Efficient transfer entropy analysis of non-stationary neural time series

PLoS ONE

Volumn 9, Issue 7, 2014, Pages

  Wollstadt, Patricia ^a   Martínez Zarzuela, Mario ^d   Vicente, Raul ^b,c   Díaz Pernas, Francisco J ^d   Wibral, Michael ^a  

^a GOETHE UNIVERSITY   (Germany)

^b FRANKFURT INSTITUTE FOR ADVANCED STUDIES   (Germany)

^c MAX PLANCK INSTITUTE FOR BRAIN RESEARCH   (Germany)

^d UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ACCURACY; ADULT; ALGORITHM; APPROXIMATE NEAREST NEIGHBOR ALGORITHM; ARTICLE; COMPUTER GRAPHICS; COMPUTER INTERFACE; CONTROLLED STUDY; FALSE POSITIVE RESULT; FEMALE; GRAPHICS PROCESSING UNIT ALGORITHM; HUMAN; HUMAN EXPERIMENT; IMAGE ANALYSIS; INFORMATION PROCESSING; K NEAREST NEIGHBOR; KRASKOV STOGBAUER GRASSBERGER ESTIMATOR; MAGNETOENCEPHALOGRAPHY; MAGNETOENCEPHALOGRAPHY SYSTEM; MALE; MATHEMATICAL COMPUTING; NEUROSCIENCE; NON STATIONARY NEURAL TIME SERIES; NORMAL HUMAN; NUCLEAR MAGNETIC RESONANCE IMAGING; NUCLEAR MAGNETIC RESONANCE SCANNER; PROBABILITY DENSITY FUNCTION; PROCESS OPTIMIZATION; RANGE SEARCH ALGORITHM; REPRODUCIBILITY; SAMPLE SIZE; SIMULATION; STATISTICAL ANALYSIS; STATISTICAL PARAMETERS; TASK PERFORMANCE; TIME SERIES ANALYSIS; TRANSFER ENTROPY; WORKFLOW; THEORETICAL MODEL;

ALGORITHMS; MODELS, THEORETICAL;

EID: 84904864048     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0102833     Document Type: Article

References (119)

