{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T21:34:56Z","timestamp":1771018496437,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T00:00:00Z","timestamp":1508803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Abstract: Modern experiments in Magnetic Confinement Nuclear Fusion can produce Gigabytes of data, mainly in form of time series. The acquired signals, composing massive databases, are typically affected by significant levels of noise. The interpretation of the time series can therefore become quite involved, particularly when tenuous causal relations have to be investigated. In the last years, synchronization experiments, to control potentially dangerous instabilities, have become a subject of intensive research. Their interpretation requires quite delicate causality analysis. In this paper, the approach of Information Geometry is applied to the problem of assessing the effectiveness of synchronization experiments on JET (Joint European Torus). In particular, the use of the Geodesic Distance on Gaussian Manifolds is shown to improve the results of advanced techniques such as Recurrent Plots and Complex Networks, when the noise level is not negligible. In cases affected by particularly high levels of noise, compromising the traditional treatments, the use of the Geodesic Distance on Gaussian Manifolds allows deriving quite encouraging results. In addition to consolidating conclusions previously quite uncertain, it has been demonstrated that the proposed approach permit to successfully analyze signals of discharges which were otherwise unusable, therefore salvaging the interpretation of those experiments.<\/jats:p>","DOI":"10.3390\/e19100569","type":"journal-article","created":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T10:39:18Z","timestamp":1508841558000},"page":"569","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Detection of Causal Relations in Time Series Affected by Noise in Tokamaks Using Geodesic Distance on Gaussian Manifolds"],"prefix":"10.3390","volume":"19","author":[{"given":"Andrea","family":"Murari","sequence":"first","affiliation":[{"name":"EUROfusion Consortium, JET, Culham Science Centre, Abingdon OX14 3DB, UK"},{"name":"Consorzio RFX (CNR, ENEA, INFN, Universita\u2019 di Padova, Acciaierie Venete SpA), I-35127 Padova, Italy"},{"name":"EUROfusion Programme Management Unit, JET, Culham Science Centre, Abingdon OX14 3DB, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0012-4260","authenticated-orcid":false,"given":"Teddy","family":"Craciunescu","sequence":"additional","affiliation":[{"name":"EUROfusion Consortium, JET, Culham Science Centre, Abingdon OX14 3DB, UK"},{"name":"National Institute for Laser, Plasma and Radiation Physics, M\u0103gurele 077126, Romania"}]},{"given":"Emmanuele","family":"Peluso","sequence":"additional","affiliation":[{"name":"EUROfusion Consortium, JET, Culham Science Centre, Abingdon OX14 3DB, UK"},{"name":"Associazione EUROfusion\u2014University of Rome \u201cTor Vergata\u201d, Via Orazio Raimondo, 18, 00173 Roma, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5158-7292","authenticated-orcid":false,"given":"Michela","family":"Gelfusa","sequence":"additional","affiliation":[{"name":"EUROfusion Consortium, JET, Culham Science Centre, Abingdon OX14 3DB, UK"},{"name":"Associazione EUROfusion\u2014University of Rome \u201cTor Vergata\u201d, Via Orazio Raimondo, 18, 00173 Roma, Italy"}]},{"name":"JET Contributors","sequence":"additional","affiliation":[]}],"member":"1968","published-online":{"date-parts":[[2017,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11D443","DOI":"10.1063\/1.4962247","article-title":"JET diagnostic enhancements in preparation for DT operations","volume":"87","author":"Figueiredo","year":"2016","journal-title":"Rev. Sci. Instrum."},{"key":"ref_2","unstructured":"Wesson, J. (2011). Tokamaks, Oxford University Press. [4th ed.]."},{"key":"ref_3","unstructured":"Khatchadourian, R. (The New Yorker, 2014). A Star in a Bottle, The New Yorker."