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Diabetic peripheral neuropathy (DPN) is a prevalent complication of chronic diabetes mellitus and has a significant impact on quality of life. DPN typically manifests itself as a symmetrical, length-dependent sensorimotor polyneuropathy with severe effects on gait. Surface electromyography (sEMG) is a valuable low-cost tool for assessing muscle activation patterns and precise identification of abnormalities. For the present study, we used information theory methods, such as cross-correlation (CC), normalized mutual information (NMI), conditional granger causality (CG-Causality), and transfer entropy (TE), to evaluate muscle network connectivity in three population groups: 33 controls (healthy volunteers, CT), 10 diabetic patients with a low risk of DPN (LW), and 17 moderate/high risk patients (MH). The results obtained indicated significant alterations in the intermuscular coupling mechanisms due to diabetes and DPN, with the TE group showing the best performance in detecting differences. The data revealed a significant increase in information transfer and muscle connectivity in the LW group over the CT group, while the MH group obtained significantly lower values for these metrics than the other two groups. These findings highlight the sEMG coupling metrics' potential to reveal neuromuscular mechanisms that could aid the development of targeted rehabilitation strategies and help monitor DPN patients. [ABSTRACT FROM AUTHOR]

Accurate runoff prediction is crucial for watershed water resource management, flood prevention, and hydropower station scheduling. Data-driven models have been increasingly applied to runoff prediction tasks and have achieved impressive results. However, existing data-driven methods may produce unreasonable predictions due to the lack of prior knowledge guidance. This study proposes a multivariate runoff prediction model that couples knowledge embedding with data-driven approaches, integrating information contained in runoff probability distributions as constraints into the data-driven model and optimizing the existing loss function with prior probability density functions (PDFs). Using the main stream in the Yellow River Basin with nine hydrological stations as an example, we selected runoff feature factors using the transfer entropy method, chose a temporal convolutional network (TCN) as the data-driven model, and optimized model parameters with the IPSO algorithm, studying univariate input models (TCN-UID), multivariable input models (TCN-MID), and the coupling model. The results indicate the following: (1) Among numerous influencing factors, precipitation, sunshine duration, and relative humidity are the key feature factors driving runoff occurrence; (2) the coupling model can effectively fit the extremes of runoff sequences, improving prediction accuracy in the training set by 6.9% and 4.7% compared to TCN-UID and TCN-MID, respectively, and by 5.7% and 2.8% in the test set. The coupling model established through knowledge embedding not only retains the advantages of data-driven models but also effectively addresses the poor prediction performance of data-driven models at extremes, thereby enhancing the accuracy of runoff predictions. [ABSTRACT FROM AUTHOR]

This study aims to employ a causal network model based on transfer entropy for the early warning of systemic risk in commodity markets. We analyzed the dynamic causal relationships of prices for 25 commodities related to China (including futures and spot prices of energy, industrial metals, precious metals, and agricultural products), validating the effect of the causal network structure among commodity markets on systemic risk. Our research results identified commodities and categories playing significant roles, revealing that industry and precious metal markets possess stronger market information transmission capabilities, with price fluctuations impacting a broader range and with greater force on other commodity markets. Under the influence of different types of crisis events, such as economic crises and the Russia–Ukraine conflict, the causal network structure among commodity markets exhibited distinct characteristics. The results of the effect of external shocks to the causal network structure of commodity markets on the entropy of systemic risk suggest that network structure indicators can warn of systemic risk. This article can assist investors and policymakers in managing systemic risk to avoid unexpected losses. [ABSTRACT FROM AUTHOR]

This paper proposes a new hybrid model for classifying stress states using EEG signals, combining multi-domain transfer entropy (TrEn) with a two-dimensional PCANet (2D-PCANet) approach. The aim is to create an automated system for identifying stress levels, which is crucial for early intervention and mental health management. A major challenge in this field lies in extracting meaningful emotional information from the complex patterns observed in EEG. Our model addresses this by initially applying independent component analysis (ICA) to purify the EEG signals, enhancing the clarity for further analysis. We then leverage the adaptability of the fractional Fourier transform (FrFT) to represent the EEG data in time, frequency, and time–frequency domains. This multi-domain representation allows for a more nuanced understanding of the brain's activity in response to stress. The subsequent stage involves the deployment of a two-layer 2D-PCANet network designed to autonomously distill EEG features associated with stress. These features are then classified by a support vector machine (SVM) to determine the stress state. Moreover, stress induction and data acquisition experiments are designed. We employed two distinct tasks known to trigger stress responses. Other stress-inducing elements that enhance the stress response were included in the experimental design, such as time limits and performance feedback. The EEG data collected from 15 participants were retained. The proposed algorithm achieves an average accuracy of over 92% on this self-collected dataset, enabling stress state detection under different task-induced conditions. [ABSTRACT FROM AUTHOR]

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X : = X t : t ∈ Z and Y : = Y t : t ∈ Z , which take values in binary alphabets. When the bivariate process (X , Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test—no causal influence—requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons. [ABSTRACT FROM AUTHOR]

This study presents a novel approach to predicting price fluctuations for U.S. sector index ETFs. By leveraging information-theoretic measures like mutual information and transfer entropy, we constructed threshold networks highlighting nonlinear dependencies between log returns and trading volume rate changes. We derived centrality measures and node embeddings from these networks, offering unique insights into the ETFs' dynamics. By integrating these features into gradient-boosting algorithm-based models, we significantly enhanced the predictive accuracy. Our approach offers improved forecast performance for U.S. sector index futures and adds a layer of explainability to the existing literature. [ABSTRACT FROM AUTHOR]

Anticipatory dynamics (AD) is unusual in that responses from an information receiver can appear ahead of triggers from the source, and direction of information flow (DIF) is needed to establish causality. Although it is believed that anticipatory dynamics is important for animals' survival, natural examples are rare. Time series (trajectories) from a pair of interacting zebrafish are used to look for the existence of AD in natural systems. In order to obtain the DIF between the two trajectories, we have made use of a special experimental design to designate information source. However, we have also used common statistical tools such as Granger causality and transfer entropy to detect DIF. In our experiments, we found that a majority of the fish pairs do not show any anticipatory behaviors and only a few pairs displayed possible AD. Interestingly, for fish in this latter group, they do not display AD all the time. Our findings suggest that the formation of schooling of fish might not need the help of AD, and new tools are needed in the detection of causality in AD system. [ABSTRACT FROM AUTHOR]

