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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.

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.

Multivariate statistical monitoring methods are proven to be effective for the dynamic tobacco strip manufacturing process. However, the traditional methods are not sensitive enough to small faults and the practical tobacco processing monitoring requires further root cause of quality issues. In this regard, this study proposed a unified framework of detection-identification-tracing. This approach developed a dissimilarity canonical variable analysis (CVA), namely, it integrated the dissimilarity analysis concept into CVA, enabling the description of incipient relationship among the process variables and quality variables. We also adopted the reconstruction-based contribution to separate the potential abnormal variable and form the candidate set. The transfer entropy method was used to identify the causal relationship between variables and establish the matrix and topology diagram of causal relationships for root cause diagnosis. We applied this unified framework to the practical operation data of tobacco strip processing from a tobacco factory. The results showed that, compared with traditional contribution plot of anomaly detection, the proposed approach cannot only accurately separate abnormal variables but also locate the position of the root cause. The dissimilarity CVA proposed in this study outperformed traditional CVA in terms of sensitiveness to faults. This method would provide theoretical support for the reliable abnormal detection and diagnosis in the tobacco production process.

In this paper, we first study the evaluation framework of Granger causality between time series. Then, the multivariate time series prediction model is constructed based on transfer entropy and graph attention network. The multivariate time series prediction model architecture has causal branches with transfer entropy, and the prediction module is executed using graph attention network. Finally, the accuracy of basketball game score prediction is analyzed, as well as comparing the accuracy of the multivariate time series prediction model with other models. The number of offensive rounds in basketball games can be predicted with a high accuracy of 67.94% using the multivariate time series prediction model. For the prediction of the scoring trend of player rotation, the ABHJI combination rotating on the court is the most efficient in scoring, and the average value of scoring is as high as 85.463. The average accuracy of the TSP reaches 72.2%, and the model has high feasibility and is suitable for scoring prediction in basketball games.

AbstractUnder global warming, the acceleration of the water cycle has increased the risk of drought in the Yellow River Basin. Revealing the drought driving mechanisms in the basin and understanding the risk situation of drought have become particularly important. This paper uses wavelet analysis and transfer entropy to analyze the drought driving mechanisms. In addition, an Improved Particle Swarm Optimization (IPSO) coupled with Long Short-Term Memory (LSTM) is used for drought risk prediction. The results are as follows: (1) Hydrological drought lags behind meteorological drought by 2–3 months, and they show two main periods on different time scales, which are 5–6 months and 8–14 months, respectively. (2) Rainfall, runoff, temperature, humidity, and vapor pressure are the main drought driving factors, with rainfall and humidity having the most significant impact. (3) The IPSO-LSTM model has improved the process of selecting model parameters based on empirical experiences in the LSTM model, improving the prediction accuracy by an average of 3.1%. This paper provides a scientific basis for water resource management and drought risk assessment in the basin, to better cope with future climate challenges.

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]

For a modern satellite, there are usually thousands of telemetry parameters. How to find the root cause of the satellite anomalies using telemetry data is an important but difficult task. This paper proposes an unsupervised root cause analysis method for satellite on-orbit anomalies based on causal discovery. The method includes a component impact analysis method based on multivariate-to-one transfer entropy, which can quickly identify components that cause system anomalies; and a pruning strategy based on the change of causality are proposed to screen and identify the parameters of the components to determine the root cause of the anomalies. Simulation experiments and real case verification show that the accuracy, recall, and F1-score of the method in this paper all reach more than 80%, which is greatly improved compared with the existing methods. The case study also shows that when anomalies occur, the root cause analysis method can detect the root cause using only 4 min of anomalous information, which helps to stop the spread of anomalies more effectively. [ABSTRACT FROM AUTHOR]

Based on the monitoring data of PM2.5 concentration in 99 cities along the Yangtze River Economic Belt, the article constructed a spatial interaction network of air pollution in the Belt using transfer entropy, and analyzed the pollutant transmission direction and transmission intensity from both the overall and local perspectives. Then, in order to make full use of the spatial correlation information of urban air pollution, the article used the spatial interaction network of air pollution to improve the graph structure of T-GCN, and constructed a prediction model based on the T-GCNTE to predict the pollutant concentrations in 99 cities of the Belt. It is found that the air pollution in each city shows strong compactness, and the information transfer of the overall network is dominated by inter-regional information transfer. Moreover, T-GCNTE can capture the spatio-temporal dependence and the influence direction of the air pollution, and better results can be obtained. Based on the above conclusions, the article provides suggestions for the development of collaborative governance system of air pollution in the Belt, strengthening industrial cooperation and improving the ecological compensation mechanism. [ABSTRACT FROM AUTHOR]