1. Turing AM (1936) On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 42: 230-265.
2. Langton CG (1990) Computation at the edge of chaos: Phase transitions and emergent computation. Physica D: Nonlinear Phenomena 42: 12-37.
3. Mitchell M (1998) Computation in cellular automata: A selected review. In: Gramß T, Bornholdt S, Groß M, Mitchell M, Pellizzari T, editors, Non-Standard Computation, Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA. pp. 95-140.
4. Lizier JT (2013) The local information dynamics of distributed computation in complex systems. Springer Theses Series. Berlin/Heidelberg: Springer.
5. Wibral M, Lizier JT, Vögler S, Priesemann V, Galuske R (2014) Local active information storage as a tool to understand distributed neural information processing. Front Neuroinform 8: 1.
6. Lizier JT, Prokopenko M, Zomaya AY (2010) Information modification and particle collisions in distributed computation. Chaos 20: 037109-037109.
7. Lizier JT, Flecker B, Williams PL (2013) Towards a synergy-based approach to measuring information modification. arXiv preprint arXiv:13033440.
8. Williams PL, Beer RD (2010) Nonnegative decomposition of multivariate information. arXiv preprint arXiv:10042515.
9. Bertschinger N, Rauh J, Olbrich E, Jost J (2012) Shared information - New insights and problems in decomposing information in complex systems. arXiv preprint arXiv:12105902.
10. Griffith V, Koch C (2012) Quantifying synergistic mutual information. arXiv preprint arXiv:12054265.
11. Harder M, Salge C, Polani D (2013) Bivariate measure of redundant information. Phys Rev E Stat Nonlin Soft Matter Phys 87: 012130.
12. Bertschinger N, Rauh J, Olbrich E, Jost J, Ay N (2014) Quantifying unique information. Entropy 16: 2161-2183.
13. Lizier JT, Prokopenko M, Zomaya AY (2012) Local measures of information storage in complex distributed computation. Inform Sciences 208: 39-54.
14. Schreiber T (2000) Measuring information transfer. Phys Rev Lett 85: 461-464.
15. Lizier JT, Prokopenko M, Zomaya AY (2008) Local information transfer as a spatiotemporal filter for complex systems. Phys Rev E Stat Nonlin Soft Matter Phys 77: 026110.
16. Lizier JT (2014) Measuring the dynamics of information processing on a local scale in time and space. In: Wibral M, Vicente R, Lizier JT, editors, Directed Information Measures in Neuroscience, Springer Berlin Heidelberg, Understanding Complex Systems. pp. 161-193.
17. Gómez C, Lizier JT, Schaum M, Wollstadt P, Grützner C, et al. (2014) Reduced predictable information in brain signals in autism spectrum disorder. Front Neuroinform 8: 9.
18. Dasgupta S, Wörgötter F, Manoonpong P (2013) Information dynamics based self-adaptive reservoir for delay temporal memory tasks. Evolving Systems: 1-15.
19. Vicente R, Wibral M, Lindner M, Pipa G (2011) Transfer entropy - a model-free measure of effective connectivity for the neurosciences. J Comput Neurosci 30: 45-67.
20. Wibral M, Rahm B, Rieder M, Lindner M, Vicente R, et al. (2011) Transfer entropy in magnetoencephalographic data: quantifying information flow in cortical and cerebellar networks. Prog Biophys Mol Biol 105: 80-97.
21. Paluš M (2001) Synchronization as adjustment of information rates: detection from bivariate time series. Phys Rev E Stat Nonlin Soft Matter Phys 63: 046211.
22. Vakorin VA, Kovacevic N, McIntosh AR (2010) Exploring transient transfer entropy based on a group-wise ICA decomposition of EEG data. Neuroimage 49: 1593-1600.
23. Vakorin VA, Krakovska OA, McIntosh AR (2009) Confounding effects of indirect connections on causality estimation. J Neurosci Methods 184: 152-160.
24. Chávez M, Martinerie J, Le Van Quyen M (2003) Statistical assessment of nonlinear causality: application to epileptic EEG signals. J Neurosci Methods 124: 113-28. (Pubitemid 36442693)
25. Amblard PO, Michel OJ (2011) On directed information theory and Granger causality graphs. J Comput Neurosci 30: 7-16.
26. Barnett L, Barrett AB, Seth AK (2009) Granger causality and transfer entropy are equivalent for Gaussian variables. Phys Rev Lett 103: 238701.
