hurst entropy a method to determine predictability in a binary series based on a fractal related process shannon s concept of information is related to predictability in a binary series the value of information relies on the frequency of 0 s and 1 s or how it is expected to occur however information entropy does not consider the bias in randomness related to autocorrelation in fact it is possible for a binary temporal series to carry both short and long term memories related to the sequential distribution of 0 s and 1 s although the hurst exponent measures the range of autocorrelation there is a lack of mathematical connection between information entropy and autocorrelation present in the series to fill this important gap we combined numerical simulations and an analytical approach to determine how information entropy changes according to the frequency of 0 s and 1 s and the hurst exponent indeed we were able to determine how predictability depends on both parameters our findings are certainly useful to several fields when binary times series are applied such as neuroscience to econophysics

generalized simulated annealing we discuss and illustrate a new stochastic algorithm generalized simulated annealing for computationally finding the global minimum of a given not necessarily convex energy cost function defined in a continuous d dimensional space this algorithm recovers as particular cases the so called classical boltzmann machine and fast cauchy machine simulated annealings and turns out to be quicker than both

distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach in this paper we introduce a multiscale symbolic information theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems more precisely we show that the multiscale complexity entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system s dynamics numerical simulations obtained from the well known and widely used mackey glass oscillator operating in a high dimensional chaotic regime were used as test beds the effect of an increased amount of observational white noise was carefully examined the results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles finally several experimental and natural time series were analyzed in order to show the applicability of this scale dependent symbolic approach in practical situations

common randomness in information theory and cryptography i secret sharing as the first part of a study of problems involving common randomness at distance locations information theoretic models of secret sharing generating a common random key at two terminals without letting an eavesdropper obtain information about this key are considered the concept of key capacity is defined single letter formulas of key capacity are obtained for several models and bounds to key capacity are derived for other models

secret key and private key constructions for simple multiterminal source models we propose an approach for constructing secret and private keys based on the long known slepian wolf code due to wyner for correlated sources connected by a virtual additive noise channel our work is motivated by results of csiszar and narayan which highlight innate connections between secrecy generation by multiple terminals that observe correlated source signals and slepian wolf near lossless data compression explicit procedures for such constructions and their substantiation are provided the performance of low density parity check channel codes in devising a new class of secret keys is examined

impulsive boundary value problems with integral boundary conditions and one dimensional p laplacian abstract by using the classical fixed point index theorem for compact maps some sufficient conditions for the existence of multiple positive solutions for a class of second order impulsive differential equations with p laplacian and integral boundary conditions are established which are the complement of previously known results meanwhile the existence of many solutions is also studied

converses for secret key agreement and secure computing we consider information theoretic secret key sk agreement and secure function computation by multiple parties observing correlated data with access to an interactive public communication channel our main result is an upper bound on the sk length which is derived using a reduction of binary hypothesis testing to multiparty sk agreement building on this basic result we derive new converses for multiparty sk agreement furthermore we derive converse results for the oblivious transfer problem and the bit commitment problem by relating them to sk agreement finally we derive a necessary condition for the feasibility of secure computation by trusted parties that seek to compute a function of their collective data using an interactive public communication that by itself does not give away the value of the function in many cases we strengthen and improve upon previously known converse bounds our results are single shot and use only the given joint distribution of the correlated observations for the case when the correlated observations consist of independent and identically distributed in time sequences we derive strong versions of previously known converses

multivariate multiscale fractional order weighted permutation entropy of nonlinear time series abstract in this letter multivariate multiscale fractional permutation entropy mmfpe and multivariate weighted multiscale fractional permutation entropy mwmfpe have been proposed to provide insights for the study of time series when measuring the dynamics of complex systems the mmfpe and mwmfpe methods are sensitive to the signal evolution meanwhile they can provide some analysis of complexity over multiple time series as well as multiple channel signals we perform these methods on synthetic tri variate time series to explore some of the interesting properties especially for negative information and information deception it can be seen that more complex system is more likely to be deceptive the amplitude information of time series which is taken into account in the mwmfpe can weaken this deception the methods are also employed to the closing prices and trade volume of financial stock markets from different areas according to the mwmfpe results the indices can be divided into three groups 1 cac40 hsi nasdaq s p500 2 n225 and 3 shencheng implying that it has a capacity to distinguish these financial stock market