Visual scanning is achieved via head motion and gaze movement for visual information acquisition and cognitive processing, which plays a critical role in undertaking common sensorimotor tasks such as driving. The coordination of the head and eyes is an important human behavior to make a key contribution to goal-directed visual scanning and sensorimotor driving. In this paper, we basically investigate the two most common patterns in eye–head coordination: "head motion earlier than eye movement" and "eye movement earlier than head motion". We utilize bidirectional transfer entropies between head motion and eye movements to determine the existence of these two eye–head coordination patterns. Furthermore, we propose a unidirectional information difference to assess which pattern predominates in head–eye coordination. Additionally, we have discovered a significant correlation between the normalized unidirectional information difference and driving performance. This result not only indicates the influence of eye–head coordination on driving behavior from a computational perspective but also validates the practical significance of our approach utilizing transfer entropy for quantifying eye–head coordination. [ABSTRACT FROM AUTHOR]

This paper provides a methodology to better understand the relationships between different aspects of vocal fold motion, which are used as features in machine learning-based approaches for detecting respiratory infections from voice recordings. The relationships are derived through a joint multivariate analysis of the vocal fold oscillations of speakers. Specifically, the multivariate setting explores the displacements and velocities of the left and right vocal folds derived from recordings of five extended vowel sounds for each speaker (/aa/, /iy/, /ey/, /uw/, and /ow/). In this multivariate setting, the differences between the bivariate and conditional interactions are analyzed by information-theoretic quantities based on transfer entropy. Incorporation of the conditional quantities reveals information regarding the confounding factors that can influence the statistical interactions among other pairs of variables. This is demonstrated on a vector autoregressive process where the analytical derivations can be carried out. As a proof of concept, the methodology is applied on a clinically curated dataset of COVID-19. The findings suggest that the interaction between the vocal fold oscillations can change according to individuals and presence of any respiratory infection, such as COVID-19. The results are important in the sense that the proposed approach can be utilized to determine the selection of appropriate features as a supplementary or early detection tool in voice-based diagnostics in future studies. [ABSTRACT FROM AUTHOR]

A key parameter when investing is Time Horizon. One of the biggest mistakes investors make is not aligning the timeline of their goals with their investment portfolio. In other words, time horizons determine the investment portfolio you should construct. We examine which portfolios are the best for long-term investing, short-term investing, and intraday trading. This study presents a novel approach for portfolio construction based on Network Science. We use daily returns of stocks that compose the Dow Jones Industrial Average (DJIA) for a 25-year period from 1998 to 2022. Stock networks are estimated from (i) Pearson correlation (undirected linear statistical correlations), as well as (ii) Transfer Entropy (directed non-linear causal relationships). Portfolios are constructed in two main ways: (a) only four stocks are selected, depending on their centrality, with Markowitz investing weights, or (b) all stocks are selected with centrality-based investing weights. Portfolio performance is evaluated in terms of the following indicators: return, risk (total and systematic), and risk-adjusted return (Sharpe ratio and Treynor ratio). Results are compared against two benchmarks: the index DJIA, and the Markowitz portfolio based on Modern Portfolio Theory. The key findings are as follows: (1) Peripheral portfolios of low centrality stocks based on Pearson correlation network are the best in the long-term, achieving an extremely high cumulative return of around 3000% as well as high risk-adjusted return; (2) Markowitz portfolio is the safest in the long-term, while on the contrary, central portfolios of high centrality stocks based on Pearson correlation network are the riskiest; (3) In times of crisis, no portfolio is always the best. However, portfolios based on Transfer Entropy network perform better in most of the crises; (4) Portfolios of all stocks selected with centrality-based investing weights outperform in both short-term investing and intraday trading. A stock brokerage company may utilize the above findings of our work to enhance its portfolio management services. [ABSTRACT FROM AUTHOR]

Geopolitical risks have recently escalated due to increased disputes and tensions between nations worldwide. Additionally, "climate change" describes the prolonged alteration of regular weather patterns, mainly due to human activities on Earth, leading to disastrous consequences for human livelihoods, the economy, and natural ecology. This study employs a novel transfer entropy spectrum-based Fourier domain to dynamically analyze the geopolitical risk index and specific climate change factors in Saudi Arabia. Our comprehensive investigation reveals a robust bidirectional causal relationship between the geopolitical risk index and key climate change variables, including total precipitation, relative humidity, temperature, and wind speed and direction. These findings provide compelling evidence of the intricate and complex links between geopolitical concerns and climate change in the region. The study offers policymakers and scholars crucial new insights into addressing the challenges posed by geopolitical instability and climate change by uncovering these causal relationships. [ABSTRACT FROM AUTHOR]

The financial system, a complex network, operates primarily through the exchange of capital, where the role of information is critical. This study utilizes the transfer entropy method to examine the strength and direction of information flow among different capital flow time series and investigate the community structure within the transfer networks. Moreover, the spreading dynamics of the capital flow transfer networks are observed, and the importance and traveling time of each node are explored. The results imply a dominant role for the food and drink industry within the Chinese market, with increased attention towards the computer industry starting in 2014. The community structure of the capital flow transfer networks significantly differs from those constructed from stock prices, with the main sector predominantly encompassing industry leaders favored by primary funds with robust capital flow connections. The average traveling time from sectors such as food and drink, coal, and utilities to other sectors is the shortest, and the dynamic flow between these sectors displays a significant role. These findings highlight that comprehension of information flow and community structure within the financial system can offer valuable insights into market dynamics and help to identify key sectors and companies. [ABSTRACT FROM AUTHOR]

The properties of cardio-respiratory coupling (CRC) are affected by various pathological conditions related to the cardiovascular and/or respiratory systems. In heart failure, one of the most common cardiac pathological conditions, the degree of CRC changes primarily depend on the type of heart-rhythm alterations. In this work, we investigated CRC in heart-failure patients, applying measures from information theory, i.e., Granger Causality (GC), Transfer Entropy (TE) and Cross Entropy (CE), to quantify the directed coupling and causality between cardiac (RR interval) and respiratory (Resp) time series. Patients were divided into three groups depending on their heart rhythm (sinus rhythm and presence of low/high number of ventricular extrasystoles) and were studied also after cardiac resynchronization therapy (CRT), distinguishing responders and non-responders to the therapy. The information-theoretic analysis of bidirectional cardio-respiratory interactions in HF patients revealed the strong effect of nonlinear components in the RR (high number of ventricular extrasystoles) and in the Resp time series (respiratory sinus arrhythmia) as well as in their causal interactions. We showed that GC as a linear model measure is not sensitive to both nonlinear components and only model free measures as TE and CE may quantify them. CRT responders mainly exhibit unchanged asymmetry in the TE values, with statistically significant dominance of the information flow from Resp to RR over the opposite flow from RR to Resp, before and after CRT. In non-responders this asymmetry was statistically significant only after CRT. Our results indicate that the success of CRT is related to corresponding information transfer between the cardiac and respiratory signal quantified at baseline measurements, which could contribute to a better selection of patients for this type of therapy. [ABSTRACT FROM AUTHOR]