27. Besserve M, Scholkopf B, Logothetis NK, Panzeri S (2010) Causal relationships between frequency bands of extracellular signals in visual cortex revealed by an information theoretic analysis. J Comput Neurosci 29: 547-566.
28. Buehlmann A, Deco G (2010) Optimal information transfer in the cortex through synchronization. PLoS Comput Biol 6: e1000934.
29. Garofalo M, Nieus T, Massobrio P, Martinoia S (2009) Evaluation of the performance of information theory-based methods and cross-correlation to estimate the functional connectivity in cortical networks. PLoS One 4: e6482.
30. Gourevitch B, Eggermont JJ (2007) Evaluating information transfer between auditory cortical neurons. J Neurophysiol 97: 2533-2543. (Pubitemid 46411182)
31. Lizier JT, Heinzle J, Horstmann A, Haynes JD, Prokopenko M (2011) Multivariate informationtheoretic measures reveal directed information structure and task relevant changes in fmri connectivity. J Comput Neurosci 30: 85-107.
32. Lüdtke N, Logothetis NK, Panzeri S (2010) Testing methodologies for the nonlinear analysis of causal relationships in neurovascular coupling. Magn Reson Imaging 28: 1113-1119.
33. Neymotin SA, Jacobs KM, Fenton AA, Lytton WW (2011) Synaptic information transfer in computer models of neocortical columns. J Comput Neurosci 30: 69-84.
34. Sabesan S, Good LB, Tsakalis KS, Spanias A, Treiman DM, et al. (2009) Information flow and application to epileptogenic focus localization from intracranial EEG. IEEE Trans Neural Syst Rehabil Eng 17: 244-53.
35. Staniek M, Lehnertz K (2009) Symbolic transfer entropy: inferring directionality in biosignals. Biomed Tech (Berl) 54: 323-8.
36. Vakorin VA, Misic B, Kraskovska O, McIntosh AR (2011) Empirical and theoretical aspects of generation and transfer of information in a neuromagnetic source network. Front Syst Neurosci 5.
37. Roux F, Wibral M, Singer W, Aru J, Uhlhaas PJ (2013) The phase of thalamic alpha activity modulates cortical gamma-band activity: evidence from resting-state meg recordings. J Neurosci 33: 17827-17835.
38. Pampu NC, Vicente R, Muresan RC, Priesemann V, Siebenhuhner F, et al. (2013) Transfer entropy as a tool for reconstructing interaction delays in neural signals. In: Signals, Circuits and Systems (ISSCS), 2013 International Symposium on. IEEE, pp. 1-4.
39. Wibral M, Vicente R, Lindner M (2014) Transfer entropy in neuroscience. In: Wibral M, Vicente R, Lizier JT, editors, Directed Information Measures in Neuroscience, Springer Berlin Heidelberg, Understanding Complex Systems. pp. 3-36.
40. Marinazzo D, Wu G, Pellicoro M, Stramaglia S (2014) Information transfer in the brain: Insights from a unified approach. In: Wibral M, Vicente R, Lizier JT, editors, Directed Information Measures in Neuroscience, Springer Berlin Heidelberg, Understanding Complex Systems. pp. 87-110.
41. Faes L, Porta A (2014) Conditional entropy-based evaluation of information dynamics in physiological systems. In: Wibral M, Vicente R, Lizier JT, editors, Directed Information Measures in Neuroscience, Springer Berlin Heidelberg, Understanding Complex Systems. pp. 61-86.
42. Faes L, Nollo G (2006) Bivariate nonlinear prediction to quantify the strength of complex dynamical interactions in short-term cardiovascular variability. Med Biol Eng Comput 44: 383-392. (Pubitemid 43949695)
43. Faes L, Nollo G, Porta A (2011) Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series. Comput Biol Med 42: 290-297.
44. Faes L, Nollo G, Porta A (2011) Information-based detection of nonlinear granger causality in multivariate processes via a nonuniform embedding technique. Phys Rev E Stat Nonlin Soft Matter Phys 83: 051112.
45. Kwon O, Yang JS (2008) Information flow between stock indices. Europhys Lett 82: 68003.
46. Kim J, Kim G, An S, Kwon YK, Yoon S (2013) Entropy-based analysis and bioinformatics-inspired integration of global economic information transfer. PLoS ONE 8: e51986.
47. Ay N, Polani D (2008) Information flows in causal networks. Adv Complex Syst 11: 17.
48. Lizier JT, Prokopenko M (2010) Differentiating information transfer and causal effect. Eur Phys J B 73: 605-615.
