Statistical Complexity Measure Research Articles

Consistent Quantification of Complex Dynamics via a Novel Statistical Complexity Measure.

Natural systems often show complex dynamics. The quantification of such complex dynamics is an important step in, e.g., characterization and classification of different systems or to investigate the effect of an external perturbation on the dynamics. Promising routes were followed in the past using concepts based on (Shannon’s) entropy. Here, we propose a new, conceptually sound measure that can be pragmatically computed, in contrast to pure theoretical concepts based on, e.g., Kolmogorov complexity. We illustrate the applicability using a toy example with a control parameter and go on to the molecular evolution of the HIV1 protease for which drug treatment can be regarded as an external perturbation that changes the complexity of its molecular evolutionary dynamics. In fact, our method identifies exactly those residues which are known to bind the drug molecules by their noticeable signal. We furthermore apply our method in a completely different domain, namely foreign exchange rates, and find convincing results as well.

Unknown fault feature extraction of rolling bearings under variable speed conditions based on statistical complexity measures

As the main transmission components of rotating machinery, rolling bearings have important research significance for fault diagnosis and state detection. However, the operating environment of mechanical equipment is complex, and the fault characteristic information of rolling bearings is often unknown. Through the complex transmission path, the bearing seat vibration sensor picks up the fault vibration response is weaker, and it is often submerged by strong noise. When the speed and load of rotating mechanical equipment change, the fault characteristic of rolling bearings is more obvious under variable speed conditions. The fault diagnosis problem of rolling bearings needs to be solved urgently under strong noise background, variable speed, and unknown fault characteristics. Therefore, this paper studies an unknown fault feature extraction method of variable speed rolling bearing based on statistical complexity measures (SCM). Order analysis preprocesses the variable speed vibration signal of rolling bearings. It is convenient for subsequent fault feature extraction and analysis. The SCM selects the optimal intrinsic mode function (IMF) component corresponding to the Empirical mode decomposition (EMD) decomposition, and it is also evaluated index for the optimal response of stochastic resonance. Therefore, the adaptive frequency shift stochastic resonance effectively extracts the unknown fault features of rolling bearings under strong noise background.

This Month in Anesthesiology

This Month in Anesthesiology

Characterizing dynamical transitions by statistical complexity measures based on ordinal pattern transition networks.

Complex network approaches have been recently emerging as novel and complementary concepts of nonlinear time series analysis that are able to unveil many features that are hidden to more traditional analysis methods. In this work, we focus on one particular approach: the application of ordinal pattern transition networks for characterizing time series data. More specifically, we generalize a traditional statistical complexity measure (SCM) based on permutation entropy by explicitly disclosing heterogeneous frequencies of ordinal pattern transitions. To demonstrate the usefulness of these generalized SCMs, we employ them to characterize different dynamical transitions in the logistic map as a paradigmatic model system, as well as real-world time series of fluid experiments and electrocardiogram recordings. The obtained results for both artificial and experimental data demonstrate that the consideration of transition frequencies between different ordinal patterns leads to dynamically meaningful estimates of SCMs, which provide prospective tools for the analysis of observational time series.

Information-theoretic characterization of eye-tracking signals with relation to cognitive tasks

Eye tracking is being increasingly used as a more powerful diagnosis instrument when compared with traditional pen-and-paper tests in psychopedagogy and psychology. This technology may significantly improve neurocognitive assessments in gathering indirect latent information about the subjects’ performance. However, the meaning and implications of these data are far from being fully understood. In this work, we present a comprehensive study of eye tracking time series in terms of statistical complexity measures. We registered the eye tracking movements of several subjects solving the two parts of the commonly applied Trail Making Test (TMT-A and TMT-B) and studied their Shannon entropy, disequilibrium, statistical complexity, and Fisher information with respect to three different probability distributions. The results show that these quantifiers reveal information about different features of the gaze depending on the distribution considered. As a meaningful result, we found that Fisher information in the position distribution reflects the difficulties encountered by the subject when solving the task. Such a characterization may be of interest to understand the underlying cognitive tasks performed by the subjects, and, additionally, it can serve as a source of valuable parameters to quantitatively assess how and why the subjects budget their attention, providing psychologists and psychopedagogues with more refined neuropsychological evaluation features and tools.

