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Information Transmission in Balanced Neuronal Networks: the Role of Matrix Non-Normality

This presentation will report the state of the work that I am doing in collaboration with the PhD student Giacomo Baggio. This is inspired by the paper [1] which proposes a model explaining how populations of neurons in motor cortex produce large amplitude transient signals during the execution of movements. The model adopted for the single neuron is the integrate and fire that is then simplified to a firing-rate model. The neuronal networks are then modeled by balanced excitatory-inhibitory networks whose nonlinearity is moderate and simple to treat [2, section 7]. The thesis of [1] is that the balanced neuronal networks that are more efficient to generate large amplitude transient signals are characterized by a large controllability Gramian (a matrix which is associated with the linear model of the network). It is finally proposed a way in which the Gramian can be increased. However, the size of the Gramian depends on two different properties of the linear model: the eigenvalues distribution of the model matrix (which determines also the stability) and its eigenvectors which are related to the so called matrix non-normality. The different influence of these two properties are not explained in [1]. In our contribution we propose a different way to interpret the role of the populations of neurons in motor cortex, which uses the notion of Shannon channel capacity and of inter-symbol interference, which are central notions in digital telecommunication. Using this interpretation we can distinguish the role of the eigenvalues and of the non-normality showing the importance of this last property for obtaining high performance information transmission in neuronal networks. The content of the presentation will be rather basic for neuroscientists but with a quite strong content of linear algebra. There will be an attempt to keep the presentation accessible also to less mathematically oriented audience.

[1] Hennequin, et al. “Optimal control of transient dynamics in balanced networks supports generation of complex movements.” Neuron, 82.6 (2014): 1394-1406.
[2] Peter Dayan and L.F. Abbott, “Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems”, The MIT Press, 2001

Type of Seminar:
Control Seminar Series
Prof. Sandro Zampieri
University of Padova
Feb 21, 2018   17:15 h

Contact Person:

Saverio Bolognani
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Biographical Sketch:
Sandro Zampieri (SM’13) received the Laurea degree in electrical engineering, and the Ph.D. degree in system engineering from the University of Padova, Padova, Italy, in 1988 and 1993, respectively. In 1991–1992, 1993, and 1996, he was a Visiting Scholar at the Laboratory for Information and Decision Systems with the Massachusetts Institute of Technology, Cambridge, MA, USA. He has held visiting positions in the Department of Mathematics of the University of Groningen, Groningen, the Netherlands, and at the Department of Mechanical Engineering of the University of California, Santa Barbara, CA, USA. Since 2002, he has been a Professor in Automatic Control with the Department of Information Engineering at the University of Padova. He has delivered several invited seminars and was a member of the technical program committee for several international conferences. He has published many journal and conference papers. His research interests include automatic control and dynamical systems theory, and, in particular, distributed control and estimation, networked control, and control under communication constraints. Prof. Zampieri was General Chair of the 1st IFAC Workshop on Estimation and Control of Networked Systems in 2009, Program Chair of the 3rd IFAC Workshop on Estimation and Control of Networked Systems in 2012, and Publication Chair of the IFAC World Congress in 2011. He was an Associate Editor of the SIAM Journal on Control and Optimization in 2002–2004 and IEEE Transactions of Automatic Control in 2013–2014. He was Chair of the IFAC technical committee Networked Systems in 2005–2008.