\newblock {\emph{\JournalTitle{Chaos: An Interdisciplinary Journal of Nonlinear Science}}} \textbf{\bibinfo{volume}{30}}, \bibinfo{pages}{113115}, \doiprefix\url{10.1063/5.0020538} (\bibinfo{year}{2020}).

[57]
\bibinfo{author}{Shannon, C.~E.}
\newblock \bibinfo{journal}{\bibinfo{title}{A mathematical theory of communication}}.
\newblock {\emph{\JournalTitle{The Bell System Technical Journal}}} \textbf{\bibinfo{volume}{27}}, \bibinfo{pages}{379--423}, \doiprefix\url{10.1002/j.1538-7305.1948.tb01338.x} (\bibinfo{year}{1948}).

[58]
\bibinfo{author}{Kullback, S.} \& \bibinfo{author}{Leibler, R.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{On information and sufficiency}}.
\newblock {\emph{\JournalTitle{Ann. Math. Stat.}}} \textbf{\bibinfo{volume}{22}}, \bibinfo{pages}{79--86} (\bibinfo{year}{1951}).

[59]
\bibinfo{author}{Kreer, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{A question of terminology}}.
\newblock {\emph{\JournalTitle{IRE Transactions on Information Theory}}} \textbf{\bibinfo{volume}{3}}, \bibinfo{pages}{208--208}, \doiprefix\url{10.1109/TIT.1957.1057418} (\bibinfo{year}{1957}).

[60]
\bibinfo{author}{Ince, R. A.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Measuring multivariate redundant information with pointwise common change in surprisal}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{19}}, \doiprefix\url{10.3390/e19070318} (\bibinfo{year}{2017}).

[61]
\bibinfo{author}{Lotka, A.~J.}
\newblock \emph{\bibinfo{title}{Elements of physical biology}} (\bibinfo{publisher}{Williams \& Wilkins}, \bibinfo{year}{1925}).

[62]
\bibinfo{author}{Volterra, V.}
\newblock \bibinfo{journal}{\bibinfo{title}{Fluctuations in the abundance of a species considered mathematically}}.
\newblock {\emph{\JournalTitle{Nature}}} \textbf{\bibinfo{volume}{118}}, \bibinfo{pages}{558--560} (\bibinfo{year}{1926}).

[63]
\bibinfo{author}{Moran, P.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{The statistical analysis of the canadian lynx cycle.}}
\newblock {\emph{\JournalTitle{Australian Journal of Zoology}}} \textbf{\bibinfo{volume}{1}}, \bibinfo{pages}{291--298} (\bibinfo{year}{1953}).

[64]
\bibinfo{author}{Ding, M.}, \bibinfo{author}{Chen, Y.} \& \bibinfo{author}{Bressler, S.}
\newblock \bibinfo{title}{Granger causality: Basic theory and application to neuroscience}.
\newblock In \bibinfo{editor}{Schelter, B.}, \bibinfo{editor}{Winterhalder, M.} \& \bibinfo{editor}{Timmer, J.} (eds.) \emph{\bibinfo{booktitle}{Handbook of Time Series Analysis: Recent Theoretical Developments and Applications}}, \bibinfo{pages}{2437--2459} (\bibinfo{publisher}{Wiley-VCH}, \bibinfo{address}{Berlin}, \bibinfo{year}{2006}).

[65]
\bibinfo{author}{May, R.~M.}
\newblock \bibinfo{journal}{\bibinfo{title}{Simple mathematical models with very complicated dynamics}}.
\newblock {\emph{\JournalTitle{Nature}}} \textbf{\bibinfo{volume}{261}}, \bibinfo{pages}{459--467} (\bibinfo{year}{1976}).

[66]
\bibinfo{author}{Lorenz, E.~N.}
\newblock \bibinfo{journal}{\bibinfo{title}{Deterministic nonperiodic flow}}.
\newblock {\emph{\JournalTitle{J. Atmos. Sci.}}} \textbf{\bibinfo{volume}{20}}, \bibinfo{pages}{130--141} (\bibinfo{year}{1963}).

[67]
\bibinfo{author}{R{\"o}ssler, O.~E.}
\newblock \bibinfo{title}{Continuous chaos}.
\newblock In \emph{\bibinfo{booktitle}{Synergetics: A Workshop Proceedings of the International Workshop on Synergetics at Schloss Elmau, Bavaria, May 2--7, 1977}}, \bibinfo{pages}{184--197} (\bibinfo{organization}{Springer}, \bibinfo{year}{1977}).

[68]
\bibinfo{author}{Richardson, L.~F.}
\newblock \emph{\bibinfo{title}{Weather Prediction by Numerical Process}} (\bibinfo{publisher}{Cambridge University Press}, \bibinfo{year}{1922}).

[69]
\bibinfo{author}{Obukhov, A.~M.}
\newblock \bibinfo{journal}{\bibinfo{title}{On the distribution of energy in the spectrum of turbulent flow}}.
\newblock {\emph{\JournalTitle{Izv. Akad. Nauk USSR, Ser. Geogr. Geofiz.}}} \textbf{\bibinfo{volume}{5}}, \bibinfo{pages}{453--466} (\bibinfo{year}{1941}).

[70]
\bibinfo{author}{Kolmogorov, A.~N.}
\newblock \bibinfo{title}{{The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large {R}eynolds' Numbers}}.
\newblock In \emph{\bibinfo{booktitle}{Dokl. Akad. Nauk SSSR}}, vol.~\bibinfo{volume}{30}, \bibinfo{pages}{301--305} (\bibinfo{year}{1941}).

[71]
\bibinfo{author}{Quiroga, R.~Q.}, \bibinfo{author}{Arnhold, J.} \& \bibinfo{author}{Grassberger, P.}
\newblock \bibinfo{journal}{\bibinfo{title}{Learning driver-response relationships from synchronization patterns}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{61}}, \bibinfo{pages}{5142--5148}, \doiprefix\url{10.1103/PhysRevE.61.5142} (\bibinfo{year}{2000}).

[72]
\bibinfo{author}{Krakovsk\'a, A.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Comparison of six methods for the detection of causality in a bivariate time series}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{97}}, \bibinfo{pages}{042207}, \doiprefix\url{10.1103/PhysRevE.97.042207} (\bibinfo{year}{2018}).

[73]
\bibinfo{author}{Javier, P. J.~E.}
\newblock \bibinfo{title}{{causal-ccm: a Python implementation of Convergent Cross Mapping}} (\bibinfo{year}{2021}).

[74]
\bibinfo{author}{Kolmogorov, A.~N.}
\newblock \bibinfo{journal}{\bibinfo{title}{A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high {Reynolds} number}}.
\newblock {\emph{\JournalTitle{J. Fluid Mech.}}} \textbf{\bibinfo{volume}{13}}, \bibinfo{pages}{82--85}, \doiprefix\url{10.1017/S0022112062000518} (\bibinfo{year}{1962}).

[75]
\bibinfo{author}{Aoyama, T.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Statistics of energy transfer in high-resolution direct numerical simulation of turbulence in a periodic box}}.
\newblock {\emph{\JournalTitle{J. Phys. Soc. Jpn.}}} \textbf{\bibinfo{volume}{74}}, \bibinfo{pages}{3202--3212} (\bibinfo{year}{2005}).

[76]
\bibinfo{author}{Falkovich, G.}
\newblock \bibinfo{journal}{\bibinfo{title}{Symmetries of the turbulent state}}.
\newblock {\emph{\JournalTitle{J. Phys. A}}} \textbf{\bibinfo{volume}{42}}, \bibinfo{pages}{123001}, \doiprefix\url{10.1088/1751-8113/42/12/123001} (\bibinfo{year}{2009}).

[77]
\bibinfo{author}{Cardesa, J.~I.}, \bibinfo{author}{Vela-Mart{\'\i}n, A.} \& \bibinfo{author}{Jim{\'e}nez, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{The turbulent cascade in five dimensions}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{357}}, \bibinfo{pages}{782--784} (\bibinfo{year}{2017}).