This study examines the complex interaction between Financial Development (FD) and Economic Growth (EG) in Algeria from 1980 to 2020 using nonlinear modeling techniques. We apply the Non-Linear Causality test with Transfer Entropy, a novel method in this literature, to confirm the nonlinear causality from FD to EG. We also use the Nonlinear Autoregressive Distributed Lag (NARDL) model and the Cumulative Dynamic Multiplier (CDM) to establish the long-run equilibrium and the short-run dynamic relationship between FD and EG. The NARDL results support the Transfer Entropy findings and show that FD has a symmetric impact on EG in both the short and long term. Positive and negative shocks on FD affect EG similarly and the imbalance is corrected in about 6 years. This study provides useful information for policymakers and stakeholders to design policies that promote (EG) and development in Algeria by enhancing FD and mitigating shocks. JEL Codes : C45, C32, E44, O16, O53 Plain Language Summary: Finance and economy in Algeria: a stable long-term relationship with short-term shocks We wanted to know how the financial sector and the economy affect each other in Algeria over the past 40 years. We used new and advanced methods to analyze the data. We found that the financial sector and the economy have a one-way relationship that is stable in the long run but can change in the short run due to shocks. We also found that the financial sector and the economy adjust to each other in about 6 years after a shock. Our study can help policymakers and stakeholders improve the financial sector and the economy in Algeria. [ABSTRACT FROM AUTHOR]

In the past decades a connection between the financial services and technology sector has evolved into a dynamic and complex relationship. However, they were not spared from the far-reaching effects that the spread of the Covid-19 pandemic brought, each responding in a distinctive manner. This paper examines the alterations in the bidirectional information flow between the financial services and technology sectors provoked by the virus outbreak by employing the concept of transfer entropy. The results document an asymmetric and modest information flow in distribution tails prior to the pandemic, with the technology sector predominating. However, as we move towards central values, the transfer intensity decreases dramatically, even reaching negative values in the flow from the financial services sector. Following the pandemic declaration, while the technology sector maintains its superior position in information transfer, its the strength, shape, and symmetry are notably altered, with transmission doubling from the financial services sector, suggesting cross-sectoral contagion in market downturns and instability of the information transfer. [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]

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Magnetic resonance-guided focused ultrasound (MRgFUS) lesioning of the ventralis intermedius nucleus (VIM) has shown promise in treating drug-refractory essential tremor (ET). It remains unknown whether focal VIM lesions by MRgFUS have broader restorative effects on information flow within the whole-brain network of ET patients. We applied an information-theoretical approach based on intrinsic ignition and the concept of transfer entropy (TE) to assess the spatiotemporal dynamics after VIM-MRgFUS. Eighteen ET patients (mean age 71.44 years) underwent repeated 3T resting-state functional magnetic resonance imaging combined with Clinical Rating Scale for Tremor (CRST) assessments one day before (T0) and one month (T1) and six months (T2) post-MRgFUS, respectively. We observed increased whole brain ignition-driven mean integration (IDMI) at T1 (p

Grouping is a common phenomenon that occurs everywhere. The leader-follower relationship inside groups has often been qualitatively characterized in previous models using simple heuristics. However, a general method is lacking to quantitatively explain leadership in an evacuating group. To understand the evolution of single-group dynamics throughout an evacuation, we developed an extended social force model integrated with a group force. A series of single-group evacuations from a room were simulated. An information-theoretic method, transfer entropy (TE), was applied to detect predefined and undeclared leadership among evacuees. The results showed that the predefined leader was correctly detected by TE, suggesting its capability in measuring leadership based on time series of evacuees’ movement information (e.g., velocity and acceleration). When evacuees were grouped together, TE was higher than when they were alone. Leaders presented a monotonically increasing cumulative influence curve over the investigated period, whereas followers showed a diminishing tendency. We found that leadership emergence correlated with evacuees’ spatial positions. The individual located in the foremost part of the group was most likely to become a leader of those in the rear, which concurred with the experimental observations. We observed how a large group split into smaller ones with undeclared leadership during evacuation. These observations were quantitatively verified by TE results. This study provides novel insights into quantifying leadership and understanding single-group dynamics during evacuations.

