Wilten Nicola
Email: wnicola at uwaterloo dot ca
My primary research interest consists of derivations and applications of mean-field systems of equations for different types of spiking neuronal networks. The mean-field systems allow for bifurcation analysis and exploration of network level phenomenon. I am also interested in other applications of mathematics to the life sciences. My purely mathematical research interests are bifurcation theory and dynamical systems, in particular non-smooth systems and higher co-dimension non-smooth bifurcations. Additionally, I am also interested in inverse problem theory, and its various applications to the sciences.
Education
PhD in Applied Mathematics, University of Waterloo. Expected Summer 2015.
Thesis Topic: Bifurcations of discontinuous pulse-coupled oscillators. Advisor: Prof. Sue Ann Campbell
HBSc Mathematics (major), and Neuroscience (Specialist), awarded 2009
Graduated with High Distinction. Undergraduate Thesis Topic: Biologically Plausible Optimal Control. Advisor: Prof. Douglas Tweed
Publications
In Preparation
Nicola, W., Scott, M. (2015) Scale-Invariant Linear Decoding for Networks of Type-I Neurons.
Ferguson, K.A., NJap, F., Nicola W., Skinner, F.K. and Campbell, S.A.. Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus.
Under Revisions
Nicola, W., Ly, C., and Campbell, S.A. (2014) One-dimensional population density approaches to recurrently coupled networks of neurons with noise. arXiv:1411.2273 (In revisions process)
Nicola, W. and Campbell S.A. (2014) Non-smooth bifurcations of mean-field systems of two-dimensional integrate and fire neurons. arXiv:1408.4767 (In revisions process)
Journals
Nicola, W. and Campbell S.A. (2013) Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons. Front. Comput. Neurosci. 7:184. doi: 10.3389/fncom.2013.00184
Nicola, W.and Campbell, S.A. (2013) Bifurcations of large networks of two-dimensional integrate and fire neurons. J. Computational Neuroscience doi: 10.1007/s10827- 013-0442-z.
M. Dur-e-Ahmad, Nicola, W., Campbell, S.A. and Skinner, F.A. (2012). Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation J. Computational
Conferences
AMMCS-CAIMS (2015), Waterloo, Ontario, Canada. Poster. Non-smooth bifurcations in the mean-field system for a network of type-I neurons with adaptation.
SIAM Dynamical systems conference (2015), Snowbird, UT, USA. Poster. Co-dimension two bifurcations in piecewise-smooth continuous dynamical systems.
CNS (2014). Quebec City, PQ, Canada. Contributed Talk. Mean-field analysis gives accurate predictions of the behavior of large networks of sparsely coupled and heterogeneous neurons.
Nonlinear dynamics and stochastic methods (2014). Pittsburgh, PA, USA. Poster. Non-smooth bifurcations for mean-field systems of networks of integrate-and-fire neurons
AMMCS (2013), Waterloo, Ontario. Contributed Talk .
Bifurcations of Networks of Heterogeneous Integrate and Fire Neurons
SIAM Dynamical systems conference (2013), Snowbird, UT, USA. Poster. Bifurcations of Large Networks of Two Dimensional Integrate and Fire Neurons
Canadian Applied and Industrial Mathematics Society (2012),Toronto, ON, Canada. Contributed Talk. Bifurcations of Large Networks of Pulse Coupled Oscillators
University of Waterloo Graduate Student Seminars,
(2012), Waterloo, ON, Canada. Seminar. Bifurcations of Large Networks of
Pulse Coupled Oscillators
Teaching Experience
Lecturer
MATH 127 - Calculus I for the Sciences, Department of Mathematics, University of Waterloo, Fall 2012
Teaching Assistant