[78]
\bibinfo{author}{Yamada, T.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Anatomy of plasma turbulence}}.
\newblock {\emph{\JournalTitle{Nature Physics}}} \textbf{\bibinfo{volume}{4}}, \bibinfo{pages}{721--725}, \doiprefix\url{10.1038/nphys1029} (\bibinfo{year}{2008}).

[79]
\bibinfo{author}{Veynante, D.} \& \bibinfo{author}{Vervisch, L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Turbulent combustion modeling}}.
\newblock {\emph{\JournalTitle{Prog. Energy Combust. Sci.}}} \textbf{\bibinfo{volume}{28}}, \bibinfo{pages}{193--266} (\bibinfo{year}{2002}).

[80]
\bibinfo{author}{Bodenschatz, E.}
\newblock \bibinfo{journal}{\bibinfo{title}{Clouds resolved}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{350}}, \bibinfo{pages}{40--41}, \doiprefix\url{10.1126/science.aad1386} (\bibinfo{year}{2015}).

[81]
\bibinfo{author}{Young, R. M.~B.} \& \bibinfo{author}{Read, P.~L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Forward and inverse kinetic energy cascades in {J}upiter's turbulent weather layer}}.
\newblock {\emph{\JournalTitle{Nat. Phys.}}} \textbf{\bibinfo{volume}{13}}, \bibinfo{pages}{1135--1140} (\bibinfo{year}{2017}).

[82]
\bibinfo{author}{Sirovich, L.} \& \bibinfo{author}{Karlsson, S.}
\newblock \bibinfo{journal}{\bibinfo{title}{Turbulent drag reduction by passive mechanisms}}.
\newblock {\emph{\JournalTitle{Nature}}} \textbf{\bibinfo{volume}{388}}, \bibinfo{pages}{753--755} (\bibinfo{year}{1997}).

[83]
\bibinfo{author}{Hof, B.}, \bibinfo{author}{De~Lozar, A.}, \bibinfo{author}{Avila, M.}, \bibinfo{author}{Tu, X.} \& \bibinfo{author}{Schneider, T.~M.}
\newblock \bibinfo{journal}{\bibinfo{title}{Eliminating turbulence in spatially intermittent flows}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{327}}, \bibinfo{pages}{1491--1494}, \doiprefix\url{10.1126/science.1186091} (\bibinfo{year}{2010}).

[84]
\bibinfo{author}{Marusic, I.}, \bibinfo{author}{Mathis, R.} \& \bibinfo{author}{Hutchins, N.}
\newblock \bibinfo{journal}{\bibinfo{title}{Predictive model for wall-bounded turbulent flow}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{329}}, \bibinfo{pages}{193--196}, \doiprefix\url{10.1126/science.1188765} (\bibinfo{year}{2010}).

[85]
\bibinfo{author}{K{\"u}hnen, J.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Destabilizing turbulence in pipe flow}}.
\newblock {\emph{\JournalTitle{Nat. Phys.}}} \textbf{\bibinfo{volume}{14}}, \bibinfo{pages}{386--390}, \doiprefix\url{10.1038/s41567-017-0018-3} (\bibinfo{year}{2018}).

[86]
\bibinfo{author}{Vela-Mart{\'\i}n, A.} \& \bibinfo{author}{Jim{\'e}nez, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{Entropy, irreversibility and cascades in the inertial range of isotropic turbulence}}.
\newblock {\emph{\JournalTitle{Journal of Fluid Mechanics}}} \textbf{\bibinfo{volume}{915}}, \bibinfo{pages}{A36} (\bibinfo{year}{2021}).

[87]
\bibinfo{author}{Vela-Mart{\'\i}n, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Subgrid-scale models of isotropic turbulence need not produce energy backscatter}}.
\newblock {\emph{\JournalTitle{Journal of Fluid Mechanics}}} \textbf{\bibinfo{volume}{937}}, \bibinfo{pages}{A14} (\bibinfo{year}{2022}).

[88]
\bibinfo{author}{Zhou, Y.}
\newblock \bibinfo{journal}{\bibinfo{title}{Degrees of locality of energy transfer in the inertial range}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{5}}, \bibinfo{pages}{1092--1094} (\bibinfo{year}{1993}).

[89]
\bibinfo{author}{Eyink, G.~L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Locality of turbulent cascades}}.
\newblock {\emph{\JournalTitle{Phys. D: Nonlinear Phenomena}}} \textbf{\bibinfo{volume}{207}}, \bibinfo{pages}{91--116} (\bibinfo{year}{2005}).

[90]
\bibinfo{author}{Mininni, P.}, \bibinfo{author}{Alexakis, A.} \& \bibinfo{author}{Pouquet, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Large-scale flow effects, energy transfer, and self-similarity on turbulence}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{74}}, \bibinfo{pages}{016303} (\bibinfo{year}{2006}).

[91]
\bibinfo{author}{Aluie, H.} \& \bibinfo{author}{Eyink, G.~L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Localness of energy cascade in hydrodynamic turbulence. ii. sharp spectral filter}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{21}}, \bibinfo{pages}{115108} (\bibinfo{year}{2009}).

[92]
\bibinfo{author}{Domaradzki, J.~A.}, \bibinfo{author}{Teaca, B.} \& \bibinfo{author}{Carati, D.}
\newblock \bibinfo{journal}{\bibinfo{title}{Locality properties of the energy flux in turbulence}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{21}}, \bibinfo{pages}{025106} (\bibinfo{year}{2009}).

[93]
\bibinfo{author}{Williams, P.~L.} \& \bibinfo{author}{Beer, R.~D.}
\newblock \bibinfo{journal}{\bibinfo{title}{Nonnegative decomposition of multivariate information}}.
\newblock {\emph{\JournalTitle{arXiv preprint arXiv:1004.2515}}}  (\bibinfo{year}{2010}).

[94]
\bibinfo{author}{Griffith, V.} \& \bibinfo{author}{Koch, C.}
\newblock \bibinfo{title}{Quantifying synergistic mutual information}.
\newblock In \emph{\bibinfo{booktitle}{Guided Self-Organization: Inception}}, \bibinfo{pages}{159--190}, \doiprefix\url{10.1007/978-3-642-53734-9_6} (\bibinfo{publisher}{Springer}, \bibinfo{address}{Berlin, Heidelberg}, \bibinfo{year}{2014}).

[95]
\bibinfo{author}{Griffith, V.} \& \bibinfo{author}{Ho, T.}
\newblock \bibinfo{journal}{\bibinfo{title}{Quantifying redundant information in predicting a target random variable}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{17}}, \bibinfo{pages}{4644--4653} (\bibinfo{year}{2015}).

[96]
\bibinfo{author}{Ince, R.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Measuring multivariate redundant information with pointwise common change in surprisal}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{19}}, \bibinfo{pages}{318} (\bibinfo{year}{2017}).

[97]
\bibinfo{author}{Gutknecht, A.~J.}, \bibinfo{author}{Wibral, M.} \& \bibinfo{author}{Makkeh, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Bits and pieces: understanding information decomposition from part-whole relationships and formal logic}}.
\newblock {\emph{\JournalTitle{Proc. R. Soc. A}}} \textbf{\bibinfo{volume}{477}}, \bibinfo{pages}{20210110}, \doiprefix\url{10.1098/rspa.2021.0110} (\bibinfo{year}{2021}).

[98]
\bibinfo{author}{Kolchinsky, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{A novel approach to the partial information decomposition}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{24}}, \bibinfo{pages}{403} (\bibinfo{year}{2022}).

[99]
\bibinfo{author}{Baptista, R.}, \bibinfo{author}{Marzouk, Y.} \& \bibinfo{author}{Zahm, O.}
\newblock \bibinfo{journal}{\bibinfo{title}{On the representation and learning of monotone triangular transport maps}}.
\newblock {\emph{\JournalTitle{Foundations of Computational Mathematics}}} \bibinfo{pages}{1--46} (\bibinfo{year}{2023}).

