Complexity-entropy Causality Plane Research Articles

Exploring the interplay of intrinsic fluctuation and complexity in intracellular calcium dynamics

The concentration of intracellular calcium ion (Ca2＋) exhibits complex oscillations, including bursting and chaos, as observed experimentally. These dynamics are influenced by inherent fluctuations within cells, which serve as crucial determinants in cellular decision-making processes and fate determination. In this study, we systematically explore the interplay between intrinsic fluctuation and the complexity of various dynamic states of intracellular cytosolic Ca2＋. To investigate this interplay, we employ complexity measures such as permutation entropy and statistical complexity. Using a stochastic chemical Langevin equation, we simulate the dynamics of cytosolic Ca2＋. Our findings reveal that permutation entropy and statistical complexity effectively characterize the diverse, dynamic states of cytosolic Ca2＋ and illustrate their interactions with intrinsic fluctuation. Permutation entropy analysis elucidates that the chaotic state is more sensitive to intrinsic fluctuation than the other periodic states. Furthermore, we identify distinct states of cytosolic Ca2＋ occupying specific locations within the theoretical bounds of the complexity–entropy causality plane. These locations indicate varying complexity and information content as intrinsic fluctuation varies. When adjusting the permutation order, the statistical complexity measure for the different periodic and chaotic states exhibits peaks in an intermediate range of intrinsic fluctuation values. Additionally, we identify scale-free or fractal patterns in this intermediate range, which are further corroborated by multifractal detrended fluctuation analysis. These high-complexity states likely correspond to optimal Ca2＋ dynamics with biological significance, revealing rich and complex dynamics shaped by the interplay of intrinsic fluctuation and complexity. Our investigation enhances our understanding of the intricate regulatory mechanisms governing intracellular Ca2＋ dynamics and how intrinsic fluctuation modulates the complexity of the various dynamics that play crucial roles in biological cells.

Daily Streamflow of Argentine Rivers Analysis Using Information Theory Quantifiers.

This paper analyzes the temporal evolution of streamflow for different rivers in Argentina based on information quantifiers such as statistical complexity and permutation entropy. The main objective is to identify key details of the dynamics of the analyzed time series to differentiate the degrees of randomness and chaos. The permutation entropy is used with the probability distribution of ordinal patterns and the Jensen-Shannon divergence to calculate the disequilibrium and the statistical complexity. Daily streamflow series at different river stations were analyzed to classify the different hydrological systems. The complexity-entropy causality plane (CECP) and the representation of the Shannon entropy and Fisher information measure (FIM) show that the daily discharge series could be approximately represented with Gaussian noise, but the variances highlight the difficulty of modeling a series of natural phenomena. An analysis of stations downstream from the Yacyretá dam shows that the operation affects the randomness of the daily discharge series at hydrometric stations near the dam. When the station is further downstream, however, this effect is attenuated. Furthermore, the size of the basin plays a relevant role in modulating the process. Large catchments have smaller values for entropy, and the signal is less noisy due to integration over larger time scales. In contrast, small and mountainous basins present a rapid response that influences the behavior of daily discharge while presenting a higher entropy and lower complexity. The results obtained in the present study characterize the behavior of the daily discharge series in Argentine rivers and provide key information for hydrological modeling.

Refined composite multivariate multiscale complexity-entropy causality plane analysis for gas-liquid two-phase flow

Abstract This paper presents a refined composite multivariate multiscale complexity-entropy causality plane (RCMMCECP) to explore the dynamics features of gas–liquid two-phase flow. Firstly, we employ a series of typical nonlinear time series to confirm the effectiveness of the RCMMCECP, including seven chaotic systems, two random processes, and one periodic process. The comparison results of the proposed method and conventional multivariate multiscale complexity-entropy causality plane (MMCECP) confirm the stability performance of the proposed RCMMCECP. Above all, the RCMMCECP enhances the reliability of the statistical complexity measure over large time scales and exhibits good continuity and noise-resistant ability in multiscale analysis. Then, we employ the RCMMCECP to analyze the upstream and downstream conductance signals. The experimental results demonstrate that the RCMMCECP can characterize the change of complexity and structural stability in the gas-liquid two-phase flow evolution process, effectively revealing its dynamics features.

