Feed-forward artificial neural network provides data-driven inference of functional connectivity.

We propose a new model-free method based on the feed-forward artificial neuronal network for detecting functional connectivity in coupled systems. The developed method which does not require large computational costs and which is able to work with short data trials can be used for analysis and reconstruction of connectivity in experimental multichannel data of different nature. We test this approach on the chaotic Rössler system and demonstrate good agreement with the previous well-known results. Then, we use our method to predict functional connectivity thalamo-cortical network of epileptic brain based on ECoG data set of WAG/Rij rats with genetic predisposition to absence epilepsy. We show the emergence of functional interdependence between cortical layers and thalamic nuclei after epileptic discharge onset.

[1]  Giulio Ruffini,et al.  Detection of Generalized Synchronization using Echo State Networks , 2017, Chaos.

[2]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Edward Ott,et al.  Attractor reconstruction by machine learning. , 2018, Chaos.

[4]  Pyragas,et al.  Weak and strong synchronization of chaos. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  A. Pikovsky,et al.  Synchronization: Theory and Application , 2003 .

[6]  M. Roulston Estimating the errors on measured entropy and mutual information , 1999 .

[7]  Steven L. Brunton,et al.  Deep learning for universal linear embeddings of nonlinear dynamics , 2017, Nature Communications.

[8]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[9]  Stefano Boccaletti,et al.  Generalized synchronization in mutually coupled oscillators and complex networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Nearest neighbors, phase tubes, and generalized synchronization. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  A. Schnitzler,et al.  Normal and pathological oscillatory communication in the brain , 2005, Nature Reviews Neuroscience.

[12]  Alexey A Koronovskii,et al.  Generalized synchronization: a modified system approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Vladimir A. Maksimenko,et al.  Betweenness centrality in multiplex brain network during mental task evaluation , 2018, Physical Review E.

[14]  A.N. Pisarchik,et al.  Optical Chaotic Communication Using Generalized and Complete Synchronization , 2010, IEEE Journal of Quantum Electronics.

[15]  Michael Small,et al.  Synchronization of chaotic systems and their machine-learning models. , 2019, Physical review. E.

[16]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[17]  Olga I. Moskalenko,et al.  On the use of chaotic synchronization for secure communication , 2009 .

[18]  Jaideep Pathak,et al.  Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data. , 2017, Chaos.

[19]  Jaideep Pathak,et al.  Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach. , 2018, Physical review letters.

[20]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Stefano Boccaletti,et al.  Macroscopic and microscopic spectral properties of brain networks during local and global synchronization. , 2017, Physical review. E.

[22]  Fernando Maestú,et al.  Artificial neural network detects human uncertainty. , 2018, Chaos.

[23]  E. van Luijtelaar,et al.  Genetic Animal Models for Absence Epilepsy: A Review of the WAG/Rij Strain of Rats , 2003, Behavior genetics.

[24]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[25]  P. Fries Rhythms for Cognition: Communication through Coherence , 2015, Neuron.

[26]  Sarah Feldt Muldoon,et al.  Small-World Propensity and Weighted Brain Networks , 2016, Scientific Reports.

[27]  Anastasiya E. Runnova,et al.  Classifying the Perceptual Interpretations of a Bistable Image Using EEG and Artificial Neural Networks , 2017, Front. Neurosci..

[28]  Gabriele Arnulfo,et al.  Modular co-organization of functional connectivity and scale-free dynamics in the human brain , 2017, Network Neuroscience.

[29]  Alexander Pisarchik,et al.  Multiscale neural connectivity during human sensory processing in the brain. , 2018, Physical review. E.

[30]  Gilles van Luijtelaar,et al.  Dynamics of networks during absence seizure's on- and offset in rodents and man , 2015, Front. Physiol..

[31]  Jan-Mathijs Schoffelen,et al.  A Tutorial Review of Functional Connectivity Analysis Methods and Their Interpretational Pitfalls , 2016, Front. Syst. Neurosci..

[32]  Alexey A. Koronovskii,et al.  Resistant to noise chaotic communication scheme exploiting the regime of generalized synchronization , 2017 .

[33]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[34]  C. Stam Modern network science of neurological disorders , 2014, Nature Reviews Neuroscience.

[35]  Evgenia Sitnikova,et al.  Thalamo-cortical mechanisms of sleep spindles and spike–wave discharges in rat model of absence epilepsy (a review) , 2010, Epilepsy Research.