This paper presents the results of an analysis of causality detection in a multi-loop control system. The investigation focuses on application of the Transfer Entropy method, which is not commonly used during the exact construction of information and material flow pathways in the field of automation. Calculations are performed on simulated multi-loop control system data obtained from a system with a structure known a priori. The model incorporates the possibility of freely changing its parameters and of applying noise with different properties. In addition, a method for determining the entropy transfer between process variables is investigated. The fitting of different variants of the probability distribution functions to the data is crucial for effective evaluation of the Transfer Entropy approach. The obtained results allow for suggestions to be formulated with respect to choosing which probability function the transfer entropy should be based upon. Moreover, we provide a proposal for the design of a causality analysis approach that can reliably obtain information relationships. [ABSTRACT FROM AUTHOR]

The quantification of causality is vital for understanding various important phenomena in nature and laboratories, such as brain networks, environmental dynamics, and pathologies. The two most widely used methods for measuring causality are Granger Causality (GC) and Transfer Entropy (TE), which rely on measuring the improvement in the prediction of one process based on the knowledge of another process at an earlier time. However, they have their own limitations, e.g., in applications to nonlinear, non-stationary data, or non-parametric models. In this study, we propose an alternative approach to quantify causality through information geometry that overcomes such limitations. Specifically, based on the information rate that measures the rate of change of the time-dependent distribution, we develop a model-free approach called information rate causality that captures the occurrence of the causality based on the change in the distribution of one process caused by another. This measurement is suitable for analyzing numerically generated non-stationary, nonlinear data. The latter are generated by simulating different types of discrete autoregressive models which contain linear and nonlinear interactions in unidirectional and bidirectional time-series signals. Our results show that information rate causalitycan capture the coupling of both linear and nonlinear data better than GC and TE in the several examples explored in the paper. [ABSTRACT FROM AUTHOR]

Cellular response to inflammatory stimuli leads to the production of eicosanoids—prostanoids (PRs) and leukotrienes (LTs)—and signaling molecules—cytokines and chemokines—by macrophages. Quantitative modeling of the inflammatory response is challenging owing to a lack of knowledge of the complex regulatory processes involved. Cybernetic models address these challenges by utilizing a well-defined cybernetic goal and optimizing a coarse-grained model toward this goal. We developed a cybernetic model to study arachidonic acid (AA) metabolism, which included two branches, PRs and LTs. We utilized a priori biological knowledge to define the branch-specific cybernetic goals for PR and LT branches as the maximization of TNFα and CCL2, respectively. We estimated the model parameters by fitting data from three experimental conditions. With these parameters, we were able to capture a novel fourth independent experimental condition as part of the model validation. The cybernetic model enhanced our understanding of enzyme dynamics by predicting their profiles. The success of the model implies that the cell regulates the synthesis and activity of the associated enzymes, through cybernetic control variables, to accomplish the chosen biological goal. The results indicated that the dominant metabolites are PGD2 (a PR) and LTB4 (an LT), aligning with their corresponding known prominent biological roles during inflammation. Using heuristic arguments, we also infer that eicosanoid overproduction can lead to increased secretion of cytokines/chemokines. This novel model integrates mechanistic knowledge, known biological understanding of signaling pathways, and data-driven methods to study the dynamics of eicosanoid metabolism. [ABSTRACT FROM AUTHOR]

Cryptocurrencies are relatively new and innovative financial assets. They are a topic of interest to investors and academics due to their distinctive features. Whether financial or not, extraordinary events are one of the biggest challenges facing financial markets. The onset of the COVID-19 pandemic crisis, considered by some authors a "black swan", is one of these events. In this study, we assess integration and contagion in the cryptocurrency market in the COVID-19 pandemic context, using two entropy-based measures: mutual information and transfer entropy. Both methodologies reveal that cryptocurrencies exhibit mixed levels of integration before and after the onset of the pandemic. Cryptocurrencies displaying higher integration before the event experienced a decline in such link after the world became aware of the first cases of pneumonia in Wuhan city. In what concerns contagion, mutual information provided evidence of its presence solely for the Huobi Token, and the transfer entropy analysis pointed out Tether and Huobi Token as its main source. As both analyses indicate no contagion from the pandemic turmoil to these financial assets, cryptocurrencies may be good investment options in case of real global shocks, such as the one provoked by the COVID-19 outbreak. [ABSTRACT FROM AUTHOR]

The present study used transfer entropy and effective transfer entropy to examine the asymmetric information flow between exchange rates, oil, and gold. The dataset is composed of daily data covering the period of 1 January 2018 to 31 December 2021. Further, the dataset is bifurcated for analysis for before and during COVID. The bidirectional information flow is observed between EUR/USD and Oil for the whole study period unlike before COVID. However, during COVID, there was a unidirectional information flow from Oil→EUR/USD. The study finds a significant unidirectional information flow from Gold→EUR/USD. The study estimates also indicate that before COVID, the direction of information flow was from Oil→Gold. However, the direction of information flow reversed during COVID from Gold→Oil. Overall, the direction of information flow among these three variables is asymmetric. The highest transfer entropy was observed for Gold→EUR/USD among all the pairs under consideration. [ABSTRACT FROM AUTHOR]

Intelligent mechanical systems are a focused area nowadays. One of the requirements of intelligent mechanical systems is to achieve intelligent fault diagnosis through the real-time acquisition and analysis of data from various sensors installed on mechanical components. In this paper, a new fault diagnosis method is proposed to solve the problems of difficulty in integrating the fault diagnosis algorithm and locating fault parts due to the complexity of modern mechanical systems. The complexity of modern industrial intelligent systems is due to the fact that the systems are composed of multiple components and there are various connections between them. Common fault diagnosis is to design specialized fault identification algorithms for the physical characteristics of each component, and the integration of different algorithms is a major challenge for system performance. Therefore, this paper investigates a general algorithm for the fault diagnosis of complex systems using the timing characteristics of sensors and transfer entropy. The fault diagnosis algorithm is based on the prediction of multi-dimensional long time series using Autoformer, and fault identification is performed based on the deviation of the predicted value from the actual value. After fault identification, a root cause analysis method of faults based on transfer entropy is proposed. The method can locate the component where the fault occurs more accurately based on the analysis of the cause–effect relationship of each component and help maintenance personnel to troubleshoot the fault. [ABSTRACT FROM AUTHOR]

