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Keywords = instantaneous causality

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19 pages, 1847 KiB  
Article
Real-Time Wave Energy Converter Control Using Instantaneous Frequency
by Inyong Kim, Ted K. A. Brekken, Solomon Yim, Brian Johnson, Yue Cao and Pranav Chandran
Appl. Sci. 2025, 15(9), 4889; https://doi.org/10.3390/app15094889 - 28 Apr 2025
Viewed by 427
Abstract
Wave Energy Converters (WECs) rely on effective Power Take-Off (PTO) control strategies to maximize energy absorption under dynamic sea conditions. Traditional hydrodynamic modeling techniques may require computationally intensive convolution calculations, making real-time control implementation challenging. This paper presents an alternative approach by leveraging [...] Read more.
Wave Energy Converters (WECs) rely on effective Power Take-Off (PTO) control strategies to maximize energy absorption under dynamic sea conditions. Traditional hydrodynamic modeling techniques may require computationally intensive convolution calculations, making real-time control implementation challenging. This paper presents an alternative approach by leveraging instantaneous frequency estimation to dynamically adjust PTO damping in response to varying wave frequencies. Two real-time frequency estimation methods are explored: the Hilbert Transform (HT) and Phase-Locked Loop (PLL). The Hilbert Transform method provides accurate frequency tracking but introduces a delayed response due to its dependence on causal data. Conversely, the PLL approach demonstrates strong potential in frequency tracking but requires careful gain tuning, particularly in complex sea states. Comparative evaluations across multiple test cases—including sinusoidal variations, amplitude steps, frequency step changes, and real-world JONSWAP spectrum waves—highlight the strengths and limitations of each method. The two different PTO control techniques across the various frequency estimation methods were tested under real-sea states using a state-space model of a point-absorbing Wave Energy Converter. The Capture Width Ratio (CWR) is used as a performance metric, with results showing that the HT achieves a 10.6% improvement, while the PLL estimation yields a 0.9% improvement relative to the fixed parameter control baseline. These results highlight the effectiveness of real-time frequency estimation in improving energy absorption compared to static control parameters. Full article
(This article belongs to the Special Issue Dynamics and Control with Applications to Ocean Renewables)
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27 pages, 4705 KiB  
Article
High-Precision Analysis Using μPMU Data for Smart Substations
by Kyung-Min Lee and Chul-Won Park
Energies 2024, 17(19), 4907; https://doi.org/10.3390/en17194907 - 30 Sep 2024
Cited by 1 | Viewed by 940
Abstract
This paper proposes a correction technique for bad data and high-precision analysis based on micro-phasor measurement unit (μPMU) data for a stable and reliable smart substation. First, a high-precision wide-area monitoring system (WAMS) with 35 μPMUs installed at Korea’s Yeonggwang substation, which is [...] Read more.
This paper proposes a correction technique for bad data and high-precision analysis based on micro-phasor measurement unit (μPMU) data for a stable and reliable smart substation. First, a high-precision wide-area monitoring system (WAMS) with 35 μPMUs installed at Korea’s Yeonggwang substation, which is connected to renewable energy sources (RESs), is introduced. Time-synchronized μPMU data are collected through the phasor data concentrator (PDC). A pre-processing program is implemented and utilized to integrate the raw data of each μPMU into a single comma-separated values (CSV) snapshot file based on the Timetag. After presenting the technique for identification and correction of event, duplicate, and spike bad data of μPMU, causal relationships are confirmed through the voltage and current fluctuations for a total of five states, such as T/L fault, tap-up, tap-down, generation, and generation shutdown. Additionally, the difference in active power between the T/L and the secondary side of the M.Tr is compared, and the fault ride through (FRT) regulations, when the fault in wind power generation (WP), etc., occurred, is analyzed. Finally, a statistical analysis, such as boxplot and kernel density, based on the instantaneous voltage fluctuation rate (IVFR) is conducted. As a result of the simulation evaluation, the proposed correction technique and precise analysis can accurately identify various phenomena in substations and reliably estimate causal relationships. Full article
(This article belongs to the Special Issue Condition Monitoring of Power System Components 2024)
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18 pages, 5361 KiB  
Article
Mining Delay Propagation Causality within an Airport Network from Historical Data
by Dan Zhu, Huawei Wang and Xianghua Tan
Aerospace 2024, 11(7), 533; https://doi.org/10.3390/aerospace11070533 - 28 Jun 2024
Cited by 1 | Viewed by 1328
Abstract
Airport networks are interconnected through flight routes, with delays at upstream airports leading to delays at downstream airports, thus causing delay propagation. Exploring the mechanisms of delay propagation in airport networks provides scientific insights for managing and controlling delays in aviation systems. Existing [...] Read more.
