E. Foxall, R. Edwards, S. Ibrahim, P. van den Driessche. A contraction argument for two-dimensional
spiking neuron models. SIAM Journal on Applied Dynamical Systems (accepted).
L. Lu and R. Edwards. Stuctural principles for complex dynamics in Glass networks. International Journal of Bifurcation and Chaos, 21:237-254 (2011) [journal site].
R. Edwards, S. Kim and P. van den Driessche. Control design for sustained oscillation in a two gene regulatory network. Journal of Mathematical Biology, 62:453-478 (2011) [pdf from journal site] [journal site].
R. Edwards and L. Collins. Lexical frequency profiles and Zipf's Law. Language Learning, 61:1-30 (2011) [pdf from journal site] [journal site].
J. Modolo, B. Bhattacharya, R. Edwards, J. Campagnaud, A. Legros and A. Beuter. Using a virtual cortical module implementing a neural field model to modulate brain rhythms in Parkinson's disease, Frontiers in Neurosience, 4:45 (2010).
[pdf from journal site]
[journal site]
R.K. Mann, R. Edwards, J. Zhou, M. Jog and C. Duval. Intra- and inter-limb coherence during stance in non-dyskinetic and dyskinetic patients with Parkinson's disease. Clinical Neurology and Neurosurgery, 112:392-399 (2010).
[pdf from journal site]
[journal site]
J. Modolo, R. Edwards, J. Campagnaud, B. Bhattacharya and A. Beuter. Past, present and future of brain stimulation. Mathematical Modeling of Natural Phenomena, 5:185-207 (2010).
[pdf from journal site]
[journal site]
R. Edwards, S. Kim and P. van den Driessche. A multigroup model for a heterosexually transmitted disease. Mathematical Biosciences, 224:87-94 (2010). [pdf from journal site] [journal site]
L. Lu and R. Edwards. Structural principles for periodic orbits in Glass networks. Journal of Mathematical Biology, 60:513-541 (2010) [pdf from journal site] [journal site]
J. Gour, R. Edwards, S. Lemieux, M. Ghassemi, M. Jog and C. Duval. Movement patterns of peak-dose levadopa-induced dyskinesias in patients with Parkinson's disease. Brain Research Bulletin 74:66-74 (2007) [pdf from journal site] [journal site]
R. Edwards, P. van den Driessche and L. Wang. Periodicity in piecewise-linear switching networks with delay. Journal of Mathematical Biology 55:271-298 (2007). [pdf from journal site] [journal site]
R. Edwards, R. Gibson, R. Illner and V. Paetkau. A stochastic model for circadian rhythms from coupled ultradian oscillators. Theoretical Biology and Medical Modelling 4:1 (2007). [pdf from journal site] [journal site]
D. Geuhl, R. Edwards, E. Cuhni, P. Burbaud, A. Rougier, J. Modolo and A. Beuter. Statistical determination of the optimal STN stimulation site in Parkinson's disease. Journal of Neurosurgery 106:101-110 (2007). [journal site] [pdf from journal site]
S. Lemieux, M. Ghassemi, M. Jog, R. Edwards and C. Duval. The influence of levodopa-induced dyskinesias on manual tracking in patients with Parkinson's disease. Experimental Brain Research 176:465-475 (2007). [pdf from journal site] [journal site]
M. Ghassemi, S. Lemieux, M.S. Jog, R. Edwards and C. Duval. Bradykinesia in patients with Parkinson's disease having Levodopa-induced dyskinesias. Brain Research Bulletin 69:512-518 (2006). [pdf from journal site] [journal site]
A. Hodge, R. Edwards, D.H. Paul and P. van den Driessche. Neuronal network models of phase separation between limb CPGs in digging sand crabs. Biological Cybernetics 95:55-68 (2006). [pdf from journal site] [journal site]
V. Paetkau, R. Edwards and R. Illner. A model for generating circadian rhythm by coupling ultradian oscillators. Theoretical Biology and Medical Modelling 3:12 (2006). [journal site] [pdf from journal site]
L. Glass, T.J. Perkins, J. Mason, H.T. Siegelmann and R. Edwards. Chaotic dynamics in an electronic model of a genetic network. Journal of Statistical Physics 121:969-994 (2005). [pdf from journal site] [journal site]
D.B. Killough and R. Edwards. Bifurcations in Glass networks. International Journal of Bifurcation and Chaos 15:395-423 (2005).