secret key generation using correlated sources and channels we study the secret key capacity in a joint source channel coding setup the terminals are connected over a discrete memoryless channel and have access to side information modelled as a pair of discrete memoryless source sequences as our main result we establish the upper and lower bounds on the secret key capacity in the lower bound expression the equivocation terms of the source and channel components are functionally additive even though the coding scheme generates a single secret key by jointly taking into account the source and channel equivocations our bounds coincide thus establishing the capacity when the underlying wiretap channel can be decomposed into a set of independent parallel and reversely degraded channels for the case of parallel gaussian channels and jointly gaussian sources we show that gaussian codebooks achieve the secret key capacity in addition when the eavesdropper also observes a correlated side information sequence we establish the secret key capacity when both the source and channel of the eavesdropper are a degraded version of the legitimate receiver we finally also treat the case when a public discussion channel is available propose a separation based coding scheme and establish its optimality when the channel output symbols of the legitimate receiver and eavesdropper are conditionally independent given the input

characterization of time series via renyi complexity entropy curves abstract one of the most useful tools for distinguishing between chaotic and stochastic time series is the so called complexity entropy causality plane this diagram involves two complexity measures the shannon entropy and the statistical complexity recently this idea has been generalized by considering the tsallis monoparametric generalization of the shannon entropy yielding complexity entropy curves these curves have proven to enhance the discrimination among different time series related to stochastic and chaotic processes of numerical and experimental nature here we further explore these complexity entropy curves in the context of the renyi entropy which is another monoparametric generalization of the shannon entropy by combining the renyi entropy with the proper generalization of the statistical complexity we associate a parametric curve the renyi complexity entropy curve with a given time series we explore this approach in a series of numerical and experimental applications demonstrating the usefulness of this new technique for time series analysis we show that the renyi complexity entropy curves enable the differentiation among time series of chaotic stochastic and periodic nature in particular time series of stochastic nature are associated with curves displaying positive curvature in a neighborhood of their initial points whereas curves related to chaotic phenomena have a negative curvature finally periodic time series are represented by vertical straight lines

characterizing time series via complexity entropy curves the search for patterns in time series is a very common task when dealing with complex systems this is usually accomplished by employing a complexity measure such as entropies and fractal dimensions however such measures usually only capture a single aspect of the system dynamics here we propose a family of complexity measures for time series based on a generalization of the complexity entropy causality plane by replacing the shannon entropy by a monoparametric entropy tsallis q entropy and after considering the proper generalization of the statistical complexity q complexity we build up a parametric curve the q complexity entropy curve that is used for characterizing and classifying time series based on simple exact results and numerical simulations of stochastic processes we show that these curves can distinguish among different long range short range and oscillating correlated behaviors also we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed we further test this technique in experimental scenarios related to chaotic laser intensity stock price sunspot and geomagnetic dynamics confirming its usefulness finally we prove that these curves enhance the automatic classification of time series with long range correlations and interbeat intervals of healthy subjects and patients with heart disease

on the public communication needed to achieve sk capacity in the multiterminal source model the focus of this paper is on the public communication required for generating a maximal rate secret key sk within the multiterminal source model of csiszar and narayan building on the prior work of tyagi for the two terminal scenario we derive a lower bound on the communication complexity r text sk defined to be the minimum rate of public communication needed to generate a maximal rate sk it is well known that the minimum rate of communication for omniscience denoted by r text co is an upper bound on r text sk for the class of pairwise independent network pin models defined on uniform hypergraphs we show that a certain type mathcal s condition which is verifiable in polynomial time guarantees that our lower bound on r text sk meets the r text co upper bound thus the pin models satisfying our condition are r text sk maximal indicating that the upper bound r text sk le r text co holds with equality this allows us to explicitly evaluate r text sk for such pin models we also give several examples of pin models that satisfy our type mathcal s condition finally we prove that for an arbitrary multiterminal source model a stricter version of our type mathcal s condition implies that communication from all terminals omnivocality is needed for establishing an sk of maximum rate for three terminal source models the converse is also true omnivocality is needed for generating a maximal rate sk only if the strict type mathcal s condition is satisfied however for the source models with four or more terminals counterexamples exist showing that the converse does not hold in general

