weighted composition operators on hardy spaces let be analytic functions defined on d such that d d the operator given by f f is called a weighted composition operator in this paper we deal with the boundedness compactness weak compactness and complete continuity of weighted composition operators on hardy spaces hp 1 p in particular we prove that such an operator is compact on h1 if and only if it is weakly compact on this space this result depends on a technique which passes the weak compactness from an operator t to operators dominated in norm by t

horizontal visibility graphs exact results for random time series networks this procedure allows us to apply methods of complex network theory for characterizing time series in this work we present the horizontal visibility algorithm a geometrically simpler and analytically solvable version of our former algorithm focusing on the mapping of random series series of independent identically distributed random variables after presenting some properties of the algorithm we present exact results on the topological properties of graphs associated with random series namely the degree distribution the clustering coefficient and the mean path length we show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape pk 1 32 3 k 2 independent of the probability distribution from which the series was generated accordingly visibility graphs with other pk are related to nonrandom series numerical simulations confirm the accuracy of the theorems for finite series in a second part we show that the method is able to distinguish chaotic series from independent and identically distributed i i d theory studying the following situations i noise free low dimensional chaotic series ii low dimensional noisy chaotic series even in the presence of large amounts of noise and iii high dimensional chaotic series coupled map lattice without needs for additional techniques such as surrogate data or noise reduction methods finally heuristic arguments are given to explain the topological properties of chaotic series and several sequences that are conjectured to be random are analyzed

the hellinger correlation in this paper the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones shown to imply other usu

complexity analysis of time series based on generalized fractional order cumulative residual distribution entropy abstract based on the theory of cumulative residual entropy and distribution entropy this paper proposes a new model cumulative residual distribution entropy crde which is more suitable for the complexity and risk analysis of time series the new model makes full use of the known information including not only the information of probability but also the information about the value of random variables additionally the crde considers the potential inherent information of vector to vector distance in the state space by combining theoretical analysis with empirical research this paper verifies that the new model has more advantages in measuring extreme events and small probability events with higher consistency stability and practicability in this paper the cumulative residual distribution entropy model is extended to the fractional order the generalized fractional cumulative residual distribution entropy gcrde can better capture the tiny evolution of time series which is more advantageous for studying the dynamic characteristics of complex systems the new model makes up for some shortcomings of traditional models and it can play a guiding role in the study of complex systems in the real world

optimal statistical decisions about some alternative financial models abstract we study neyman pearson testing and bayesian decision making based on observations of the price dynamics x t t 0 t of a financial asset when the hypothesis is the classical geometric brownian motion with a given constant growth rate and the alternative is a different random diffusion process with a given possibly price dependent growth rate examples of asset price observations are introduced and used throughout the paper to demonstrate the applicability of the theory by a rigorous mathematical approach we obtain exact formulae and bounds for the most common statistical characteristics of testing and decision making such as the power of test type ii error probability the bayes factor and its moments power divergences and the bayes risk or bayes error these bounds can be much more easily evaluated than the exact formulae themselves and consequently they are useful for practical applications an important theoretical conclusion of this paper is that for the class of alternatives considered neither the risk nor the errors converge to zero faster than exponentially in the observation time t we illustrate in concrete decision situations that the actual rate of convergence is well approximated by the bounds given in the paper

an algorithm for the n lyapunov exponents of an n dimensional unknown dynamical system abstract an algorithm for estimating lyapunov exponents of an unknown dynamical system is designed the algorithm estimates not only the largest but all lyapunov exponents of the unknown system the estimation is carried out by a multivariate feedforward network estimation technique we focus our attention on deterministic as well as noisy system estimation the performance of the algorithm is very satisfactory in the presence of noise as well as with limited number of observations