[100]
\bibinfo{author}{Cobey, S.} \& \bibinfo{author}{Baskerville, E.~B.}
\newblock \bibinfo{journal}{\bibinfo{title}{Limits to causal inference with state-space reconstruction for infectious disease}}.
\newblock {\emph{\JournalTitle{PLOS ONE}}} \textbf{\bibinfo{volume}{11}}, \bibinfo{pages}{1--22}, \doiprefix\url{10.1371/journal.pone.0169050} (\bibinfo{year}{2016}).

[101]
\bibinfo{author}{Mønster, D.}, \bibinfo{author}{Fusaroli, R.}, \bibinfo{author}{Tylén, K.}, \bibinfo{author}{Roepstorff, A.} \& \bibinfo{author}{Sherson, J.~F.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causal inference from noisy time-series data — testing the convergent cross-mapping algorithm in the presence of noise and external influence}}.
\newblock {\emph{\JournalTitle{Future Generation Computer Systems}}} \textbf{\bibinfo{volume}{73}}, \bibinfo{pages}{52--62}, \doiprefix\url{10.1016/j.future.2016.12.009} (\bibinfo{year}{2017}).

[102]
\bibinfo{author}{Runge, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{{Causal network reconstruction from time series: From theoretical assumptions to practical estimation}}}.
\newblock {\emph{\JournalTitle{Chaos: An Interdisciplinary Journal of Nonlinear Science}}} \textbf{\bibinfo{volume}{28}}, \bibinfo{pages}{075310}, \doiprefix\url{10.1063/1.5025050} (\bibinfo{year}{2018}).

[103]
\bibinfo{author}{DeWeese, M.~R.} \& \bibinfo{author}{Meister, M.}
\newblock \bibinfo{journal}{\bibinfo{title}{How to measure the information gained from one symbol}}.
\newblock {\emph{\JournalTitle{Network: Computation in Neural Systems}}} \textbf{\bibinfo{volume}{10}}, \bibinfo{pages}{325}, \doiprefix\url{10.1088/0954-898X/10/4/303} (\bibinfo{year}{1999}).

[104]
\bibinfo{author}{Lizier, J.~T.}
\newblock \bibinfo{journal}{\bibinfo{title}{{JIDT: An Information-Theoretic Toolkit for Studying the Dynamics of Complex Systems}}}.
\newblock {\emph{\JournalTitle{Frontiers in Robotics and AI}}} \textbf{\bibinfo{volume}{1}}, \doiprefix\url{10.3389/frobt.2014.00011} (\bibinfo{year}{2014}).

[105]
\bibinfo{author}{Akaike, H.}
\newblock \bibinfo{title}{Akaike’s information criterion}.
\newblock In \bibinfo{editor}{Lovric, M.} (ed.) \emph{\bibinfo{booktitle}{International Encyclopedia of Statistical Science}}, \doiprefix\url{10.1007/978-3-642-04898-2_110} (\bibinfo{publisher}{Springer}, \bibinfo{address}{Berlin, Heidelberg}, \bibinfo{year}{2011}).

[106]
\bibinfo{author}{Cardesa, J.~I.}, \bibinfo{author}{Vela-Mart\'in, A.}, \bibinfo{author}{Dong, S.} \& \bibinfo{author}{Jim\'enez, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{The temporal evolution of the energy flux across scales in homogeneous turbulence}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{27}}, \bibinfo{pages}{111702}, \doiprefix\url{10.1063/1.4935812} (\bibinfo{year}{2015}).

[107]
\bibinfo{author}{Rosales, C.} \& \bibinfo{author}{Meneveau, C.}
\newblock \bibinfo{journal}{\bibinfo{title}{Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{17}}, \bibinfo{pages}{095106} (\bibinfo{year}{2005}).

\end{thebibliography}

% \begin{thebibliography}{100}
\urlstyle{rm}
\expandafter\ifx\csname url\endcsname\relax
\def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\expandafter\ifx\csname doiprefix\endcsname\relax\def\doiprefix{DOI: }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

[1]
\bibinfo{author}{Pearl, J.}
\newblock \emph{\bibinfo{title}{Causality: Models, Reasoning, and Inference}} (\bibinfo{publisher}{Cambridge University Press}, \bibinfo{address}{New York, NY, USA}, \bibinfo{year}{2000}).

[2]
\bibinfo{author}{Bunge, M.}
\newblock \emph{\bibinfo{title}{Causality and Modern Science}} (\bibinfo{publisher}{Dover Publications}, \bibinfo{year}{1979}).

[3]
\bibinfo{author}{Runge, J.}, \bibinfo{author}{Gerhardus, A.}, \bibinfo{author}{Varando, G.}, \bibinfo{author}{Eyring, V.} \& \bibinfo{author}{Camps-Valls, G.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causal inference for time series}}.
\newblock {\emph{\JournalTitle{Nature Reviews Earth {\&} Environment}}} \textbf{\bibinfo{volume}{4}}, \bibinfo{pages}{487--505}, \doiprefix\url{10.1038/s43017-023-00431-y} (\bibinfo{year}{2023}).

[4]
\bibinfo{author}{Razi, A.} \& \bibinfo{author}{Friston, K.~J.}
\newblock \bibinfo{journal}{\bibinfo{title}{The connected brain: causality, models, and intrinsic dynamics}}.
\newblock {\emph{\JournalTitle{IEEE Signal Processing Magazine}}} \textbf{\bibinfo{volume}{33}}, \bibinfo{pages}{14--35} (\bibinfo{year}{2016}).

[5]
\bibinfo{author}{Chiou-Wei, S.~Z.}, \bibinfo{author}{Chen, C.-F.} \& \bibinfo{author}{Zhu, Z.}
\newblock \bibinfo{journal}{\bibinfo{title}{Economic growth and energy consumption revisited — evidence from linear and nonlinear granger causality}}.
\newblock {\emph{\JournalTitle{Energy Economics}}} \textbf{\bibinfo{volume}{30}}, \bibinfo{pages}{3063--3076}, \doiprefix\url{10.1016/j.eneco.2008.02.002} (\bibinfo{year}{2008}).
\newblock \bibinfo{note}{Technological Change and the Environment}.

[6]
\bibinfo{author}{Rothman, K.~J.} \& \bibinfo{author}{Greenland, S.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causation and causal inference in epidemiology}}.
\newblock {\emph{\JournalTitle{American journal of public health}}} \textbf{\bibinfo{volume}{95}}, \bibinfo{pages}{S144--S150} (\bibinfo{year}{2005}).

[7]
\bibinfo{author}{Hedstr{\"o}m, P.} \& \bibinfo{author}{Ylikoski, P.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causal mechanisms in the social sciences}}.
\newblock {\emph{\JournalTitle{Annual review of sociology}}} \textbf{\bibinfo{volume}{36}}, \bibinfo{pages}{49--67} (\bibinfo{year}{2010}).

[8]
\bibinfo{author}{Lozano-Dur{\'a}n, A.}, \bibinfo{author}{Bae, H.~J.} \& \bibinfo{author}{Encinar, M.~P.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causality of energy-containing eddies in wall turbulence}}.
\newblock {\emph{\JournalTitle{Journal of Fluid Mechanics}}} \textbf{\bibinfo{volume}{882}}, \bibinfo{pages}{A2} (\bibinfo{year}{2020}).

[9]
\bibinfo{author}{Mart{\'\i}nez-S{\'a}nchez, {\'A}.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causality analysis of large-scale structures in the flow around a wall-mounted square cylinder}}.
\newblock {\emph{\JournalTitle{Journal of Fluid Mechanics}}} \textbf{\bibinfo{volume}{967}}, \bibinfo{pages}{A1} (\bibinfo{year}{2023}).

[10]
\bibinfo{author}{Eichler, M.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causal inference with multiple time series: principles and problems}}.
\newblock {\emph{\JournalTitle{Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}}} \textbf{\bibinfo{volume}{371}}, \bibinfo{pages}{20110613}, \doiprefix\url{10.1098/rsta.2011.0613} (\bibinfo{year}{2013}).

[11]
\bibinfo{author}{Barndorff-Nielsen, O.~E.} \& \bibinfo{author}{Kluppelberg, C.}
\newblock \emph{\bibinfo{title}{Complex stochastic systems}} (\bibinfo{publisher}{Chapman and Hall, CRC, Boca Raton}, \bibinfo{year}{2001}).