Investor sentiment transmission is significantly influential over financial markets. Prior studies do not reach a consensus about the multi-scale transmission patterns of investor sentiment. Our study proposed a composite set of methods based on wavelet, transfer entropy, and network analysis to explore the transmission patterns of investor sentiment among firms. By taking 137 new energy vehicle-related listed firms as an example, the results show three key findings: (1) the transmission of investor sentiment presents more active in the short term and takes place in a local range; (2) the transmission of investor sentiment presents patterns of continuity and growth from short term to long term; and (3) the transmission patterns of investor sentiment will have specific evolutions from short term to long term. Suggestions are offered to investors, managers and policymakers to better monitor the financial market using investor sentiment transmission. [ABSTRACT FROM AUTHOR]

Accurate workload prediction plays a key role in intelligent scheduling decisions on cloud platforms. There are massive amounts of short-workload sequences in the cloud platform, and the small amount of data and the presence of outliers make accurate workload sequence prediction a challenge. For the above issues, this paper proposes an ensemble learning method based on sample weight transfer and long short-term memory (LSTM), termed as Tr-Predictor. Specifically, a selection method of similar sequences combining time warp edit distance (TWED) and transfer entropy (TE) is proposed to select a source domain dataset with higher similarity for the target workload sequence. Then, we upgrade the basic learner of the ensemble model two-stage TrAdaBoost.R2 to LSTM in the deep model and enhance the ability of the ensemble model to extract sequence features. To optimize the weight adjustment strategy, we adopt a two-stage weight adjustment strategy and select the best weight for the learner according to the sample error and model error. Finally, the above process determines the parameters of the target model and uses the target model to predict the short-task sequences. In the experimental validation, we arbitrarily select nine sets of short-workload data from the Google dataset and three sets of short-workload data from the Alibaba cluster to verify the prediction effectiveness of the proposed algorithm. The experimental results show that compared with the commonly used cloud workload prediction methods Tr-Predictor has higher prediction accuracy on the small-sample workload. The prediction indicators of the ablation experiments show the performance gain of each part in the proposed method. [ABSTRACT FROM AUTHOR]

The relationship between three different groups of COVID-19 news series and stock market volatility for several Latin American countries and the U.S. are analyzed. To confirm the relationship between these series, a maximal overlap discrete wavelet transform (MODWT) was applied to determine the specific periods wherein each pair of series is significantly correlated. To determine if the news series cause Latin American stock markets' volatility, a one-sided Granger causality test based on transfer entropy (GC-TE) was applied. The results confirm that the U.S. and Latin American stock markets react differently to COVID-19 news. Some of the most statistically significant results were obtained from the reporting case index (RCI), A-COVID index, and uncertainty index, in that order, which are statistically significant for the majority of Latin American stock markets. Altogether, the results suggest these COVID-19 news indices could be used to forecast stock market volatility in the U.S. and Latin America. [ABSTRACT FROM AUTHOR]

This paper aims to empirically examine long memory and bi-directional information flow between estimated volatilities of highly volatile time series datasets of five cryptocurrencies. We propose the employment of Garman and Klass (GK), Parkinson's, Rogers and Satchell (RS), and Garman and Klass-Yang and Zhang (GK-YZ), and Open-High-Low-Close (OHLC) volatility estimators to estimate cryptocurrencies' volatilities. The study applies methods such as mutual information, transfer entropy (TE), effective transfer entropy (ETE), and Rényi transfer entropy (RTE) to quantify the information flow between estimated volatilities. Additionally, Hurst exponent computations examine the existence of long memory in log returns and OHLC volatilities based on simple R/S, corrected R/S, empirical, corrected empirical, and theoretical methods. Our results confirm the long-run dependence and non-linear behavior of all cryptocurrency's log returns and volatilities. In our analysis, TE and ETE estimates are statistically significant for all OHLC estimates. We report the highest information flow from BTC to LTC volatility (RS). Similarly, BNB and XRP share the most prominent information flow between volatilities estimated by GK, Parkinson's, and GK-YZ. The study presents the practicable addition of OHLC volatility estimators for quantifying the information flow and provides an additional choice to compare with other volatility estimators, such as stochastic volatility models. [ABSTRACT FROM AUTHOR]

Agents interacting with their environments, machine or otherwise, arrive at decisions based on their incomplete access to data and their particular cognitive architecture, including data sampling frequency and memory storage limitations. In particular, the same data streams, sampled and stored differently, may cause agents to arrive at different conclusions and to take different actions. This phenomenon has a drastic impact on polities—populations of agents predicated on the sharing of information. We show that, even under ideal conditions, polities consisting of epistemic agents with heterogeneous cognitive architectures might not achieve consensus concerning what conclusions to draw from datastreams. Transfer entropy applied to a toy model of a polity is analyzed to showcase this effect when the dynamics of the environment is known. As an illustration where the dynamics is not known, we examine empirical data streams relevant to climate and show the consensus problem manifest. [ABSTRACT FROM AUTHOR]

The major issue in the evolution of housing prices is risk of housing price contagion. To model this issue, we constructed housing multilayer networks using transfer entropy, generalized variance decomposition, directed minimum spanning trees, and directed planar maximally filtered graph methods, as well as China's comprehensive indices of housing price and urban real housing prices from 2012 to 2021. The results of our housing multilayer networks show that the topological indices (degree, PageRank, eigenvector, etc.) of new first-tier cities (Tianjin, Qingdao, and Shenyang) rank higher than those of conventional first-tier cities (Beijing, Shanghai, Guangzhou, and Shenzheng). [ABSTRACT FROM AUTHOR]