a comparison of high frequency cross correlation measures on a high frequency scale the time series are not homogeneous therefore standard correlation measures can not be directly applied to the raw data there are two ways to deal with this problem the time series can be homogenised through an interpolation method 1 linear or previous tick and then the pearson correlation statistic computed recently methods that can handle raw non synchronous time series have been developed 2 4 this paper compares two traditional methods that use interpolation with an alternative method applied directly to the actual time series

relationship between decentralized controller design using h sub spl infin and stochastic risk averse criteria considers discrete time decentralized risk averse leqg linear exponential of quadratic cost gaussian teams and shows that the team optimal solutions are identical to one of the solutions for minimax team problems the author first gives the result for static teams and extends the result to dynamic teams with a quasi classical information pattern using a dynamic programming argument in the process the author also establishes differences between the two problems by pointing out the existence of multiple solutions to the minimax team problem while there exists a unique solution to the leqg team problem

difference of weighted composition operators abstract we obtain complete characterizations in terms of carleson measures for bounded compact differences of weighted composition operators acting on the standard weighted bergman spaces over the unit disk unlike the known results we allow the weight functions to be non holomorphic and unbounded as a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the hardy spaces in terms of carleson measures and as a nontrivial application of this we show that compact differences of composition operators with univalent symbols on the hardy spaces are exactly the same as those on the weighted bergman spaces as another application we show that an earlier characterization due to acharyya and wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of non holomorphic weights we also include some explicit examples related to our results

time reversibility from visibility graphs of nonstationary processes visibility algorithms are a family of methods to map time series into networks with the aim of describing the structure of time series and their underlying dynamical properties in graph theoretical terms here we explore some properties of both natural and horizontal visibility graphs associated to several nonstationary processes and we pay particular attention to their capacity to assess time irreversibility nonstationary signals are infinitely irreversible by definition independently of whether the process is markovian or producing entropy at a positive rate and thus the link between entropy production and time series irreversibility has only been explored in nonequilibrium stationary states here we show that the visibility formalism naturally induces a new working definition of time irreversibility which allows us to quantify several degrees of irreversibility for stationary and nonstationary series yielding finite values that can be used to efficiently assess the presence of memory and off equilibrium dynamics in nonstationary processes without the need to differentiate or detrend them we provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes

compact differences of composition operators abstract a characterization of compact difference is given for composition operators acting on the standard weighted bergman spaces and necessary conditions are given on a larger scale of weighted dirichlet spaces conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts the additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component

a characterization of horizontal visibility graphs and combinatorics on words abstract a horizontal visibility graph hvg is defined in association with an ordered set of non negative reals hvgs realize a methodology in the analysis of time series their degree distribution being a good discriminator between randomness and chaos luque et al b luque l lacasa f ballesteros j luque horizontal visibility graphs exact results for random time series phys rev e 80 2009 046103 we prove that a graph is an hvg if and only if it is outerplanar and has a hamilton path therefore an hvg is a noncrossing graph as defined in algebraic combinatorics flajolet and noy p flajolet m noy analytic combinatorics of noncrossing configurations discrete math 204 1999 203 229 our characterization of hvgs implies a linear time recognition algorithm treating ordered sets as words we characterize subfamilies of hvgs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair with this technique we determine asymptotically the average number of edges of hvgs

weighted network analysis of high frequency cross correlation measures in this paper we implement a fourier method to estimate high frequency correlation matrices from small data sets the fourier estimates are shown to be considerably less noisy than the standard pearson correlation measures and thus capable of detecting subtle changes in correlation matrices with just a month of data the evolution of correlation at different time scales is analyzed from the full correlation matrix and its minimum spanning tree representation the analysis is performed by implementing measures from the theory of random weighted networks

brief paper comparisons among robust stability criteria for linear systems with affine parameter uncertainties this paper is concerned with the problem of comparisons among robust stability criteria for a class of uncertain linear systems where the system state matrices considered are affinely dependent on the uncertain parameters at first a robust stability criterion for the class of systems to be affinely quadratically stable aqs is derived based on the vertex separator approach where affine parameter dependent lyapunov functions are exploited to prove stability then comparison results between the robust stability criterion and the existing tests for aqs are given in terms of degree of conservatism a numerical example is given to illustrate the results

