Estimation of effective connectivity using multi-layer perceptron artificial neural network

  • Nasibeh Talebi
  • Ali Motie Nasrabadi
  • Iman Mohammad-Rezazadeh
Research Article
  • 130 Downloads

Abstract

Studies on interactions between brain regions estimate effective connectivity, (usually) based on the causality inferences made on the basis of temporal precedence. In this study, the causal relationship is modeled by a multi-layer perceptron feed-forward artificial neural network, because of the ANN’s ability to generate appropriate input–output mapping and to learn from training examples without the need of detailed knowledge of the underlying system. At any time instant, the past samples of data are placed in the network input, and the subsequent values are predicted at its output. To estimate the strength of interactions, the measure of “Causality coefficient” is defined based on the network structure, the connecting weights and the parameters of hidden layer activation function. Simulation analysis demonstrates that the method, called “CREANN” (Causal Relationship Estimation by Artificial Neural Network), can estimate time-invariant and time-varying effective connectivity in terms of MVAR coefficients. The method shows robustness with respect to noise level of data. Furthermore, the estimations are not significantly influenced by the model order (considered time-lag), and the different initial conditions (initial random weights and parameters of the network). CREANN is also applied to EEG data collected during a memory recognition task. The results implicate that it can show changes in the information flow between brain regions, involving in the episodic memory retrieval process. These convincing results emphasize that CREANN can be used as an appropriate method to estimate the causal relationship among brain signals.

Keywords

Effective connectivity Multi-layer perceptron artificial neural network Multivariate autoregressive Causality Memory recognition 

Notes

Acknowledgements

We are thankful to Professor Tim Curran and his co-authors for providing the EEG data. This research is supported by Cognitive Sciences and technologies Council of Iran, under the Grant Number 2688.