Featured Application: Loop regions in β2AR are critical hot spot regions, likely in other GPCRs, and can be used as potential allosteric drug targets. Two independent 1.5 μs long MD simulations were conducted for the fully atomistic model of the human beta2-adrenergic receptor (β2AR) in a complex with a G protein to investigate the signal transmission in a fully active state via mutual information and transfer entropy based on α-carbon displacements and rotameric states of backbone and side-chain torsion angles. Significant correlations between fluctuations in α-Carbon displacements were mostly detected between transmembrane (TM) helices, especially TM5 and TM6 located at each end of ICL3 and TM7. Signal transmission across β2-AR was quantified by shared mutual information; a high amount of correspondence was distinguished in almost all loop regions when rotameric states were employed. Moreover, polar residues, especially Arg, made the most contribution to signal transmission via correlated side-chain rotameric fluctuations as they were more frequently observed in loop regions than hydrophobic residues. Furthermore, transfer entropy identified all loop regions as major entropy donor sites, which drove future rotameric states of torsion angles of residues in transmembrane helices. Polar residues appeared as donor sites from which entropy flowed towards hydrophobic residues. Overall, loops in β2AR were recognized as potential allosteric hot spot regions, which play an essential role in signal transmission and should likely be used as potential drug targets. [ABSTRACT FROM AUTHOR]

In this study, causalities of COVID-19 across a group of seventy countries are analyzed with effective transfer entropy. To reveal the causalities, a weighted directed network is constructed. In this network, the weights of the links reveal the strength of the causality which is obtained by calculating effective transfer entropies. Transfer entropy has some advantages over other causality evaluation methods. Firstly, transfer entropy can quantify the strength of the causality and secondly it can detect nonlinear causal relationships. After the construction of the causality network, it is analyzed with well-known network analysis methods such as eigenvector centrality, PageRank, and community detection. Eigenvector centrality and PageRank metrics reveal the importance and the centrality of each node country in the network. In community detection, node countries in the network are divided into groups such that countries in each group are much more densely connected. [ABSTRACT FROM AUTHOR]

The relationship between the Chinese market and the US market is widely concerned by researchers and investors. This paper uses transfer entropy and local random permutation ( L R P ) surrogates to detect the information flow dynamics between two markets. We provide a detailed analysis of the relationship between the two markets using long-term daily and weekly data. Calculations show that there is an asymmetric information flow between the two markets, in which the US market significantly affects the Chinese market. Dynamic analysis based on weekly data shows that the information flow evolves, and includes three significant periods between 2004 and 2021. We also used daily data to analyze the dynamics of information flow in detail over the three periods and found that changes in the intensity of information flow were accompanied by major events affecting the market, such as the 2008 financial crisis and the COVID-19 pandemic period. In particular, we analyzed the impact of the S&P500 index on different industry indices in the Chinese market and found that the dynamics of information flow exhibit multiple patterns. This study reveals the complex information flow between two markets from the perspective of nonlinear dynamics, thereby helping to analyze the impact of major events and providing quantitative analysis tools for investment practice. [ABSTRACT FROM AUTHOR]

Valued in hundreds of billions of Malaysian ringgit, the Bursa Malaysia Financial Services Index's constituents comprise several of the strongest performing financial constituents in Bursa Malaysia's Main Market. Although these constituents persistently reside mostly within the large market capitalization (cap), the existence of the individual constituent's causal influence or intensity relative to each other's performance during uncertain or even certain times is unknown. Thus, the key purpose of this paper is to identify and analyze the individual constituent's causal intensity, from early 2018 (pre-COVID-19) to the end of the year 2021 (post-COVID-19) using Granger causality and Schreiber transfer entropy. Furthermore, network science is used to measure and visualize the fluctuating causal degree of the source and the effected constituents. The results show that both the Granger causality and Schreiber transfer entropy networks detected patterns of increasing causality from pre- to post-COVID-19 but with differing causal intensities. Unexpectedly, both networks showed that the small- and mid-caps had high causal intensity during and after COVID-19. Using Bursa Malaysia's sub-sector for further analysis, the Insurance sub-sector rapidly increased in causality as the year progressed, making it one of the index's largest sources of causality. Even after removing large amounts of weak causal intensities, Schreiber transfer entropy was still able to detect higher amounts of causal sources from the Insurance sub-sector, whilst Granger causal sources declined rapidly post-COVID-19. The method of using directed temporal networks for the visualization of temporal causal sources is demonstrated to be a powerful approach that can aid in investment decision making. [ABSTRACT FROM AUTHOR]

Predicting the values of a financial time series is mainly a function of its price history, which depends on several factors, internal and external. With this history, it is possible to build an ∊-machine for predicting the financial time series. This work proposes considering the influence of a financial series through the transfer of entropy when the values of the other financial series are known. A method is proposed that considers the transfer of entropy for breaking the ties that occur when calculating the prediction with the ∊-machine. This analysis is carried out using data from six financial series: two American, the S&P 500 and the Nasdaq; two Asian, the Hang Seng and the Nikkei 225; and two European, the CAC 40 and the DAX. This work shows that it is possible to influence the prediction of the closing value of a series if the value of the influencing series is known. This work showed that the series that transfer the most information through entropy transfer are the American S&P 500 and Nasdaq, followed by the European DAX and CAC 40, and finally the Asian Nikkei 225 and Hang Seng. [ABSTRACT FROM AUTHOR]

Highlights: An new analysis method for vibration-transmission paths based on CEEMDAN-SVD-TE is proposed. It is verified that the CEEMDAN-SVD-TE method has higher effectiveness and is superior to the single TE algorithm. The feasibility of CEEMDAN-SVD-TE in practical engineering is verified by engineering examples from the Quxue hydropower house. By using the information-transmission rate, it is identified that the lower frame foundation is an essential node for vibration transmission. The analysis of the vibration-transmission path is one of the keys to the vibration control and safety monitoring of a hydropower house, and the vibration source of the hydropower house is complex, making it more difficult to analyze the vibration-transmission path. In order to accurately identify the transmission path of the vibration in a hydropower house, an identification method for the vibration-transmission path based on CEEMDAN-SVD-TE is presented in this paper. First of all, this paper verifies that the CEEMDAN-SVD-TE method has higher effectiveness and is superior to the single transfer-entropy (TE) algorithm in information-transmission-direction identification; secondly, based on the measured field-vibration data, CEEMDAN-SVD noise-reduction technology is used to adaptively decompose the characteristics according to the signal energy; finally, the transfer-entropy theory and the information-transmission rate are used to determine the vibration-transmission path of the hydropower house. The results show that the main transmission path of the vibration caused by tailwater fluctuation is tailwater pipe (top cover measurement point)→turbine pier (stator foundation measurement point, lower frame foundation measurement point)→generator floor (generator floor measurement point). This research can offer a reference for vibration control and safety monitoring of hydropower houses, and provide a new idea for structural vibration reduction. [ABSTRACT FROM AUTHOR]