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

on compactness of the difference of composition operators abstract let and be analytic self maps of the unit disc and denote by c and c the induced composition operators the compactness and weak compactness of the difference t c c are studied on h p spaces of the unit disc and l p spaces of the unit circle it is shown that the compactness of t on h p is independent of p 1 the compactness of t on l 1 and m the space of complex measures is characterized and examples of and are constructed such that t is compact on h 1 but non compact on l 1 other given results deal with l weakly compact counterparts of the previous results and a conjecture of j e shapiro

asymptotic distribution theory for nonparametric entropy measures of serial dependence entropy is a classical statistical concept with appealing properties establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging in this paper we develop an asymptotic theory for a class of kernel based smoothed nonparametric entropy measures of serial dependence in a time series context we use this theory to derive the limiting distribution of granger and lin s 1994 normalized entropy measure of serial dependence which was previously not available in the literature we also apply our theory to construct a new entropy based test for serial dependence providing an alternative to robinson s 1991 approach to obtain accurate inferences we propose and justify a consistent smoothed bootstrap procedure the naive bootstrap is not consistent for our test our test is useful in for example testing the random walk hypothesis evaluating density forecasts and identifying important lags of a time series it is asymptotically locally more powerful than robinson s 1991 test as is confirmed in our simulation an application to the daily s p 500 stock price index illustrates our approach

an r squared measure of goodness of fit for some common nonlinear regression models abstract for regression models other than the linear model r squared type goodness of fit summary statistics have been constructed for particular models using a variety of methods we propose an r squared measure of goodness of fit for the class of exponential family regression models which includes logit probit poisson geometric gamma and exponential this r squared is defined as the proportionate reduction in uncertainty measured by kullback leibler divergence due to the inclusion of regressors under further conditions concerning the conditional mean function it can also be interpreted as the fraction of uncertainty explained by the fitted model

the topological invariance of lyapunov exponents in embedded dynamics abstract there are two contributions of this paper one is to provide a theoretical ground for the jacobian methods by showing that n of the lyapunov exponents of the estimated jacobian are the lyapunov exponents of an n dimensional unknown dynamical system the second is to show that it is necessary that the lyapunov exponents be calculated in the tangent space of the attractor in the embedding the method of reconstruction is to form vectors of m consecutive observations which for m 2 n is generically an embedding this is takens result a function of m variables is then fit to the data and the jacobian matrix is constructed at each point in the orbit of the data when embedding occurs at dimension m n then the lyapunov exponents of the reconstructed dynamics are the lyapunov exponents of the original dynamics this is the case for the henon the lorenz and the mackey glass systems with a first component observer however if embedding only occurs for an m n then the jacobian method yields m lyapunov exponents only n of which are the lyapunov exponents of the original system the problem is that as currently used the jacobian method is applied to the full m dimensional space of the reconstruction and not just to the n dimensional manifold that is the image of the embedding map our examples show that it is possible to get spurious lyapunov exponents that are even larger than the largest lyapunov exponent of the original system

a comment on measuring the hurst exponent of financial time series abstract a fundamental hypothesis of quantitative finance is that stock price variations are independent and can be modeled using brownian motion in recent years it was proposed to use rescaled range analysis and its characteristic value the hurst exponent to test for independence in financial time series theoretically independent time series should be characterized by a hurst exponent of 1 2 however finite brownian motion data sets will always give a value of the hurst exponent larger than 1 2 and without an appropriate statistical test such a value can mistakenly be interpreted as evidence of long term memory we obtain a more precise statistical significance test for the hurst exponent and apply it to real financial data sets our empirical analysis shows no long term memory in some financial returns suggesting that brownian motion cannot be rejected as a model for price dynamics