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:=Xt:t∈Z and Y:=Yt: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.

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]

We evaluate causal dependencies between thirteen indices that represent large-scale climate patterns (El Nino/Southern Oscillation, the North Atlantic Oscillation, the Pacific Decadal Oscillation, etc.) using a recently proposed approach based on a linear approximation of the transfer entropy. We demonstrate that this methodology identifies causal relations that are well-known, as well as it uncovers some relations which, to the best of our knowledge, have not yet been reported in the literature. We also identify significant changes in causal dependencies that have occurred in the last three decades. [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]

Connectivity analysis using modern approaches like Granger causality, partial directed coherence and transfer entropy always demands additional statistical evaluation of the obtained measures for significance. Although for very simple linear autoregressive processes and quasilinear oscillatory activities theoretical estimates are available, the real biological signals are too complex for application of analytical approaches and surrogate data come into use. When pathological activity like epileptic seizures is studied, the question can also rise in a somewhat different way: one asks whether the studied activity is different from the normal one rather than whether connectivity exists. The similar question is also valid if one compares connectivity in different physiological states like sleep and wakefulness. Here, we study two different approaches to statistical evaluation of transfer entropy estimates in application to the study of spike–wave discharges (SWDs), the main encephalographic manifestation of absence epilepsy, registered in local field potentials of WAG/Rij rats (genetic models). The first approach is to compare distributions of the estimators for the baseline and different stages of pathological activity using traditional measures like t-test with additional corrections for multiple testing. The second approach is to make surrogate data and test whether the achieved estimators differ for surrogate series and for real ones. To support our findings and to understand the methods better, the series simulated using simple oscillatory models of epileptic activity are evaluated in the same way as the experimental data. We show that the most pronounced phenomena like bidirectional increase in coupling between frontal and parietal cortical areas during SWDs in comparison to baseline activity are considered to be significant by both approaches. But when the less expressed coupling changes are under consideration, the approach base on surrogate data provides less false positives. These results confirm that the primary outcomes of connectivity analysis for absence epilepsy (and not only it) achieved previously are valid although the statistical evaluation of the connectivity estimators was suboptimal. [ABSTRACT FROM AUTHOR]

Based on the daily stock closing price data of 14 A-share listed banks in China from January 2009 to June 2021, this paper makes a comparative analysis of the contagion effect of risks in the banking industry before and after the outbreak of COVID-19. Based on the transfer entropy method, this paper calculates the correlation network matrix of inter-bank risk contagion effect and empirically studies the contagion effect of risks in the banking industry before and after the outbreak by using social network analysis method, depicting the network structure of systemic risk contagion in Chinese banking industry. This study found that the risk of inter-bank system increased significantly after the outbreak and the key nodes of bank risk contagion have also changed before and after the outbreak; state-owned banks are less risky, joint-stock banks and local financial institutions are riskier, and the contagion effect of risks between banks is asymmetric. [ABSTRACT FROM AUTHOR]

Modulation of the amplitude of high-frequency cortical field activity locked to changes in the phase of a slower brain rhythm is known as phase-amplitude coupling (PAC). The study of this phenomenon has been gaining traction in neuroscience because of several reports on its appearance in normal and pathological brain processes in humans as well as across different mammalian species. This has led to the suggestion that PAC may be an intrinsic brain process that facilitates brain inter-area communication across different spatiotemporal scales. Several methods have been proposed to measure the PAC process, but few of these enable detailed study of its time course. It appears that no studies have reported details of PAC dynamics including its possible directional delay characteristic. Here, we study and characterize the use of a novel information theoretic measure that may address this limitation: local transfer entropy. We use both simulated and actual intracranial electroencephalographic data. In both cases, we observe initial indications that local transfer entropy can be used to detect the onset and offset of modulation process periods revealed by mutual information estimated phase-amplitude coupling (MIPAC). We review our results in the context of current theories about PAC in brain electrical activity, and discuss technical issues that must be addressed to see local transfer entropy more widely applied to PAC analysis. The current work sets the foundations for further use of local transfer entropy for estimating PAC process dynamics, and extends and complements our previous work on using local mutual information to compute PAC (MIPAC).