[12]
\bibinfo{author}{Spirtes, P.}, \bibinfo{author}{Glymour, C.} \& \bibinfo{author}{Scheines, R.}
\newblock \emph{\bibinfo{title}{{Causation, Prediction, and Search}}} (\bibinfo{publisher}{The MIT Press}, \bibinfo{year}{2001}).

[13]
\bibinfo{author}{Dawid, A.~P.}
\newblock \bibinfo{journal}{\bibinfo{title}{Influence diagrams for causal modelling and inference}}.
\newblock {\emph{\JournalTitle{International Statistical Review}}} \textbf{\bibinfo{volume}{70}}, \bibinfo{pages}{161--189}, \doiprefix\url{10.1111/j.1751-5823.2002.tb00354.x} (\bibinfo{year}{2002}).

[14]
\bibinfo{author}{Kampa, M.} \& \bibinfo{author}{Castanas, E.}
\newblock \bibinfo{journal}{\bibinfo{title}{Human health effects of air pollution}}.
\newblock {\emph{\JournalTitle{Environmental pollution}}} \textbf{\bibinfo{volume}{151}}, \bibinfo{pages}{362--367} (\bibinfo{year}{2008}).

[15]
\bibinfo{author}{Altman, N.} \& \bibinfo{author}{Krzywinski, M.}
\newblock \bibinfo{journal}{\bibinfo{title}{Association, correlation and causation}}.
\newblock {\emph{\JournalTitle{Nature Methods}}} \textbf{\bibinfo{volume}{12}}, \bibinfo{pages}{899--900}, \doiprefix\url{10.1038/nmeth.3587} (\bibinfo{year}{2015}).

[16]
\bibinfo{author}{Pearson, K.} \& \bibinfo{author}{Galton, F.}
\newblock \bibinfo{journal}{\bibinfo{title}{{VII. Note on regression and inheritance in the case of two parents}}}.
\newblock {\emph{\JournalTitle{Proceedings of the Royal Society of London}}} \textbf{\bibinfo{volume}{58}}, \bibinfo{pages}{240--242}, \doiprefix\url{10.1098/rspl.1895.0041} (\bibinfo{year}{1895}).

[17]
\bibinfo{author}{Spearman, C.}
\newblock \bibinfo{journal}{\bibinfo{title}{The proof and measurement of association between two things}}.
\newblock {\emph{\JournalTitle{The American Journal of Psychology}}} \textbf{\bibinfo{volume}{100}}, \bibinfo{pages}{441--471} (\bibinfo{year}{1987}).

[18]
\bibinfo{author}{Agresti, A.} \& \bibinfo{author}{Franklin, C.}
\newblock \bibinfo{journal}{\bibinfo{title}{The art and science of learning from data}}.
\newblock {\emph{\JournalTitle{Upper Saddle River, New Jersey}}} \textbf{\bibinfo{volume}{88}} (\bibinfo{year}{2007}).

[19]
\bibinfo{author}{Horn, K.~J.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{{Growth and survival relationships of 71 tree species with nitrogen and sulfur deposition across the conterminous U.S.}}}
\newblock {\emph{\JournalTitle{PLOS ONE}}} \textbf{\bibinfo{volume}{13}}, \bibinfo{pages}{1--19}, \doiprefix\url{10.1371/journal.pone.0205296} (\bibinfo{year}{2018}).

[20]
\bibinfo{author}{Duan, R.-R.}, \bibinfo{author}{Hao, K.} \& \bibinfo{author}{Yang, T.}
\newblock \bibinfo{journal}{\bibinfo{title}{Air pollution and chronic obstructive pulmonary disease}}.
\newblock {\emph{\JournalTitle{Chronic Diseases and Translational Medicine}}} \textbf{\bibinfo{volume}{6}}, \bibinfo{pages}{260--269}, \doiprefix\url{https://doi.org/10.1016/j.cdtm.2020.05.004} (\bibinfo{year}{2020}).

[21]
\bibinfo{author}{Camps-Valls, G.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Discovering causal relations and equations from data}}.
\newblock {\emph{\JournalTitle{Physics Reports}}} \textbf{\bibinfo{volume}{1044}}, \bibinfo{pages}{1--68}, \doiprefix\url{10.1016/j.physrep.2023.10.005} (\bibinfo{year}{2023}).

[22]
\bibinfo{author}{Eberhardt, F.} \& \bibinfo{author}{Scheines, R.}
\newblock \bibinfo{journal}{\bibinfo{title}{Interventions and causal inference}}.
\newblock {\emph{\JournalTitle{Philosophy of Science}}} \textbf{\bibinfo{volume}{74}}, \bibinfo{pages}{981--995} (\bibinfo{year}{2007}).

[23]
\bibinfo{author}{Runge, J.}, \bibinfo{author}{Nowack, P.}, \bibinfo{author}{Kretschmer, M.}, \bibinfo{author}{Flaxman, S.} \& \bibinfo{author}{Sejdinovic, D.}
\newblock \bibinfo{journal}{\bibinfo{title}{Detecting and quantifying causal associations in large nonlinear time series datasets}}.
\newblock {\emph{\JournalTitle{Science Advances}}} \textbf{\bibinfo{volume}{5}}, \bibinfo{pages}{eaau4996}, \doiprefix\url{10.1126/sciadv.aau4996} (\bibinfo{year}{2019}).

[24]
\bibinfo{author}{Wiener, N.}
\newblock \emph{\bibinfo{title}{{The theory of prediction. Modern mathematics for engineers}}}, vol. \bibinfo{volume}{165} (\bibinfo{publisher}{New York}, \bibinfo{year}{1956}).

[25]
\bibinfo{author}{Granger, C. W.~J.}
\newblock \bibinfo{journal}{\bibinfo{title}{Investigating causal relations by econometric models and cross-spectral methods}}.
\newblock {\emph{\JournalTitle{Econometrica}}} \textbf{\bibinfo{volume}{37}}, \bibinfo{pages}{424--438} (\bibinfo{year}{1969}).

[26]
\bibinfo{author}{Geweke, J.~F.}
\newblock \bibinfo{journal}{\bibinfo{title}{Measures of conditional linear dependence and feedback between time series}}.
\newblock {\emph{\JournalTitle{Journal of the American Statistical Association}}} \textbf{\bibinfo{volume}{79}}, \bibinfo{pages}{907--915} (\bibinfo{year}{1984}).

[27]
\bibinfo{author}{Barnett, L.}, \bibinfo{author}{Barrett, A.~B.} \& \bibinfo{author}{Seth, A.~K.}
\newblock \bibinfo{journal}{\bibinfo{title}{Granger causality and transfer entropy are equivalent for gaussian variables}}.
\newblock {\emph{\JournalTitle{Physical Review Letters}}} \textbf{\bibinfo{volume}{103}}, \bibinfo{pages}{238701} (\bibinfo{year}{2009}).

[28]
\bibinfo{author}{Barnett, L.} \& \bibinfo{author}{Seth, A.~K.}
\newblock \bibinfo{journal}{\bibinfo{title}{{The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference}}}.
\newblock {\emph{\JournalTitle{Journal of Neuroscience Methods}}} \textbf{\bibinfo{volume}{223}}, \bibinfo{pages}{50--68}, \doiprefix\url{10.1016/j.jneumeth.2013.10.018} (\bibinfo{year}{2014}).

[29]
\bibinfo{author}{Barnett, L.} \& \bibinfo{author}{Seth, A.~K.}
\newblock \bibinfo{journal}{\bibinfo{title}{Granger causality for state-space models}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{91}}, \bibinfo{pages}{040101}, \doiprefix\url{10.1103/PhysRevE.91.040101} (\bibinfo{year}{2015}).