modeling the predictive power of the singular value decomposition based entropy empirical evidence from the dow jones global titans 50 index abstract in this paper we are analyzing the predictive power of the singular value decomposition entropy for the dow jones global titans 50 djgt index of the new york stock exchange nyse market for the correlation matrix of the djgt index components we then calculate the entropy of the singular value decomposition granger causality test was used to prove that entropy has a predictive power for stock market dynamics of the djgt index the results of our paper are revealing the importance of considering structural breaks when analyzing financial stock markets our analysis is conducting to the conclusion that the singular value decomposition entropy has predictive power for the nyse djgt index

entropy and predictability of stock market returns abstract we examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties we compare our results with a number of traditional measures the metric entropy is capable of detecting nonlinear dependence within the returns series and is also capable of detecting nonlinear affinity between the returns and their predictions obtained from various models thereby serving as a measure of out of sample goodness of fit or model adequacy several models are investigated including the linear and neural network models as well as nonparametric and recursive unconditional mean models we find significant evidence of small nonlinear unconditional serial dependence within the returns series but fragile evidence of superior conditional predictability profit opportunity when using market switching versus buy and hold strategies

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

on the recovery of joint distributions from limited information the paper considers the role of entropy and other information theoretic concepts in the description and formation of joint distributions for m random variables the discussion includes a review of methods for constructing discrete and continuous joint distributions from the component marginal distributions we then propose a minimum cross entropy approach that recovers continuous joint distributions from the joint and marginal moments and the marginal densities the large sample properties of the associated estimator are outlined and a simple demonstration problem that highlights the advantages and drawbacks of the proposed method is presented

unbiased determination of production technologies abstract to determine whether an industry exhibits constant returns to scale whether the production function is homothetic or whether inputs are separable a common approach is to specify a cost function estimate its parameters using data such as prices and quantities of inputs and then test the parametric restrictions corresponding to constant returns a homothetic technology or separability statistically such inferences are valid if the true cost function is a member of the parametric class considered otherwise the inference is biased that is the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test the use of fixed parameter flexible functional forms such as the translog the generalized leontief or the box cox will not alleviate this problem the fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound depending on the number of parameters on the error as measured by the sobolev norm of approximation to an arbitrary cost function thus it is possible to construct statistical tests for constant returns a homothetic technology or separability which are asymptotically size by letting the number of parameters of the fourier flexible form depend on sample size that is the true rejection probability converges to the nominal size of the test as sample size tends to infinity the rate of convergence depends on the smoothness of the true cost function the more times is differentiable the true cost function the faster the convergence the method is illustrated using the data on aggregate u s manufacturing of berndt and wood 1975 1979 and berndt and khaled 1979

fractionally integrated process for transition economics we analyze the european transition economics and show that many time series of major indices exhibit i power law correlations in their values ii power law correlations in their magnitudes and iii an asymmetric probability distribution applying the phase randomization procedure to these time series we show that magnitude correlations completely vanish we propose a stochastic model that can generate time series with features i ii and iii and we show by means of numerical simulations that this model is capable of reproducing these three features found in the empirical data

visibility graph analysis of economy policy uncertainty indices abstract uncertainty plays an important role in the global economy in this paper the economic policy uncertainty epu indices of the united states and china are selected as the proxy variable corresponding to the uncertainty of national economic policy by adopting the visibility graph algorithm the four economic policy uncertainty indices of the united states and china are mapped into complex networks and the topological properties of the corresponding networks are studied the hurst exponents of all the four indices are within 0 5 1 which implies that the economic policy uncertainty is persistent the degree distributions of the epu networks have power law tails and thus the networks are scale free the average clustering coefficients of the four epu networks are high and close to each other while these networks exhibit weak assortative mixing we also find that the epu network in united states based on daily data shows the small world feature since the average shortest path length increases logarithmically with the network size such that l n 0 626 ln n 0 405 our research highlights the possibility to study the epu from the view angle of complex networks