This paper addresses the subject of causality analysis using simulation data and data collected from a real control system. Simulated data includes Gaussian and Cauchy noise signals. Real-time series include various, mostly unknown distortions, like trends, oscillations, and noises. Presented research focuses on the oscillatory component in data and its propagation in multi-loop control systems. Oscillation identification is based on a deep decomposition process for control error time series. Identified periodic signals are used for further causality processing. The analysis uses the Transfer Entropy approach. This method belongs to the group of model-free methods. The determination of information pathways is conducted without any model or a priori process knowledge. The research investigates the impact of the oscillation time-series component on the Transfer Entropy causality analysis. The summary shows the observations obtained for given simulated datasets and those collected from real processes. The obtained results show that simulated analysis works properly. On the contrary, the direct application of the oscillation decomposition in real industrial cases may be misleading. Large datasets demand modification in the methodology. Different variants are tested. They show that oscillation propagation is biased in real systems and, therefore, the decomposition should be applied with caution. Furthermore, it is important to remember that the algorithm transition from simulated data to real industrial ones is demanding and should be done with the utmost care. [ABSTRACT FROM AUTHOR]

Lithosphere-ionosphere non-linear interactions create a complex system where links between different phenomena can remain hidden. The statistical correlation between West Pacific strong earthquakes and high-energy electron bursts escaping trapped conditions was demonstrated in past works. Here, it is investigated from the point of view of information. Starting from the conditional probability statistical model, which was deduced from the correlation, the Shannon entropy, the joint entropy, and the conditional entropy are calculated. Time-delayed mutual information and transfer entropy have also been calculated analytically here for binary events: by including correlations between consecutive earthquake events, and between consecutive earthquakes and electron bursts. These quantities have been evaluated for the complex dynamical system of lithosphere-ionosphere; although the expressions calculated by probabilities resulted in being valid for each pair of binary events. Peaks occurred for the same time delay as in the correlations, Δt = 1.5–3.5 h, and as well as for a new time delay, Δt = −58.5–−56.5 h, for the transfer entropy; this last is linked to EQ self-correlations from the analysis. Even if the low number of self-correlated EQs makes this second peak insignificant in this case, it is of interest to separate the non-linear contribution of the transfer entropy of binary events in the study of a complex system. [ABSTRACT FROM AUTHOR]

Cross-frequency interactions, a form of oscillatory neural activity, are thought to play an essential role in the integration of distributed information in the brain. Indeed, phase-amplitude interactions are believed to allow for the transfer of information from large-scale brain networks, oscillating at low frequencies, to local, rapidly oscillating neural assemblies. A promising approach to estimating such interactions is the use of transfer entropy (TE), a non-linear, information-theory-based effective connectivity measure. The conventional method involves feeding instantaneous phase and amplitude time series, extracted at the target frequencies, to a TE estimator. In this work, we propose that the problem of directed phase-amplitude interaction detection is recast as a phase TE estimation problem, under the hypothesis that estimating TE from data of the same nature, i.e., two phase time series, will improve the robustness to the common confounding factors that affect connectivity measures, such as the presence of high noise levels. We implement our proposal using a kernel-based TE estimator, defined in terms of Renyi's α entropy, which has successfully been used to compute single-trial phase TE. We tested our approach on the synthetic data generated through a simulation model capable of producing a time series with directed phase-amplitude interactions at two given frequencies, and on EEG data from a cognitive task designed to activate working memory, a memory system whose underpinning mechanisms are thought to include phase–amplitude couplings. Our proposal detected statistically significant interactions between the simulated signals at the desired frequencies for the synthetic data, identifying the correct direction of the interaction. It also displayed higher robustness to noise than the alternative methods. The results attained for the working memory data showed that the proposed approach codes connectivity patterns based on directed phase–amplitude interactions, that allow for the different cognitive load levels of the working memory task to be differentiated. [ABSTRACT FROM AUTHOR]

Neural oscillations are present in the brain at different spatial and temporal scales, and they are linked to several cognitive functions. Furthermore, the information carried by their phases is fundamental for the coordination of anatomically distributed processing in the brain. The concept of phase transfer entropy refers to an information theory-based measure of directed connectivity among neural oscillations that allows studying such distributed processes. Phase TE is commonly obtained from probability estimations carried out over data from multiple trials, which bars its use as a characterization strategy in brain–computer interfaces. In this work, we propose a novel methodology to estimate TE between single pairs of instantaneous phase time series. Our approach combines a kernel-based TE estimator defined in terms of Renyi's α entropy, which sidesteps the need for probability distribution computation with phase time series obtained by complex filtering the neural signals. Besides, a kernel-alignment-based relevance analysis is added to highlight relevant features from effective connectivity-based representation supporting further classification stages in EEG-based brain–computer interface systems. Our proposal is tested on simulated coupled data and two publicly available databases containing EEG signals recorded under motor imagery and visual working memory paradigms. Attained results demonstrate how the introduced effective connectivity succeeds in detecting the interactions present in the data for the former, with statistically significant results around the frequencies of interest. It also reflects differences in coupling strength, is robust to realistic noise and signal mixing levels, and captures bidirectional interactions of localized frequency content. Obtained results for the motor imagery and working memory databases show that our approach, combined with the relevance analysis strategy, codes discriminant spatial and frequency-dependent patterns for the different conditions in each experimental paradigm, with classification performances that do well in comparison with those of alternative methods of similar nature. [ABSTRACT FROM AUTHOR]

Anticipatory dynamics (AD) is unusual in that responses from an information receiver can appear ahead of triggers from the source, and direction of information flow (DIF) is needed to establish causality. Although it is believed that anticipatory dynamics is important for animals' survival, natural examples are rare. Time series (trajectories) from a pair of interacting zebrafish are used to look for the existence of AD in natural systems. In order to obtain the DIF between the two trajectories, we have made use of a special experimental design to designate information source. However, we have also used common statistical tools such as Granger causality and transfer entropy to detect DIF. In our experiments, we found that a majority of the fish pairs do not show any anticipatory behaviors and only a few pairs displayed possible AD. Interestingly, for fish in this latter group, they do not display AD all the time. Our findings suggest that the formation of schooling of fish might not need the help of AD, and new tools are needed in the detection of causality in AD system.

