fractional kinetic equations and universal decoupling of a memory function in mesoscale region it is proved that kinetic equations containing non integer integrals and derivatives appear in the result of reduction of a set of micromotions to some averaged collective motion in the mesoscale region in other words it means that after a proper statistical average the microscopic dynamics is converted into a collective motion in the mesoscopic regime a fractal medium containing weakly and strongly correlated relaxation units has been considered it is shown that in most cases the original of the memory function recovers the riemann liouville integral for a strongly correlated fractal medium a generalization of the riemann liouville integral is obtained for the fractal branched processes one can derive the stretched exponential law of relaxation that is widely used for description of relaxation phenomena in disordered media it is shown that the generalized stretched exponential function describes the averaged collective motion in the fractal branched complex systems it is confirmed that the generalized stretched exponential law can be definitely applicable for description of a set of spontaneous evoked postsynaptic signals in the living matter the application of these fractional kinetic equations for the description of the dielectric relaxation phenomena is also discussed these kinetic equations and their generalizations can be applicable for the description of different relaxation or diffusion processes in the intermediate mesoscale region

sensitivity to evidence in gaussian bayesian networks using mutual information we introduce a methodology for sensitivity analysis of evidence variables in gaussian bayesian networks knowledge of the posterior probability distribution of the target variable in a bayesian network given a set of evidence is desirable however this evidence is not always determined in fact additional information might be requested to improve the solution in terms of reducing uncertainty in this study we develop a procedure based on shannon entropy and information theory measures that allows us to prioritize information according to its utility in yielding a better result some examples illustrate the concepts and methods introduced

firing variability is higher than deduced from the empirical coefficient of variation a convenient and often used summary measure to quantify the firing variability in neurons is the coefficient of variation cv defined as the standard deviation divided by the mean it is therefore important to find an estimator that gives reliable results from experimental data that is the estimator should be unbiased and have low estimation variance when the cv is evaluated in the standard way empirical standard deviation of interspike intervals divided by their average then the estimator is biased underestimating the true cv especially if the distribution of the interspike intervals is positively skewed moreover the estimator has a large variance for commonly used distributions the aim of this letter is to quantify the bias and propose alternative estimation methods if the distribution is assumed known or can be determined from data parametric estimators are proposed which not only remove the bias but also decrease the estimation errors if no distribution is assumed and the data are very positively skewed we propose to correct the standard estimator when defining the corrected estimator we simply use that it is more stable to work on the log scale for positively skewed distributions the estimators are evaluated through simulations and applied to experimental data from olfactory receptor neurons in rats

fluctuation noise spectroscopy and a universal fitting function of amplitudes of random sequences abstract a universal fitting function has been recognized that makes use of the eigen coordinates method physica a 285 2000 547 to accurately describe the distribution of ordered amplitudes within random sequences taken from a diversity of sources it is shown that sequences with a discrete structure can be described in terms of specific distributions of relative frequencies with respect to the number of quantum levels an investigation of these quantum distributions leads to an increase in both sensitivity and selectivity when attempting the statistical detection of various predominant factors of the hidden signals the physical meaning of this new function is discussed and a proposal is made as the basis of a new fluctuation noise spectroscopy in which the recognized function can be used for the detection of small signals and or the forerunners of strong signals that are hidden within the random sequences analyzed

complex fractal dimensions describe the hierarchical structure of diffusion limited aggregate clusters we analyze large diffusion limited aggregates and uncover a ital discrete scaling invariance in their inner structure which can be quantified by the introduction of a set of ital complex fractal dimensions we provide a theoretical framework and prediction of their values based on renormalization group theory and a previous wavelet analysis copyright ital 1996 the american physical society

log periodic oscillations for biased diffusion on random lattice abstract random walks with a fixed bias direction on randomly diluted cubic lattices far above the percolation threshold exhibit log periodic oscillations in the effective exponent versus time a scaling argument accounts for the numerical results in the limit of large biases and small dilution and shows the importance of the interplay of these two ingredients in the generation of the log periodicity these results show that log periodicity is the dominant effect compared to previous predictions of and reports on anomalous diffusion