References

  1. Addis DR, Moscovitch M, McAndrews MP (2007) Consequences of hippocampal damage across the autobiographical memory network in left temporal lobe epilepsy. Brain 130(Pt 9):2327–2342. doi:10.1093/brain/awm166 PubMedCrossRefGoogle Scholar
  2. Ashby FG, Ell SW, Valentin VV, Casale MB (2005) FROST: a distributed neurocomputational model of working memory maintenance. J Cogn Neurosci 17(11):1728–1743. doi:10.1162/089892905774589271 PubMedCrossRefGoogle Scholar
  3. Astolfi L, Cincotti F, Babiloni C, Carducci F, Basilisco A, Rossini PM, Babiloni F (2005) Estimation of the cortical connectivity by high-resolution EEG and structural equation modeling: simulations and application to finger tapping data. IEEE Trans Biomed Eng 52(5):757–768. doi:10.1109/TBME.2005.845371 PubMedCrossRefGoogle Scholar
  4. Astolfi L, Cincotti F, Mattia D, Marciani MG, Baccala LA, de Vico Fallani F, Babiloni F (2006) Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data. IEEE Trans Biomed Eng 53(9):1802–1812. doi:10.1109/TBME.2006.873692 PubMedCrossRefGoogle Scholar
  5. Astolfi L, Cincotti F, Mattia D, Marciani MG, Baccala LA, de Vico Fallani F, Babiloni F (2007) Comparison of different cortical connectivity estimators for high-resolution EEG recordings. Hum Brain Mapp 28(2):143–157. doi:10.1002/hbm.20263 PubMedCrossRefGoogle Scholar
  6. Astolfi L, Cincotti F, Mattia D, De Vico Fallani F, Tocci A, Colosimo A, Babiloni F (2008) Tracking the time-varying cortical connectivity patterns by adaptive multivariate estimators. IEEE Trans Biomed Eng 55(3):902–913. doi:10.1109/TBME.2007.905419 PubMedCrossRefGoogle Scholar
  7. Atmanspacher H, Rotter S (2008) Interpreting neurodynamics: concepts and facts. Cogn Neurodyn 2(4):297–318. doi:10.1007/s11571-008-9067-8 PubMedPubMedCentralCrossRefGoogle Scholar
  8. Baba K, Enbutu I, Yoda M (1990) Explicit representation of knowledge acquired from plant historical data using neural network. Paper presented at the 1990 IJCNN International Joint Conference on Neural Networks, 1990Google Scholar
  9. Baccala LA, Alvarenga MY, Sameshima K, Jorge CL, Castro LH (2004) Graph theoretical characterization and tracking of the effective neural connectivity during episodes of mesial temporal epileptic seizure. J Integr Neurosci 3(4):379–395. doi:10.1142/S0219635204000610 PubMedCrossRefGoogle Scholar
  10. Behnam H, Sheikhani A, Mohammadi MR, Noroozian M, Golabi P (2008) Abnormalities in connectivity of quantitative electroencephalogram background activity in autism disorders especially in left hemisphere and right temporal. Paper presented at the tenth international conference on computer modeling and simulation (uksim 2008)Google Scholar
  11. Biswas SK, Marbaniang L, Purkayastha B, Chakraborty M, Singh HR, Bordoloi M (2016) Rainfall forecasting by relevant attributes using artificial neural networks-a comparative study. Int J Big Data Intell 3(2):111–121CrossRefGoogle Scholar
  12. Bitan T, Booth JR, Choy J, Burman DD, Gitelman DR, Mesulam MM (2005) Shifts of effective connectivity within a language network during rhyming and spelling. J Neurosci 25(22):5397–5403. doi:10.1523/JNEUROSCI.0864-05.2005 PubMedPubMedCentralCrossRefGoogle Scholar
  13. Boger Z, Guterman H (1997) Knowledge extraction from artificial neural network models. Paper presented at the 1997 IEEE international conference on systems, man, and cybernetics, 1997. Computational cybernetics and simulationGoogle Scholar
  14. Bowden GJ, Dandy GC, Maier HR (2005) Input determination for neural network models in water resources applications. Part 1—background and methodology. J Hydrol 301(1):75–92. doi:10.1016/j.jhydrol.2004.06.021 CrossRefGoogle Scholar
  15. Bressler SL, Richter CG, Chen Y, Ding M (2007) Cortical functional network organization from autoregressive modeling of local field potential oscillations. Stat Med 26(21):3875–3885. doi:10.1002/sim.2935 PubMedCrossRefGoogle Scholar
  16. Brodmann K (2006) Brodmann’s: localisation in the cerebral cortex (Garey LJ, trans.). Springer USGoogle Scholar
  17. Broman KW, Speed TP (2002) A model selection approach for the identification of quantitative trait loci in experimental crosses. J R Stat Soc Ser B (Stat Methodol) 64(4):641–656. doi:10.1111/1467-9868.00354 CrossRefGoogle Scholar