[journal site]
[pdf from journal site]
R. Edwards, J.J. MacDonald and M.J. Tsatsomeros. On matrices with common invariant cones with applications in neural and gene networks. Linear Algebra and its Applications 398:37-67 (2005). [pdf from journal site]
S.A. Campbell, R. Edwards and P. van den Driessche. Delayed coupling between two neural network loops. SIAM Journal on Applied Mathematics 65:316-335 (2004). [pdf from journal site]
M.S. Titcombe, R. Edwards and A. Beuter. Mathematical modelling of parkinsonian tremor. Nonlinear Studies 11:363-384 (2004).
[preprint]
A. Webber, N. Virji-Babul, R. Edwards and M. Lesperance. Stiffness and postural stability in adults with Down syndrome. Experimental Brain Research 155:450-458 (2004).
[journal site]
[pdf from journal site]
A. Beuter and R. Edwards. Effect of chronic exposure to methylmercury on eye movements in Cree subjects. International Archives of Occupational and Environmental Health 77:97-107 (2004).
[journal site] [pdf from journal site]
C.S. Bohun, S.J. McCollum, R. Edwards and R. Illner. Generic emergence of cognitive behaviour in self-generating neural networks, Nonlinear Dynamics and Systems Theory, 3: 43-63 (2003). [journal site]
K. Kappler, R. Edwards and L. Glass. Dynamics in high dimensional model gene networks, Signal Processing, 83:789-798 (2003). [pdf from journal site] [journal site]
R. Edwards and P. Gill. On synchronization and cross-talk in parallel networks, Dynamics of Continuous, Discrete and Impulsive Systems B, 10:287-300 (2003). [journal site]
A. Beuter and R. Edwards. Kinetic tremor during tracking movements in
patients with Parkinson's disease, Parkinsonism and Related Disorders,
8:361-368 (2002). [pdf from journal site] [journal site]
A. Beuter and R. Edwards. Caractérisation et discrimination du
tremblement cinétique dans la maladie de Parkinson, Revue Neurologique,
158:338-340 (2002). [journal site]
R. Edwards. Chaos in neural and gene networks with hard switching,
Differential Equations and Dynamical Systems, 9:187-220 (2001).
[preprint] [journal site]
R. Edwards, H. T. Siegelmann, K. Aziza and L. Glass. Symbolic dynamics and
computation in model gene networks, Chaos, 11:160-169 (2001). [pdf from journal site] [journal site]
R. Edwards and L. Glass. Combinatorial explosion in model gene networks,
Chaos, 10:691-704 (2000). [pdf from journal site] [journal site]
A. Beuter, R. Edwards and D. Lamoureux. Neuromotor profiles: What are they
and what can we learn from them?, Brain and Cognition, 43:39-44 (2000). [pdf from journal site] [journal site]
A. Beuter, R. Edwards and A. Boucher. Physiological tremor: Does handedness
make a difference?, International Journal of Neuroscience, 101:9-19 (2000).
R. Edwards and A. Beuter. Using time domain characteristics to discriminate
physiologic and parkinsonian tremors. Journal of Clinical Neurophysiology,
17:87-100 (2000). [journal site]
R. Edwards, A. Beuter and L. Glass. Parkinsonian tremor and simplification
in network dynamics, Bulletin of Mathematical Biology, 61:157-177 (1999).
K. Norman, R. Edwards and A. Beuter. The measurement of tremor using a
velocity transducer: comparison to simultaneous recordings using transducers of
displacement, acceleration and muscle activity, Journal of Neuroscience
Methods, 92:41-54 (1999). [pdf from journal site] [journal site]
A. Beuter and R. Edwards. Using frequency domain characteristics to
discriminate physiologic and parkinsonian tremors, Journal of Clinical
Neurophysiology, 16:484-494 (1999). [journal site]
K.E. Norman, R. Edwards, C. Duval, S. Patenaude and A. Beuter.
