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Deng J, Sun B, Scheel N, Renli AB, Zhu DC, Zhu D, Ren J, Li T, Zhang R. Causalized convergent cross-mapping and its approximate equivalence with directed information in causality analysis. PNAS NEXUS 2024; 3:pgad422. [PMID: 38169910 PMCID: PMC10758925 DOI: 10.1093/pnasnexus/pgad422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 11/27/2023] [Indexed: 01/05/2024]
Abstract
Convergent cross-mapping (CCM) has attracted increased attention recently due to its capability to detect causality in nonseparable systems under deterministic settings, which may not be covered by the traditional Granger causality. From an information-theoretic perspective, causality is often characterized as the directed information (DI) flowing from one side to the other. As information is essentially nondeterministic, a natural question is: does CCM measure DI flow? Here, we first causalize CCM so that it aligns with the presumption in causality analysis-the future values of one process cannot influence the past of the other, and then establish and validate the approximate equivalence of causalized CCM (cCCM) and DI under Gaussian variables through both theoretical derivations and fMRI-based brain network causality analysis. Our simulation result indicates that, in general, cCCM tends to be more robust than DI in causality detection. The underlying argument is that DI relies heavily on probability estimation, which is sensitive to data size as well as digitization procedures; cCCM, on the other hand, gets around this problem through geometric cross-mapping between the manifolds involved. Overall, our analysis demonstrates that cross-mapping provides an alternative way to evaluate DI and is potentially an effective technique for identifying both linear and nonlinear causal coupling in brain neural networks and other settings, either random or deterministic, or both.
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Affiliation(s)
- Jinxian Deng
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
| | - Boxin Sun
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
| | - Norman Scheel
- Department of Radiology, Michigan State University, East Lansing, MI 48824, USA
| | - Alina B Renli
- Department of Neuroscience, Michigan State University, East Lansing, MI 48824, USA
| | - David C Zhu
- Department of Radiology, Michigan State University, East Lansing, MI 48824, USA
| | - Dajiang Zhu
- Department of Computer Science and Engineering, University of Texas, Arlington, TX 76010, USA
| | - Jian Ren
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
| | - Tongtong Li
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
| | - Rong Zhang
- Institute for Exercise and Environmental Medicine, Texas Health Presbyterian Hospital Dallas, Dallas, TX 75231, USA
- Departments of Neurology and Internal Medicine, University of Texas Southwestern Medical Center, Dallas, TX 75390, USA
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Platiša MM, Radovanović NN, Pernice R, Barà C, Pavlović SU, Faes L. Information-Theoretic Analysis of Cardio-Respiratory Interactions in Heart Failure Patients: Effects of Arrhythmias and Cardiac Resynchronization Therapy. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1072. [PMID: 37510019 PMCID: PMC10378632 DOI: 10.3390/e25071072] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 07/06/2023] [Accepted: 07/13/2023] [Indexed: 07/30/2023]
Abstract
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.