Airport networks are interconnected through flight routes, with delays at upstream airports leading to delays at downstream airports, thus causing delay propagation. Exploring the mechanisms of delay propagation in airport networks provides scientific insights for managing and controlling delays in aviation systems. Existing methods, such as Granger causality tests and transfer entropy, must be revised to address the nonlinear causal relationships of delays in airport networks. So, this paper proposes a causality mining method for delay propagation in airport networks based on partial correlation-based multivariate conditional independence (PCMCI). This method comprehensively considers all airports and causality mining in two stages. The first stage uses conditional independence tests to obtain the parent node set of the target airport, which includes both true and false causal relationships. The second stage employs instantaneous conditional independence tests to eliminate false causal relationships and obtain test statistics representing the strength of causality. Based on historical delay data from US airports over a year, the experimental results show that multiple factors cause delay propagation in airport networks rather than a single causal relationship. The scope of delay propagation is limited, mainly affecting a few airports closely connected to it. Delays at airports with small flight volumes are more likely to propagate. Few airport pairs in the network mutually propagate delays and, often, delays at airports affected by a particular airport’s delay also exhibit causal relationships with each other. This method provides a new perspective for deepening the understanding of delay propagation mechanisms in airport networks. Full article
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11 pages, 25015 KiB  
Article
Study on the Mechanism of Natural Gas Hydrate Decomposition and Seabed Seepage Triggered by Mass Transport Deposits
by Pengqi Liu, Wei Zhang, Shuang Mao, Pibo Su, Huaizhen Chen and Liguo Hu
J. Mar. Sci. Eng. 2024, 12(4), 646; https://doi.org/10.3390/jmse12040646 - 12 Apr 2024
Cited by 1 | Viewed by 1412
Abstract
Previous studies indicate that mass transport deposits are related to the dynamic accumulation of natural gas hydrates and gas leakage. This research aims to elucidate the causal mechanism of seabed seepage in the western region of the southeastern Qiongdongnan Basin through the application [...] Read more.
Previous studies indicate that mass transport deposits are related to the dynamic accumulation of natural gas hydrates and gas leakage. This research aims to elucidate the causal mechanism of seabed seepage in the western region of the southeastern Qiongdongnan Basin through the application of seismic interpretation and attribute fusion techniques. The mass transport deposits, bottom simulating reflector, submarine mounds, and other phenomena were identified through seismic interpretation techniques. Faults and fractures were identified by utilizing variance attribute analysis. Gas chimneys were identified using instantaneous frequency attribute analysis. Free gas and paleo-seepage points were identified using sweetness attributes, enabling the analysis of fluid seepage pathways and the establishment of a seepage evolution model. Research has shown that in areas where the mass transport deposits develop thicker layers, there is a greater uplift of the bottom boundary of the gas hydrate stability zone, which can significantly alter the seafloor topography. Conversely, the opposite is true. The research indicates that the upward migration of the gas hydrate stability zone, induced by the mass transport deposits in the study area, can result in the rapid decomposition of gas hydrates. The gas generated from the decomposition of gas hydrates is identified as the principal factor responsible for inducing seabed seepage. Moderate- and low-speed natural gas seepage can create spiny seamounts and domed seamounts, respectively. Full article
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59 pages, 89375 KiB  
Article
Information Geometry Theoretic Measures for Characterizing Neural Information Processing from Simulated EEG Signals
by Jia-Chen Hua, Eun-jin Kim and Fei He
Entropy 2024, 26(3), 213; https://doi.org/10.3390/e26030213 - 28 Feb 2024
Cited by 3 | Viewed by 1510
Abstract
In this work, we explore information geometry theoretic measures for characterizing neural information processing from EEG signals simulated by stochastic nonlinear coupled oscillator models for both healthy subjects and Alzheimer’s disease (AD) patients with both eyes-closed and eyes-open conditions. In particular, we employ [...] Read more.