accurate estimator of correlations between asynchronous signals abstract the estimation of the correlation between time series is often hampered by the asynchronicity of the signals cumulating data within a time window suppresses this source of noise but weakens the statistics we present a method to estimate correlations without applying long time windows we decompose the correlations of data cumulated over a long window using decay of lagged correlations as calculated from short window data this increases the accuracy of the estimated correlation significantly and decreases the necessary effort of calculations both in real and computer experiments

long term memory and volatility clustering in high frequency price changes abstract we studied the long term memory in diverse stock market indices and foreign exchange rates using detrended fluctuation analysis dfa for all high frequency market data studied no significant long term memory property was detected in the return series while a strong long term memory property was found in the volatility time series the possible causes of the long term memory property were investigated using the return data filtered by the ar 1 model reflecting the short term memory property the garch 1 1 model reflecting the volatility clustering property and the figarch model reflecting the long term memory property of the volatility time series the memory effect in the ar 1 filtered return and volatility time series remained unchanged while the long term memory property diminished significantly in the volatility series of the garch 1 1 filtered data notably there is no long term memory property when we eliminate the long term memory property of volatility by the figarch model for all data used although the hurst exponents of the volatility time series changed considerably over time those of the time series with the volatility clustering effect removed diminish significantly our results imply that the long term memory property of the volatility time series can be attributed to the volatility clustering observed in the financial time series

centralized versus decentralized optimization of distributed stochastic differential decision systems with different information structures part i a general theory decentralized optimization of distributed stochastic dynamical systems with two or more controls of the decision makers dms has been an active area of research for over half a century although such decentralized optimization problems are often formulated utilizing static team and person by person pbp optimality criteria the corresponding static team theory results have not been extended to dynamical systems in this first part of the two part paper we derive team and pbp optimality conditions for distributed stochastic differential systems when the controls of the dms generate actions based on different information structures the necessary conditions are given by a hamiltonian system described by coupled backward and forward stochastic differential equations sdes and a conditional hamiltonian conditioned on the information structures available to the controls of the dms the sufficient conditions state that pbp optimality implies team optimality if the hamiltonian is convex in the state and or actions spaces of the controls of the dms we show existence of relaxed team optimal strategies when the information structures are not affected by the controls of the dms throughout the paper we discuss similarities to analogous optimality conditions of centralized decision or control of stochastic systems and we note a connections to mean field stochastic optimal control problems

time series analysis of s p 500 index a horizontal visibility graph approach the behavior of stock prices has been thoroughly studied throughout the last century and contradictory results have been reported in the corresponding literature in this paper a network theoretical approach is provided to investigate how crises affected the behavior of us stock prices we analyze high frequency data from s p500 via the horizontal visibility graph method and find that all major crises that took place worldwide in the last twenty years affected significantly the behavior of the price index nevertheless we observe that each of those crises impacted the index in a different way and magnitude interestingly our results suggest that the predictability of the price index series increases during the periods of crises

measurement of linear dependence and feedback between multiple time series abstract measures of linear dependence and feedback for multiple time series are defined the measure of linear dependence is the sum of the measure of linear feedback from the first series to the second linear feedback from the second to the first and instantaneous linear feedback the measures are nonnegative and zero only when feedback causality of the relevant type is absent the measures of linear feedback from one series to another can be additively decomposed by frequency a readily usable theory of inference for all of these measures and their decompositions is described the computations involved are modest

nonlinearity in high frequency stock returns evidence from the athens stock exchange abstract this study investigates empirically the presence of nonlinearities in the athens composite share price index high frequency returns a preliminary analysis indicates that volatility exhibits a periodic intraday inverse j shaped pattern associated with the opening and closing of the market periodicity is then removed employing a flexible fourier form subsequently an arma figarch model over several frequencies yields that return volatility is long memory and self similar nonlinear analysis with the use of the embedding dimension suggests that the filtered return process does not exhibit deterministic or higher order stochastic nonlinearity rather it is reminiscent of a random process we conclude that the acspi data are nonlinear however nonlinearity is attributed to persistent arch effects