Precursor detection of thermoacoustic instability using statistical complexity and artificial neural network

Thermoacoustic instability (TAI) is a critical challenge for modern lean-burn combustion systems. This phenomenon is commonly undesired and should be avoided or suppressed to maintain high efficiency and structural safety. This paper proposes a methodology for categorizing combustion dynamical states and detecting the precursor of TAI. Statistical complexity of the acoustic pressure signals is captured by the complexity-entropy causality plane (CECP), and the precursor is detected by applying an artificial neural network (ANN) in CECP. The estimation provides an indicator of the proximity of the dynamical state to the onset of oscillatory instability and is well-validated in an annular combustor. It has been proven that ANN is more generalizable than the K-medoid clustering and can detect the transition ahead of those conventional methods indicated, namely, the temporal kurtosis and the root mean square. This study constitutes the demonstration of a novel framework that is particularly advantageous for detecting the onset of oscillatory instabilities of combustion systems.

Characterizing river discharge along River Niger using complexity–entropy causality plane

Characterizing river discharge along River Niger using complexity–entropy causality plane

Chaotic dynamics of the Hénon map and neuronal input-output: A comparison with neurophysiological data.

In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson's and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input-output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher's information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity-entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.

Hydrological changes caused by the construction of dams and reservoirs: The CECP analysis.

We investigated the influence of the construction of cascade dams and reservoirs on the predictability and complexity of the streamflow of the São Francisco River, Brazil, by using complexity entropy causality plane (CECP) in its standard and weighted form. We analyzed daily streamflow time series recorded in three fluviometric stations: São Francisco (upstream of cascade dams), Juazeiro (downstream of Sobradinho dam), and Pão de Açúcar station (downstream of Sobradinho and Xingó dams). By comparing the values of CECP information quantifiers (permutation entropy and statistical complexity) for the periods before and after the construction of Sobradinho (1979) and Xingó (1994) dams, we found that the reservoirs' operations changed the temporal variability of streamflow series toward the less predictable regime as indicated by higher entropy (lower complexity) values. Weighted CECP provides some finer details in the predictability of streamflow due to the inclusion of amplitude information in the probability distribution of ordinal patterns. The time evolution of streamflow predictability was analyzed by applying CECP in 2 year sliding windows that revealed the influence of the Paulo Alfonso complex (located between Sobradinho and Xingó dams), construction of which started in the 1950s and was identified through the increased streamflow entropy in the downstream Pão de Açúcar station. The other streamflow alteration unrelated to the construction of the two largest dams was identified in the upstream unimpacted São Francisco station, as an increase in the entropy around 1960s, indicating that some natural factors could also play a role in the decreased predictability of streamflow dynamics.

High short interest stocks performance during the Covid-19 crisis: an informational efficacy measure based on permutation-entropy approach

PurposeThe author examine the performance of a number of high short interest stocks along with the prices of the GameStop stock and three major stock exchange indices, particularly for the period after the eruption of the Covid-19 crisis.Design/methodology/approachWith the employment of the complexity–entropy causality plane approach, the author categorize the stock prices in terms of the level of informational efficiency.FindingsThe author reported that the efficiency level for the index of the high short interest stocks falls considerably, not only at the onset of the Covid-19 crisis but during the health crisis period at hand. This is translated into proof of less uncertainty in predicting the stock prices of these specific stocks. On the other hand, the GameStop prices exhibit the same behavior as those with the high short interest firms, but change considerably in the middle of the crisis. The reversal of the behavior, by obtaining higher informational efficiency levels, is attributed to the short squeeze frenzy that increased the price of the stock many times over. Among the stock market indices, the Dow Jones Industrial Average and the S&P 500 decreased their efficiency levels marginally, after the surge of the crisis, while the Russell 2000 index kept the level intact. The high and stable degree of randomness could be attributed to the measures taken concurrently by the Federal Reserve and the government immediately after the outbreak of the crisis.Originality/valueThis is one of the few studies that examine the impact of short selling behavior on the efficiency level of certain stocks' prices, particularly during the health public crisis. It provides an alternative approach to measuring quantitatively the degree of inefficiency and randomness.