  18. Brunet D, Murray MM, Michel CM (2011) Spatiotemporal analysis of multichannel EEG: CARTOOL. Comput Intell Neurosci 2011:813870. doi:10.1155/2011/813870 PubMedPubMedCentralCrossRefGoogle Scholar
  19. Buckner RL (2003) Functional–anatomic correlates of control processes in memory. J Neurosci 23(10):3999–4004PubMedGoogle Scholar
  20. Burge J, Lane T, Link H, Qiu S, Clark VP (2009) Discrete dynamic Bayesian network analysis of fMRI data. Hum Brain Mapp 30(1):122–137. doi:10.1002/hbm.20490 PubMedPubMedCentralCrossRefGoogle Scholar
  21. Cadotte AJ, Mareci TH, DeMarse TB, Parekh MB, Rajagovindan R, Ditto WL, Carney PR (2009) Temporal lobe epilepsy: anatomical and effective connectivity. IEEE Trans Neural Syst Rehabil Eng 17(3):214–223. doi:10.1109/TNSRE.2008.2006220 PubMedCrossRefGoogle Scholar
  22. Cansino S, Maquet P, Dolan RJ, Rugg MD (2002) Brain activity underlying encoding and retrieval of source memory. Cereb Cortex 12(10):1048–1056PubMedCrossRefGoogle Scholar
  23. Cheung BL, Nowak R, Lee HC, van Drongelen W, Van Veen BD (2012) Cross validation for selection of cortical interaction models from scalp EEG or MEG. IEEE Trans Biomed Eng 59(2):504–514. doi:10.1109/TBME.2011.2174991 PubMedCrossRefGoogle Scholar
  24. Chuang CH, Huang CS, Lin CT, Ko LW, Chang JY, Yang JM (2012, 4-6 June 2012) Mapping information flow of independent source to predict conscious level: a granger causality based brain–computer interface. Paper presented at the 2012 international symposium on computer, consumer and controlGoogle Scholar
  25. Coben R, Chabot RJ, Hirshberg L (2013) EEG analyses in the assessment of autistic disorders. In: Casanova MF, El-Baz AS, Suri JS (eds) Imaging the brain in autism. Springer, New York, pp 349–370CrossRefGoogle Scholar
  26. Coben R, Mohammad-Rezazadeh I, Cannon RL (2014) Using quantitative and analytic EEG methods in the understanding of connectivity in autism spectrum disorders: a theory of mixed over- and under-connectivity. Front Hum Neurosci 8(45). doi:10.3389/fnhum.2014.00045
  27. Cohen M, Cauwenberghs G (1998) Blind separation of linear convolutive mixtures through parallel stochastic optimization. Paper presented at the proceedings of the 1998 IEEE international symposium on circuits and systems, 1998. ISCAS’98Google Scholar
  28. Curran T, DeBuse C, Woroch B, Hirshman E (2006) Combined pharmacological and electrophysiological dissociation of familiarity and recollection. J Neurosci 26(7):1979–1985. doi:10.1523/JNEUROSCI.5370-05.2006 PubMedCrossRefGoogle Scholar
  29. Danckert S, Gati J, Menon R, Köhler S (2007) Perirhinal and hippocampal contributions to visual recognition memory can be distinguished from those of occipito-temporal structures based on conscious awareness of prior occurrence. Hippocampus 17(11):1081–1092PubMedCrossRefGoogle Scholar
  30. Dietz NA, Jones KM, Gareau L, Zeffiro TA, Eden GF (2005) Phonological decoding involves left posterior fusiform gyrus. Hum Brain Mapp 26(2):81–93. doi:10.1002/hbm.20122 PubMedCrossRefGoogle Scholar
  31. Eichenbaum H, Yonelinas AP, Ranganath C (2007) The medial temporal lobe and recognition memory. Annu Rev Neurosci 30:123–152. doi:10.1146/annurev.neuro.30.051606.094328 PubMedPubMedCentralCrossRefGoogle Scholar
  32. Faes L, Nollo G (2010) Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions. Biol Cybern 103(5):387–400. doi:10.1007/s00422-010-0406-6 PubMedCrossRefGoogle Scholar
  33. Frankland PW, Bontempi B (2005) The organization of recent and remote memories. Nat Rev Neurosci 6(2):119–130. doi:10.1038/nrn1607 PubMedCrossRefGoogle Scholar
  34. Friston K (1994) Functional and effective connectivity in neuroimaging: a synthesis. Hum Brain Mapp 2(1–2):56–78CrossRefGoogle Scholar
  35. Friston KJ, Harrison L, Penny W (2003) Dynamic causal modelling. Neuroimage 19(4):1273–1302PubMedCrossRefGoogle Scholar
  36. Friston K, Harrison L, Daunizeau J, Kiebel S, Phillips C, Trujillo-Barreto N, Mattout J (2008) Multiple sparse priors for the M/EEG inverse problem. Neuroimage 39(3):1104–1120. doi:10.1016/j.neuroimage.2007.09.048 PubMedCrossRefGoogle Scholar
  37. Gevrey M, Dimopoulos I, Lek S (2003) Review and comparison of methods to study the contribution of variables in artificial neural network models. Ecol Model 160(3):249–264. doi:10.1016/s0304-3800(02)00257-0 CrossRefGoogle Scholar