mutual information a measure of dependency for nonlinear time series abstract the main goal of the paper is to show how mutual information can be used as a measure of dependence in financial time series one major advantage of this approach resides precisely in its ability to account for nonlinear dependencies with no need to specify a theoretical probability distribution or use of a mean variance model

noisy chaos in intraday financial data evidence from the american index the presence of chaos in financial markets was inconclusive due mainly to test misspecification and data type although noisy chaos was investigated in recent studies it was only explored in daily returns which does not necessary mean that continuous intra daily data will exhibit the same dynamics high level noisy chaos is tested in the standard poor s 500 index returns over 4 different frequencies weekly daily 30 min and 5 min basis the dynamics in all frequencies are non chaotic

the maximum number of 3 and 4 cliques within a planar maximally filtered graph abstract planar maximally filtered graphs pmfg are an important tool for filtering the most relevant information from correlation based networks such as stock market networks one of the main characteristics of a pmfg is the number of its 3 and 4 cliques recently in a few high impact papers it was stated that based on heuristic evidence the maximum number of 3 and 4 cliques that can exist in a pmfg with n vertices is 3 n 8 and n 4 respectively in this paper we prove that this is indeed the case

joint carleson measure and the difference of composition operators on aαp bn we introduce a concept of joint carleson measure and characterize when the difference of two composition operators on a p bn the weighted bergman space over the unit ball bn in cn is bounded or compact we apply this joint carleson measure characterization to composition operators with smooth symbols and construct an interesting example which shows that the boundedness or the compactness depends on p when n 2 this is in sharp contrast with the single composition operator case where the boundedness or the compactness is independent of p 0 moreover the compact difference on the weighted bergman spaces over the unit disc is known to be independent of p 0 and the compact difference on a p bn is known to be independent of p 0 if each composition operator is bounded on a p bn for some 1 2

static team problems part ii affine control laws projections algorithms and the legt problem team problems over the set of affine team control laws are solved as constrained parameter optimization problems this methodology eases both the notational and computational difficulties for the lqgt linear quadratic gaussian team and the legt linear exponential gaussian team problems the constrained parameter optimization approach leads to the representation of the optimal team control gains as explicit projections of the optimal centralized gains the projection representation offers insight into the team solution and suggests an algorithm for computing the optimal gains for the legt problem the legt problem behavior is compared to lqgt behavior for an example which consists of a static team with garbled decision implementation

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

a practical method for calculating largest lyapunov exponents from small data sets detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest lyapunov exponent lyapunov exponents quantify the exponential divergence of initially close state space trajectories and estimate the amount of chaos in a system we present a new method for calculating the largest lyapunov exponent from an experimental time series the method follows directly from the definition of the largest lyapunov exponent and is accurate because it takes advantage of all the available data we show that the algorithm is fast easy to implement and robust to changes in the following quantities embedding dimension size of data set reconstruction delay and noise level furthermore one may use the algorithm to calculate simultaneously the correlation dimension thus one sequence of computations will yield an estimate of both the level of chaos and the system complexity

on the connected component of compact composition operators on the hardy space we show that there exist non compact composition operators in the connected component of the compact ones on the classical hardy space h2 this answers a question posed by shapiro and sundberg in 1990 we also establish an improved version of a theorem of maccluer giving a lower bound for the essential norm of a difference of composition operators in terms of the angular derivatives of their symbols as a main tool we use aleksandrov clark measures