49. Chicharro D, Ledberg A (2012) When two become one: the limits of causality analysis of brain dynamics. PLoS One 7: e32466.
50. Lizier JT, Rubinov M (2012) Multivariate construction of effective computational networks from observational data. Max Planck Institute for Mathematics in the Sciences Preprint 25/2012.
51. Stramaglia S, Wu GR, Pellicoro M, Marinazzo D (2012) Expanding the transfer entropy to identify information circuits in complex systems. Phys Rev E Stat Nonlin Soft Matter Phys 86: 066211.
52. Bettencourt LM, Stephens GJ, Ham MI, Gross GW (2007) Functional structure of cortical neuronal networks grown in vitro. Phys Rev E Stat Nonlin Soft Matter Phys 75: 021915.
53. Wibral M, Pampu N, Priesemann V, Siebenhühner F, Seiwert H, et al. (2013) Measuring information-transfer delays. PloS one 8: e55809.
54. Wibral M, Wollstadt P, Meyer U, Pampu N, Priesemann V, et al. (2012) Revisiting Wiener's principle of causality - interaction-delay reconstruction using transfer entropy and multivariate analysis on delay-weighted graphs. Conf Proc IEEE Eng Med Biol Soc 2012: 3676-3679.
55. Gomez-Herrero G, Wu W, Rutanen K, Soriano M, Pipa G, et al. (2010) Assessing coupling dynamics from an ensemble of time series. arXiv preprint arXiv:10080539.
56. Lindner M, Vicente R, Priesemann V, Wibral M (2011) TRENTOOL: A MATLAB open source toolbox to analyse information flow in time series data with transfer entropy. BMC Neurosci 12: 119.
57. Kraskov A, Stoegbauer H, Grassberger P (2004) Estimating mutual information. Phys Rev E Stat Nonlin Soft Matter Phys 69: 066138.
58. Owens JD, Houston M, Luebke D, Green S, Stone JE, et al. (2008) GPU computing. Proc IEEE 96: 879-899.
59. Brodtkorb AR, Hagen TR, Sætra ML (2013) Graphics processing unit (GPU) programming strategies and trends in GPU computing. J Parallel Distr Com 73: 4-13.
60. Lee D, Dinov I, Dong B, Gutman B, Yanovsky I, et al. (2012) CUDA optimization strategies for compute- and memory-bound neuroimaging algorithms. Comput Methods Programs Biomed 106: 175-187.
61. Martínez-Zarzuela M, Gómez C, Díaz-Pernas FJ, Fernández A, Hornero R (2013) Crossapproximate entropy parallel computation on GPUs for biomedical signal analysis. Application to MEG recordings. Comput Methods Programs Biomed 112: 189-199.
62. Konstantinidis EI, Frantzidis CA, Pappas C, Bamidis PD (2012) Real time emotion aware applications: A case study employing emotion evocative pictures and neuro-physiological sensing enhanced by graphic processor units. Comput Methods Programs Biomed 107: 16-27.
63. Arefin AS, Riveros C, Berretta R, Moscato P (2012) GPU-FS-kNN: A software tool for fast and scalable kNN computation using GPUs. PLoS One 7: e44000.
64. Wilson JA, Williams JC (2009) Massively parallel signal processing using the graphics processing unit for real-time brain-computer interface feature extraction. Front Neuroeng 2: 11.
65. Chen D, Wang L, Ouyang G, Li X (2011) Massively parallel neural signal processing on a manycore platform. Comput Sci Eng 13: 42-51.
66. Liu Y, Schmidt B, Liu W, Maskell DL (2010) CUDA-MEME: Accelerating motif discovery in biological sequences using CUDA-enabled graphics processing units. Pattern Recognit Lett 31: 2170-2177.
67. Merkwirth C, Parlitz U, Lauterborn W (2000) Fast nearest-neighbor searching for nonlinear signal processing. Phys Rev E Stat Nonlin Soft Matter Phys 62: 2089-2097.
68. Gardner WA, Napolitano A, Paura L (2006) Cyclostationarity: Half a century of research. Signal Process 86: 639-697. (Pubitemid 43242966)
69. Williams PL, Beer RD (2011) Generalized measures of information transfer. arXiv preprint arXiv:11021507.
70. Takens F (1981) Dynamical Systems and Turbulence, Warwick 1980, Springer, volume 898 of Lecture Notes in Mathematics, chapter Detecting Strange Attractors in Turbulence. pp. 366-381.
71. Ragwitz M, Kantz H (2002) Markov models from data by simple nonlinear time series predictors in delay embedding spaces. Phys Rev E Stat Nonlin Soft Matter Phys 65: 056201.
72. Kozachenko L, Leonenko N (1987) Sample estimate of entropy of a random vector. Probl Inform Transm 23: 95-100.
