From dynamics to links: a sparse reconstruction of the topology of a neural network

• Main Authors: Aletti Giacomo, Lonardoni Davide, Naldi Giovanni, Nieus Thierry
• Format: Article
• Language: English
• Published: Sciendo 2019-01-01
• Series: Communications in Applied and Industrial Mathematics
• Subjects: neural networks; sparse reconstruction; lasso method
• Online Access: https://doi.org/10.2478/caim-2019-0002

One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal transduction have been studied intensively and a better knowledge and understanding of some basic processes of information handling by neurons has been achieved. In contrast, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor electrical activity of a large number of neurons in real time. Then, the qualitative and quantitative analysis of the spiking activity of individual neurons is a very valuable tool for the study of the dynamics and architecture of the neural networks. Such activity is not due to the sole intrinsic properties of the individual neural cells but it is mostly the consequence of the direct influence of other neurons. The deduction of the effective connectivity between neurons, whose experimental spike trains are observed, is of crucial importance in neuroscience: first for the correct interpretation of the electro-physiological activity of the involved neurons and neural networks, and, for correctly relating the electrophysiological activity to the functional tasks accomplished by the network. In this work, we propose a novel method for the identification of connectivity of neural networks using recorded voltages. Our approach is based on the assumption that the network has a topology with sparse connections. After a brief description of our method, we will report the performances and compare it to the cross-correlation computed on the spike trains, which represents a gold standard method in the field.