quantification of heart rate variability by discrete nonstationary non markov stochastic processes we develop the statistical theory of discrete nonstationary non markov random processes in complex systems the objective of this paper is to find the chain of finite difference non markov kinetic equations for time correlation functions tcf in terms of nonstationary effects the developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of initial and final states and nonstationary normalized tcf using the projection operators technique we find the chain of finite difference non markov kinetic equations for discrete nonstationary tcf and for the set of nonstationary discrete memory functions mf s the last one contains supplementary information about nonstationary properties of the complex system on the whole another relevant result of our theory is the construction of the set of dynamic parameters of nonstationarity which contains some information of the nonstationarity effects the full set of dynamic spectral and kinetic parameters and kinetic functions tcf short mf s statistical spectra of non markovity parameter and statistical spectra of nonstationarity parameter has made it possible to acquire the in depth information about discreteness non markov effects long range memory and nonstationarity of the underlying processes the developed theory is applied to analyze the long time holter series of rr intervals of human ecg s we had two groups of patients the healthy ones and the patients after myocardial infarction in both groups we observed effects of fractality standard and restricted self organized criticality and also a certain specific arrangement of spectral lines the received results demonstrate that the power spectra of all orders n 1 2 mf m n t exhibit the neatly expressed fractal feat ures we have found out that the full sets of non markov discrete and nonstationary parameters can serve as reliable and powerful means of diagnosis of the cardiovascular system states and can he used to distinguish healthy data from pathologic data

convergence analysis of deflected conditional approximate subgradient methods subgradient methods for nondifferentiable optimization benefit from deflection i e defining the search direction as a combination of the previous direction and the current subgradient in the constrained case they also benefit from projection of the search direction onto the feasible set prior to computing the steplength that is from the use of conditional subgradient techniques however combining the two techniques is not straightforward especially if an inexact oracle is available which can only compute approximate function values and subgradients we present a convergence analysis of several different variants both conceptual and implementable of approximate conditional deflected subgradient methods our analysis extends the available results in the literature by using the main stepsize rules presented so far while allowing deflection in a more flexible way furthermore to allow for diminishing square summable rules where the stepsize is tightly controlled a priori we propose a new class of deflection restricted approaches where it is the deflection parameter rather than the stepsize which is dynamically adjusted using the target value of the optimization sequence for both polyak type and diminishing square summable stepsizes we propose a correction of the standard formula which shows that in the inexact case knowledge about the error computed by the oracle which is available in several practical applications can be exploited in order to strengthen the convergence properties of the method the analysis allows for several variants of the algorithm at least one of them is likely to show numerical performances similar to these of heavy ball subgradient methods popular within backpropagation approaches to train neural networks while possessing stronger convergence properties

algorithms for the continuous nonlinear resource allocation problem new implementations and numerical studies patriksson 2008 provided a then up to date survey on the continuous separable differentiable and convex resource allocation problem with a single resource constraint since the publication of that paper the interest in the problem has grown several new applications have arisen where the problem at hand constitutes a subproblem and several new algorithms have been developed for its efficient solution this paper therefore serves three purposes first it provides an up to date extension of the survey of the literature of the field complementing the survey in patriksson 2008 with more then 20 books and articles second it contributes improvements of some of these algorithms in particular with an improvement of the pegging that is variable fixing process in the relaxation algorithm and an improved means to evaluate subsolutions third it numerically evaluates several relaxation primal and breakpoint dual algorithms incorporating a variety of pegging strategies as well as a quasi newton method our conclusion is that our modification of the relaxation algorithm performs the best at least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

possibility between earthquake and explosion seismogram differentiation by discrete stochastic non markov processes and local hurst exponent analysis the basic scientific point of this paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature one example of such kinds of signals is presented by seismograms containing recordings of earthquakes eq s and technogenic explosions te s eq s are among the most dramatic phenomena in nature we propose here a discrete stochastic model for possible solution of a problem of strong eq forecasting and differentiation of te s from the weak eq s theoretical analysis is performed by two independent methods by using statistical theory of discrete non markov stochastic processes phys rev e 62 6178 2000 and the local hurst exponent the following earth states have been considered among them before ib and during i strong eq during weak eq ii and during te iii and in a calm state of earth s core iv the estimation of states i ii and iii has been made on the particular examples of turkey 1999 eq s state iv has been taken as an example of earth s state before underground te time recordings of seismic signals of the first four dynamic orthogonal collective variables six various planes of phase portrait of four dimensional phase space of orthogonal variables and the local hurst exponent have been calculated for the dynamic analysis of states of systems i char21 iv the analysis of statistical properties of seismic time series i char21 iv has been realized with the help of a set of discrete time dependent functions time correlation function and first three memory functions their power spectra and the first three points in the statistical spectrum of non markovity parameters in all systems studied we have found a bizarre combination of the following spectral characteristics the fractal frequency spectra adjustable by phenomena of usual and restricted self organized criticality spectra of white and color noises and unusual alternation of markov and non markov effects of long range memory detected earlier j phys a 27 5363 1994 only for hydrodynamic systems our research demonstrates that discrete non markov stochastic processes and long range memory effects play a crucial role in the behavior of seismic systems i char21 iv the approaches permitting us to obtain an algorithm of strong eq forecasting and to differentiate te s from weak eq s have been developed

