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

bandt pompe approach to the classical quantum transition abstract by regarding the celebrated classical quantum transition problem as one pertaining to the domain of dynamic systems theory we present a discussion that exhibits the superiority of the bandt pompe approach to the extraction of a probability distribution from time series values

acoustic scattering from an arbitrarily rough surface a method is described for dealing with acoustic scattering from a time independent pressure release surface as in work by previous authors the problem is formulated as an integral equation on the surface this formulation takes account of arbitrarily large surface roughness and multiple scattering phenomena at the surface the problem may be considered naturally in two stages the first part of the problem is to invert the integral equation to find the pressure gradient on the surface the eigenfunction expansion method used by holford j acoust soc am 70 1116 1128 1981 for periodic surfaces is extended to deal with more general aperiodic surfaces it is then shown that this approach is almost exactly equivalent to a direct collocation method the second part of the problem is to evaluate the scattered pressure away from the surface the method used here is to calculate the reflection coefficients from the fourier transform of the pressure gradient on the surface the reflection coefficients giv

the entropy as a tool for analysing statistical dependences in financial time series abstract the entropy is a concept which may serve to define quantities such as the conditional entropy and the mutual information using a novel algorithm for the estimation of the mutual information from data we analyse several financial time series and demonstrate the usefulness of this new approach the issues of long range dependence and non stationarity are discussed

characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments we study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep deep sleep and rapid eye movement rem sleep using the detrended fluctuation analysis method we find short range anticorrelations in the sign time series which are strong during deep sleep weaker during light sleep and even weaker during rem sleep in contrast we find long range positive correlations in the magnitude time series which are strong during rem sleep and weaker during light sleep we observe uncorrelated behavior for the magnitude during deep sleep since the magnitude series relates to the nonlinear properties of the original time series while the sign series relates to the linear properties our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during rem sleep thus the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages

new irreversibility measure and complexity analysis based on singular value decomposition abstract visibility graph algorithm is a powerful tool for visualization and analysis of complex dynamical system kullback leibler divergence kld based on the horizontal visibility graph algorithm has received largely extensive attention in the field of irreversibility analysis in this paper we will propose a new irreversibility measure built on the multi scale theory i e the kld based on singular value decomposition kld svd furthermore since matrix singular value can reflect the basic characteristics of the complex system we further bring forward the definition of shannon entropy with singular value decomposition se svd after considering that the shannon entropy has been well defined as a complexity measure in order to show the advantages of these two new measures in detecting the complexity of systems several simulation and real data experiments are chosen to examine the performance of them through these results we find that the average and variance of kld svd corresponding to each time series is less than that of the kld moreover kld svd s volatility is significantly weaker than kld s as there is a conceptual link between predictability and irreversibility we can argue that kld svd algorithm implies the higher predictability and lower confusion on the other hand se svd can do well in revealing the internal complexity of the different time series meanwhile it is useful to mention that se svd is robust against noise efficiently

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

scattering by infinite one dimensional rough surfaces we consider the dirichlet boundary value problem for the helmholtz equation in a non locally perturbed half plane this problem models time harmonic electromagnetic scattering by a one dimensional infinite rough perfectly conducting surface the same problem arises in acoustic scattering by a sound soft surface chandler wilde and zhang have suggested a radiation condition for this problem a generalization of the rayleigh expansion condition for diffraction gratings and uniqueness of solution has been established recently an integral equation formulation of the problem has also been proposed and in the special case when the whole boundary is both lyapunov and a small perturbation of a flat boundary the unique solvability of this integral equation has been shown by chandler wilde and ross by operator perturbation arguments in this paper we study the general case with no limit on surface amplitudes or slopes and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers as an important corollary we prove that for a variety of incident fields including the incident plane wave the dirichlet boundary value problem for the scattered field has a unique solution

characterization of the causality between spike trains with permutation conditional mutual information uncovering the causal relationship between spike train recordings from different neurons is a key issue for understanding the neural coding this paper presents a method called permutation conditional mutual information pcmi for characterizing the causality between a pair of neurons the performance of this method is demonstrated with the spike trains generated by the poisson point process model and the izhikevich neuronal model including estimation of the directionality index and detection of the temporal dynamics of the causal link simulations show that the pcmi method is superior to the transfer entropy and causal entropy methods at identifying the coupling direction between the spike trains the advantages of pcmi are twofold it is able to estimate the directionality index under the weak coupling and against the missing and extra spikes