  38. Ghasemi M, Mahloojifar A (2012, 20–21 Dec. 2012) Directed transform function approach for functional network analysis in resting state fMRI data of Parkinson disease. Paper presented at the 2012 19th Iranian conference of biomedical engineering (ICBME)Google Scholar
  39. Giannakakis GA, Nikita KS (2008) Estimation of time-varying causal connectivity on EEG signals with the use of adaptive autoregressive parameters. Paper presented at the Engineering in Medicine and Biology Society, 2008. EMBS 2008. 30th annual international conference of the IEEEGoogle Scholar
  40. Gourévitch B, Le Bouquin-Jeannès R, Faucon G (2006) Linear and nonlinear causality between signals: methods, examples and neurophysiological applications. Biol Cybern 95(4):349–369PubMedCrossRefGoogle Scholar
  41. Gravier A, Quek C, Duch W, Wahab A, Gravier-Rymaszewska J (2016) Neural network modelling of the influence of channelopathies on reflex visual attention. Cogn Neurodyn 10(1):49–72. doi:10.1007/s11571-015-9365-x PubMedCrossRefGoogle Scholar
  42. Hampstead BM, Stringer AY, Stilla RF, Deshpande G, Hu X, Moore AB, Sathian K (2011) Activation and effective connectivity changes following explicit-memory training for face-name pairs in patients with mild cognitive impairment: a pilot study. Neurorehabil Neural Repair 25(3):210–222. doi:10.1177/1545968310382424 PubMedCrossRefGoogle Scholar
  43. Hang X, HaoT, Yu-He L (2009, 12–15 July 2009) Time series prediction based on NARX neural networks: an advanced approach. Paper presented at the 2009 international conference on machine learning and cyberneticsGoogle Scholar
  44. Hannart A, Naveau P (2012) An improved Bayesian information criterion for multiple change-point models. Technometrics 54(3):256–268CrossRefGoogle Scholar
  45. He B, Yang L, Wilke C, Yuan H (2011) Electrophysiological imaging of brain activity and connectivity-challenges and opportunities. IEEE Trans Biomed Eng 58(7):1918–1931. doi:10.1109/TBME.2011.2139210 PubMedPubMedCentralCrossRefGoogle Scholar
  46. Hemmelmann D, Ungureanu M, Hesse W, Wüstenberg T, Reichenbach J, Witte O, Leistritz L (2009) Modelling and analysis of time-variant directed interrelations between brain regions based on BOLD-signals. Neuroimage 45(3):722–737PubMedCrossRefGoogle Scholar
  47. 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 Methods 124(1):27–44PubMedCrossRefGoogle Scholar
  48. Hill DC, McMillan D, Bell KR, Infield D (2012) Application of auto-regressive models to UK wind speed data for power system impact studies. IEEE Trans Sustain Energy 1:134–141CrossRefGoogle Scholar
  49. Horwitz B (2003) The elusive concept of brain connectivity. Neuroimage 19(2 Pt 1):466–470PubMedCrossRefGoogle Scholar
  50. Hytti H, Takalo R, Ihalainen H (2006) Tutorial on multivariate autoregressive modelling. J Clin Monit Comput 20(2):101–108. doi:10.1007/s10877-006-9013-4 PubMedCrossRefGoogle Scholar
  51. Khadem A, Hossein-Zadeh GA (2014) Estimation of direct nonlinear effective connectivity using information theory and multilayer perceptron. J Neurosci Methods 229:53–67PubMedCrossRefGoogle Scholar
  52. Kim H (2013) Differential neural activity in the recognition of old versus new events: an activation likelihood estimation meta-analysis. Hum Brain Mapp 34(4):814–836. doi:10.1002/hbm.21474 PubMedCrossRefGoogle Scholar
  53. Kundu B, Sutterer DW, Emrich SM, Postle BR (2013) Strengthened effective connectivity underlies transfer of working memory training to tests of short-term memory and attention. J Neurosci 33(20):8705–8715. doi:10.1523/JNEUROSCI.5565-12.2013 PubMedPubMedCentralCrossRefGoogle Scholar
  54. Lee CY, Zhang BT (2014) Effective EEG connectivity analysis of episodic memory retrieval. Paper presented at the proceedings of annual meeting of the Cognitive Science Society (CogSci 2014)Google Scholar
  55. Lehnertz K (2011) Assessing directed interactions from neurophysiological signals—an overview. Physiol Meas 32(11):1715–1724. doi:10.1088/0967-3334/32/11/R01 PubMedCrossRefGoogle Scholar
  56. Liu Z, Zhang Y, Bai L, Yan H, Dai R, Zhong C, Feng Y (2012) Investigation of the effective connectivity of resting state networks in Alzheimer’s disease: a functional MRI study combining independent components analysis and multivariate Granger causality analysis. NMR Biomed 25(12):1311–1320PubMedCrossRefGoogle Scholar