Organisms have evolved sensory mechanisms to extract pertinent information from their environment, enabling them to assess their situation and act accordingly. For social organisms travelling in groups, like the fish in a school or the birds in a flock, sharing information can further improve their situational awareness and reaction times. Data on the benefits and costs of social coordination, however, have largely allowed our understanding of why collective behaviours have evolved to outpace our mechanistic knowledge of how they arise. Recent studies have begun to correct this imbalance through fine-scale analyses of group movement data. One approach that has received renewed attention is the use of information theoretic (IT) tools like mutual information, transfer entropy and causation entropy, which can help identify causal interactions in the type of complex, dynamical patterns often on display when organisms act collectively. Yet, there is a communications gap between studies focused on the ecological constraints and solutions of collective action with those demonstrating the promise of IT tools in this arena. We attempt to bridge this divide through a series of ecologically motivated examples designed to illustrate the benefits and challenges of using IT tools to extract deeper insights into the interaction patterns governing group-level dynamics. We summarize some of the approaches taken thus far to circumvent existing challenges in this area and we conclude with an optimistic, yet cautionary perspective.

Objective To study the changes of heart-brain coupling indexes after cerebral ischemia in a rat model of middle cerebral artery occlusion (MCAO) and the relationship with prognosis in the early stage. Methods Twenty male SD rats(7~8 weeks old, body weight 290±25 g) were randomly divided into 2 groups (n=10): the cerebral ischemia group (MCAO group) and the control group (Sham group). Lead Ⅱ electrocardiography (ECG) and dual-channel electroencephalogram (EEG) were recorded at the baseline and 0~4 h after the surgery. Neurofunctional recovery was evaluated by neurological deficit score(NDS) via a series of behavior tests every 24 h and survival time was recorded. The heart rate variability (HRV) indicators were extracted by the collected ECG signals, including RR interval (RRI), low frequency (LF), high frequency (HF) and LF/HF ratio. The power spectrum of δ, θ, α and β waves were calculated from EEG signal. The heart-brain network was constructed based on the indicators mentioned, and the transfer entropy algorithm was used to quantify the coupling strength applied to the prognosis for survival which was analyzed and compared by the area under curve (AUC) among nodes of different networks. Results There was a bidirectional interaction between the brain and the heart, and the strength of two-way coupling increased after ischemia. There was obviously increased coupling between HRV LF and EEG δ wave. Transfer entropy (AUC=0.717, P=0.010) was superior to the HRV (AUC=0.571, P=0.404) and EEG power spectrum (AUC=0.583, P=0.329) in prognostication. Conclusion The low-frequency coupling between heart and brain enhanced after cerebral ischemia, and the coupling index of heart and brain can improve the prognostic performance.

The accurate estimation of time delays is crucial in traffic congestion analysis, as this information can be used to address fundamental questions regarding the origin and propagation of traffic congestion. However, the exact measurement of time delays during congestion remains a challenge owing to the complex propagation process between roads and high uncertainty regarding future behavior. To overcome this challenge, we propose a novel time delay estimation method for the propagation of traffic congestion due to accidents using lag-specific transfer entropy (TE). The proposed method adopts Markov bootstrap techniques to quantify uncertainty in the time delay estimator. To the best of our knowledge, our proposed method is the first to estimate time delays based on causal relationships between adjacent roads. We validated the method's efficacy using simulated data, as well as real user trajectory data obtained from a major GPS navigation system in South Korea.

The synchronicity effect between the financial market and online response for time-series forecasting is an important task with wide applications. This study combines data from the Baidu index (BDI), Google trends (GT), and transfer entropy (TE) to forecast a wide range of futures prices with a focus on China. A forecasting model based on a hybrid gray wolf optimizer (GWO), convolutional neural network (CNN), and long short-term memory (LSTM) is developed. First, Baidu and Google dual-platform search data were selected and constructed as Internet-based consumer price index (ICPI) using principal component analysis. Second, TE is used to quantify the information between online behavior and futures markets. Finally, the effective Internet-based consumer price index (ICPI) and TE are introduced into the GWO-CNN-LSTM model to forecast the daily prices of corn, soybean, polyvinyl chloride (PVC), egg, and rebar futures. The results show that the GWO-CNN-LSTM model has a significant improvement in predicting future prices. Internet-based CPI built on Baidu and Google platforms has a high degree of real-time performance and reduces the platform and language bias of the search data. Our proposed framework can provide predictive decision support for government leaders, market investors, and production activities.