randomizing nonlinear maps via symbolic dynamics abstract pseudo random number generators prng have attracted intense attention due to their obvious importance for many branches of science and technology a randomizing technique is a procedure designed to improve the prng randomness degree according the specific requirements it is obviously important to quantify its effectiveness in order to classify randomizing techniques based on a symbolic dynamics approach we advance a novel physically motivated representation based on the statistical properties of chaotic systems recourse is made to a plane that has as coordinates i the shannon entropy and ii a form of the statistical complexity measure each statistical quantifier incorporates a different probability distribution function generating thus a representation that i sheds insight into just how each randomizing technique operates and also ii quantifies its effectiveness using the logistic map and the three way bernoulli map as typical examples of chaotic dynamics it is shown that our methodology allows for choosing the more convenient randomizing technique in each instance comparison with measures of complexity based on diagonal lines on the recurrence plots n marwan m c romano m thiel j kurths phys rep 438 2007 237 support the main conclusions of this paper

forbidden patterns permutation entropy and stock market inefficiency abstract in this paper we introduce two new quantifiers for the stock market inefficiency the number of forbidden patterns and the normalized permutation entropy they are model independent measures thus they have more general applicability we find robust evidence that degree of market inefficiency is positively correlated with the number of forbidden patterns and negatively correlated with the permutation entropy our empirical results suggest that these two physical tools are useful to discriminate the stage of stock market development and can be easily implemented

weighted permutation entropy based on different symbolic approaches for financial time series abstract in this paper we introduce weighted permutation entropy wpe and three different symbolic approaches to investigate the complexities of stock time series containing amplitude coded information and explore the influence of using different symbolic approaches on obtained wpe results we employ wpe based on symbolic approaches to the us and chinese stock markets and make a comparison between the results of us and chinese stock markets three symbolic approaches are able to help the complexity containing in the stock time series by wpe method drop whatever the embedding dimension is the similarity between these stock markets can be detected by the wpe based on binary coding method while the difference between them can be revealed by the wpe based on method max min method the combinations of the symbolic approaches method and max min method and wpe method are capable of reflecting the multiscale structure of complexity by different time delay and analyze the differences between complexities of stock time series in more detail and more accurately furthermore the correlations between stock markets in the same region and the similarities hidden in the s p500 and dji shangzheng and shencheng are uncovered by the comparison of the wpe based on binary coding method of six stock markets

an investigation of oil water two phase flow instability using multivariate multi scale weighted permutation entropy abstract the present study is devoted to the investigation of oil water two phase flow instability using multivariate multi scale weighted permutation entropy mwmpe four typical multivariate multi scale entropies namely mwmpe multivariate multi scale permutation entropy mmpe multivariate multi scale sample entropy mmse and multivariate multi scale approximate entropy mmae are applied in lorenz system with the addition of different kinds of noises the comparison results indicate that mwmpe presents the superiorities of being sensitive to the variation in scale showing a monotonous increasing trend as well as the best anti noise ability accordingly with the fluctuating signals from an eight electrode rotating electrical field conductance sensor used for the measurement of oil water flows we extract mwmpe for the whole experimental flow conditions in terms of which the effects of mixture velocity and water cut on oil water two phase flow instability are illuminated our research provides an effective method for uncovering the underlying evolution instability of the flow structures in oil water flows

large scale antenna selection and precoding for interference exploitation we propose several low complexity transmit antenna selection tas and precoding schemes for massive multi input multi output m mimo it is well established that large antenna arrays in m mimo lead to particularly high hardware overheads as they require an equally large number of radio frequency chains and antenna selection is envisaged as a solution to reducing this hardware complexity accordingly in the proposed schemes both hardware and computational complexity of m mimo systems are addressed by jointly optimizing tas and precoding we first introduce a mixed integer programming approach that simultaneously identifies the transmitting antennas subset and solves the precoding problem by employing a unified metric based on constructive interference ci concept we then propose three sub optimal techniques that allow a reduction of the computational complexity required to solve the joint optimization our analyses and results prove that the proposed joint tas and precoding schemes based on ci exploitation are able to outperform the state of the art while providing a favorable performance complexity tradeoff

pre scaling optimization for space shift keying based on semidefinite relaxation the performance of space shift keying ssk is known to be dominated by the minimum euclidean distance med in the received ssk constellation in this paper we propose a method of enhancing the med in the received ssk constellation and improving both the attainable performance and the power efficiency by means of symbol scaling at the transmitter to this aim we formulate a pair of optimization problems one for maximizing the med subject to a specific transmit power constraint and one for minimizing the transmit power subject to a med threshold as these problems are np hard we re formulate their optimization using semidefinite relaxations which results in convex problem formulations that can be efficiently solved using standard approaches moreover we design pre scaling techniques for imperfect channel state information at the transmitter where the existing approaches are inapplicable our results show that the proposed schemes substantially improve the power efficiency of ssk systems with respect to state of the art techniques by offering an improved performance for specific transmit power requirements or equivalently a transmit power reduction for a given med threshold