Visual scanning is achieved via head motion and gaze movement for visual information acquisition and cognitive processing, which plays a critical role in undertaking common sensorimotor tasks such as driving. The coordination of the head and eyes is an important human behavior to make a key contribution to goal-directed visual scanning and sensorimotor driving. In this paper, we basically investigate the two most common patterns in eye-head coordination: "head motion earlier than eye movement" and "eye movement earlier than head motion". We utilize bidirectional transfer entropies between head motion and eye movements to determine the existence of these two eye-head coordination patterns. Furthermore, we propose a unidirectional information difference to assess which pattern predominates in head-eye coordination. Additionally, we have discovered a significant correlation between the normalized unidirectional information difference and driving performance. This result not only indicates the influence of eye-head coordination on driving behavior from a computational perspective but also validates the practical significance of our approach utilizing transfer entropy for quantifying eye-head coordination.

We introduce an information-theoretical approach for analyzing information transfer between time series. Rather than using the Transfer Entropy (TE), we define and apply the Transfer Information Energy (TIE), which is based on Onicescu's Information Energy. Whereas the TE can be used as a measure of the reduction in uncertainty about one time series given another, the TIE may be viewed as a measure of the increase in certainty about one time series given another. We compare the TIE and the TE in two known time series prediction applications. First, we analyze stock market indexes from the Americas, Asia/Pacific and Europe, with the goal to infer the information transfer between them (i.e., how they influence each other). In the second application, we take a bivariate time series of the breath rate and instantaneous heart rate of a sleeping human suffering from sleep apnea, with the goal to determine the information transfer heart → breath vs. breath → heart. In both applications, the computed TE and TIE values are strongly correlated, meaning that the TIE can substitute the TE for such applications, even if they measure symmetric phenomena. The advantage of using the TIE is computational: we can obtain similar results, but faster. [ABSTRACT FROM AUTHOR]

The Kullback-Leibler (KL) divergence is a fundamental measure of information geometry that is used in a variety of contexts in artificial intelligence. We show that, when system dynamics are given by distributed nonlinear systems, this measure can be decomposed as a function of two information-theoretic measures, transfer entropy and stochastic interaction. More specifically, these measures are applicable when selecting a candidate model for a distributed system, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed acyclic graph (DAG) that characterises the unidirectional coupling between subsystems. Standard approaches to structure learning are not applicable in this framework due to the hidden variables; however, we can exploit the properties of certain dynamical systems to formulate exact methods based on differential topology. We approach the problem by using reconstruction theorems to derive an analytical expression for the KL divergence of a candidate DAG from the observed dataset. Using this result, we present a scoring function based on transfer entropy to be used as a subroutine in a structure learning algorithm. We then demonstrate its use in recovering the structure of coupled Lorenz and Rössler systems. [ABSTRACT FROM AUTHOR]

The validation of numerical models is an important component of modeling to ensure reliability of model outputs under prescribed conditions. In river deltas, robust validation of models is paramount given that models are used to forecast land change and to track water, solid, and solute transport through the deltaic network. We propose using transfer entropy (TE) to validate model results. TE quantifies the information transferred between variables in terms of strength, timescale, and direction. Using water level data collected in the distributary channels and inter-channel islands of Wax Lake Delta, Louisiana, USA, along withmodeled water level data generated for the same locations using Delft3D, we assess how well couplings between external drivers (river discharge, tides, wind) and modeled water levels reproduce the observed data couplings.We perform this operation through time using ten-day windows. Modeled and observed couplings compare well; their differences reflect the spatial parameterization of wind and roughness in the model, which prevents the model from capturing high frequency fluctuations of water level. The model captures couplings better in channels than on islands, suggesting that mechanisms of channel-island connectivity are not fully represented in the model. Overall, TE serves as an additional validation tool to quantify the couplings of the system of interest at multiple spatial and temporal scales. [ABSTRACT FROM AUTHOR]

Iterated games are an important framework of economic theory and application, at least since the original work of Axelrod's computational tournaments of the early 80's. Recent theoretical results have shown that games (the economic context) and game theory (the decision-making process) are both formally equivalent to computational logic gates. Here these results are extended to behavioural data obtained from an experiment in which rhesus monkeys sequentially played thousands of the "matching pennies" game, an empirical example similar to Axelrod's tournaments in which algorithms played against one another. The results show that the monkeys exhibit a rich variety of behaviours, both between and within subjects when playing opponents of varying complexity. Despite earlier suggestions, there is no clear evidence that the win-stay, lose-switch strategy is used, however there is evidence of non-linear strategy-based interactions between the predictors of future choices. It is also shown that there is consistent evidence across protocols and across individuals that the monkeys extract non-markovian information, i.e., information from more than just the most recent state of the game. This work shows that the use of information theory in game theory can test important hypotheses that would otherwise be more difficult to extract using traditional statistical methods. [ABSTRACT FROM AUTHOR]

Transfer entropy (TE) is a model-free approach based on information theory to capture causality between variables, which has been used for the modeling and monitoring of, and fault diagnosis in, complex industrial processes. It is able to detect the causality between variables without assuming any underlying model, but it is computationally burdensome. To overcome this limitation, a hybrid method of TE and the modified conditional mutual information (CMI) approach is proposed by using generated multi-valued alarm series. In order to obtain a process topology, TE can generate a causal map of all sub-processes and modified CMI can be used to distinguish the direct connectivity from the above-mentioned causal map by using multi-valued alarm series. The effectiveness and accuracy rate of the proposed method are validated by simulated and real industrial cases (the Tennessee-Eastman process) to capture process topology by using multi-valued alarm series. [ABSTRACT FROM AUTHOR]

Accurately determining dependency structure is critical to understanding a complex system's organization. We recently showed that the transfer entropy fails in a key aspect of this--measuring information flow--due to its conflation of dyadic and polyadic relationships. We extend this observation to demonstrate that Shannon information measures (entropy and mutual information, in their conditional and multivariate forms) can fail to accurately ascertain multivariate dependencies due to their conflation of qualitatively different relations among variables. This has broad implications, particularly when employing information to express the organization and mechanisms embedded in complex systems, including the burgeoning efforts to combine complex network theory with information theory. Here, we do not suggest that any aspect of information theory is wrong. Rather, the vast majority of its informational measures are simply inadequate for determining the meaningful relationships among variables within joint probability distributions. We close by demonstrating that such distributions exist across an arbitrary set of variables. [ABSTRACT FROM AUTHOR]