a library for continuous convex separable quadratic knapsack problems abstract the continuous convex separable quadratic knapsack problem cqknp is an easy but useful model that has very many different applications although the problem can be solved quickly it must typically be solved very many times within approaches to much more difficult models hence an efficient solution approach is required we present and discuss a small open source library for its solution that we have recently developed and distributed

projected perspective reformulations with applications in design problems the perspective relaxation pr is a general approach for constructing tight approximations to mixed integer nonlinear programs minlp with semicontinuous variables the pr of a minlp can be formulated either as a mixed integer second order cone program mi socp provided that the original objective function is socp representable or as a semi infinite minlp in this paper we show that under some further assumptions rather restrictive but satisfied in several practical applications the pr of a mixed integer quadratic program miqp can also be reformulated as a piecewise quadratic program qp ultimately yielding a qp relaxation of roughly the same size of the standard continuous relaxation furthermore if the original problem has some exploitable structure then this structure is typically preserved in the reformulation thus allowing the construction of specialized approaches for solving the pr we report on implementing these ideas on two miqps with appropriate structure a sensor placement problem and a quadratic cost single commodity network design problem

stochastic dynamics of time correlation in complex systems with discrete time in this paper we present the concept of description of random processes in complex systems with discrete time it involves the description of kinetics of discrete processes by means of the chain of finite difference non markov equations for time correlation functions tcfs we have introduced the dynamic time dependent information shannon entropy s i t where i 0 1 2 3 ellipsis as an information measure of stochastic dynamics of time correlation i 0 and time memory i 1 2 3 ellipsis the set of functions s i t constitute the quantitative measure of time correlation disorder i 0 and time memory disorder i 1 2 3 ellipsis in complex system the theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states we examine two stochastic processes involving the creation and annihilation of time correlation or time memory in details we carry out the analysis of vectors dynamics employing finite difference equations for random variables and the evolution operator describing their natural motion the existence of tcf results in the construction of the set of projection operators by the usage of scalar product operation harnessing the infinite set of orthogonal dynamic random variables on a basis of gram shmidt orthogonalization procedure tends to creation of infinite chain of finite difference non markov kinetic equations for discrete tcfs and memory functions mfs the solution of the equations above thereof brings to the recurrence relations between the tcf and mf of senior and junior orders this offers new opportunities for detecting the frequency spectra of power of entropy function s i t for time correlation i 0 and time memory i 1 2 3 ellipsis the results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems application of this technique on the analysis of stochastic dynamics of rr intervals from human ecg s shows convincing evidence for a non markovian phenomemena associated with a peculiarities in short and long range scaling this method may be of use in distinguishing healthy from pathologic data sets based in differences in these non markovian properties

a survey on the continuous nonlinear resource allocation problem our problem of interest consists of minimizing a separable convex and differentiable function over a convex set defined by bounds on the variables and an explicit constraint described by a separable convex function applications are abundant and vary from equilibrium problems in the engineering and economic sciences through resource allocation and balancing problems in manufacturing statistics military operations research and production and financial economics to subproblems in algorithms for a variety of more complex optimization models this paper surveys the history and applications of the problem as well as algorithmic approaches to its solution the most common techniques are based on finding the optimal value of the lagrange multiplier for the explicit constraint most often through the use of a type of line search procedure we analyze the most relevant references especially regarding their originality and numerical findings summarizing with remarks on possible extensions and future research 2006 elsevier b v all rights reserved