[30]
\bibinfo{author}{Hiemstra, C.} \& \bibinfo{author}{Jones, J.~D.}
\newblock \bibinfo{journal}{\bibinfo{title}{{Testing for Linear and Nonlinear Granger Causality in the Stock Price-Volume Relation}}}.
\newblock {\emph{\JournalTitle{The Journal of Finance}}} \textbf{\bibinfo{volume}{49}}, \bibinfo{pages}{1639--1664}, \doiprefix\url{10.1111/j.1540-6261.1994.tb04776.x} (\bibinfo{year}{1994}).

[31]
\bibinfo{author}{Bell, D.}, \bibinfo{author}{Kay, J.} \& \bibinfo{author}{Malley, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{A non-parametric approach to non-linear causality testing}}.
\newblock {\emph{\JournalTitle{Economics Letters}}} \textbf{\bibinfo{volume}{51}}, \bibinfo{pages}{7--18}, \doiprefix\url{10.1016/0165-1765(95)00791-1} (\bibinfo{year}{1996}).

[32]
\bibinfo{author}{Abhyankar, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Linear and nonlinear granger causality: Evidence from the uk stock index futures market}}.
\newblock {\emph{\JournalTitle{The Journal of Futures Markets (1986-1998)}}} \textbf{\bibinfo{volume}{18}}, \bibinfo{pages}{519} (\bibinfo{year}{1998}).

[33]
\bibinfo{author}{Tissot, G.}, \bibinfo{author}{Lozano-Dur{\'a}n, A.}, \bibinfo{author}{Jim{\'e}nez, J.}, \bibinfo{author}{Cordier, L.} \& \bibinfo{author}{Noack, B.~R.}
\newblock \bibinfo{journal}{\bibinfo{title}{Granger causality in wall-bounded turbulence}}.
\newblock {\emph{\JournalTitle{J. Phys. Conf. Ser}}} \textbf{\bibinfo{volume}{506}}, \bibinfo{pages}{012006}, \doiprefix\url{10.1088/1742-6596/506/1/012006} (\bibinfo{year}{2014}).

[34]
\bibinfo{author}{Ancona, N.}, \bibinfo{author}{Marinazzo, D.} \& \bibinfo{author}{Stramaglia, S.}
\newblock \bibinfo{journal}{\bibinfo{title}{Radial basis function approach to nonlinear granger causality of time series}}.
\newblock {\emph{\JournalTitle{Physical Review E}}} \textbf{\bibinfo{volume}{70}}, \bibinfo{pages}{056221} (\bibinfo{year}{2004}).

[35]
\bibinfo{author}{Bueso, D.}, \bibinfo{author}{Piles, M.} \& \bibinfo{author}{Camps-Valls, G.}
\newblock \bibinfo{journal}{\bibinfo{title}{Explicit granger causality in kernel hilbert spaces}}.
\newblock {\emph{\JournalTitle{Physical Review E}}} \textbf{\bibinfo{volume}{102}}, \bibinfo{pages}{062201} (\bibinfo{year}{2020}).

[36]
\bibinfo{author}{Sugihara, G.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Detecting causality in complex ecosystems}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{338}}, \bibinfo{pages}{496--500}, \doiprefix\url{10.1126/science.1227079} (\bibinfo{year}{2012}).

[37]
\bibinfo{author}{McCracken, J.~M.} \& \bibinfo{author}{Weigel, R.~S.}
\newblock \bibinfo{journal}{\bibinfo{title}{Convergent cross-mapping and pairwise asymmetric inference}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{90}}, \bibinfo{pages}{062903}, \doiprefix\url{10.1103/PhysRevE.90.062903} (\bibinfo{year}{2014}).

[38]
\bibinfo{author}{Clark, A.~T.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Spatial convergent cross mapping to detect causal relationships from short time series}}.
\newblock {\emph{\JournalTitle{Ecology}}} \textbf{\bibinfo{volume}{96}}, \bibinfo{pages}{1174--1181}, \doiprefix\url{10.1890/14-1479.1} (\bibinfo{year}{2015}).

[39]
\bibinfo{author}{Leng, S.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Partial cross mapping eliminates indirect causal influences}}.
\newblock {\emph{\JournalTitle{Nature Communications}}} \textbf{\bibinfo{volume}{11}}, \bibinfo{pages}{2632}, \doiprefix\url{10.1038/s41467-020-16238-0} (\bibinfo{year}{2020}).

[40]
\bibinfo{author}{Brouwer, E.~D.}, \bibinfo{author}{Arany, A.}, \bibinfo{author}{Simm, J.} \& \bibinfo{author}{Moreau, Y.}
\newblock \bibinfo{title}{Latent convergent cross mapping}.
\newblock In \emph{\bibinfo{booktitle}{International Conference on Learning Representations}} (\bibinfo{year}{2021}).

[41]
\bibinfo{author}{Takens, F.}
\newblock \bibinfo{title}{Detecting strange attractors in turbulence}.
\newblock In \bibinfo{editor}{Rand, D.} \& \bibinfo{editor}{Young, L.-S.} (eds.) \emph{\bibinfo{booktitle}{Dynamical Systems and Turbulence, Warwick 1980}}, \bibinfo{pages}{366--381} (\bibinfo{publisher}{Springer Berlin Heidelberg}, \bibinfo{address}{Berlin, Heidelberg}, \bibinfo{year}{1981}).

[42]
\bibinfo{author}{Massey, J.}
\newblock \bibinfo{title}{Causality, feedback and directed information}.
\newblock In \emph{\bibinfo{booktitle}{Proc. 1990 Int. Symp. on Infom. Theory and its Applications}}, \bibinfo{pages}{27--30} (\bibinfo{year}{1990}).

[43]
\bibinfo{author}{Kramer, G.}
\newblock \emph{\bibinfo{title}{Directed information for channels with feedback}}.
\newblock \bibinfo{type}{{PhD Thesis}}, \bibinfo{school}{ETH Z\"urich}, \bibinfo{address}{Z\"urich} (\bibinfo{year}{1998}).
\newblock \doiprefix\url{10.3929/ethz-a-001988524}.

[44]
\bibinfo{author}{Schreiber, T.}
\newblock \bibinfo{journal}{\bibinfo{title}{Measuring information transfer}}.
\newblock {\emph{\JournalTitle{Phys. Rev. Lett.}}} \textbf{\bibinfo{volume}{85}}, \bibinfo{pages}{461} (\bibinfo{year}{2000}).

[45]
\bibinfo{author}{Verdes, P.}
\newblock \bibinfo{journal}{\bibinfo{title}{Assessing causality from multivariate time series}}.
\newblock {\emph{\JournalTitle{Physical Review E}}} \textbf{\bibinfo{volume}{72}}, \bibinfo{pages}{026222} (\bibinfo{year}{2005}).

[46]
\bibinfo{author}{Lizier, J.~T.}, \bibinfo{author}{Prokopenko, M.} \& \bibinfo{author}{Zomaya, A.~Y.}
\newblock \bibinfo{journal}{\bibinfo{title}{Local information transfer as a spatiotemporal filter for complex systems}}.
\newblock {\emph{\JournalTitle{Physical Review E}}} \textbf{\bibinfo{volume}{77}}, \bibinfo{pages}{026110} (\bibinfo{year}{2008}).

[47]
\bibinfo{author}{Lizier, J.~T.}, \bibinfo{author}{Prokopenko, M.} \& \bibinfo{author}{Zomaya, A.~Y.}
\newblock \bibinfo{journal}{\bibinfo{title}{Information modification and particle collisions in distributed computation}}.
\newblock {\emph{\JournalTitle{Chaos: An Interdisciplinary Journal of Nonlinear Science}}} \textbf{\bibinfo{volume}{20}} (\bibinfo{year}{2010}).

[48]
\bibinfo{author}{Bossomaier, T.}, \bibinfo{author}{Barnett, L.}, \bibinfo{author}{Harré, M.} \& \bibinfo{author}{Lizier, J.~T.}
\newblock \emph{\bibinfo{title}{An Introduction to Transfer Entropy: Information Flow in Complex Systems}} (\bibinfo{publisher}{Springer International Publishing}, \bibinfo{address}{Cham}, \bibinfo{year}{2016}), \bibinfo{edition}{1st ed. 2016.} edn.