Two-dimensional geometry and electromyography
of spontaneous and imitated parkinsonian wrist tremor, Brain and Cognition, 40:207-211 (1999). [pdf from journal site] [journal site]
R. Edwards and A. Beuter. Indexes for identification of abnormal tremor using
computer tremor evaluation systems, IEEE Transactions on Biomedical Engineering, 46:895-898 (1999). [pdf from journal site] [journal site]
A. Beuter, R. Edwards, A. de Geoffroy, D. Mergler and K. Hudnell.
Quantification of neuromotor function for detection of the effects of manganese exposure,
Neurotoxicology, 20:355-366 (1999).
D. Mergler, M. Baldwin, S. Bélanger, A. Beuter,
R. Edwards, A. de Geoffroy, F. Larribe, M. Panisset,
M.-P. Sassine and K. Hudnell. Manganese neurotoxicity, a continuum
of dysfunction: Preliminary results from a community based study,
Neurotoxicology, 20:327-342 (1999).
A. Beuter, A. de Geoffroy and R. Edwards.
Quantitative analysis of rapid pointing movements in Cree subjects
exposed to mercury and in subjects with neurological deficits, Environmental
Research A, 80:50-63 (1999).
A. Beuter, A. de Geoffroy and R. Edwards.
Analysis of rapid alternating movements in Cree subjects exposed
to methylmercury and in subjects with neurological deficits, Environmental
Research A, 80:64-79 (1999).
A. Beuter and R. Edwards. Tremor in Cree subjects exposed to
methylmercury: A preliminary study, Neurotoxicology and Teratology,
20:581-589 (1998).
R. Edwards and A. Beuter. Sensitivity and specificity of a
portable system measuring postural tremor,
Neurotoxicology and Teratology, 19:95-104 (1997).
R. Edwards and A. Beuter. How to handle intermittent phenomena in time series analysis:
A case study of neuromotor deficit, Brain and Cognition, 32:262-266
(1996).
R. Edwards. Stable patterns in spatially discrete reaction-diffusion
equations, Dynamic Systems and Applications, 5:245-262 (1996).
R. Edwards. Approximation of neural network dynamics by
reaction-diffusion
equations, Mathematical Methods in the Applied Sciences,
19:651-677 (1996).
Articles in refereed conference proceedings:
A. Beuter and R. Edwards. Is tremor in Parkinson's disease a simplification in network dynamics?. in: The Basal Ganglia VI (A.M. Graybiel, M.R. DeLong, S.T. Kitai, eds.), pp.51-60, Plenum, New York (2003). (Proceedings of the 6th triennial meeting of the IBAGS, Oct. 1998.)
R. Edwards. Chaos in a continuous-time Boolean network. Proceedings of the 3rd International Conference on Dynamic Systems and Applications, Atlanta, May 1999, pp.185-192, Dynamic Publishing (2001).
L. Batten, C. S. Bohun, A. Bona, K. Cheng, T. Doman, J. Drew, R. Edwards, S. Kutay, C. Laflamme, D. McCrae, W. Myrvold, F. Ruskey, J. Sawada, P. van den Driessche, J. Vander Kloet and K. L. B. Wood. Classification of chemical compound pharmacophore structures. 3rd PIMS Industrial Problem Solving Workshop, June 1999, pp.83-93, PIMS (2000).
K.E. Norman, R. Edwards, S. Patenaude, C. Duval and A. Beuter.
Comparisons among simultaneous recordings of human finger tremor in displacement,
velocity, acceleration and electromyography, in: Proceedings of
the 12th ISEK (International Society of Electrophysiology and Kinesiology) Congress,
Montréal, June 1998, pp.110-111 (1998).
Book chapters:
R. Edwards and L. Glass. A calculus for relating the dynamics and structure of complex biological networks, in: Adventures in Chemical Physics, R.S. Berry and J. Jortner (eds.) (Advances in Chemical Physics, vol.132), pp.151-178, Hoboken, New Jersey: Wiley, 2006.
A. Beuter, R. Edwards and M. Titcombe. Data analysis and mathematical modeling of human tremor, in: Nonlinear Dynamics in Physiology and Medicine, A. Beuter, L. Glass, M.C. Mackey and M.S. Titcombe (eds.), pp.303-355, New York: Springer-Verlag, 2003.
Introduction to special issue:
A. Beuter, R. Edwards and D. Mottet. Insights from mathematical approaches to complex dynamics of physiological systems. Nonlinear Studies 11:301-303 (2004).