analysis of crude oil markets with improved multiscale weighted permutation entropy abstract entropy measures are recently extensively used to study the complexity property in nonlinear systems weighted permutation entropy wpe can overcome the ignorance of the amplitude information of time series compared with pe and shows a distinctive ability to extract complexity information from data having abrupt changes in magnitude improved or sometimes called composite multi scale ms method possesses the advantage of reducing errors and improving the accuracy when applied to evaluate multiscale entropy values of not enough long time series in this paper we combine the merits of wpe and improved ms to propose the improved multiscale weighted permutation entropy imwpe method for complexity investigation of a time series then it is validated effective through artificial data white noise and 1 f noise and real market data of brent and daqing crude oil meanwhile the complexity properties of crude oil markets are explored respectively of return series volatility series with multiple exponents and eemd produced intrinsic mode functions imfs which represent different frequency components of return series moreover the instantaneous amplitude and frequency of brent and daqing crude oil are analyzed by the hilbert transform utilized to each imf

binary indices of time series complexity measures and entropy plane abstract complexity of time series is an important feature of dynamical systems such as financial systems in order to bring out the complete non linear behavior of financial time series non linear tools of complexity measurement like entropy measures are indispensable sample entropy sampen and distribution entropy disten are popular methods of assessing the complexity in various fields however both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets therefore we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane in order to further improve the accuracy of the research results we take the embedding dimension m as the variable expand the entropy point into the entropy curve for further research furthermore considering the shortcomings of sample entropy and distribution entropy in practical application we generalize them by i replacing sample entropy and distribution entropy with multi scale sample entropy and multi scale distribution entropy ii generalizing shannon entropy as tsallis entropy also scale factor and entropic index q are taken respectively as variables to get the entropy curves by using the artificial data we confirm the rationality of using entropy points and entropy curves to study the complexity of time series finally we apply this method to measure the complexity of real world financial time series the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences

sunspot cycle a driven nonlinear oscillator a property of nonlinear oscillators mutual dependence between their instantaneous amplitude and frequency is tested in the yearly and monthly records of the sunspot numbers using the histogramadjusted isospectral surrogate data and the barnes model as the autoregressive moving average surrogates the instantaneous amplitudes and frequencies are obtained by means of the analytic signal approach using the discrete hilbert transform in several tests the amplitude frequency correlation has been found significant on levels ranging from p 0 03 to p 0 07 which supports the hypothesis of a driven nonlinear oscillator as a mechanism underlying the sunspot cycle

complexity entropy causality plane a useful approach for distinguishing songs nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies this is particularly true when dealing with music databases in this context it is essential to have techniques and tools able to discriminate properties from these massive sets in this work we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure building up the complexity entropy causality plane the results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs additionally we believe that the here reported method may be applied in practical situations since it is simple robust and has a fast numerical implementation

secret key agreement by public discussion from common information the problem of generating a shared secret key s by two parties knowing dependent random variables x and y respectively but not sharing a secret key initially is considered an enemy who knows the random variable z jointly distributed with x and y according to some probability distribution p sub xyz can also receive all messages exchanged by the two parties over a public channel the goal of a protocol is that the enemy obtains at most a negligible amount of information about s upper bounds on h s as a function of p sub xyz are presented lower bounds on the rate h s n as n to infinity are derived for the case in which x x sub 1 x sub n y y sub 1 y sub n and z z sub 1 z sub n result from n independent executions of a random experiment generating x sub i y sub i and z sub i for i 1 n it is shown that such a secret key agreement is possible for a scenario in which all three parties receive the output of a binary symmetric source over independent binary symmetric channels even when the enemy s channel is superior to the other two channels

coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming abstract in this paper the existence and iterative approximation of coupled fixed points for mixed monotone condensing set valued operators are discussed the results presented here extend and improve the corresponding results of d guo and v lakshmikantham coupled fixed points of nonlinear operators 1 2 as an application we utilize the results obtained in section 2 to study the existence problem of solutions for a class of functional equations arising in dynamic programming

comments on information theoretic key agreement of multiple terminals part i theorem 5 of a gohari v anantharam ieee transactions on information theory vol 56 no 8 pp 3973 3996 2010 states an upper bound on the secrecy capacity for the source model problem it has a three page proof given in appendix b of the paper unfortunately we show that this bound does not provide any improvement over the simpler bound given in corollary 1 of the paper we also provide an example of a family of two agent source model problems where the one way secrecy rate in each direction is zero but the secrecy rate is nonzero and can be determined exactly as a conditional mutual information