ASSESSMENT OF SECTOR BOND, EQUITY INDICES AND GREEN BOND INDEX USING INFORMATION THEORY QUANTIFIERS AND CLUSTERS TECHNIQUES

Green bonds are financial assets similar to classic debt securities used to finance sustainable investments. Given this, they are a long-term investment alternative that effectively contributes to the planet’s future by preserving the environment and encouraging sustainable development. This research encompasses a rich dataset of equity and bond sectors, general indices, and the S&P Green Bond Index. We estimate the permutation entropy [Formula: see text], an appropriate statistical complexity measure [Formula: see text], and Fisher Information measure [Formula: see text]. Therefore, we employ these complexity measures to construct two 2D maps, the complexity-entropy causality plane ([Formula: see text] ×[Formula: see text]) and the Shannon–Fisher causality plane ([Formula: see text] ×[Formula: see text]). Also, we use the information theory quantifiers to rank these indices’ efficiency analogous to the complexity hierarchy. From a mathematical point of view, the complexity-entropy causality plane (CECP) is a map that considers the global analysis, while the SFCP is a map that simultaneously feels the global and local analysis. Our findings reveal that both 2D maps indicated the most efficient (b_info_tech) and least efficient (b_energy) assets. There are peculiarities in the ranking performed considering the information theory quantifiers used to build each map due to the mathematical distinction that underlies the construction of each map. Moreover, we applied two clustering approaches ([Formula: see text]-means and Hierarchical cluster) that categorically converged in the indication of four distinct groups, which allowed us to verify that, in an overview, equities present a unique dynamic when compared to bonds and the Green bond index.

ASSESSMENT THE PREDICTABILITY IN THE PRICE DYNAMICS FOR THE TOP 10 CRYPTOCURRENCIES: THE IMPACTS OF RUSSIA–UKRAINE WAR

This paper has investigated the predictability of the top 10 cryptocurrencies’ price dynamics, ranked by their daily market capitalization and trade volume, via the information theory quantifiers. Our analysis considers the Complexity-entropy causality plane to study the temporal evolution of the price of these cryptocurrencies and their respective locations along this 2D map, bearing in mind after and during the Russia–Ukraine war. Moreover, we apply the permutation entropy and the Jensen–Shannon statistical complexity measure to rank these cryptocurrencies similarly to a complexity hierarchy. Our findings reflect that the Russian–Ukraine war affects the informational efficiency of cryptocurrency dynamics. Specifically, the cryptocurrencies notably showed a decrease in informational inefficiency (USD-coin, Binance-USD, BNB, Dogecoin, and XRP). At the same time, the cryptocurrencies with more expressiveness for the financial market, considering the volume traded and the capitalized market, were strongly impacted, presenting an increase in informational inefficiency (Tether, Cardano, Ethereum, and Bitcoin). It clarifies the potential of cryptocurrencies to mitigate exogenous shocks and their capability to use with portfolio selection, risk diversification and herding behavior.

Generalized weighted permutation entropy.

A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods: Permutation entropy and Weighted permutation entropy. The method introduces a scaling parameter to discern the disorder and complexity of ordinal patterns with small and large fluctuations. Using this scaling parameter, the complexity-entropy causality plane is generalized to the complexity-entropy-scale causality box. Simulations conducted on synthetic series generated by stochastic, chaotic, and random processes, as well as real world data, are shown to produce unique signatures in this three dimensional representation.