73. Victor JD (2005) Binless strategies for estimation of information from neural data. Phys Rev E Stat Nonlin Soft Matter Phys 72: 051903.
74. Vicente R, Wibral M (2014) Efficient estimation of information transfer. In: Wibral M, Vicente R, Lizier JT, editors, Directed Information Measures in Neuroscience, Springer Berlin Heidelberg, Understanding Complex Systems. pp. 37-58.
75. NVIDIA Corporation (2013). CUDA toolkit documentation. Available: http://docs.nvidia.com/cuda. Accessed 7 November 2013.
76. Maris E, Oostenveld R (2007) Nonparametric statistical testing of EEG- and MEG-data. J Neurosci Methods 164: 177-90. (Pubitemid 46950991)
77. Bentley JL, Friedman JH (1979) Data structures for range searching. ACM Comput Surv 11: 397-409.
78. Arya S, Mount DM, Netanyahu NS, Silverman R, Wu AY (1998) An optimal algorithm for approximate nearest neighbor searching fixed dimensions. J ACM 45: 891-923.
79. Muja M, Lowe DG (2009) Fast approximate nearest neighbors with automatic algorithm configuration. In: In VISAPP International Conference on Computer Vision Theory and Applications. pp. 331-340.
80. Garcia V, Debreuve E, Nielsen F, Barlaud M (2010) K-nearest neighbor search: Fast GPU-based implementations and application to high-dimensional feature matching. In: Image Processing (ICIP), 2010 17th IEEE International Conference on. pp. 3757-3760.
81. Sismanis N, Pitsianis N, Sun X (2012) Parallel search of k-nearest neighbors with synchronous operations. In: High Performance Extreme Computing (HPEC), 2012 IEEE Conference on. pp. 1-6.
82. Brown S, Snoeyink J. GPU nearest neighbor searches using a minimal kd-tree. Available: http://cs.unc.edu/~shawndb. Accessed 7 November 2013.
83. Li S, Simons LC, Pakaravoor JB, Abbasinejad F, Owens JD, et al. (2012) kANN on the GPU with shifted sorting. In: Dachsbacher C, Munkberg J, Pantaleoni J, editors, Proceedings of the Fourth ACM SIGGRAPH/Eurographics conference on High-Performance Graphics. High Performance Graphics 2012, The Eurographics Association, pp. 39-47.
84. Pan J, Manocha D (2012) Bi-level locality sensitive hashing for k-nearest neighbor computation. In: Data Engineering (ICDE), 2012 IEEE 28th International Conference on. pp. 378-389. doi: 10.1109/ICDE.2012.40.
85. Khronos OpenCL Working Group, Munshi A (2009). The OpenCL specification version: 1.0 document revision: 48. Available: http://www.khronos.org/registry/ cl/specs/opencl-1.0.pdf. Accessed 30 May 2014.
86. Grützner C, Uhlhaas PJ, Genc E, Kohler A, Singer W, et al. (2010) Neuroelectromagnetic correlates of perceptual closure processes. J Neurosci 30: 8342-8352.
87. Kraskov A (2004) Synchronization and Interdependence measures and their application to the electroencephalogram of epilepsy patients and clustering of data. Ph.D. thesis, University of Wuppertal.
88. Mooney CM, Ferguson GA (1951) A new closure test. Can J Psychol 5: 129-133.
89. Oostenveld R, Fries P, Maris E, Schoffelen JM (2011) FieldTrip: Open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data. Comput Intell Neurosci 2011: 156869.
90. Gross J, Kujala J, Hamalainen M, Timmermann L, Schnitzler A, et al. (2001) Dynamic imaging of coherent sources: studying neural interactions in the human brain. Proc Natl Acad Sci U S A 98: 694-699. (Pubitemid 32105105)
91. Brookes MJ, Vrba J, Robinson SE, Stevenson CM, Peters AM, et al. (2008) Optimising experimental design for meg beamformer imaging. Neuroimage 39: 1788-1802.
92. Bar M, Kassam KS, Ghuman AS, Boshyan J, Schmid AM, et al. (2006) Top-down facilitation of visual recognition. P Natl Acad Sci USA 103: 449-454. (Pubitemid 43122421)
93. Cavanagh P (1991) Whats up in top-down processing. In: Gorea A, editor, Representations of vision: Trends and tacit assumptions in vision research, Cambridge University Press. pp. 295-304.
94. Verdes PF (2005) Assessing causality from multivariate time series. Phys Rev E Stat Nonlin Soft Matter Phys 72: 026222.
95. Pompe B, Runge J (2011) Momentary information transfer as a coupling measure of time series. Phys Rev E Stat Nonlin Soft Matter Phys 83: 051122.
96. Marschinski R, Kantz H (2002) Analysing the information flow between financial time series. Eur Phys J B 30: 275-281.