[49]
\bibinfo{author}{Lozano-Dur\'an, A.} \& \bibinfo{author}{Arranz, G.}
\newblock \bibinfo{journal}{\bibinfo{title}{Information-theoretic formulation of dynamical systems: Causality, modeling, and control}}.
\newblock {\emph{\JournalTitle{Phys. Rev. Res.}}} \textbf{\bibinfo{volume}{4}}, \bibinfo{pages}{023195}, \doiprefix\url{10.1103/PhysRevResearch.4.023195} (\bibinfo{year}{2022}).

[50]
\bibinfo{author}{Liang, X.~S.} \& \bibinfo{author}{Kleeman, R.}
\newblock \bibinfo{journal}{\bibinfo{title}{Information transfer between dynamical system components}}.
\newblock {\emph{\JournalTitle{Phys. Rev. Lett.}}} \textbf{\bibinfo{volume}{95}}, \bibinfo{pages}{244101}, \doiprefix\url{10.1103/PhysRevLett.95.244101} (\bibinfo{year}{2006}).

[51]
\bibinfo{author}{Spirtes, P.} \& \bibinfo{author}{Glymour, C.}
\newblock \bibinfo{journal}{\bibinfo{title}{An algorithm for fast recovery of sparse causal graphs}}.
\newblock {\emph{\JournalTitle{Social Science Computer Review}}} \textbf{\bibinfo{volume}{9}}, \bibinfo{pages}{62--72} (\bibinfo{year}{1991}).

[52]
\bibinfo{author}{Runge, J.}
\newblock \bibinfo{title}{Conditional independence testing based on a nearest-neighbor estimator of conditional mutual information}.
\newblock In \bibinfo{editor}{Storkey, A.} \& \bibinfo{editor}{Perez-Cruz, F.} (eds.) \emph{\bibinfo{booktitle}{Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}}, vol.~\bibinfo{volume}{84} of \emph{\bibinfo{series}{Proceedings of Machine Learning Research}}, \bibinfo{pages}{938--947} (\bibinfo{publisher}{PMLR}, \bibinfo{year}{2018}).

[53]
\bibinfo{author}{Runge, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{Modern causal inference approaches to investigate biodiversity-ecosystem functioning relationships}}.
\newblock {\emph{\JournalTitle{Nature Communications}}} \textbf{\bibinfo{volume}{14}}, \bibinfo{pages}{1917}, \doiprefix\url{10.1038/s41467-023-37546-1} (\bibinfo{year}{2023}).

[54]
\bibinfo{author}{Runge, J.}
\newblock \bibinfo{title}{Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets}.
\newblock In \emph{\bibinfo{booktitle}{Conference on Uncertainty in Artificial Intelligence}}, \bibinfo{pages}{1388--1397} (\bibinfo{organization}{PMLR}, \bibinfo{year}{2020}).

[55]
\bibinfo{author}{Gerhardus, A.} \& \bibinfo{author}{Runge, J.}
\newblock \bibinfo{title}{High-recall causal discovery for autocorrelated time series with latent confounders}.
\newblock In \bibinfo{editor}{Larochelle, H.}, \bibinfo{editor}{Ranzato, M.}, \bibinfo{editor}{Hadsell, R.}, \bibinfo{editor}{Balcan, M.} \& \bibinfo{editor}{Lin, H.} (eds.) \emph{\bibinfo{booktitle}{Advances in Neural Information Processing Systems}}, vol.~\bibinfo{volume}{33}, \bibinfo{pages}{12615--12625} (\bibinfo{publisher}{Curran Associates, Inc.}, \bibinfo{year}{2020}).

[56]
\bibinfo{author}{Saggioro, E.}, \bibinfo{author}{de~Wiljes, J.}, \bibinfo{author}{Kretschmer, M.} \& \bibinfo{author}{Runge, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{{Reconstructing regime-dependent causal relationships from observational time series}}}.
\newblock {\emph{\JournalTitle{Chaos: An Interdisciplinary Journal of Nonlinear Science}}} \textbf{\bibinfo{volume}{30}}, \bibinfo{pages}{113115}, \doiprefix\url{10.1063/5.0020538} (\bibinfo{year}{2020}).

[57]
\bibinfo{author}{Shannon, C.~E.}
\newblock \bibinfo{journal}{\bibinfo{title}{A mathematical theory of communication}}.
\newblock {\emph{\JournalTitle{The Bell System Technical Journal}}} \textbf{\bibinfo{volume}{27}}, \bibinfo{pages}{379--423}, \doiprefix\url{10.1002/j.1538-7305.1948.tb01338.x} (\bibinfo{year}{1948}).

[58]
\bibinfo{author}{Kullback, S.} \& \bibinfo{author}{Leibler, R.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{On information and sufficiency}}.
\newblock {\emph{\JournalTitle{Ann. Math. Stat.}}} \textbf{\bibinfo{volume}{22}}, \bibinfo{pages}{79--86} (\bibinfo{year}{1951}).

[59]
\bibinfo{author}{Kreer, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{A question of terminology}}.
\newblock {\emph{\JournalTitle{IRE Transactions on Information Theory}}} \textbf{\bibinfo{volume}{3}}, \bibinfo{pages}{208--208}, \doiprefix\url{10.1109/TIT.1957.1057418} (\bibinfo{year}{1957}).

[60]
\bibinfo{author}{Ince, R. A.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Measuring multivariate redundant information with pointwise common change in surprisal}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{19}}, \doiprefix\url{10.3390/e19070318} (\bibinfo{year}{2017}).

[61]
\bibinfo{author}{Lotka, A.~J.}
\newblock \emph{\bibinfo{title}{Elements of physical biology}} (\bibinfo{publisher}{Williams \& Wilkins}, \bibinfo{year}{1925}).

[62]
\bibinfo{author}{Volterra, V.}
\newblock \bibinfo{journal}{\bibinfo{title}{Fluctuations in the abundance of a species considered mathematically}}.
\newblock {\emph{\JournalTitle{Nature}}} \textbf{\bibinfo{volume}{118}}, \bibinfo{pages}{558--560} (\bibinfo{year}{1926}).

[63]
\bibinfo{author}{Moran, P.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{The statistical analysis of the canadian lynx cycle.}}
\newblock {\emph{\JournalTitle{Australian Journal of Zoology}}} \textbf{\bibinfo{volume}{1}}, \bibinfo{pages}{291--298} (\bibinfo{year}{1953}).

[64]
\bibinfo{author}{Ding, M.}, \bibinfo{author}{Chen, Y.} \& \bibinfo{author}{Bressler, S.}
\newblock \bibinfo{title}{Granger causality: Basic theory and application to neuroscience}.
\newblock In \bibinfo{editor}{Schelter, B.}, \bibinfo{editor}{Winterhalder, M.} \& \bibinfo{editor}{Timmer, J.} (eds.) \emph{\bibinfo{booktitle}{Handbook of Time Series Analysis: Recent Theoretical Developments and Applications}}, \bibinfo{pages}{2437--2459} (\bibinfo{publisher}{Wiley-VCH}, \bibinfo{address}{Berlin}, \bibinfo{year}{2006}).

[65]
\bibinfo{author}{May, R.~M.}
\newblock \bibinfo{journal}{\bibinfo{title}{Simple mathematical models with very complicated dynamics}}.
\newblock {\emph{\JournalTitle{Nature}}} \textbf{\bibinfo{volume}{261}}, \bibinfo{pages}{459--467} (\bibinfo{year}{1976}).

[66]
\bibinfo{author}{Lorenz, E.~N.}
\newblock \bibinfo{journal}{\bibinfo{title}{Deterministic nonperiodic flow}}.
\newblock {\emph{\JournalTitle{J. Atmos. Sci.}}} \textbf{\bibinfo{volume}{20}}, \bibinfo{pages}{130--141} (\bibinfo{year}{1963}).

[67]
\bibinfo{author}{R{\"o}ssler, O.~E.}
\newblock \bibinfo{title}{Continuous chaos}.
\newblock In \emph{\bibinfo{booktitle}{Synergetics: A Workshop Proceedings of the International Workshop on Synergetics at Schloss Elmau, Bavaria, May 2--7, 1977}}, \bibinfo{pages}{184--197} (\bibinfo{organization}{Springer}, \bibinfo{year}{1977}).