interpretation of the extreme physical information principle in terms of shift information it is shown that fisher information fi can be considered as a limiting case of a related form of kullback information char22 a shift information si the compatibility of the use of si with a basic physical principle of uncertainty is demonstrated the scope of fi based theory is extended to the nonlinear klein gordon equation

the quantified histograms detection of the hidden unsteadiness abstract for a given level of digitization a number of relative frequencies presented by a histogram constructed for a short sample defined as a segment of a random series related in a certain way to both the length of the sampling l and the number of decompositions k may form a set of some levels possessing a discrete spectrum this spectrum can be defined as a quantified histogram qh the structure of parameters of a certain qh can be analyzed via both the number of quantum levels nql and the proper collection of relative frequencies on every level these parameters form kind of specific fingerprints which characterizes statistical properties of the segment of random series treated in this way qhs allow us to introduce the concept of a standard noise sn which can be used as a noise ruler to compare random series of distinct nature this standard noise turns out to be very useful in the detection of both a hidden unsteadiness and superweak signals existing in random series in the capacity of an example of the application of this new method a comparison of statistically sensible distinctions between noises accompanying either earthquakes or technogenic explosions is given distinctions thus obtained called earthquake forerunner can be used for earthquakes forecasting

measures of statistical dispersion based on shannon and fisher information concepts we propose and discuss two information based measures of statistical dispersion of positive continuous random variables the entropy based dispersion and fisher information based dispersion although standard deviation is the most frequently employed dispersion measure we show that it is not well suited to quantify some aspects that are often expected intuitively such as the degree of randomness the proposed dispersion measures are not entirely independent though each describes the quality of probability distribution from a different point of view we discuss relationships between the measures describe their extremal values and illustrate their properties on the pareto the lognormal and the lognormal mixture distributions application possibilities are also mentioned

chernoff information between gaussian trees abstract in this paper we deal with gaussian graphical classifiaction problem we aim to provide a systematic study of the relationship between chernoff information and topological as well as algebraic properties of the corresponding gaussian graphs for the underlying graphical testing problems we first show the relationship between chernoff information and generalized eigenvalues of the associated covariance matrices it is then proved that chernoff information between two gaussian trees sharing certain local subtree structures can be transformed into that of two smaller trees in this way we provide a sequence of equivalent gaussian tree pairs in terms of chernoff information under our proposed grafting operations bottleneck gaussian trees namely gaussian trees connected by one such operation can thus be simplified into two 3 node gaussian trees thereafter we provide a thorough study about how chernoff information changes when small differences are accumulated into bigger ones via concatenated grafting operations as well as partial ordering in the end we propose an optimal linear dimension reduction method based on generalized eigenvalues for the purpose of classification which is proved to achieve maximum chernoff information among all linear transformations

recognition of nonextensive statistical distributions by the eigencoordinates method nonextensive statistical distributions suggested by tsallis are studied in the framework of the so called eigencoordinates ecs method which allows to recognize them with high level of authenticity at first the possibilities of the ecs method have been demonstrated on model files to exhibit some peculiarities of this new method then the amplitude distributions of the real noise tracks before and after earthquakes have been analyzed it has been shown that this type of noise is fractal and strongly correlated histograms of the noise amplitudes with high level of reliability are really described by a distribution coming from nonextensive statistics the possibilities and recommendations for the application of the ecs method to identify theoretical curves claimed for the description of experimental data are discussed

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

the effect of block parameter perturbations in gaussian bayesian networks sensitivity and robustness in this work we study the effects of model inaccuracies on the description of a gaussian bayesian network with a set of variables of interest and a set of evidential variables using the kullback leibler divergence measure we compare the output of two different networks after evidence propagation the original network and a network with perturbations representing uncertainties in the quantitative parameters we describe two methods for analyzing the sensitivity and robustness of a gaussian bayesian network on this basis in the sensitivity analysis different expressions are obtained depending on which set of parameters is considered inaccurate this fact makes it possible to determine the set of parameters that most strongly disturbs the network output if all of the divergences are small we can conclude that the network output is insensitive to the proposed perturbations the robustness analysis is similar but considers all potential uncertainties jointly it thus yields only one divergence which can be used to confirm the overall sensitivity of the network some practical examples of this method are provided including a complex real world problem