constructive multiuser interference in symbol level precoding for the miso downlink channel this paper investigates the problem of interference among the simultaneous multiuser transmissions in the downlink of multiple antenna systems using symbol level precoding a new approach to exploit the multiuser interference is discussed the concept of exploiting the interference between spatial multiuser transmissions by jointly utilizing data information di and channel state information csi in order to design symbol level precoders is proposed to this end the interference between data streams is transformed under certain conditions into useful signal that can improve the signal to interference noise ratio sinr of the downlink transmissions we propose a maximum ratio transmission mrt based algorithm that jointly exploits di and csi to glean the benefits from constructive multiuser interference subsequently a relation between the constructive interference downlink transmission and physical layer multicasting is established in this context novel constructive interference precoding techniques that tackle the transmit power minimization min power with individual sinr constraints at each user s receivers is proposed furthermore fairness through maximizing the weighted minimum sinr max min sinr of the users is addressed by finding the link between the min power and max min sinr problems moreover heuristic precoding techniques are proposed to tackle the weighted sum rate problem finally extensive numerical results show that the proposed schemes outperform other state of the art techniques

intensive statistical complexity measure of pseudorandom number generators abstract a statistical complexity measure has been recently proposed to quantify the performance of chaotic pseudorandom number generators prng physica a 354 2005 281 here we revisit this quantifier and introduce two important improvements i consideration of an intensive statistical complexity physica a 334 2004 119 and ii following the prescription of brand and pompe phys rev lett 88 2002 174102 1 in evaluating the probability distribution associated with the prng the ensuing new measure is applied to a very well tested prng advanced by marsaglia

evidence of increment of efficiency of the mexican stock market through the analysis of its variations abstract it is well known that there exist statistical and structural differences between the stock markets of developed and emerging countries in this work and in order to find out if the efficiency of the mexican stock market has been changing over time we have performed and compared several analyses of the variations of the mexican stock market index ipc and dow jones industrial average index djia for different periods of their historical daily data we have analyzed the returns autocorrelation function acf and used detrended fluctuation analysis dfa to study returns variations we also analyze the volatility mean value and standard deviation of both markets and compare their evolution we conclude from the overall result of these studies that they show compelling evidence of the increment of efficiency of the mexican stock market over time the data samples analyzed here correspond to daily values of the ipc and djia for the period 10 30 1978 02 28 2006

transmit selection diversity for unitary precoded multiuser spatial multiplexing systems with linear receivers multiuser spatial multiplexing is a downlink transmission technique that uses linear transmit precoding to multiplex multiple users and precancel interuser interference in such a system the spatial degrees of freedom are used for interference mitigation and generally come at the expense of diversity gain this paper proposes two precoding methods that use extra transmit antennas beyond the minimum required to provide additional degrees of diversity the approach taken is to solve for a unitary transmit precoder under a zero interuser interference constraint that minimizes an upper bound on the symbol error rate ser for each user solutions where all transmit antennas are employed as well as subsets of antennas to reduce analog components are described numerical results confirm a dramatic improvement in terms of ser and mutual information over single user multiple input multiple output mimo methods and static allocation methods for example the proposed techniques achieve a signal to noise ratio snr improvement of 6 10 db at an uncoded ser of 10 3 with only one extra transmit antenna

multiscale tsallis permutation entropy analysis for complex physiological time series abstract discussing the complexity of time series has been a long standing problem including the use of information entropy to determine the complexity of the sequence permutation entropy pe has been regarded as a learning process to investigate the complexity of time series such as financial time series and physiological time series the permutation entropy which is based on the shannon entropy se has undeniable shortcomings in dealing with some specific problems hence in this paper we propose the multiscale tsallis permutation entropy mtpe as an improved measuring tool for assessing the hidden temporal correlations in time series the modified method not only presents a different way showing clear characteristics but also provides more significant results compared with the se robustness of the hypothesis is proved by the correlation between tsallis permutation entropy tpe and hurst exponent obtained from the sequences which are generated from fractional brownian motion stochastic model experimental results of autoregressive sequences ar and electroencephalograph time series eeg make the advantages of tsallis permutation entropy more obvious which also well validate the efficiency and integrity of principle of maximum entropy pme multiscale analysis provides us with another perspective to analyze permutation entropy which also allows us to better analyze the complexity of the sequence