[68]
\bibinfo{author}{Richardson, L.~F.}
\newblock \emph{\bibinfo{title}{Weather Prediction by Numerical Process}} (\bibinfo{publisher}{Cambridge University Press}, \bibinfo{year}{1922}).

[69]
\bibinfo{author}{Obukhov, A.~M.}
\newblock \bibinfo{journal}{\bibinfo{title}{On the distribution of energy in the spectrum of turbulent flow}}.
\newblock {\emph{\JournalTitle{Izv. Akad. Nauk USSR, Ser. Geogr. Geofiz.}}} \textbf{\bibinfo{volume}{5}}, \bibinfo{pages}{453--466} (\bibinfo{year}{1941}).

[70]
\bibinfo{author}{Kolmogorov, A.~N.}
\newblock \bibinfo{title}{{The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large {R}eynolds' Numbers}}.
\newblock In \emph{\bibinfo{booktitle}{Dokl. Akad. Nauk SSSR}}, vol.~\bibinfo{volume}{30}, \bibinfo{pages}{301--305} (\bibinfo{year}{1941}).

[71]
\bibinfo{author}{Quiroga, R.~Q.}, \bibinfo{author}{Arnhold, J.} \& \bibinfo{author}{Grassberger, P.}
\newblock \bibinfo{journal}{\bibinfo{title}{Learning driver-response relationships from synchronization patterns}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{61}}, \bibinfo{pages}{5142--5148}, \doiprefix\url{10.1103/PhysRevE.61.5142} (\bibinfo{year}{2000}).

[72]
\bibinfo{author}{Krakovsk\'a, A.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Comparison of six methods for the detection of causality in a bivariate time series}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{97}}, \bibinfo{pages}{042207}, \doiprefix\url{10.1103/PhysRevE.97.042207} (\bibinfo{year}{2018}).

[73]
\bibinfo{author}{Javier, P. J.~E.}
\newblock \bibinfo{title}{{causal-ccm: a Python implementation of Convergent Cross Mapping}} (\bibinfo{year}{2021}).

[74]
\bibinfo{author}{Kolmogorov, A.~N.}
\newblock \bibinfo{journal}{\bibinfo{title}{A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high {Reynolds} number}}.
\newblock {\emph{\JournalTitle{J. Fluid Mech.}}} \textbf{\bibinfo{volume}{13}}, \bibinfo{pages}{82--85}, \doiprefix\url{10.1017/S0022112062000518} (\bibinfo{year}{1962}).

[75]
\bibinfo{author}{Aoyama, T.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Statistics of energy transfer in high-resolution direct numerical simulation of turbulence in a periodic box}}.
\newblock {\emph{\JournalTitle{J. Phys. Soc. Jpn.}}} \textbf{\bibinfo{volume}{74}}, \bibinfo{pages}{3202--3212} (\bibinfo{year}{2005}).

[76]
\bibinfo{author}{Falkovich, G.}
\newblock \bibinfo{journal}{\bibinfo{title}{Symmetries of the turbulent state}}.
\newblock {\emph{\JournalTitle{J. Phys. A}}} \textbf{\bibinfo{volume}{42}}, \bibinfo{pages}{123001}, \doiprefix\url{10.1088/1751-8113/42/12/123001} (\bibinfo{year}{2009}).

[77]
\bibinfo{author}{Cardesa, J.~I.}, \bibinfo{author}{Vela-Mart{\'\i}n, A.} \& \bibinfo{author}{Jim{\'e}nez, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{The turbulent cascade in five dimensions}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{357}}, \bibinfo{pages}{782--784} (\bibinfo{year}{2017}).

[78]
\bibinfo{author}{Yamada, T.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Anatomy of plasma turbulence}}.
\newblock {\emph{\JournalTitle{Nature Physics}}} \textbf{\bibinfo{volume}{4}}, \bibinfo{pages}{721--725}, \doiprefix\url{10.1038/nphys1029} (\bibinfo{year}{2008}).

[79]
\bibinfo{author}{Veynante, D.} \& \bibinfo{author}{Vervisch, L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Turbulent combustion modeling}}.
\newblock {\emph{\JournalTitle{Prog. Energy Combust. Sci.}}} \textbf{\bibinfo{volume}{28}}, \bibinfo{pages}{193--266} (\bibinfo{year}{2002}).

[80]
\bibinfo{author}{Bodenschatz, E.}
\newblock \bibinfo{journal}{\bibinfo{title}{Clouds resolved}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{350}}, \bibinfo{pages}{40--41}, \doiprefix\url{10.1126/science.aad1386} (\bibinfo{year}{2015}).

[81]
\bibinfo{author}{Young, R. M.~B.} \& \bibinfo{author}{Read, P.~L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Forward and inverse kinetic energy cascades in {J}upiter's turbulent weather layer}}.
\newblock {\emph{\JournalTitle{Nat. Phys.}}} \textbf{\bibinfo{volume}{13}}, \bibinfo{pages}{1135--1140} (\bibinfo{year}{2017}).

[82]
\bibinfo{author}{Sirovich, L.} \& \bibinfo{author}{Karlsson, S.}
\newblock \bibinfo{journal}{\bibinfo{title}{Turbulent drag reduction by passive mechanisms}}.
\newblock {\emph{\JournalTitle{Nature}}} \textbf{\bibinfo{volume}{388}}, \bibinfo{pages}{753--755} (\bibinfo{year}{1997}).

[83]
\bibinfo{author}{Hof, B.}, \bibinfo{author}{De~Lozar, A.}, \bibinfo{author}{Avila, M.}, \bibinfo{author}{Tu, X.} \& \bibinfo{author}{Schneider, T.~M.}
\newblock \bibinfo{journal}{\bibinfo{title}{Eliminating turbulence in spatially intermittent flows}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{327}}, \bibinfo{pages}{1491--1494}, \doiprefix\url{10.1126/science.1186091} (\bibinfo{year}{2010}).

[84]
\bibinfo{author}{Marusic, I.}, \bibinfo{author}{Mathis, R.} \& \bibinfo{author}{Hutchins, N.}
\newblock \bibinfo{journal}{\bibinfo{title}{Predictive model for wall-bounded turbulent flow}}.
\newblock {\emph{\JournalTitle{Science}}} \textbf{\bibinfo{volume}{329}}, \bibinfo{pages}{193--196}, \doiprefix\url{10.1126/science.1188765} (\bibinfo{year}{2010}).

[85]
\bibinfo{author}{K{\"u}hnen, J.} \emph{et~al.}
\newblock \bibinfo{journal}{\bibinfo{title}{Destabilizing turbulence in pipe flow}}.
\newblock {\emph{\JournalTitle{Nat. Phys.}}} \textbf{\bibinfo{volume}{14}}, \bibinfo{pages}{386--390}, \doiprefix\url{10.1038/s41567-017-0018-3} (\bibinfo{year}{2018}).

[86]
\bibinfo{author}{Vela-Mart{\'\i}n, A.} \& \bibinfo{author}{Jim{\'e}nez, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{Entropy, irreversibility and cascades in the inertial range of isotropic turbulence}}.
\newblock {\emph{\JournalTitle{Journal of Fluid Mechanics}}} \textbf{\bibinfo{volume}{915}}, \bibinfo{pages}{A36} (\bibinfo{year}{2021}).

[87]
\bibinfo{author}{Vela-Mart{\'\i}n, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Subgrid-scale models of isotropic turbulence need not produce energy backscatter}}.
\newblock {\emph{\JournalTitle{Journal of Fluid Mechanics}}} \textbf{\bibinfo{volume}{937}}, \bibinfo{pages}{A14} (\bibinfo{year}{2022}).

[88]
\bibinfo{author}{Zhou, Y.}
\newblock \bibinfo{journal}{\bibinfo{title}{Degrees of locality of energy transfer in the inertial range}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{5}}, \bibinfo{pages}{1092--1094} (\bibinfo{year}{1993}).