97. Sauseng P, Klimesch W, Gruber WR, Hanslmayr S, Freunberger R, et al. (2007) Are event-related potential components generated by phase resetting of brain oscillations? A critical discussion. Neuroscience 146: 1435-1444. (Pubitemid 46783212)
98. Makeig S, Debener S, Onton J, Delorme A (2004) Mining event-related brain dynamics. Trends Cogn Sci 8: 204-210. (Pubitemid 38543249)
99. Shah AS, Bressler SL, Knuth KH, Ding M, Mehta AD, et al. (2004) Neural dynamics and the fundamental mechanisms of event-related brain potentials. Cereb Cortex 14: 476-483. (Pubitemid 38579648)
100. Jervis BW, Nichols MJ, Johnson TE, Allen E, Hudson NR (1983) A fundamental investigation of the composition of auditory evoked potentials. IEEE Trans Biomed Eng: 43-50.
101. Mangun GR (1992) Human brain potentials evoked by visual stimuli: induced rhythms or timelocked components? In: Basar E, Bullock TH, editors, Induced rhythms in the brain, Boston, MA: Birkhauser. pp. 217-231.
102. Schroeder CE, Steinschneider M, Javitt DC, Tenke CE, Givre SJ, et al. (1995) Localization of ERP generators and identification of underlying neural processes. Electroen Clin Neuro Suppl 44: 55.
103. Sayers BM, Beagley H, Henshall W (1974) The mechanism of auditory evoked EEG responses. Nature 247: 481-483.
104. Makeig S, Westerfield M, Jung TP, Enghoff S, Townsend J, et al. (2002) Dynamic brain sources of visual evoked responses. Science 295: 690-694. (Pubitemid 34111830)
105. Jansen BH, Agarwal G, Hegde A, Boutros NN (2003) Phase synchronization of the ongoing EEG and auditory EP generation. Clin Neurophysiol 114: 79-85. (Pubitemid 35454175)
106. Klimesch W, Schack B, Schabus M, Doppelmayr M, Gruber W, et al. (2004) Phase-locked alpha and theta oscillations generate the P1-N1 complex and are related to memory performance. Cognitive Brain Res 19: 302-316. (Pubitemid 38520024)
107. Turi G, Gotthardt S, Singer W, Vuong TA, Munk M, et al. (2012) Quantifying additive evoked contributions to the event-related potential. Neuroimage 59: 2607-2624.
108. Möller E, Schack B, Arnold M, Witte H (2001) Instantaneous multivariate EEG coherence analysis by means of adaptive high-dimensional autoregressive models. J Neurosci Meth 105: 143-158. (Pubitemid 32223935)
109. Ding M, Bressler SL, Yang W, Liang H (2000) Short-window spectral analysis of cortical eventrelated potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment. Biol Cybern 83: 35-45.
110. Hesse W, Möller E, Arnold M, Schack B (2003) The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies. J Neurosci Meth 124: 27-44. (Pubitemid 36315806)
111. Leistritz L, Hesse W, Arnold M, Witte H (2006) Development of interaction measures based on adaptive non-linear time series analysis of biomedical signals. Biomed Tech 51: 64-69.
112. Wibral M, Turi G, Linden DEJ, Kaiser J, Bledowski C (2008) Decomposition of working memoryrelated scalp ERPs: crossvalidation of fMRI-constrained source analysis and ICA. Int J Psychophysiol 67: 200-211. (Pubitemid 351273441)
113. Andrzejak RG, Ledberg A, Deco G (2006) Detecting event-related time-dependent directional couplings. New Journal of Physics 8: 6.
114. Strong SP, de Ruyter van Steveninck RR, Bialek W, Koberle R (1998) On the application of information theory to neural spike trains. Pac Symp Biocomput: 621-632.
115. Georgieva SS, Todd JT, Peeters R, Orban GA (2008) The extraction of 3D shape from texture and shading in the human brain. Cereb Cortex 18: 2416-2438.
116. Kanwisher N, Tong F, Nakayama K (1998) The effect of face inversion on the human fusiform face area. Cognition 68: B1-B11. (Pubitemid 128424122)
117. Andrews TJ, Schluppeck D (2004) Neural responses to Mooney images reveal a modular representation of faces in human visual cortex. Neuroimage 21: 91-98. (Pubitemid 38115000)
118. McKeeff TJ, Tong F (2007) The timing of perceptual decisions for ambiguous face stimuli in the human ventral visual cortex. Cerebral Cortex 17: 669-678.
119. Faes L, Nollo G, Porta A (2013) Compensated transfer entropy as a tool for reliably estimating information transfer in physiological time series. Entropy 15: 198-219.