  57. Marinazzo D, Liao W, Chen H, Stramaglia S (2011) Nonlinear connectivity by Granger causality. Neuroimage 58(2):330–338. doi:10.1016/j.neuroimage.2010.01.099 PubMedCrossRefGoogle Scholar
  58. May RJ, Maier HR, Dandy GC, Fernando TMKG (2008) Non-linear variable selection for artificial neural networks using partial mutual information. Environ Model Softw 23(10):1312–1326. doi:10.1016/j.envsoft.2008.03.007 CrossRefGoogle Scholar
  59. Mayes AR (1988) Human organic memory disorders. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  60. McIntosh AR (1999) Mapping cognition to the brain through neural interactions. Memory 7(5–6):523–548PubMedCrossRefGoogle Scholar
  61. McNorgan C, Joanisse MF (2014) A connectionist approach to mapping the human connectome permits simulations of neural activity within an artificial brain. Brain Connect 4(1):40–52PubMedGoogle Scholar
  62. Neumaier A, Schneider T (2001) Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans Math Softw: (TOMS) 27(1):27–57CrossRefGoogle Scholar
  63. Nunez PL, Srinivasan R (2006) Electric fields of the brain: the neurophysics of EEG. Oxford University Press, OxfordCrossRefGoogle Scholar
  64. Omidvarnia A, Azemi G, Boashash B, O’Toole JM, Colditz PB, Vanhatalo S (2014) Measuring time-varying information flow in scalp EEG signals: orthogonalized partial directed coherence. IEEE Trans Biomed Eng 61(3):680–693. doi:10.1109/TBME.2013.2286394 PubMedCrossRefGoogle Scholar
  65. Parker A, Bussey TJ, Wilding EL (2005) The cognitive neuroscience of memory: encoding and retrieval, vol 1. Psychology Press, LondonGoogle Scholar
  66. Pereda E, Quiroga RQ, Bhattacharya J (2005) Nonlinear multivariate analysis of neurophysiological signals. Prog Neurobiol 77(1–2):1–37. doi:10.1016/j.pneurobio.2005.10.003 PubMedCrossRefGoogle Scholar
  67. Porcaro C, Zappasodi F, Rossini PM, Tecchio F (2009) Choice of multivariate autoregressive model order affecting real network functional connectivity estimate. Clin Neurophysiol 120(2):436–448. doi:10.1016/j.clinph.2008.11.011 PubMedCrossRefGoogle Scholar
  68. Protopapa F, Siettos CI, Myatchin I, Lagae L (2016) Children with well controlled epilepsy possess different spatio-temporal patterns of causal network connectivity during a visual working memory task. Cogn Neurodyn 10(2):99–111. doi:10.1007/s11571-015-9373-x PubMedPubMedCentralCrossRefGoogle Scholar
  69. Rajapakse JC, Zhou J (2007) Learning effective brain connectivity with dynamic Bayesian networks. Neuroimage 37(3):749–760. doi:10.1016/j.neuroimage.2007.06.003 PubMedCrossRefGoogle Scholar
  70. Roulston MS (1999) Estimating the errors on measured entropy and mutual information. Physica D 125(3):285–294CrossRefGoogle Scholar
  71. Rugg MD, Henson RN (2002) Episodic memory retrieval: an (event-related) functional neuroimaging perspective. In: The cognitive neuroscience of memory encoding and retrieval, pp 3–37Google Scholar
  72. Rugg MD, Fletcher PC, Frith CD, Frackowiak RS, Dolan RJ (1996) Differential activation of the prefrontal cortex in successful and unsuccessful memory retrieval. Brain 119(Pt 6):2073–2083PubMedCrossRefGoogle Scholar
  73. Saad EW, Wunsch DC II (2007) Neural network explanation using inversion. Neural Netw 20(1):78–93PubMedCrossRefGoogle Scholar
  74. Sarvas J (1987) Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys Med Biol 32(1):11–22PubMedCrossRefGoogle Scholar
  75. Schneider T, Neumaier A (2001) Algorithm 808: ARfit—a Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans Math Softw: (TOMS) 27(1):58–65CrossRefGoogle Scholar
  76. Schoffelen JM, Gross J (2009) Source connectivity analysis with MEG and EEG. Hum Brain Mapp 30(6):1857–1865. doi:10.1002/hbm.20745 PubMedCrossRefGoogle Scholar
  77. Sharma A (2000) Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: part 1—a strategy for system predictor identification. J Hydrol 239(1):232–239CrossRefGoogle Scholar
  78. Shibata R (1984) Approximate efficiency of a selection procedure for the number of regression variables. Biometrika 71(1):43–49CrossRefGoogle Scholar
  79. Slotnick SD, Schacter DL (2006) The nature of memory related activity in early visual areas. Neuropsychologia 44(14):2874–2886. doi:10.1016/j.neuropsychologia.2006.06.021 PubMedCrossRefGoogle Scholar