information theoretic key agreement of multiple terminals part i we study the problem of information theoretically secure secret key agreement under the well known source model and channel model in both of these models multiple terminals wish to create a shared secret key that is secure from a passive eavesdropper the terminals have access to a noiseless public communication channel and an additional resource that depends on the model in the source model the resource is an external source that repeatedly beams correlated randomness to the terminals whereas in the channel model the resource is a secure but noisy discrete memoryless broadcast channel we derive new lower and upper bounds on the secret key capacity under both the source model and the channel model the technique used for deriving our bound for the source model is to find certain properties of functions of joint probability distributions which applied to the joint distribution of the source will imply that they dominate the secret key capacity and then prove the bound by a verification argument a similar technique is used for the channel model finally we also define a problem of communication for omniscience by a neutral observer and establish the equivalence between this new problem and the problem of secret key agreement this generalizes an earlier result of csiszar and narayan

multiple fixed points of a sum operator and applications this paper considers existence of multiple positive fixed points for some nonlinear operators a particular case of the operators is sum of an e concave operator and an e convex operator then we apply the results to nonlinear integral equations

permutation entropy and statistical complexity quantifier of nonstationarity effect in the vertical velocity records how the nonstationarity in the atmosphere turbulent vertical velocity series affects its organization degree of multiscale structures is quantified by permutation entropy pe and complexity entropy causality plane cecp and marked pe and cecp differences are detected between the nonstationary and stationary series we find that the value of pe is lower in the nonstationary vertical velocity series than the stationary counterparts both types of series locate near the region of the higher complexity value in the cecp as chaotic systems but the pe is smaller and the complexity degree is larger in the nonstationary series than the stationary with smaller time delays due to the close relationship between pe and the multiscale shannon entropy we show that the pe and cecp can be also taken as an indicator to quantify the different organization degrees of the multiscale structures existing between the stationary and nonstationary surface vertical velocity records

bounds on entanglement distillation and secret key agreement for quantum broadcast channels the squashed entanglement of a quantum channel is an additive function of quantum channels which finds application as an upper bound on the rate at which secret key and entanglement can be generated when using a quantum channel a large number of times in addition to unlimited classical communication this quantity has led to an upper bound of log 1 eta 1 eta on the capacity of a pure loss bosonic channel for such a task where eta is the average fraction of photons that make it from the input to the output of the channel the purpose of this paper is to extend these results beyond the single sender single receiver setting to the more general case of a single sender and multiple receivers a quantum broadcast channel we employ multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglement can be generated between any subset of the users of such a channel along the way developing several new properties of these measures we apply our results to the case of a pure loss broadcast channel with one sender and two receivers

existence of fixed points for some convex operators and applications to multi point boundary value problems existence results of fixed points for some convex operators are given by means of fixed point theorem of cone expansion and compression then they are applied to nonlinear multi point boundary value problems

generalized entropy plane based on large deviations theory for financial time series abstract complexity entropy causality plane analysis and large deviations spectrums theory are proposed to study time series the entropy plane analysis depicts the complexity of a system in two dimensional plane while large deviations theory shows the spectral structure of time series in the way of multifractal in this paper we combine the characteristics of these two popular methods and propose a generalized entropy plane model based on the large deviation theory the methodology is applied to both synthetic data and financial markets we discuss the impact of the parameters on the results in detail besides the modified model can distinguish different time series meanwhile we compare our results with the original complexity entropy causality plane and large deviations spectrums and the consistency of these results is confirmed the method can provide abundant dynamical properties of complex systems

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

secrecy capacities for multiple terminals we derive single letter characterizations of strong secrecy capacities for models with an arbitrary number of terminals each of which observes a distinct component of a discrete memoryless multiple source with unrestricted and interactive public communication permitted between the terminals a subset of these terminals can serve as helpers for the remaining terminals in generating secrecy according to the extent of an eavesdropper s knowledge three kinds of secrecy capacity are considered secret key sk private key pk and wiretap secret key wsk capacity the characterizations of the sk and pk capacities highlight the innate connections between secrecy generation and multiterminal source coding without secrecy requirements a general upper bound for wsk capacity is derived which is tight in the case when the eavesdropper can wiretap noisy versions of the components of the underlying multiple source provided randomization is permitted at the terminals these secrecy capacities are seen to be achievable with noninteractive communication between the terminals the achievability results are also shown to be universal