In this work, we explore information geometry theoretic measures for characterizing neural information processing from EEG signals simulated by stochastic nonlinear coupled oscillator models for both healthy subjects and Alzheimer’s disease (AD) patients with both eyes-closed and eyes-open conditions. In particular, we employ information rates to quantify the time evolution of probability density functions of simulated EEG signals, and employ causal information rates to quantify one signal’s instantaneous influence on another signal’s information rate. These two measures help us find significant and interesting distinctions between healthy subjects and AD patients when they open or close their eyes. These distinctions may be further related to differences in neural information processing activities of the corresponding brain regions, and to differences in connectivities among these brain regions. Our results show that information rate and causal information rate are superior to their more traditional or established information-theoretic counterparts, i.e., differential entropy and transfer entropy, respectively. Since these novel, information geometry theoretic measures can be applied to experimental EEG signals in a model-free manner, and they are capable of quantifying non-stationary time-varying effects, nonlinearity, and non-Gaussian stochasticity presented in real-world EEG signals, we believe that they can form an important and powerful tool-set for both understanding neural information processing in the brain and the diagnosis of neurological disorders, such as Alzheimer’s disease as presented in this work. Full article
(This article belongs to the Special Issue Entropy Applications in Electroencephalography)
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16 pages, 2855 KiB  
Article
Energy Consumption Minimization in Unmanned Aerial Vehicle-Enabled Secure Wireless Sensor Networks
by Xufei Ding, Wen Tian, Guangjie Liu and Xiaopeng Ji
Sensors 2023, 23(23), 9411; https://doi.org/10.3390/s23239411 - 26 Nov 2023
Cited by 2 | Viewed by 1383
Abstract
In wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs) are considered an effective data collection tool. In this paper, we investigate the energy-efficient data collection problem in a UAV-enabled secure WSN without knowing the instantaneous channel state information of the eavesdropper (Eve). Specifically, [...] Read more.
In wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs) are considered an effective data collection tool. In this paper, we investigate the energy-efficient data collection problem in a UAV-enabled secure WSN without knowing the instantaneous channel state information of the eavesdropper (Eve). Specifically, the UAV collected the information from all the wireless sensors at the scheduled time and forward it to the fusion center while Eve tries to eavesdrop on this confidential information from the UAV. To surmount this intractable and convoluted mixed-integer non-convex problem, we propose an efficient iterative optimization algorithm using the block coordinate descent (BCD) method to minimize the maximum energy consumption of the ground sensor nodes (GSNs) under the constraints of secrecy outage probability (SOP), connection outage probability (COP), minimum secure data, information causality, and UAV trajectory. Numerical results demonstrate the superiority of the algorithm we proposed in energy consumption and secrecy rate compared with other schemes. Full article
(This article belongs to the Section Communications)
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12 pages, 2209 KiB  
Article
Open Hardware Implementation of Real-Time Phase and Amplitude Estimation for Neurophysiologic Signals
by José Ángel Ochoa, Irene Gonzalez-Burgos, María Jesús Nicolás and Miguel Valencia
Bioengineering 2023, 10(12), 1350; https://doi.org/10.3390/bioengineering10121350 - 23 Nov 2023
Cited by 1 | Viewed by 1839
Abstract
Adaptive deep brain stimulation (aDBS) is a promising concept in the field of DBS that consists of delivering electrical stimulation in response to specific events. Dynamic adaptivity arises when stimulation targets dynamically changing states, which often calls for a reliable and fast causal [...] Read more.
Adaptive deep brain stimulation (aDBS) is a promising concept in the field of DBS that consists of delivering electrical stimulation in response to specific events. Dynamic adaptivity arises when stimulation targets dynamically changing states, which often calls for a reliable and fast causal estimation of the phase and amplitude of the signals. Here, we present an open-hardware implementation that exploits the concepts of resonators and Hilbert filters embedded in an open-hardware platform. To emulate real-world scenarios, we built a hardware setup that included a system to replay and process different types of physiological signals and test the accuracy of the instantaneous phase and amplitude estimates. The results show that the system can provide a precise and reliable estimation of the phase even in the challenging scenario of dealing with high-frequency oscillations (~250 Hz) in real-time. The framework might be adopted in neuromodulation studies to quickly test biomarkers in clinical and preclinical settings, supporting the advancement of aDBS. Full article
(This article belongs to the Section Biosignal Processing)
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13 pages, 380 KiB  
Article
Superluminal Local Operations in Quantum Field Theory: A Ping-Pong Ball Test
by Albert Much and Rainer Verch
Universe 2023, 9(10), 447; https://doi.org/10.3390/universe9100447 - 11 Oct 2023
Cited by 3 | Viewed by 1817
Abstract
It is known that, in quantum field theory, localized operations, e.g., given by unitary operators in local observable algebras, may lead to non-causal, or superluminal, state changes within their localization region. In this article, it is shown that, both in quantum field theory [...] Read more.