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Connor, J.W., Kirk, A., and Wilson, H.R. (2008). Edge Localised Modes (ELMs): Experiments and Theory. AIP Conf. Proc., 1013.","DOI":"10.1063\/1.2939030"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"026006","DOI":"10.1088\/0029-5515\/56\/2\/026006","article-title":"Application of transfer entropy to causality detection and synchronization experiments in Tokamaks","volume":"56","author":"Murari","year":"2016","journal-title":"Nucl. Fusion"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"036027","DOI":"10.1088\/1741-4326\/aa53b6","article-title":"Sawtooth pacing with on-axis ICRH modulation in JET-ILW","volume":"57","author":"Lerche","year":"2017","journal-title":"Nucl. Fusion"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"076008","DOI":"10.1088\/0029-5515\/56\/7\/076008","article-title":"How to assess the efficiency of synchronization experiments in Tokamaks","volume":"56","author":"Murari","year":"2016","journal-title":"Nucl. Fusion"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1209\/0295-5075\/4\/9\/004","article-title":"Recurrence Plots of Dynamical Systems","volume":"5","author":"Eckmann","year":"1987","journal-title":"Europhys. Lett."},{"key":"ref_9","first-page":"026702","article-title":"Recurrence plot based measures of complexity and its application to heart rate variability data","volume":"66","author":"Marwan","year":"2012","journal-title":"Phys. Rev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0375-9601(92)90426-M","article-title":"Embeddings and delays as derived from quantification of recurrence plots","volume":"171","author":"Zbilut","year":"1992","journal-title":"Phys. Lett. A"},{"key":"ref_11","unstructured":"Newman, M., Barab\u00e1si, A.L., and Watts, D.J. (2006). The Structure and Dynamics of Networks, Princeton University Press."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Meyers, R.A. (2009). Encyclopedia of Complexity and Systems Science, Springer.","DOI":"10.1007\/978-0-387-30440-3"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"016218","DOI":"10.1103\/PhysRevE.75.016218","article-title":"Detecting temporal and spatial correlations in pseudoperiodic time series","volume":"75","author":"Zhang","year":"2007","journal-title":"Phys. Rev. E Stat. Nonlinear Soft Matter Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4972","DOI":"10.1073\/pnas.0709247105","article-title":"From time series to complex networks: The visibility graph","volume":"105","author":"Lacasa","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"De Berg, M., van Kreveld, M., Overmans, M., and Schwarzkopf, O. (2001). Computational Geometry: Algorithms and Applications, Springer.","DOI":"10.1007\/978-3-662-04245-8"},{"key":"ref_16","unstructured":"Zhang, Y. (2012). Visibility algorithms: A short review. Graph Theory, InTech."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"046103","DOI":"10.1103\/PhysRevE.80.046103","article-title":"Horizontal visibility graphs: Exact results for random time series","volume":"80","author":"Luque","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"50011","DOI":"10.1209\/0295-5075\/103\/50011","article-title":"Coupling between time series: A network view","volume":"103","author":"Mehraban","year":"2015","journal-title":"EPL"},{"key":"ref_19","unstructured":"Barabasi, A.L., and Posfal, M. (2016). Network Science, Cambridge University Press."},{"key":"ref_20","unstructured":"Amari, S.-I., and Nagaoka, H. (2000). Methods of Information Geometry, Oxford University Press and the American Mathematical Society."},{"key":"ref_21","first-page":"8191","article-title":"Information and accuracy attainable in the estimation of statistical parameters","volume":"37","author":"Rao","year":"1945","journal-title":"Bull. Calcutta Math. Soc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3403","DOI":"10.1103\/PhysRevA.45.3403","article-title":"Determining embedding dimension for phase-space reconstruction using a geometrical construction","volume":"45","author":"Kennel","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_23","unstructured":"(2016, May 25). CRP Toolbox for Matlab. Available online: http:\/\/tocsy.agnld.uni-potsdam.de."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Craciunescu, T., and Murari, A. (2016). Geodesic distance on Gaussian Manifolds for the robust identification of chaotic systems. Nonlinear Dyn., 86.","DOI":"10.1007\/s11071-016-2915-x"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/10\/569\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:48:18Z","timestamp":1760208498000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/10\/569"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,24]]},"references-count":24,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["e19100569"],"URL":"https:\/\/doi.org\/10.3390\/e19100569","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,24]]}}}