a fixed point theorem for a general epidemic model abstract epidemic type models typically undergo a phase transition when the infection rate surpasses the epidemic threshold however for networks having degree degree correlations the epidemic threshold has never formally been defined and there is a shortage of rigorous mathematics describing epidemic phase transitions in the context of disease spreading on top of a complex network this paper provides a set of necessary and sufficient conditions for the occurrence of a persistent infected state as a proof of principle we demonstrate that the percolation and sis sir epidemic models on complex correlated networks satisfy the assumptions necessary for a single phase transition this paper attempts to highlight commonalities in a variety of different interacting particle systems

modified permutation entropy analysis of heartbeat dynamics heart rate variability hrv contains important information about the modulation of the cardiovascular system various methods of nonlinear dynamics e g estimating lyapunov exponents and complexity measures e g correlation dimension or entropies have been applied to hrv analysis permutation entropy which was proposed recently has been widely used in many fields due to its conceptual and computational simplicity it maps a time series onto a symbolic sequence of permutation ranks the original permutation entropy assumes the time series under study has a continuous distribution thus equal values are rare and can be ignored by ranking them according to their order of emergence or broken by adding small random perturbations to ensure every symbol in a sequence is different however when the observed time series is digitized with lower resolution leading to a greater number of equal values or the equalities represent certain characteristic sequential patterns of the system it may not be rational to simply ignore or break them in the present paper a modified permutation entropy is proposed that by mapping the equal value onto the same symbol rank allows for a more accurate characterization of system states the application of the modified permutation entropy to the analysis of hrv is investigated using clinically collected data results show that modified permutation entropy can greatly improve the ability to distinguish the hrv signals under different physiological and pathological conditions it can characterize the complexity of hrv more effectively than the original permutation entropy

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

fixed point theorems for τ φ concave operators and applications in this paper by introducing t f concave operators and using the properties of cones and monotone iterative technique some new existence and uniqueness theorems of fixed points for increasing operators with such concavity are established under more extensive conditions in ordered banach spaces as an application we study the existence and uniqueness of positive solutions of generalized three point boundary value problems for second order differential equations the results obtained here improve and generalize many known results

missing ordinal patterns in correlated noises abstract recent research aiming at the distinction between deterministic or stochastic behavior in observational time series has looked into the properties of the ordinal patterns c bandt b pompe phys rev lett 88 2002 174102 in particular new insight has been obtained considering the emergence of the so called forbidden ordinal patterns j m amigo s zambrano m a f sanjuan europhys lett 79 2007 50001 it was shown that deterministic one dimensional maps always have forbidden ordinal patterns in contrast with time series generated by an unconstrained stochastic process in which all the patterns appear with probability one techniques based on the comparison of this property in an observational time series and in white gaussian noise were implemented however the comparison with correlated stochastic processes was not considered in this paper we used the concept of missing ordinal patterns to study their decay rate as a function of the time series length in three stochastic processes with different degrees of correlation fractional brownian motion fractional gaussian noise and noises with f k power spectrum we show that the decay rate of missing ordinal patterns in these processes depend on their correlation structures we finally discuss the implications of the present results for the use of these properties as a tool for distinguishing deterministic from stochastic processes

coding for positive rate in the source model key agreement problem a two party key agreement problem with public discussion known as the source model problem is considered by relating key agreement to hypothesis testing a new coding scheme is developed that yields a sufficient condition to achieve a positive secret key sk rate in terms of renyi divergence the merits of this coding scheme are illustrated by applying it to an erasure model for eve s side information and by deriving an upper bound on eve s erasure probabilities for which the sk capacity is zero this bound strictly improves on the best known single letter lower bound on the sk capacity moreover the bound is tight when alice s or bob s source is binary which extends a previous result for a doubly symmetric binary source the results motivate a new measure for the correlation between two random variables which is of independent interest

multi key generation over a cellular model with a helper the problem of simultaneously generating multiple keys for a cellular source model with a helper is investigated in the model considered there are four terminals mathcal x 0 mathcal x 1 mathcal x 2 and mathcal x 3 each of which observes one component of a vector source terminal mathcal x 0 wishes to generate two secret keys k 1 and k 2 respectively with terminals mathcal x 1 and mathcal x 2 under the help of terminal mathcal x 3 all terminals are allowed to communicate over a public channel an eavesdropper is assumed to have access to the public discussion both symmetric and asymmetric key generations are considered in symmetric key generation models model 1a with a trusted helper requires that the two keys are concealed from the eavesdropper and model 1b with an untrusted helper further requires that the two keys are concealed from the helper in addition to the eavesdropper the asymmetric key generation models 2a and 2b are the same as symmetric key generation models 1a and 1b respectively except that the key k 2 is further required to be concealed from terminal mathcal x 1 for all models studied the key capacity region is established by designing a unified achievable strategy to achieve the cut set outer bounds we also study the problem of generating more than two keys and characterize its key capacity region when all the cellular terminals are required to generate independent keys with the base station