receive antenna selection for mimo spatial multiplexing theory and algorithms this paper discusses the problem of receive antenna subset selection in multiple input multiple output spatial multiplexing mimo sm systems we develop selection algorithms for maximizing the channel capacity one algorithm in particular allows tractable statistical analysis of performance we leverage this to prove that the capacity of the system through receive antenna selection is statistically lower bounded by the capacity of a set of parallel independent single input multiple output simo channels each with selection diversity this provides the crucial step in proving the next main result the diversity order achievable through antenna selection is the same as that of the full system the result sets up strong motivation for introducing receive selection in mimo sm systems the remainder of the paper discusses selection algorithms for two popular mimo sm systems namely ordered successive interference cancellation with independently encoded layers and minimum mean square error mmse receiver with joint encoding of data streams extensive monte carlo simulations are presented to validate and demonstrate performance

relationship between efficiency and predictability in stock price change abstract in this study we evaluate the relationship between efficiency and predictability in the stock market the efficiency which is the issue addressed by the weak form efficient market hypothesis is calculated using the hurst exponent and the approximate entropy apen the predictability corresponds to the hit rate this is the rate of consistency between the direction of the actual price change and that of the predicted price change as calculated via the nearest neighbor prediction method we determine that the hurst exponent and the apen value are negatively correlated however predictability is positively correlated with the hurst exponent

a new treatment of rough surface scattering this paper treats the problem of the scattering of a narrow beam at a randomly rough surface where the height distribution is gaussian and the correlation of heights is gaussian the field at the surface is assumed to satisfy a dirichlet boundary condition the problem is formulated using the standard integral equation approach in the case when the rms height is very large numerical solution of this equation for a realization of the surface involves the solution of a very large matrix problem particularly if the beam is scattered to other parts of the surface that are at a considerable distance from the initial illumination here we provide a straightforward technique motivated by ray theory that allows only those parts of the surface that are actually illuminated at any stage to be treated thus for the first reflection of the beam one solves an integral equation over the initially illuminated area this solution is used to determine the parts of the surface which give rise to doubly scattered waves and one then solves the integral equation over the newly illuminated area and so on until all reflections have been accounted for this procedure can be carried out with no explicit reference to any ray model working simply with the discrete matrix form of the integral equation in particular for one dimensional surface variation a strategy of successive sweeps from left to right and back again for a beam incident from the left is shown to be successful any standard iterative or direct solution technique can be used for the sequence of sub problems so introduced the general method is also applicable to scattering from surfaces varying in two dimensions

per antenna constant envelope precoding for large multi user mimo systems we consider the multi user mimo broadcast channel with m single antenna users and n transmit antennas under the constraint that each antenna emits signals having constant envelope ce the motivation for this is that ce signals facilitate the use of power efficient rf power amplifiers analytical and numerical results show that under certain mild conditions on the channel gains for a fixed m an array gain is achievable even under the stringent per antenna ce constraint essentially for a fixed m at sufficiently large n the total transmitted power can be reduced with increasing n while maintaining a fixed information rate to each user simulations for the i i d rayleigh fading channel show that the total transmit power can be reduced linearly with increasing n i e an o n array gain we also propose a precoding scheme which finds near optimal ce signals to be transmitted and has o mn complexity also in terms of the total transmit power required to achieve a fixed desired information sum rate despite the stringent per antenna ce constraint the proposed ce precoding scheme performs close to the sum capacity achieving scheme for an average only total transmit power constrained channel

permutation information theory approach to unveil delay dynamics from time series analysis in this paper an approach to identify delay phenomena from time series is developed we show that it is possible to perform a reliable time delay identification by using quantifiers derived from information theory more precisely permutation entropy and permutation statistical complexity these quantifiers show clear extrema when the embedding delay of the symbolic reconstruction matches the characteristic time delay s of the system numerical data originating from a time delay system based on the well known mackey glass equations operating in the chaotic regime were used as test beds we show that our method is straightforward to apply and robust to additive observational and dynamical noise moreover we find that the identification of the time delay is even more efficient in a noise environment our permutation approach is also able to recover the time delay in systems with low feedback rate or high nonlinearity

linear transmit processing in mimo communications systems we examine and compare the different types of linear transmit processing for multiple input multiple output systems where we assume that the receive filter is independent of the transmit filter contrary to the joint optimization of transmit and receive filters we can identify three filter types similar to receive processing the transmit matched filter the transmit zero forcing filter and the transmit wiener filter we show that the transmit filters are based on similar optimizations as the respective receive filters with an additional constraint for the transmit power moreover the transmit wiener filter has similar convergence properties as the receive wiener filter i e it converges to the matched filter and the zero forcing filter for low and high signal to noise ratio respectively we give closed form solutions for all transmit filters and present the fundamental result that their mean square errors are equal to the errors of the respective receive filters if the information symbols and the additive noise are uncorrelated however our simulations reveal that the bit error ratio results of the transmit filters differ from the results for the respective receive filters