It is known that, in quantum field theory, localized operations, e.g., given by unitary operators in local observable algebras, may lead to non-causal, or superluminal, state changes within their localization region. In this article, it is shown that, both in quantum field theory as well as in classical relativistic field theory, there are localized operations which correspond to “instantaneous” spatial rotations (leaving the localization region invariant) leading to superluminal effects within the localization region. This shows that “impossible measurement scenarios” which have been investigated in the literature, and which rely on the presence of localized operations that feature superluminal effects within their localization region, do not only occur in quantum field theory, but also in classical field theory. Full article
(This article belongs to the Special Issue The Physics of Time Travel)
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14 pages, 2105 KiB  
Article
How a Subclinical Unilateral Vestibular Signal Improves Binocular Vision
by Frédéric Xavier, Emmanuelle Chouin, Véronique Serin-Brackman and Alexandra Séverac Cauquil
J. Clin. Med. 2023, 12(18), 5847; https://doi.org/10.3390/jcm12185847 - 8 Sep 2023
Cited by 3 | Viewed by 1436
Abstract
The present study aimed to determine if an infra-liminal asymmetric vestibular signal could account for some of the visual complaints commonly encountered in chronic vestibular patients. We used infra-liminal galvanic vestibular stimulation (GVS) to investigate its potential effects on visuo-oculomotor behavior. A total [...] Read more.
The present study aimed to determine if an infra-liminal asymmetric vestibular signal could account for some of the visual complaints commonly encountered in chronic vestibular patients. We used infra-liminal galvanic vestibular stimulation (GVS) to investigate its potential effects on visuo-oculomotor behavior. A total of 78 healthy volunteers, 34 aged from 20 to 25 years old and 44 aged from 40 to 60 years old, were included in a crossover study to assess the impact of infra-liminal stimulation on convergence, divergence, proximal convergence point, and stereopsis. Under GVS stimulation, a repeated measures ANOVA showed a significant variation in near convergence (p < 0.001), far convergence (p < 0.001), and far divergence (p = 0.052). We also observed an unexpected effect of instantaneous blocking of the retest effect on the far divergence measurement. Further investigations are necessary to establish causal relationships, but GVS could be considered a behavioral modulator in non-pharmacological vestibular therapies. Full article
(This article belongs to the Special Issue Molecular and Cellular Mechanisms in Vestibular Disorders)
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25 pages, 2869 KiB  
Article
Detecting Nonlinear Interactions in Complex Systems: Application in Financial Markets
by Akylas Fotiadis, Ioannis Vlachos and Dimitris Kugiumtzis
Entropy 2023, 25(2), 370; https://doi.org/10.3390/e25020370 - 17 Feb 2023
Cited by 6 | Viewed by 3110
Abstract
Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point [...] Read more.
Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point detection may not be sensitive to it. In this article, we present a novel scheme for detecting structural breaks through the occurrence or vanishing of nonlinear causal relationships in a complex system. A significance resampling test was developed for the null hypothesis (H0) of no nonlinear causal relationships using (a) an appropriate Gaussian instantaneous transform and vector autoregressive (VAR) process to generate the resampled multivariate time series consistent with H0; (b) the modelfree Granger causality measure of partial mutual information from mixed embedding (PMIME) to estimate all causal relationships; and (c) a characteristic of the network formed by PMIME as test statistic. The significance test was applied to sliding windows on the observed multivariate time series, and the change from rejection to no-rejection of H0, or the opposite, signaled a non-trivial change of the underlying dynamics of the observed complex system. Different network indices that capture different characteristics of the PMIME networks were used as test statistics. The test was evaluated on multiple synthetic complex and chaotic systems, as well as on linear and nonlinear stochastic systems, demonstrating that the proposed methodology is capable of detecting nonlinear causality. Furthermore, the scheme was applied to different records of financial indices regarding the global financial crisis of 2008, the two commodity crises of 2014 and 2020, the Brexit referendum of 2016, and the outbreak of COVID-19, accurately identifying the structural breaks at the identified times. Full article
(This article belongs to the Special Issue Granger Causality and Transfer Entropy for Financial Networks)
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23 pages, 3033 KiB  
Article
Emotional Imagery Influences the Adaptive Force in Young Women: Unpleasant Imagery Reduces Instantaneously the Muscular Holding Capacity
by Laura V. Schaefer, Silas Dech, Lara L. Wolff and Frank N. Bittmann
Brain Sci. 2022, 12(10), 1318; https://doi.org/10.3390/brainsci12101318 - 29 Sep 2022
Cited by 6 | Viewed by 2374
Abstract
The link between emotions and motor function has been known for decades but is still not clarified. The Adaptive Force (AF) describes the neuromuscular capability to adapt to increasing forces and was suggested to be especially vulnerable to interfering inputs. This study investigated [...] Read more.
