IC Colloquium : Some of the upcoming challenges in computational and mathematical neuroscience
Event details
| Date | 19.11.2012 |
| Hour | 16:30 › 17:45 |
| Speaker | Olivier Faugeras, INRIA |
| Location | |
| Category | Conferences - Seminars |
Abstract
The CNS, like all complex systems, features a large variety of spatial and temporal scales. A given scale is usually accessible through a class of measurement modalities, e.g. electro-encephalography gives us access to the "mean" activity of very large populations of neurons whereas a micro-electrode can record from a single neuron. It is therefore important to be able to both develop theories that account for phenomena at a given scale, for example at the single neuron level the Hodgkin-Huxley equations can reproduce many of the observed behaviours, and are able to seamlessly traverse the scales from the finest to the coarsest, e.g. to develop a (mesoscopic) theory of say, a cortical column, from the (microscopic) description of its individual neurons and of their connections.
In the first part of this talk I describe some current attempts in my research group to rigourously bridge the gap between theories of individual neurons behaviours and those of large populations of interconnected such neurons. This raises several important issues such as the role of the uncertainty, the noise, in these theories, and the optimal encoding of information. I also mention the difficulties that one encounters when developing such mean field theories, hence the challenges, as well as underline their differences with what may be called "naive" mean field theories.
In the second part of the talk I focus on an existing theory for describing the behaviours of entire cortical areas such as those that make up the visual system of human and non-human primates. The theory of neural fields can probably be deduced from that of individual neurons by methods such as those sketched out in the first part of the talk but I will rather concentrate on two of its important features, in relation to visual perception, because I think that they are both universal in the way neuronal populations operate and unfamiliar to many of those working in computer vision or engineering in general. The first point is related to the idea of the symmetries of a system, the second to the idea of the bifurcations of the solutions to the equations that describe this system. As in the first part I will also mention a number of problems with neural fields theories, hence again the challenges.
The talk will be relatively light on the mathematics, emphasizing more the concepts than the technicalities.
Biography
Olivier FAUGERAS is a graduate from the Ecole Polytechnique, France (1971). He holds a PhD in Computer Science and Electrical Engineering from the University of Utah (1976) and a Doctorate of Science in Mathematics from Paris VI University (1981). He is currently a Senior Scientist ("Directeur de Recherche" in French) at INRIA (Mathematics, Informatics), where he leads the NeuroMathComp project team, joint scientific venture between Inria (Mathematics, Computer Science) and the JAD Laboratory (Mathematics) at Nice Sophia Antipolis University.
His research interests are in mathematical and computational neuroscience, i.e. in applying mathematics and computers to model populations of neurons. Applications of his work include computer and biological visual perception, neuronal diseases, plasticity and learning, models of functional imaging modalities (MR, MEG, EEG).
He has published extensively in archival Journals, International Conferences, has contributed chapters to many books and is the author of "Artificial 3-D Vision" published in 1993 by MIT Press and, with Quang-Tuan Luong and Théo Papadopoulo, of "The Geometry of Multiple Images" which appeared in March 2001, also at MIT Press. He has co-edited with Nikos Paragios and Yunmei Chen "The Handbook of Mathematical Models in Computer Vision" published in 2005 by Springer. He was an adjunct Professor from 1996 to 2001 in the Electrical Engineering and Computer Science Department of the Massachusetts Institute of Technology and a member of the AI Lab. He has served as Associate Editor for IEEE PAMI from 1987 to 1990 and as co-Editor-in-Chief of the International Journal of Computer Vision from 1991 to 2004. In 2011, together with Stephen Coombes from the University of Nottingham, he started the Open Access Journal of Mathematical Neuroscience (JMN) published by Springer. He is a member of the French Academy of Sciences and the French Academy of Technology. He was awarded by the European Research Council (ERC) an advanced grant entitled "From single neurons to visual perception" dealing with the mathematical foundations of neuroscience.
The CNS, like all complex systems, features a large variety of spatial and temporal scales. A given scale is usually accessible through a class of measurement modalities, e.g. electro-encephalography gives us access to the "mean" activity of very large populations of neurons whereas a micro-electrode can record from a single neuron. It is therefore important to be able to both develop theories that account for phenomena at a given scale, for example at the single neuron level the Hodgkin-Huxley equations can reproduce many of the observed behaviours, and are able to seamlessly traverse the scales from the finest to the coarsest, e.g. to develop a (mesoscopic) theory of say, a cortical column, from the (microscopic) description of its individual neurons and of their connections.
In the first part of this talk I describe some current attempts in my research group to rigourously bridge the gap between theories of individual neurons behaviours and those of large populations of interconnected such neurons. This raises several important issues such as the role of the uncertainty, the noise, in these theories, and the optimal encoding of information. I also mention the difficulties that one encounters when developing such mean field theories, hence the challenges, as well as underline their differences with what may be called "naive" mean field theories.
In the second part of the talk I focus on an existing theory for describing the behaviours of entire cortical areas such as those that make up the visual system of human and non-human primates. The theory of neural fields can probably be deduced from that of individual neurons by methods such as those sketched out in the first part of the talk but I will rather concentrate on two of its important features, in relation to visual perception, because I think that they are both universal in the way neuronal populations operate and unfamiliar to many of those working in computer vision or engineering in general. The first point is related to the idea of the symmetries of a system, the second to the idea of the bifurcations of the solutions to the equations that describe this system. As in the first part I will also mention a number of problems with neural fields theories, hence again the challenges.
The talk will be relatively light on the mathematics, emphasizing more the concepts than the technicalities.
Biography
Olivier FAUGERAS is a graduate from the Ecole Polytechnique, France (1971). He holds a PhD in Computer Science and Electrical Engineering from the University of Utah (1976) and a Doctorate of Science in Mathematics from Paris VI University (1981). He is currently a Senior Scientist ("Directeur de Recherche" in French) at INRIA (Mathematics, Informatics), where he leads the NeuroMathComp project team, joint scientific venture between Inria (Mathematics, Computer Science) and the JAD Laboratory (Mathematics) at Nice Sophia Antipolis University.
His research interests are in mathematical and computational neuroscience, i.e. in applying mathematics and computers to model populations of neurons. Applications of his work include computer and biological visual perception, neuronal diseases, plasticity and learning, models of functional imaging modalities (MR, MEG, EEG).
He has published extensively in archival Journals, International Conferences, has contributed chapters to many books and is the author of "Artificial 3-D Vision" published in 1993 by MIT Press and, with Quang-Tuan Luong and Théo Papadopoulo, of "The Geometry of Multiple Images" which appeared in March 2001, also at MIT Press. He has co-edited with Nikos Paragios and Yunmei Chen "The Handbook of Mathematical Models in Computer Vision" published in 2005 by Springer. He was an adjunct Professor from 1996 to 2001 in the Electrical Engineering and Computer Science Department of the Massachusetts Institute of Technology and a member of the AI Lab. He has served as Associate Editor for IEEE PAMI from 1987 to 1990 and as co-Editor-in-Chief of the International Journal of Computer Vision from 1991 to 2004. In 2011, together with Stephen Coombes from the University of Nottingham, he started the Open Access Journal of Mathematical Neuroscience (JMN) published by Springer. He is a member of the French Academy of Sciences and the French Academy of Technology. He was awarded by the European Research Council (ERC) an advanced grant entitled "From single neurons to visual perception" dealing with the mathematical foundations of neuroscience.
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Practical information
- Informed public
- Free
- This event is internal
Organizer
- Host : Prof. Pascal Fua
Contact
- Christine Moscioni / Simone Muller