  80. Sommerlade L, Henschel K, Wohlmuth J, Jachan M, Amtage F, Hellwig B, Schelter B (2009) Time-variant estimation of directed influences during Parkinsonian tremor. J Physiol Paris 103(6):348–352. doi:10.1016/j.jphysparis.2009.07.005 PubMedCrossRefGoogle Scholar
  81. Stam CJ, Reijneveld JC (2007) Graph theoretical analysis of complex networks in the brain. Nonlinear Biomed Phys 1(1):3. doi:10.1186/1753-4631-1-3 PubMedPubMedCentralCrossRefGoogle Scholar
  82. Stam C, Van Dijk B (2002) Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets. Physica D 163(3):236–251CrossRefGoogle Scholar
  83. Stoica P, Selen Y (2004) Model-order selection: a review of information criterion rules. IEEE Signal Process Mag 21(4):36–47CrossRefGoogle Scholar
  84. Supp GG, Schlogl A, Trujillo-Barreto N, Muller MM, Gruber T (2007) Directed cortical information flow during human object recognition: analyzing induced EEG gamma-band responses in brain’s source space. PLoS ONE 2(8):e684. doi:10.1371/journal.pone.0000684 PubMedPubMedCentralCrossRefGoogle Scholar
  85. Tulving E (1985) Elements of episodic memory. Oup, OxfordGoogle Scholar
  86. Tuncer O, Shanker B, Kempel L (2012) Tetrahedral-based vector generalized finite element method and its applications. IEEE Antennas Wirel Propag Lett 11:945–948CrossRefGoogle Scholar
  87. Valdes-Sosa PA, Roebroeck A, Daunizeau J, Friston K (2011) Effective connectivity: influence, causality and biophysical modeling. Neuroimage 58(2):339–361. doi:10.1016/j.neuroimage.2011.03.058 PubMedPubMedCentralCrossRefGoogle Scholar
  88. van der Velde F, de Kamps M (2015) The necessity of connection structures in neural models of variable binding. Cogn Neurodyn 9(4):359–370. doi:10.1007/s11571-015-9331-7 PubMedPubMedCentralCrossRefGoogle Scholar
  89. Vilberg KL, Rugg MD (2008) Memory retrieval and the parietal cortex: a review of evidence from a dual-process perspective. Neuropsychologia 46(7):1787–1799. doi:10.1016/j.neuropsychologia.2008.01.004 PubMedPubMedCentralCrossRefGoogle Scholar
  90. Wagner AD, Shannon BJ, Kahn I, Buckner RL (2005) Parietal lobe contributions to episodic memory retrieval. Trends Cogn Sci 9(9):445–453. doi:10.1016/j.tics.2005.07.001 PubMedCrossRefGoogle Scholar
  91. Wang R, Zhu Y (2016) Can the activities of the large scale cortical network be expressed by neural energy? A brief review. Cogn Neurodyn 10(1):1–5. doi:10.1007/s11571-015-9354-0 PubMedCrossRefGoogle Scholar
  92. Ward J (2015) The student’s guide to cognitive neuroscience. Psychology Press, LondonGoogle Scholar
  93. Watrous AJ, Tandon N, Conner CR, Pieters T, Ekstrom AD (2013) Frequency-specific network connectivity increases underlie accurate spatiotemporal memory retrieval. Nat Neurosci 16(3):349–356. doi:10.1038/nn.3315 PubMedPubMedCentralCrossRefGoogle Scholar
  94. Weis S, Klaver P, Reul J, Elger CE, Fernández G (2004) Temporal and cerebellar brain regions that support both declarative memory formation and retrieval. Cereb Cortex 14(3):256–267. doi:10.1093/cercor/bhg125 PubMedCrossRefGoogle Scholar
  95. Wennekers T, Ay N (2005) Finite state automata resulting from temporal information maximization and a temporal learning rule. Neural Comput 17(10):2258–2290. doi:10.1162/0899766054615671 PubMedCrossRefGoogle Scholar
  96. Winterhalder M, Schelter B, Hesse W, Schwab K, Leistritz L, Klan D, Witte H (2005) Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems. Signal Process 85(11):2137–2160CrossRefGoogle Scholar
  97. Wu X, Li J, Yao L (2012) Determining effective connectivity from FMRI data using a gaussian dynamic bayesian network. Paper presented at the neural information processingGoogle Scholar
  98. Zeng LL, Liao Y, Zhou Z, Shen H, Liu Y, Liu X, Hu D (2016) Default network connectivity decodes brain states with simulated microgravity. Cogn Neurodyn 10(2):113–120. doi:10.1007/s11571-015-9359-8 PubMedCrossRefGoogle Scholar
  99. Zhang NR, Siegmund DO (2007) A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data. Biometrics 63(1):22–32. doi:10.1111/j.1541-0420.2006.00662.x PubMedCrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Nasibeh Talebi
    • 1
  • Ali Motie Nasrabadi
    • 1
  • Iman Mohammad-Rezazadeh
    • 2
  1. 1.Department of Biomedical Engineering, Faculty of EngineeringShahed UniversityTehranIran
  2. 2.HRL Laboratories, LLCMalibuUSA

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