The link between emotions and motor function has been known for decades but is still not clarified. The Adaptive Force (AF) describes the neuromuscular capability to adapt to increasing forces and was suggested to be especially vulnerable to interfering inputs. This study investigated the influence of pleasant and unpleasant food imagery on the manually assessed AF of elbow and hip flexors objectified by a handheld device in 12 healthy women. The maximal isometric AF was significantly reduced during unpleasant vs. pleasant imagery and baseline (p < 0.001, dz = 0.98–1.61). During unpleasant imagery, muscle lengthening started at 59.00 ± 22.50% of maximal AF, in contrast to baseline and pleasant imagery, during which the isometric position could be maintained mostly during the entire force increase up to ~97.90 ± 5.00% of maximal AF. Healthy participants showed an immediately impaired holding function triggered by unpleasant imagery, presumably related to negative emotions. Hence, AF seems to be suitable to test instantaneously the effect of emotions on motor function. Since musculoskeletal complaints can result from muscular instability, the findings provide insights into the understanding of the causal chain of linked musculoskeletal pain and mental stress. A case example (current stress vs. positive imagery) suggests that the approach presented in this study might have future implications for psychomotor diagnostics and therapeutics. Full article
(This article belongs to the Section Sensory and Motor Neuroscience)
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8 pages, 431 KiB  
Article
Observations of Bell Inequality Violations with Causal Isolation between Source and Detectors
by Marc Jean Jose Fleury
Entropy 2022, 24(9), 1230; https://doi.org/10.3390/e24091230 - 1 Sep 2022
Cited by 2 | Viewed by 2789
Abstract
We report the experimental observations of Bell inequality violations (BIV) in entangled photons causally separated by a rotating mirror. A Foucault mirror gating geometry is used to causally isolate the entangled photon source and detectors. We report an observed BIV of CHSH- [...] Read more.
We report the experimental observations of Bell inequality violations (BIV) in entangled photons causally separated by a rotating mirror. A Foucault mirror gating geometry is used to causally isolate the entangled photon source and detectors. We report an observed BIV of CHSH-S=2.30±0.07>2.00. This result rules out theories that explain correlations with traveling communication between source and detectors, including super-luminal and instantaneous communication. Full article
(This article belongs to the Special Issue Completeness of Quantum Theory: Still an Open Question)
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20 pages, 309 KiB  
Article
Quantum Gravity If Non-Locality Is Fundamental
by Stuart A. Kauffman
Entropy 2022, 24(4), 554; https://doi.org/10.3390/e24040554 - 15 Apr 2022
Cited by 10 | Viewed by 3975
Abstract
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. [...] Read more.
I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful. Full article
23 pages, 443 KiB  
Article
Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality
by Angeliki Papana
Entropy 2021, 23(12), 1570; https://doi.org/10.3390/e23121570 - 25 Nov 2021
Cited by 5 | Viewed by 5585
Abstract
The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the [...] Read more.
The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance. Full article
(This article belongs to the Special Issue Granger Causality and Transfer Entropy for Financial Networks)
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15 pages, 2177 KiB  
Article
Frequency Domain Repercussions of Instantaneous Granger Causality
by Luiz A. Baccalá and Koichi Sameshima
Entropy 2021, 23(8), 1037; https://doi.org/10.3390/e23081037 - 12 Aug 2021
Cited by 7 | Viewed by 2386
Abstract
Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow [...] Read more.
Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected. Full article
(This article belongs to the Special Issue Brain Connectivity and Information Theory)
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