[89]
\bibinfo{author}{Eyink, G.~L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Locality of turbulent cascades}}.
\newblock {\emph{\JournalTitle{Phys. D: Nonlinear Phenomena}}} \textbf{\bibinfo{volume}{207}}, \bibinfo{pages}{91--116} (\bibinfo{year}{2005}).

[90]
\bibinfo{author}{Mininni, P.}, \bibinfo{author}{Alexakis, A.} \& \bibinfo{author}{Pouquet, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Large-scale flow effects, energy transfer, and self-similarity on turbulence}}.
\newblock {\emph{\JournalTitle{Phys. Rev. E}}} \textbf{\bibinfo{volume}{74}}, \bibinfo{pages}{016303} (\bibinfo{year}{2006}).

[91]
\bibinfo{author}{Aluie, H.} \& \bibinfo{author}{Eyink, G.~L.}
\newblock \bibinfo{journal}{\bibinfo{title}{Localness of energy cascade in hydrodynamic turbulence. ii. sharp spectral filter}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{21}}, \bibinfo{pages}{115108} (\bibinfo{year}{2009}).

[92]
\bibinfo{author}{Domaradzki, J.~A.}, \bibinfo{author}{Teaca, B.} \& \bibinfo{author}{Carati, D.}
\newblock \bibinfo{journal}{\bibinfo{title}{Locality properties of the energy flux in turbulence}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{21}}, \bibinfo{pages}{025106} (\bibinfo{year}{2009}).

[93]
\bibinfo{author}{Williams, P.~L.} \& \bibinfo{author}{Beer, R.~D.}
\newblock \bibinfo{journal}{\bibinfo{title}{Nonnegative decomposition of multivariate information}}.
\newblock {\emph{\JournalTitle{arXiv preprint arXiv:1004.2515}}}  (\bibinfo{year}{2010}).

[94]
\bibinfo{author}{Griffith, V.} \& \bibinfo{author}{Koch, C.}
\newblock \bibinfo{title}{Quantifying synergistic mutual information}.
\newblock In \emph{\bibinfo{booktitle}{Guided Self-Organization: Inception}}, \bibinfo{pages}{159--190}, \doiprefix\url{10.1007/978-3-642-53734-9_6} (\bibinfo{publisher}{Springer}, \bibinfo{address}{Berlin, Heidelberg}, \bibinfo{year}{2014}).

[95]
\bibinfo{author}{Griffith, V.} \& \bibinfo{author}{Ho, T.}
\newblock \bibinfo{journal}{\bibinfo{title}{Quantifying redundant information in predicting a target random variable}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{17}}, \bibinfo{pages}{4644--4653} (\bibinfo{year}{2015}).

[96]
\bibinfo{author}{Ince, R.~A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Measuring multivariate redundant information with pointwise common change in surprisal}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{19}}, \bibinfo{pages}{318} (\bibinfo{year}{2017}).

[97]
\bibinfo{author}{Gutknecht, A.~J.}, \bibinfo{author}{Wibral, M.} \& \bibinfo{author}{Makkeh, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{Bits and pieces: understanding information decomposition from part-whole relationships and formal logic}}.
\newblock {\emph{\JournalTitle{Proc. R. Soc. A}}} \textbf{\bibinfo{volume}{477}}, \bibinfo{pages}{20210110}, \doiprefix\url{10.1098/rspa.2021.0110} (\bibinfo{year}{2021}).

[98]
\bibinfo{author}{Kolchinsky, A.}
\newblock \bibinfo{journal}{\bibinfo{title}{A novel approach to the partial information decomposition}}.
\newblock {\emph{\JournalTitle{Entropy}}} \textbf{\bibinfo{volume}{24}}, \bibinfo{pages}{403} (\bibinfo{year}{2022}).

[99]
\bibinfo{author}{Baptista, R.}, \bibinfo{author}{Marzouk, Y.} \& \bibinfo{author}{Zahm, O.}
\newblock \bibinfo{journal}{\bibinfo{title}{On the representation and learning of monotone triangular transport maps}}.
\newblock {\emph{\JournalTitle{Foundations of Computational Mathematics}}} \bibinfo{pages}{1--46} (\bibinfo{year}{2023}).

[100]
\bibinfo{author}{Cobey, S.} \& \bibinfo{author}{Baskerville, E.~B.}
\newblock \bibinfo{journal}{\bibinfo{title}{Limits to causal inference with state-space reconstruction for infectious disease}}.
\newblock {\emph{\JournalTitle{PLOS ONE}}} \textbf{\bibinfo{volume}{11}}, \bibinfo{pages}{1--22}, \doiprefix\url{10.1371/journal.pone.0169050} (\bibinfo{year}{2016}).

[101]
\bibinfo{author}{Mønster, D.}, \bibinfo{author}{Fusaroli, R.}, \bibinfo{author}{Tylén, K.}, \bibinfo{author}{Roepstorff, A.} \& \bibinfo{author}{Sherson, J.~F.}
\newblock \bibinfo{journal}{\bibinfo{title}{Causal inference from noisy time-series data — testing the convergent cross-mapping algorithm in the presence of noise and external influence}}.
\newblock {\emph{\JournalTitle{Future Generation Computer Systems}}} \textbf{\bibinfo{volume}{73}}, \bibinfo{pages}{52--62}, \doiprefix\url{10.1016/j.future.2016.12.009} (\bibinfo{year}{2017}).

[102]
\bibinfo{author}{Runge, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{{Causal network reconstruction from time series: From theoretical assumptions to practical estimation}}}.
\newblock {\emph{\JournalTitle{Chaos: An Interdisciplinary Journal of Nonlinear Science}}} \textbf{\bibinfo{volume}{28}}, \bibinfo{pages}{075310}, \doiprefix\url{10.1063/1.5025050} (\bibinfo{year}{2018}).

[103]
\bibinfo{author}{DeWeese, M.~R.} \& \bibinfo{author}{Meister, M.}
\newblock \bibinfo{journal}{\bibinfo{title}{How to measure the information gained from one symbol}}.
\newblock {\emph{\JournalTitle{Network: Computation in Neural Systems}}} \textbf{\bibinfo{volume}{10}}, \bibinfo{pages}{325}, \doiprefix\url{10.1088/0954-898X/10/4/303} (\bibinfo{year}{1999}).

[104]
\bibinfo{author}{Lizier, J.~T.}
\newblock \bibinfo{journal}{\bibinfo{title}{{JIDT: An Information-Theoretic Toolkit for Studying the Dynamics of Complex Systems}}}.
\newblock {\emph{\JournalTitle{Frontiers in Robotics and AI}}} \textbf{\bibinfo{volume}{1}}, \doiprefix\url{10.3389/frobt.2014.00011} (\bibinfo{year}{2014}).

[105]
\bibinfo{author}{Akaike, H.}
\newblock \bibinfo{title}{Akaike’s information criterion}.
\newblock In \bibinfo{editor}{Lovric, M.} (ed.) \emph{\bibinfo{booktitle}{International Encyclopedia of Statistical Science}}, \doiprefix\url{10.1007/978-3-642-04898-2_110} (\bibinfo{publisher}{Springer}, \bibinfo{address}{Berlin, Heidelberg}, \bibinfo{year}{2011}).

[106]
\bibinfo{author}{Cardesa, J.~I.}, \bibinfo{author}{Vela-Mart\'in, A.}, \bibinfo{author}{Dong, S.} \& \bibinfo{author}{Jim\'enez, J.}
\newblock \bibinfo{journal}{\bibinfo{title}{The temporal evolution of the energy flux across scales in homogeneous turbulence}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{27}}, \bibinfo{pages}{111702}, \doiprefix\url{10.1063/1.4935812} (\bibinfo{year}{2015}).

[107]
\bibinfo{author}{Rosales, C.} \& \bibinfo{author}{Meneveau, C.}
\newblock \bibinfo{journal}{\bibinfo{title}{Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties}}.
\newblock {\emph{\JournalTitle{Phys. Fluids}}} \textbf{\bibinfo{volume}{17}}, \bibinfo{pages}{095106} (\bibinfo{year}{2005}).

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