LIGHTING THE POPULATIONAL IMPACT OF COVID-19 VACCINES IN BRAZIL

This paper examines the populational impact of the COVID-19 vaccinations for Brazil. Therefore, our analysis takes into account the time series of the daily number of deaths related to COVID-19 from March 17, 2020 until October 19, 2021 with 582 observations. Specifically, we apply the permutation entropy ([Formula: see text]), statistical complexity ([Formula: see text]) and Fisher information measure ([Formula: see text]) to investigate the predictability of the daily deaths for COVID-19 considering two pandemic scenarios (until and after the extreme day). Based on these complexity measures, we construct the Complexity-Entropy causality plane (CECP) and Shannon–Fisher causality plane (SFCP), which allows us to assess the disorder and estimate randomness inherent to the time series of the daily deaths for COVID-19 concerning these two pandemic scenarios. Our empirical results indicate that after the extreme day, the increase in the vaccinated population contingent led to a lower entropy, higher predictability, and lower death cases. Given this, we conclude that the COVID-19 vaccines in Brazil were a highly effective public health action. In the most extreme situation, Brazil had 4249 records of daily deaths on April 8, 2021, approximately 3.5 months after the first dose of the vaccine. After this extreme situation on April 9, 2021, the daily records of deaths decrease to a minimum of 130 deaths on October 19, 2021. Thus, there is a percentage variation of −96.44% in records of daily deaths. To the best of our knowledge, this work is the first to provide empirical evidence for the populational impact related to COVID-19 vaccines.

Complexity-Entropy Causality Plane Analysis of Air Pollution Series

In this study, we explore the subtle temporal structure of environmental data using symbolic information-theory approach. The newly developed multivariate multiscale permutation entropy and complexity-entropy causality plane methodology are applied to the six pollutants data recorded in Beijing during 2013–2016, which is a powerful tool to discriminate nonlinear deterministic and stochastic dynamics. The obtained results showed that pollutant series exhibit significant randomness and a lower level of predictability in spring and summer, and more temporal correlations in winter and fall. In addition, surrogate analysis is implemented to avoid biased conclusion. We also define the relative complexity measure of multivariate series to reflect the complexity of a system. The highest relative complexity in winter is in line with the physical behavior of the pollution phenomenon.

Complexity entropy-analysis of monthly rainfall time series in northeastern Brazil

In this work we analyze predictability and complexity of monthly rainfall temporal series recorded from 1950 to 2012, at 133 gauging stations in Pernambuco state, northeastern Brazil. To this end we use the complexity entropy causality plane (CECP) and Fisher Shannon plane (FS) formed by information quantifiers permutation entropy, permutation statistical complexity, and Fisher information measure, which serve to evaluate randomness and structural organization of the underlying process. By comparing the locations of analyzed stations in CECP and FS and performing statistical significance test, we distinguish rainfall regime in the deep inland, drier Sertão region, from the intermediate inland Agreste, and coastal, tropical humid Zona da Mata regions. We also perform time dependent CECP and FS analysis and for Sertão region identify the periods of higher entropy (lower complexity and Fisher information measure) which are related to El Niño episodes and historical droughts in northeastern Brazil. Our work represents a contribution to establishing the use of information theory based methods in climatological studies.

Transition-based complexity-entropy causality diagram: A novel method to characterize complex systems

Complexity-entropy causality plane (CECP) and ordinal transition network (OTN) are both crucial tools to reveal the characteristics of time series and distinguish complex systems. However, when the parameters of the system to be distinguished have a wide range of values, the distinguishing function of CECP is weakened. Therefore, we propose a new measure called transition Fisher information (TFI) based on the probability transition matrix in OTN. The TFI is combined with conditional entropy of ordinal patterns and complexity measure to form a novel three-dimensional graph, called transition-based complexity-entropy causality diagram(TB-CECD). These three statistics depict the complex system from different angles. Through simulation experiments, we prove that even if the parameters of complex systems are wide-ranging, the systems of different properties can be assigned to different areas of the graph. Moreover, we find that the trace of the transition probability matrix can be seen as a function of time delay and used to reflect the periodic information of the system. For applications, the proposed methods are applied to vehicle dynamic response data to diagnose periodic short-wave defects such as rail corrugation. The financial time series and Electroencephalographic (EEG) time series are also researched.

