary symbolic sequence into stationary subsequences and apply this method to dna sequences which are known to be nonstationary on a wide range of different length scales

jensen divergence based on fisher s information the measure of jensen fisher divergence between probability distributions is introduced and its theoretical grounds set up this quantity in contrast to the remaining jensen divergences grasps the fluctuations of the probability distributions because it is controlled by the local fisher information which is a gradient functional of the distribution so it is appropriate and informative when studying the similarity of distributions mainly for those having oscillatory character the new jensen fisher divergence shares with the jensen shannon divergence the following properties non negativity additivity when applied to an arbitrary number of probability densities symmetry under exchange of these densities vanishing under certain conditions and definiteness even when these densities present non common zeros moreover the jensen fisher divergence is shown to be expressed in terms of the relative fisher information as the jensen shannon divergence does in terms of the kullback leibler or relative shannon entropy finally the jensen shannon and jensen fisher divergences are compared for the following three large non trivial and qualitatively different families of probability distributions the sinusoidal generalized gamma like and rakhmanov hermite distributions which are closely related to the quantum mechanical probability densities of numerous physical systems