Information theory and Wigner crystallization: A model perspective

AbstractAccurate restricted Hartree‐Fock (RHF) wave‐functions are used to investigate information theoretic properties of the model problem of two interacting electrons confined within an infinite spherical potential of radius R. Benchmark quality calculations are performed to characterize this system via a range of information measures as a function of the tunable parameter R, across the full electron correlation regime (low to high correlation; small R to large R). Both the Shannon information entropy and a statistical complexity measure provide quantitative insight regarding the onset of the formation of a “Wigner molecule” state for this system.

Characterizing dynamics of time series via Hill-index complexity measure.

The ordinal patterns of time series provide a variety of information about the dynamic characteristics of the underlying process. With the ordinal symbolic approach, recently, a permutation-based Hill's diversity index has been proposed as a useful tool for complex system analysis. However, this method just measures the complexity of the system from the perspective of uncertainty, while the underlying structural information of the system dynamics can hardly be captured. To overcome this deficiency, this paper introduces a Hill-index complexity measure (HICM). The numerical applications suggest that the proposed HICM has greater discriminating power than the conventional statistical complexity measure (SCM). With parameter r, even between chaotic systems with extremely similar dynamics, HICM can make a clear differentiation, which can barely be achieved by SCM. Besides, HICM with appropriate r is relatively more robust against noise than SCM. In the empirical application to financial markets, the approach adopted in this paper could differentiate the stage of stock market development. Combined with multidimensional scaling based on the dynamic time wrapping distance, the method could reveal the potential similarities among the stock market dynamics and give a refined classification of these world indices.

Alternative fault detection and diagnostic using information theory quantifiers based on vibration time-waveforms from condition monitoring systems: Application to operational wind turbines

Wind turbines operate almost uninterruptedly, and their operation is often subject to harsh environments, as well as complex and dynamic loads. Fourier analysis, a standard diagnostic technique, presents some limitations regarding the use of non-stationary, non-periodic, noisy data, which is precisely the case with wind turbine data. Due to these limitations, unseen faults could progress and cause severe, and even catastrophic, failure in wind turbines. Information theory quantifiers, such as entropy, divergence, and, statistical complexity measure, are proposed to evaluate the health status of wind turbine components. In this work, this is done via the decomposition of the signal in time, frequency, and time-frequency domain, namely via Bandt and Pompe, power spectrum, and wavelet packet decomposition. Two different real data sets from operational wind turbines were characterized by the proposed methods. Results demonstrate that the proposed method can distinguish (cluster) well between the states of fault, but also presented some limitations, mainly related to the complexity of the signal from operational wind turbines. Based on these results, new methods, complementary to Fourier analysis, are proposed to be employed in wind turbine data, aiming to increase the capability of detecting faults in such a complex environment.

Complexity analysis of multiscale multivariate time series based on entropy plane via vector visibility graph

Vector visibility graph (VVG) is an algorithm that transforms multivariate time series into directed complex networks. However, at present, the researches of VVG mainly focus on its degree distribution. Considering the limitation of using the degree distribution of vector visibility graph alone to analyze the complexity of multivariate time series, we use the normalized Shannon entropy and the statistical complexity measure to analyze the complexity of multivariate time series based on the results of the degree distribution. We introduce the multivariate multiscale entropy plane to measure the dynamical complexity of multivariate systems. The effectiveness of the proposed method is validated by numerical simulation from several kinds of systems. In addition, we also observe that it is immune to different levels of noise in a wide range. Then, it is applied to evaluate the dynamic classification of financial time series from stock markets. Our results indicate that this method is effective to research the physical structures of stock markets.

An analysis of Brazilian agricultural commodities using permutation – information theory quantifiers: The influence of food crisis

Abstract We analyze predictability of selected Brazilian agricultural commodity prices (cotton, sugar, coffee, soybean and cattle) during the period 1997–2018 which encompasses the periods of agricultural commodities prices spikes between 2007 and 2011. We use information theory based methods entropy-complexity plane (HC) and entropy –Fisher information plane (HF), where Shannon entropy, statistical complexity and Fisher information measure are calculated for empirical Brandt-Pompe probability distribution of ordinal patterns. We find that coffee market shows lowest predictability (highest efficiency), while pork market shows highest predictability (lowest efficiency). By analyzing temporal evolution of efficiency index derived from Shannon entropy and Fisher information measure we observe that coffee and soybeans price series exhibit high and stable informational efficiency for all analyzed period, the efficiency of sugar market shows steady increase, while the efficiency of cattle and cotton market first decreases (until the crisis) and then increases in the post crisis period.