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Affiliation(s)
- Mirjana M Platiša
- Laboratory for Biosignals, Institute of Biophysics, Faculty of Medicine, University of Belgrade, Višegradska 26-2, 11000 Belgrade, Serbia
| | - Nikola N Radovanović
- Pacemaker Center, University Clinical Center of Serbia, University of Belgrade, 11000 Belgrade, Serbia
| | - Riccardo Pernice
- Department of Engineering, University of Palermo, Viale delle Scienze, Building 9, 90128 Palermo, Italy
| | - Chiara Barà
- Department of Engineering, University of Palermo, Viale delle Scienze, Building 9, 90128 Palermo, Italy
| | - Siniša U Pavlović
- Pacemaker Center, University Clinical Center of Serbia, University of Belgrade, 11000 Belgrade, Serbia
| | - Luca Faes
- Department of Engineering, University of Palermo, Viale delle Scienze, Building 9, 90128 Palermo, Italy
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Bahamonde AD, Montes RM, Cornejo P. Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series. ROYAL SOCIETY OPEN SCIENCE 2023; 10:221590. [PMID: 37448474 PMCID: PMC10336384 DOI: 10.1098/rsos.221590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/09/2022] [Accepted: 06/21/2023] [Indexed: 07/15/2023]
Abstract
Causality detection methods are valuable tools for detecting causal links in complex systems. The efficiency of continuity scaling (CS) and the convergent cross sorting (CSS) methods to detect causality was analysed. Usefulness and limitations of both methods in their application to simulated and real-world time series was explored under different scenarios. We find that CS is more robust and efficient than the CSS method for all simulated systems, even when increasing noise levels were considered. Both methods were not able to infer causality when time series with a marked difference in their main frequencies were analysed. Minimum time-series length required for the detection of a causal link depends on intrinsic system dynamics and on the method selected to detect it. Using simulated time series, only the CS method was capable to detect bidirectional causality. Causality detection, using the CS method, should at least include: (i) causality strength convergence analysis, (ii) statistical tests of significance, (iii) time-series standardization, and (iv) causality strength ratios as a strength indicator of relative causality between systems. Causality cannot be detected by either method in simulated time series that exhibit generalized synchronization.
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Affiliation(s)
- Adolfo D Bahamonde
- Interdisciplinary Center for Aquaculture Research (INCAR), University of Concepción, O'Higgins 1695, Concepción, Chile
| | - Rodrigo M Montes
- Interdisciplinary Center for Aquaculture Research (INCAR), University of Concepción, O'Higgins 1695, Concepción, Chile
| | - Pablo Cornejo
- Interdisciplinary Center for Aquaculture Research (INCAR), University of Concepción, O'Higgins 1695, Concepción, Chile
- Mechanical Engineering Department, University of Concepción, Concepción, Chile
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Tao P, Wang Q, Shi J, Hao X, Liu X, Min B, Zhang Y, Li C, Cui H, Chen L. Detecting dynamical causality by intersection cardinal concavity. FUNDAMENTAL RESEARCH 2023. [DOI: 10.1016/j.fmre.2023.01.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023] Open
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Leonardis EJ, Breston L, Lucero-Moore R, Sena L, Kohli R, Schuster L, Barton-Gluzman L, Quinn LK, Wiles J, Chiba AA. Interactive neurorobotics: Behavioral and neural dynamics of agent interactions. Front Psychol 2022; 13:897603. [PMID: 36059768 PMCID: PMC9431369 DOI: 10.3389/fpsyg.2022.897603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 06/27/2022] [Indexed: 11/13/2022] Open
Abstract
Interactive neurorobotics is a subfield which characterizes brain responses evoked during interaction with a robot, and their relationship with the behavioral responses. Gathering rich neural and behavioral data from humans or animals responding to agents can act as a scaffold for the design process of future social robots. This research seeks to study how organisms respond to artificial agents in contrast to biological or inanimate ones. This experiment uses the novel affordances of the robotic platforms to investigate complex dynamics during minimally structured interactions that would be difficult to capture with classical experimental setups. We then propose a general framework for such experiments that emphasizes naturalistic interactions combined with multimodal observations and complementary analysis pipelines that are necessary to render a holistic picture of the data for the purpose of informing robotic design principles. Finally, we demonstrate this approach with an exemplar rat-robot social interaction task which included simultaneous multi-agent tracking and neural recordings.
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Affiliation(s)
- Eric J. Leonardis
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
| | - Leo Breston
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
- Program in Neurosciences, University of California, San Diego, San Diego, CA, United States
| | - Rhiannon Lucero-Moore
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
| | - Leigh Sena
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
| | - Raunit Kohli
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
| | - Luisa Schuster
- Center for Neural Science, New York University, New York, NY, United States
| | - Lacha Barton-Gluzman
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
| | - Laleh K. Quinn
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
| | - Janet Wiles
- School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, QLD, Australia
| | - Andrea A. Chiba
- Department of Cognitive Science, University of California, San Diego, San Diego, CA, United States
- Program in Neurosciences, University of California, San Diego, San Diego, CA, United States
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