The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based on nonparametric entropy estimates for which the development of formal asymptotic theory turns out to be challenging. In this paper, we provide numerical comparisons for simulation-based tests to gain some insights into the statistical behavior of nonparametric transfer entropy-based tests. In particular, surrogate algorithms and smoothed bootstrap procedures are described and compared. We conclude this paper with a financial application to the detection of spillover effects in the global equity market. [ABSTRACT FROM AUTHOR]

Sleep is a central activity in human adults and characterizes most of the newborn infant life. During sleep, autonomic control acts to modulate heart rate variability (HRV) and respiration. Mechanisms underlying cardiorespiratory interactions in different sleep states have been studied but are not yet fully understood. Signal processing approaches have focused on cardiorespiratory analysis to elucidate this co-regulation. This manuscript proposes to analyze heart rate (HR), respiratory variability and their interrelationship in newborn infants to characterize cardiorespiratory interactions in different sleep states (active vs. quiet). We are searching for indices that could detect regulation alteration or malfunction, potentially leading to infant distress. We have analyzed inter-beat (RR) interval series and respiration in a population of 151 newborns, and followed up with 33 at 1 month of age. RR interval series were obtained by recognizing peaks of the QRS complex in the electrocardiogram (ECG), corresponding to the ventricles depolarization. Univariate time domain, frequency domain and entropy measures were applied. In addition, Transfer Entropy was considered as a bivariate approach able to quantify the bidirectional information flow from one signal (respiration) to another (RR series). Results confirm the validity of the proposed approach. Overall, HRV is higher in active sleep, while high frequency (HF) power characterizes more quiet sleep. Entropy analysis provides higher indices for SampEn and Quadratic Sample entropy (QSE) in quiet sleep. Transfer Entropy values were higher in quiet sleep and point to a major influence of respiration on the RR series. At 1 month of age, time domain parameters show an increase in HR and a decrease in variability. No entropy differences were found across ages. The parameters employed in this study help to quantify the potential for infants to adapt their cardiorespiratory responses as they mature. Thus, they could be useful as early markers of risk for infant cardiorespiratory vulnerabilities. [ABSTRACT FROM AUTHOR]

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date, very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent's next action by introducing two new classes of games: "invertible games" and "cyclical games". By explicitly expanding out the mutual information between past states and the next action we show under what circumstances the explicit values of the utility are irrelevant for iterated games and this is then related to revealed preferences theory of classical economics. These information measures are then applied to the Traveler's Dilemma game and the Prisoner's Dilemma game, the Prisoner's Dilemma being invertible, to illustrate their use. In the Prisoner's Dilemma, a novel connection is made between the computational principles of logic gates and both the structure of games and the agents' decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: "Tit-for-Tat" and "Win-Stay, Lose-Switch". [ABSTRACT FROM AUTHOR]

We study information transfer routes among cross-industry and cross-region electricity consumption data based on transfer entropy and the MST (Minimum Spanning Tree) model. First, we characterize the information transfer routes with transfer entropy matrixes, and find that the total entropy transfer of the relatively developed Guangdong Province is lower than others, with significant industrial cluster within the province. Furthermore, using a reshuffling method, we find that driven industries contain much more information flows than driving industries, and are more influential on the degree of order of regional industries. Finally, based on the Chu-Liu-Edmonds MST algorithm, we extract the minimum spanning trees of provincial industries. Individual MSTs show that the MSTs follow a chain-like formation in developed provinces and star-like structures in developing provinces. Additionally, all MSTs with the root of minimal information outflow industrial sector are of chain-form. [ABSTRACT FROM AUTHOR]

Transfer Entropy has been applied to experimental datasets to unveil causality between variables. In particular, its application to non-stationary systems has posed a great challenge due to restrictions on the sample size. Here, we have investigated the minimum sample size that produces a reliable causal inference. The methodology has been applied to two prototypical models: the linear model autoregressive-moving average and the non-linear logistic map. The relationship between the Transfer Entropy value and the sample size has been systematically examined. Additionally, we have shown the dependence of the reliable sample size and the strength of coupling between the variables. Our methodology offers a realistic lower bound for the sample size to produce a reliable outcome. [ABSTRACT FROM AUTHOR]

Supply networks existing today in many industries can behave as complex adaptive systems making them more difficult to analyze and assess. Being able to fully understand both the complex static and dynamic structures of a complex adaptive supply network (CASN) are key to being able to make more informed management decisions and prioritize resources and production throughout the network. Previous efforts to model and analyze CASN have been impeded by the complex, dynamic nature of the systems. However, drawing from other complex adaptive systems sciences, information theory provides a model-free methodology removing many of those barriers, especially concerning complex network structure and dynamics. With minimal information about the network nodes, transfer entropy can be used to reverse engineer the network structure while local transfer entropy can be used to analyze the network structure’s dynamics. Both simulated and real-world networks were analyzed using this methodology. Applying the methodology to CASNs allows the practitioner to capitalize on observations from the highly multidisciplinary field of information theory which provides insights into CASN’s self-organization, emergence, stability/instability, and distributed computation. This not only provides managers with a more thorough understanding of a system’s structure and dynamics for management purposes, but also opens up research opportunities into eventual strategies to monitor and manage emergence and adaption within the environment. [ABSTRACT FROM AUTHOR]

Complex network methodology is very useful for complex system exploration. However, the relationships among variables in complex systems are usually not clear. Therefore, inferring association networks among variables from their observed data has been a popular research topic. We propose a method, named small-shuffle symbolic transfer entropy spectrum (SSSTES), for inferring association networks from multivariate time series. The method can solve four problems for inferring association networks, i.e., strong correlation identification, correlation quantification, direction identification and temporal relation identification. The method can be divided into four layers. The first layer is the so-called data layer. Data input and processing are the things to do in this layer. In the second layer, we symbolize the model data, original data and shuffled data, from the previous layer and calculate circularly transfer entropy with different time lags for each pair of time series variables. Thirdly, we compose transfer entropy spectrums for pairwise time series with the previous layer's output, a list of transfer entropy matrix. We also identify the correlation level between variables in this layer. In the last layer, we build a weighted adjacency matrix, the value of each entry representing the correlation level between pairwise variables, and then get the weighted directed association network. Three sets of numerical simulated data from a linear system, a nonlinear system and a coupled Rossler system are used to show how the proposed approach works. Finally, we apply SSSTES to a real industrial system and get a better result than with two other methods. [ABSTRACT FROM AUTHOR]