Taxonomy of commodities assets via complexity-entropy causality plane

Abstract This paper promotes insights based on an empirical analysis of the complex dynamics of 12 significant assets of the commodity market. We applied the Complexity-entropy causality plane (CECP) to quantify the permutation entropy and appropriate statistical complexity measures consider time series of monthly spot and futures prices of these records, which made it possible to map the commodities assets and their respective locations along the CECP. The results obtained from our procedure fitting show that the price dynamics behavior varies widely along the plane from the lower-right region, characterized by high entropy and low complexity to the middle region of the plane, marked by more complex and less entropic. It suggests that the commodities that are located in the lower-right region are closer to their fundamental prices, so they are more efficient, while the commodities start pricing lies significantly farther from the right corner are more susceptible to speculative activities and present a low degree of efficiency. We also used the Bandt-Pompe permutation entropy and the Jensen-Shannon statistical complexity to elaborate the taxonomy of this market based on the complexity hierarchy, which expands the understanding inherent of the phenomenology of this important economic aggregate and can support the work of policymakers. Additionally, we proposed a novel Macrophysics policy that can be adopted as an alternative complementary of the classical fundamentals of macroeconomics used by policymakers to develop more efficient policies.

Entropy-Based Measure of Statistical Complexity of a Game Strategy.

In this note, we introduce excess strategic entropy—an entropy-based measure of complexity of the strategy. It measures complexity and predictability of the (mixed) strategy of a player. We show and discuss properties of this measure and its possible applications.

Complexity and information measures in planar characterization of chaos and noise

In this work, we present a comprehensive assessment of the Fisher information measure and statistical complexity measures based on Euclidean distance, Wootters distance and Jensen–Shannon divergence, regarding their abilities to (planar-) distinguish between/among (1) chaos and periodicity; (2) different degrees of periodicities; (3) different chaotic regimes; and (4) chaos and noise, and characterize delay dynamics. The Bandt–Pompe approach is used to build up the probability space to generate the entropy-complexity/information plane. The effect of embedding parameters on the evaluation is also considered. Within this framework, complexity measures based on the Wootters distance and Jensen–Shannon divergence are superior to the Fisher information measure in capturing subtle details of chaotic dynamics. The Fisher information measure shows advantages in robustness to additive noises and in planar-behavior representation of chaos and noise. Moreover, all measures are able to properly characterize the intrinsic delay dynamics of chaotic and stochastic systems. Nevertheless, the complexity measure based on the Euclidean distance is not valid by definition, thus, not applicable at any cases.

The implementation of ring oscillator based PUF designs in Field Programmable Gate Arrays using of different challenge

Physically Unclonable Functions (PUFs) are the components of integrated circuits that produce sign, peculiar to each chip, based on the uncontrollable processes that occur during integrated circuit manufacture. There are various use areas of Physically Unclonable Functions circuits such as authentication, key generation and random number generation. Secure key generation in cryptography depends on the fact the random numbers produced are true random numbers. There are numerous methods to generate true random numbers such as thermal noise, anthropogenic interactions and ring oscillator. In order to use the random numbers produced in the article in the field of cryptography, a random number generator based on a ring oscillator (RO)-based Physically Unclonable Functions has been used in an Field Programmable Gate Array environment. Challenges that have periodic and non-periodic structures are used with the aim of increasing the randomness of acquired random numbers and preventing the attacks that Physically Unclonable Functions are exposed to. The statistical qualities of responses produced by these challenges are examined. The responses produced were subject to a statistical test (NIST), a statistical complexity measure (SCM), auto correlation and scale index. The statistical test results shows that the proposed system produces successful results.

Application of Information and Complexity Measures to Neutron Stars Structure

We apply several information and statistical complexity measures to neutron stars structure. Neutron stars is a classical example where the gravitational field and quantum behaviour are combined and produce a macroscopic dense object. We concentrate our study on the connection between complexity and neutron star properties, like maximum mass and the corresponding radius, applying a specific set of realistic equation of states. Moreover, the effect of the strength of the gravitational field on the neutron star structure and consequently on the complexity measure is also investigated. It is seen that neutron stars, consistent with astronomical observations so far, are ordered systems (low complexity), which cannot grow in complexity as their mass increases. This is a result of the interplay of gravity, the short-range nuclear force and the very short-range weak interaction.