fixed points of generalized e concave generalized e convex operators and their applications in this paper we present the definitions of generalized e concave operators and generalized e convex operators which are the generalizations of e concave operators and e convex operators respectively without compactness or continuity assumption of generalized e concave operators and generalized e convex operators we have proved the existence uniqueness and monotone iterative techniques of their fixed points our results are even new to e concave operators and e convex operators finally we apply the results to the singular boundary value problems for second order differential equations

secret key agreement general capacity and second order asymptotics we revisit the problem of secret key agreement using interactive public communication for two parties and propose a new secret key agreement protocol the protocol attains the secret key capacity for general observations and attains the second order asymptotic term in the maximum length of a secret key for independent and identically distributed observations in contrast to the previously suggested secret key agreement protocols the proposed protocol uses interactive communication in fact the standard one way communication protocol used prior to this paper fails to attain the asymptotic results above our converse proofs rely on a recently established upper bound for secret key lengths both our lower and upper bounds are derived in a single shot setup and the asymptotic results are obtained as corollaries

coupled fixed points of nonlinear operators with applications a partir de quasi solutions couplees des problemes aux valeurs initiales pour des equations differentielles ordinaires on introuit le concept de points fixes couples abstraits pour certains operateurs on donne des theoremes d existence

modeling persistence in hydrological time series using fractional differencing the class of autoregressive integrated moving average arima time series models may be generalized by permitting the degree of differencing d to take fractional values models including fractional differencing are capable of representing persistent series d 0 or short memory series d 0 the class of fractionally differenced arima processes provides a more flexible way than has hitherto been available of simultaneously modeling the long term and short term behavior of a time series in this paper some fundamental properties of fractionally differenced arima processes are presented methods of simulating these processes are described estimation of the parameters of fractionally differenced arima models is discussed and an approximate maximum likelihood method is proposed the methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures

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

causality and the entropy complexity plane robustness and missing ordinal patterns abstract we deal here with the issue of determinism versus randomness in time series one wishes to identify their relative weights in a given time series two different tools have been advanced in the literature to such effect namely i the causal entropy complexity plane o a rosso h a larrondo m t martin a plastino m a fuentes distinguishing noise from chaos phys rev lett 99 2007 154102 and ii the estimation of the decay rate of missing ordinal patterns j m amigo s zambrano m a f sanjuan true and false forbidden patterns in deterministic and random dynamics europhys lett 79 2007 50001 l c carpi p m saco o a rosso missing ordinal patterns in correlated noises physica a 389 2010 2020 2029 in this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation the chaotic series studied here was via the logistic map r 4 to which we added correlated noise colored noise with f k power spectrum 0 k 2 of varying amplitudes in such a fashion important insights pertaining to the deterministic component of the original time series can be gained we find that in the entropy complexity plane this goal can be achieved without additional computations

infeasibility proof and information state in network information theory in this paper we revisit the structure of infeasibility results in network information theory based on a notion of information state we also discuss ideas for generalizing a known outer bound for lossless transmission of independent sources over a network to one of lossy transmission of dependent sources over the same network to concretely demonstrate this we apply our ideas and prove new results for lossy transmission of dependent sources by generalizing 1 the cut set bound 2 the best known outer bound on the capacity region of a general broadcast channel and 3 the outer bound part of the result of maric yates and kramer on strong interference channels with a common message

fractional brownian motion fractional gaussian noise and tsallis permutation entropy abstract in this work we analyze two important stochastic processes the fractional brownian motion and fractional gaussian noise within the framework of the tsallis permutation entropy this entropic measure evaluated after using the bandt pompe method to extract the associated probability distribution is shown to be a powerful tool to characterize fractal stochastic processes it allows for a better discrimination of the processes than the shannon counterpart for appropriate ranges of values of the entropic index moreover we find the optimum value of this entropic index for the stochastic processes under study