My work in nonlinear dynamics is often inspired by problems in neural modeling and, more generally, in physiology and biology. I am particularly interested in the response properties of models of cells or systems of cells to deterministic and/or stochastic inputs, and on the role of feedback. My current research activity involves work on delay-differential equations, chaos, noise-induced transitions, noise shaping, neural field equations, stochastic resonance, multistability, dynamical memory, and nonlinear time series and point process analysis aimed at guiding and testing modelling studies. I also am interested in emergent computation, i.e. in the new properties that arise through the interaction of simpler nonlinear elements.
A lot of the computational and theoretical neuroscience work in my group revolves around the weakly electric fish, due to close interactions with two experimental groups at the University of Ottawa (Maler and Lewis). These animals have a sufficiently simple brain (compared e.g. to monkeys), yet exhibit sufficiently interesting behaviors, to enable us to figure out how information is processed and stored in their brains - thus revealing the building blocks of processing in more complex brains. Thus, apart from generating a wealth of knowledge on the neural functioning of the whole class of wave-type electric fish, this work leads to general principles of neural organization that applies in many cases to higher mammals.
Recently I have begun investigating the learning properties of small neural networks which can be monitored using optical techniques including two-photon imaging. We are figuring out the circuitry that underlies the detection of a "novel" stimulus and how this leads to the activation of immediate early genes. This is done in the context of navigation and foraging as well as of social interactions in pulse-type (rather than wave-type as above) electric fish species.
Further, I have projects in visual neuroscience and psychophysics. For example, I work on the problem of the dynamics of eye saccade programming, on the dynamics of attention shifts, and on the link between the two. I am also working on motor control and internal models, e.g. in the context of posture control.
I also study how the nervous system can disambiguate mixtures of signals (as in the cocktail party effect), and in particular, why certain mixtures are significant and lead to specific behaviors. This is relevant to musical consonance and to social communication in a variety of animal species (especially electric fish). It is also particularly relevant to the design of novel prosthetic devices such as cochlear implants.
I am also working on modeling how abnormal firing (includig ectopic firing) occurs after traumatic impacts on nerve fibers, on the associated onset of pain responses, and on the alteration of propagation delays between different parts of the nervous system in MS and other conditions and their functional consequences. I am also doing modeling work on the activity of cingulate cortex in response to familiar and non-familiar stimuli, and how this is perturbed in different psychiatric conditions. This involves collaborations with MRI and mental health researchers.
The long term goals of my research are to understand how neurons and other biological units self-organize and perform computations, and what links cellular biophysics and biological complexity. At the core of this work is the physical understanding of how deterministic dynamics and stochasticity (i.e. noise sources) interact in nonlinear systems, producing complex, and often unpredictable behaviors.
My research also aims to understand how nature solved signal processing problems, and to use this knowledge for the design of new signal processing strategies for e.g. bionic, robotic, prosthetic and enhanced learning applications. The goal of my research on physiological regulation problems from the point of view of nonlinear stochastic dynamics is the design of novel therapies for treament of certain diseases or of novel criteria for intervention in the intensive care unit.
My main collaborators these days are:
UNIVERSITY OF OTTAWA:
Len Maler, Cellular and Molecular Medicine: sensory coding and feedback, memory and novelty detection, weakly electric fish.
John Lewis, Biology: bioelectric field modeling, plasticity and feedback, weakly electric fish
Victor LeBlanc, Mathematics and Statistics: neural field models, excitable media, bifurcations in delayed feedback systems.
Jean-Claude Beique, Cellular and Molecular Medicine: neural plasticity, neurophotonics.
Jean-Philippe Thivierge, Psychology, multi-electrode arrays and network dynamics.
Andrew Seely, Department of Surgery, Faculty of Medicine: physiological variability and autonomous nervous system control.
Cathy Morris (Ottawa-Health Research Institutes) and Bela Joos (Physics): nerve propagation in trauma and multiple sclerosis.
Georg Northoff (Institute of Mental Health Research, U. Ottawa): disruption of resting state activity in mental health.
plus a number of national and international collaborators.