optimal control of systems with delayed observation sharing patterns via input output methods abstract in this paper we present an input output point of view of certain optimal control problems with constraints on the processing of the measurement data in particular we consider norm minimization optimal control problems under the so called one step delay observation sharing pattern we present a youla parametrization approach that leads to their solution by converting them to nonstandard yet convex model matching problems this conversion is always possible whenever the part of the plant that relates controls to measurements possesses the same structure in its feedthrough term with the one imposed by the observation pattern on the feedthrough term of the controller i e block diagonal when that is not the case it amounts to the so called non classical information pattern problems for the h case using loop shifting ideas a simple sufficient condition is given under which the problem can be still converted to a convex model matching problem we also demonstrate that there are several nontrivial classes of problems satisfying this condition finally we extend these ideas to the case of a n step delay observation sharing pattern

ordering univariate distributions by entropy and variance this paper examines the role of variance and entropy in ordering distributions and random prospects there is no universal relation between entropy and variance orderings of distributions but we place their relationship in the context of a stronger ordering relation known as dispersion ordering further some conditions are identified under which variance and entropy order similarly when continuous variables are transformed we also analyze parametric changes which do not disturb the agreement between these rankings the results are conveniently tabulated in terms of distribution parameters

multiscale shannon entropy and its application in the stock market abstract in this paper we perform a multiscale entropy analysis on the dow jones industrial average index using the shannon entropy the stock index shows the characteristic of multi scale entropy that caused by noise in the market the entropy is demonstrated to have significant predictive ability for the stock index in both long term and short term and empirical results verify that noise does exist in the market and can affect stock price it has important implications on market participants such as noise traders

a versatile and robust metric entropy test of time reversibility and other hypotheses abstract we examine the performance of a metric entropy statistic as a robust test for time reversibility tr symmetry and serial dependence it also serves as a measure of goodness of fit the statistic provides a consistent and unified basis in model search and is a powerful diagnostic measure with surprising ability to pinpoint areas of model failure we provide empirical evidence comparing the performance of the proposed procedure with some of the modern competitors in nonlinear time series analysis such as robust implementations of the bds and characteristic function based tests of tr along with correlation based competitors such as the ljung box q statistic unlike our procedure each of its competitors is motivated for a different specific context and hypothesis our evidence is based on monte carlo simulations along with an application to several stock indices for the us equity market

a model for social networks social networks are organized into communities with dense internal connections giving rise to high values of the clustering coefficient in addition these networks have been observed to be assortative i e highly connected vertices tend to connect to other highly connected vertices and have broad degree distributions we present a model for an undirected growing network which reproduces these characteristics with the aim of producing efficiently very large networks to be used as platforms for studying sociodynamic phenomena the communities arise from a mixture of random attachment and implicit preferential attachment the structural properties of the model are studied analytically and numerically using the k clique method for quantifying the communities r 2006 elsevier b v all rights reserved

estimating the intrinsic dimension of data with a fractal based method in this paper the problem of estimating the intrinsic dimension of a data set is investigated a fractal based approach using the grassberger procaccia algorithm is proposed since the grassberger procaccia algorithm 1983 performs badly on sets of high dimensionality an empirical procedure that improves the original algorithm has been developed the procedure has been tested on data sets of known dimensionality and on time series of santa fe competition

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

relative entropy measures of multivariate dependence abstract there has been a lot of work on measures of dependence or association for bivariate probability distributions or bivariate data these measures usually assume that the variables are both continuous or both categorical in comparison there is very little work on multivariate or conditional measures of dependence the purpose of this article is to discuss measures of multivariate dependence and measures of conditional dependence based on relative entropies these measures are conceptually very general as they can be used for a set of variables that can be a mixture of continuous ordinal categorical and nominal categorical variables for continuous or ordinal categorical variables a certain transformation of relative entropy to the interval 0 1 leads to generalizations of the correlation multiple correlation and partial correlation coefficients if all variables are nominal categorical the relative entropies are standardized to take a maximum of 1 and then transformed so that in the bivar

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

components of linear fractional composition operators abstract we determine when two linear fractional composition operators on the hardy space h 2 belong to the same component in the collection of all composition operators on h 2 we show that two such composition operators in the same component may fail to have compact difference which answers a question raised by joel shapiro and carl sundberg