Abstract How to capture the temporal evolution of synaptic weights from measures of dynamic functional connectivity between the activity of different simultaneously recorded neurons is an important and open problem in systems neuroscience. Here, we report methodological progress to address this issue. We first simulated recurrent neural network models of spiking neurons with spike timing-dependent plasticity mechanisms that generate time-varying synaptic and functional coupling. We then used these simulations to test analytical approaches that infer fixed and time-varying properties of synaptic connectivity from directed functional connectivity measures, such as cross-covariance and transfer entropy. We found that, while both cross-covariance and transfer entropy provide robust estimates of which synapses are present in the network and their communication delays, dynamic functional connectivity measured via cross-covariance better captures the evolution of synaptic weights over time. We also established how measures of information transmission delays from static functional connectivity computed over long recording periods (i.e., several hours) can improve shorter time-scale estimates of the temporal evolution of synaptic weights from dynamic functional connectivity. These results provide useful information about how to accurately estimate the temporal variation of synaptic strength from spiking activity measures.

Correlations between two time series, including the linear Pearson correlation and the nonlinear transfer entropy, have attracted significant attention. In this work, we studied the correlations between multiple stock data with the introduction of a time delay and a rolling window. In most cases, the Pearson correlation and transfer entropy share the same tendency, where a higher correlation provides more information for predicting future trends from one stock to another, but a lower correlation provides less. Considering the computational complexity of the transfer entropy and the simplicity of the Pearson correlation, using the linear correlation with time delays and a rolling window is a robust and simple method to quantify the mutual information between stocks. Predictions made by the long short-term memory method with mutual information outperform those made only with self-information when there are high correlations between two stocks.

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]

Magnetic resonance-guided focused ultrasound (MRgFUS) lesioning of the ventralis intermedius nucleus (VIM) has shown promise in treating drug-refractory essential tremor (ET). It remains unknown whether focal VIM lesions by MRgFUS have broader restorative effects on information flow within the whole-brain network of ET patients. We applied an information-theoretical approach based on intrinsic ignition and the concept of transfer entropy (TE) to assess the spatiotemporal dynamics after VIM-MRgFUS. Eighteen ET patients (mean age 71.44 years) underwent repeated 3T resting-state functional magnetic resonance imaging combined with Clinical Rating Scale for Tremor (CRST) assessments one day before (T0) and one month (T1) and six months (T2) post-MRgFUS, respectively. We observed increased whole brain ignition-driven mean integration (IDMI) at T1 (p < 0.05), along with trend increases at T2. Further, constraining to motor network nodes, we identified significant increases in information-broadcasting (bilateral supplementary motor area (SMA) and left cerebellar lobule III) and information-receiving (right precentral gyrus) at T1. Remarkably, increased information-broadcasting in bilateral SMA was correlated with relative improvement of the CRST in the treated hand. In addition, causal TE-based effective connectivity (EC) at T1 showed an increase from right SMA to left cerebellar lobule crus II and from left cerebellar lobule III to right thalamus. In conclusion, results suggest a change in information transmission capacity in ET after MRgFUS and a shift towards a more integrated functional state with increased levels of global and directional information flow. • For the first time, functional consequences of a focal VIM-lesion, are described by advanced information theory-based measures. • Information broadcasting between hubs of the tremor network is improved post-MRgFUS, correlating with tremor improvement. • VIM-MRgFUS improves global information transfer, as evidenced by increased mean integration, suggesting restorative effects. [ABSTRACT FROM AUTHOR]

The transfer entropy (TE) based causality analysis is able to provide a typical solution for fault rooting of industrial processes. However, short-term disturbances that occur during nominal operations of chemical processes are usually neglected because of the fixed time window of TE for global data distributions. Inspired by the selective attention idea, we propose attention transfer entropy (ATE) that helps to locate prominent targets. Concerning temporal features of industrial time series, prior knowledge is employed for constructing an interpretable model. We verify the reliability and effectiveness of the method with coal gasification process data. Additionally, the algorithm is compared to conventional causality analysis methods, proving that ATE enjoys excellent performances in rooting short-term disturbances with lower calculation burden. • The attention transfer entropy (ATE) with adjustable sliding windows is proposed. • The ATE-based causality analysis is suggested for short-term disturbance rooting. • The ATE algorithm is verified by data collected from a coal gasification process. [ABSTRACT FROM AUTHOR]