Generalized entropy plane based on multiscale weighted multivariate dispersion entropy for financial time series

Abstract In recent years, complexity-entropy causality plane, Shannon-Fisher information plane and Renyi-Tsalli entropy plane methods have been proposed to study one-dimensional nonlinear complex systems and widely applied in many fields. However, it is much less common for these definitions to extend to two-dimensional or higher-dimensional data. Dispersion entropy shows superior performance in complex system analysis. We propose the above three generalized entropy plane methods based on multivariate dispersion entropy (MDE) and weighted multivariate dispersion entropy (WMDE) to evaluate the complexity of two-dimensional data. The performance of these methods is compared by analyzing the simulated data. Applying these methods to the study of multivariate stock time series, the complexity-entropy causality plane shows more great performance, not only obtains the classification of the stock market indices, but distinguishes the development states of different stock market indices. At the same time, we also propose multiscale multivariate dispersion entropy (MMDE) and multiscale weighted multivariate dispersion entropy (MWMDE), and reveal the ordinal structure of stock market indices from the view of multiscale.

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.

The Fisher-DisEn plane: A novel approach to distinguish different complex systems

In this work, we propose the Fisher-DisEn plane by the discrete Fisher information measure and dispersion entropy to analyze complex dynamic systems. Multiple trials with different artificial chaos and noises are carried out, regarding their capability on: (i) distinguishing different levels of chaos; (ii) distinguishing different chaos; (iii) distinguishing different noise; (iv) distinguishing between chaos and noise. Compared with the original complexity-entropy causality plane, our method is more superior in extracting more subtle details to distinguish different dynamic systems. In the experiments with the financial series, our method is found to be more reasonable in discriminating stock markets from different parts of the world by making comparisons with original method.

Permutation Entropy and Statistical Complexity Analysis of Brazilian Agricultural Commodities

Agricultural commodities are considered perhaps the most important commodities, as any abrupt increase in food prices has serious consequences on food security and welfare, especially in developing countries. In this work, we analyze predictability of Brazilian agricultural commodity prices during the period after 2007/2008 food crisis. We use information theory based method Complexity/Entropy causality plane (CECP) that was shown to be successful in the analysis of market efficiency and predictability. By estimating information quantifiers permutation entropy and statistical complexity, we associate to each commodity the position in CECP and compare their efficiency (lack of predictability) using the deviation from a random process. Coffee market shows highest efficiency (lowest predictability) while pork market shows lowest efficiency (highest predictability). By analyzing temporal evolution of commodities in the complexity–entropy causality plane, we observe that during the analyzed period (after 2007/2008 crisis) the efficiency of cotton, rice, and cattle markets increases, the soybeans market shows the decrease in efficiency until 2012, followed by the lower predictability and the increase of efficiency, while most commodities (8 out of total 12) exhibit relatively stable efficiency, indicating increased market integration in post-crisis period.

Early detection of thermoacoustic combustion oscillations using a methodology combining statistical complexity and machine learning.

We conduct an experimental study on early detection of thermoacoustic combustion oscillations using a method combining statistical complexity and machine learning, including the characterization of intermittent combustion oscillations. Abrupt switching from aperiodic small-amplitude oscillations to periodic large-amplitude oscillations and vice versa appears in pressure fluctuations. The dynamic behavior of aperiodic small-amplitude pressure fluctuations represents chaos. The complexity-entropy causality plane effectively captures the subtle changes in the combustion state during a transition to well-developed combustion oscillations. The feature space of the complexity-entropy causality plane, which is obtained by a support vector machine, has potential use for detecting a precursor of combustion oscillations.