Feature Extraction of Ship-Radiated Noise Based on Intrinsic Time-Scale Decomposition and a Statistical Complexity Measure

Extracting effective features from ship-radiated noise is an important way to improve the detection and recognition performance of passive sonar. Complexity features of ship-radiated noise have attracted increasing amounts of attention. However, the traditional definition of complexity based on entropy (information stored in the system) is not accurate. To this end, a new statistical complexity measure is proposed in this paper based on spectrum entropy and disequilibrium. Since the spectrum features are unique to the class of the ship, our method can distinguish different ships according to their location in the two-dimensional plane composed of complexity and spectrum entropy (CSEP). To weaken the influence of ocean ambient noise, the intrinsic time-scale decomposition (ITD) is applied to preprocess the data in this study. The effectiveness of the proposed method is validated through a classification experiment of four types of marine vessels. The recognition rate of the ITD-CSEP methodology achieved 94%, which is much higher than that of traditional feature extraction methods. Moreover, the ITD-CSEP is fast and parameter free. Hence, the method can be applied in the real time processing practical applications.

A space transformational crow search algorithm for optimization problems

New and efficient meta-heuristic algorithms are always in demand to solve real world optimization problems due to its exploiting capability in the search domain to generate the global optimal solution. Crow search algorithm (CSA) is one of the latest meta-heuristic algorithms introduced in the literature to solve optimization tasks. The clever behaviour of crows attracted the researchers to think how to achieve a better optimization by using crow as a base element. Like other optimization algorithms, the CSA suffers with local optima and stagnation problem. In addition, for complex real world problems, CSA has not sufficient exploration capability. Therefore, in the current work, an attempt is made to enhance the explorative behaviour of the CSA by combining the space transform search (STS) method. The proposed algorithm is named as STS-CSA. The proposed STS-CSAintegrates space transformation search technique and computes the solution in current search space and transformed search space simultaneously to generate solutions that is closer to global optimum solution. To assess the performance in solving optimization problems, STS-CSA has been evaluated by applying standard IEEE CEC 2017 benchmark functions. Three real-world engineering problems are also verified to assess the effectiveness of the proposed algorithm in solving the practical problems. The performed analysis such as statistical measure, convergence analysis and complexity measure reveal that the proposed method is reliable and efficient in solving practical optimization problems.

A nonlinear matter-field Hamiltonian analyzed with Renyi and Tsallis statistics

We study the dynamics of a nonlinear matter-field system, using as tools 1) entropic and 2) statistical complexity measures. For 1) we mean here Renyi and Tsallis measures and for 2) the Jensen associated complexities. Our goal is to attain some clarity regarding features that could not be successfully tackled in previous similar work that employs Boltzmann–Gibbs–Shannon and Tsallis measures. The new tools allow for a determination of statistical complexity maxima, no accessible in previous efforts. Other kind of results acquire rotund robustness in being encountered in three distinct statistical scenarios.

Physicochemical Properties and Complexity of Amino Acids beyond Our Biosphere: Analysis of the Isoleucine Group from Meteorites

Understanding the physicochemical properties of biomolecules and how these properties drive the emergence of complexity in the assembly/condensation of such systems is important for understanding a variety of reactions taking place in astrophysical environments, in particular those where polymerization processes occur on mineral surfaces or solid organic matter form in cold-chemistry processes. Here, a computational study of the structural and electronic properties of the gas and condensed phases of the isoleucine group of amino acids, found with large enantiomeric excess in Antarctic meteorites, is presented. An analysis of a statistical complexity measure related to their electronic properties, of the degree of chirality, and of the H-bond patterns is also reported. The results, based on Density Functional Theory, Many Body Perturbation Theory, and Moller–Plesset perturbation theory, show that a) the condensed amino acids keep reminiscence of structural and electronic properties of the gas phase molecules, b) the proteinogenic l-isoleucine gains in complexity and chirality upon condensation, contrary to its diastereomer, which is absent in living systems, and c) the complexity based on electronic properties can contrast with the notion of structural/geometrical complexity. The findings suggest that future scoring strategies of organic molecules should rely on both structural/geometrical molecular complexity and on the electronic properties, which in different states of matter are determined by other degrees of freedom (configurational or chiral) to a different extent, as well as on information storage capability of self-assembly configurations constrained by an atomistic chemistry perspective.

Complexity study of [formula omitted]-deformed quantum harmonic oscillator

The statistical complexity measure defined by López-Ruiz, Mancini, and Calbet is reported for a single particle under q-deformed quantum harmonic oscillator. It is found that q-deformation leads to typically a different behavior in complexity. An interesting variation appears in the exponential Shannon information entropy and disequilibrium. The product of these, which defines the statistical complexity are reported and discussed. It is shown that the deformation parameter q can be used to tune the statistical complexity of the quantum harmonic oscillator.