This study revisits stock market integration in Africa using an information‐theoretic framework that quantifies the flow of information between exchanges. We use daily return data for seven MSCI‐classified African stock exchanges between 2011 and 2021. As Bitcoin has become an important asset class on the African continent, we also explore whether this cryptocurrency confers any diversification benefits. Our method holds that stock markets are integrated if there is a significant flow of information between exchanges. The results reveal a statistically insignificant flow of information among African stock exchanges, and for the few cases in which information flow is statistically significant, the magnitudes are low. South Africa is the most influential stock market, as it transmits most of the total transfer entropy (informational value) in the system. We also observe that African stock exchanges are weakly integrated with Bitcoin. [ABSTRACT FROM AUTHOR]

Introduction: The right and left-hand motor imagery (MI) analysis based on the electroencephalogram (EEG) signal can directly link the central nervous system to a computer or a device. This study aims to identify a set of robust and nonlinear effective brain connectivity features quantified by transfer entropy (TE) to characterize the relationship between brain regions from EEG signals and create a hierarchical feature selection and classification for discrimination of right and lefthand MI tasks. Methods: TE is calculated among EEG channels as the distinctive, effective connectivity features. TE is a model-free method that can measure nonlinear effective connectivity and analyze multivariate dependent directed information flow among neural EEG channels. Then four feature subset selection methods namely relief-F, Fisher, Laplacian, and local learningbased clustering (LLCFS) algorithms are used to choose the most significant effective connectivity features and reduce redundant information. Finally, support vector machine (SVM) and linear discriminant analysis (LDA) methods are used for classification. Results: Results show that the best performance in 29 healthy subjects and 60 trials is achieved using the TE method via the Relief-F algorithm as feature selection and support vector machine (SVM) classification with 91.02% accuracy. Conclusion: The TE index and a hierarchical feature selection and classification can be useful for the discrimination of right- and left-hand MI tasks from multichannel EEG signals. [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]

This study presents a data-driven framework for modeling complex systems, with a specific emphasis on traffic modeling. Traditional methods in traffic modeling often rely on assumptions regarding vehicle interactions. Our approach comprises two steps: first, utilizing information- theoretic (IT) tools to identify interaction directions and candidate variables thus eliminating assumptions, and second, employing the sparse identification of nonlinear systems (SINDy) tool to establish functional relationships. We validate the framework’s efficacy using synthetic data from two distinct traffic models, while considering measurement noise. Results show that IT tools can reliably detect directions of interaction as well as instances of no interaction. SINDy proves instrumental in creating precise functional relationships and determining coefficients in tested models. The innovation of our framework lies in its ability to use data-driven approach to model traffic dynamics without relying on assumptions, thus offering applications in various complex systems beyond traffic.

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.

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.

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.

In the field of neuroscience, it is very important to evaluate the causal coupling characteristics between bioelectrical signals accurately and effectively. Transfer entropy is commonly used to analyze complex data, especially the causal relationship between data with non-linear, multidimensional characteristics. However, traditional transfer entropy needs to estimate the probability density function of the variable, which is computationally complex and unstable. In this paper, a new and effective method for entropy transfer is proposed, by means of applying R-vine copula function estimation. The effectiveness of R-vine copula transfer entropy is first verified on several simulations, and then applied to intermuscular coupling analysis to explore the characteristics of the intermuscular coupling network of muscles in non-fatigue and fatigue conditions. The experiment results show that as the muscle group enters the fatigue state, the community structure can be adjusted and the muscle nodes participating in the exercise are fully activated, enabling the two-way interaction between different communities. Finally, it comes to the conclusion that the proposed method can make accurate inferences about complex causal coupling. Moreover, the characteristics of the intermuscular coupling network in both non-fatigue and fatigue states can provide a new theoretical perspective for the diagnosis of neuromuscular fatigue and sports rehabilitation, which has good application value.

The accurate estimation of time delays is crucial in traffic congestion analysis, as this information can be used to address fundamental questions regarding the origin and propagation of traffic congestion. However, the exact measurement of time delays during congestion remains a challenge owing to the complex propagation process between roads and high uncertainty regarding future behavior. To overcome this challenge, we propose a novel time delay estimation method for the propagation of traffic congestion due to accidents using lag-specific transfer entropy (TE). The proposed method adopts Markov bootstrap techniques to quantify uncertainty in the time delay estimator. To the best of our knowledge, our proposed method is the first to estimate time delays based on causal relationships between adjacent roads. We validated the method's efficacy using simulated data, as well as real user trajectory data obtained from a major GPS navigation system in South Korea. [ABSTRACT FROM AUTHOR]

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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]