Rod Edwards, Dept. of Mathematics & Statistics, University of Victoria


Publications

Refereed journal articles:

  1. M. Hall, N.K. Mohtaram, S.M. Willerth and R. Edwards. Modelling the behaviour of human induced pluripotent stem cells seeded on melt electrospun scaffolds. Journal of Biological Engineering, 11:38 (2017) (20 pages) [journal site].
  2. S. Odense and R. Edwards. Universal approximation results for the temporal restricted Boltzmann machine and the recurrent temporal restricted Boltzmann machine. Journal of Machine Learning Research, 17 (158):1−21 (2016) [journal site].
  3. R.K. Mann, R. Edwards and J. Zhou. Robust designs for experiments with blocks. Communications in Statistics - Theory and Methods, 45:5363-5379 (2016) [journal site].
  4. D. Hudson and R. Edwards. Dynamics of transcription-translation networks. Physica D, 331:102-113 (2016) [journal site].
  5. E. Foxall, R. Edwards and P. van den Driessche. Social contact processes and the partner model. Annals of Applied Probability, 26:1297-1328 (2016) [journal site].
  6. R. Edwards, A. Machina, G. McGregor and P. van den Driessche. A modelling framework for gene regulatory networks involving transcription and translation. Bulletin of Mathematical Biology, 77:953-983 (2015) [journal site].
  7. P. Shahrear, L. Glass and R. Edwards. Chaotic dynamics and diffusion in a piecewise linear equation. Chaos, 25, 033103 (2015) [journal site].
  8. M. Li, R. Illner, R. Edwards and J. Ma. Marketing new products: Bass models on random graphs. Communications in Mathematical Sciences, 13:497-509 (2015) [journal site].
  9. P. Shahrear, L. Glass, R. Wilds and R. Edwards. Dynamics in piecewise linear and continuous models of complex switching networks. Mathematics and Computers in Simulation, 110:33-39 (2015) [journal site].
  10. R. Edwards and L. Glass. Dynamics in genetic networks. American Mathematical Monthly, 121:793-809 (2014) [journal site].
  11. T.J. Perkins, E. Foxall, L. Glass and R. Edwards. A scaling law for random walks on networks. Nature Communications, 5:5121 (2014) [journal site].
  12. F. Rahimi, C. Bee, C. Duval, P. Boissy, R. Edwards, M. Jog and the EMAP group. Using ecological whole body kinematics to evaluate effects of medication adjustment in Parkinson Disease. Journal of Parkinson's Disease, 4:617-627 (2014) [journal site].
  13. R. Edwards and L. Ironi. Periodic solutions of gene networks with steep sigmoidal regulatory functions. Physica D, 282:1:15 (2014) [journal site].
  14. A. Machina, R. Edwards and P. van den Driessche. Sensitive dependence on initial conditions in gene networks. Chaos, 23:025101 (2013) [journal site].
  15. A. Machina, R. Edwards and P. van den Driessche. Singular dynamics in gene network models. SIAM Journal on Applied Dynamical Systems, 12:95-125 (2013) [journal site].
  16. R. Edwards, E. Foxall and T. Perkins. Scaling properties of paths on graphs. Electronic Journal of Linear Algebra, 23:966-988 (2012) [journal site].
  17. R.K. Mann, R. Edwards, J. Zhou, A. Fenney, M. Jog and C. Duval. Comparing movement patterns associated with Huntington's chorea and Parkinson's dyskinesia. Experimental Brain Research, 218:639-654 (2012) [journal site].
  18. R. Edwards, E. Farcot and E. Foxall. Explicit construction of chaotic attractors in Glass networks. Chaos, Solitons and Fractals, 45:666-680 (2012) [journal site].
  19. R. Edwards and D.J. Leeming. The exact number of real roots of the Bernoulli polynomials. Journal of Approximation Theory, 164:754-775 (2012) [journal site].
  20. E. Foxall, R. Edwards, S. Ibrahim and P. van den Driessche. A contraction argument for two-dimensional spiking neuron models. SIAM Journal on Applied Dynamical Systems, 11:540-566 (2012) [journal site].
  21. 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].
  22. 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) [journal site].
  23. R. Edwards and L. Collins. Lexical frequency profiles and Zipf's Law. Language Learning, 61:1-30 (2011) [journal site].
  24. 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). [journal site]
  25. 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). [journal site]
  26. J. Modolo, R. Edwards, J. Campagnaud, B. Bhattacharya and A. Beuter. Past, present and future of brain stimulation. Mathematical Modeling of Natural Phenomena, 5(2):185-207 (2010). [journal site]
  27. R. Edwards, S. Kim and P. van den Driessche. A multigroup model for a heterosexually transmitted disease. Mathematical Biosciences, 224:87-94 (2010). [journal site]
  28. L. Lu and R. Edwards. Structural principles for periodic orbits in Glass networks. Journal of Mathematical Biology, 60:513-541 (2010) [journal site]
  29. 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) [journal site]
  30. 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). [journal site]
  31. 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). [journal site]
  32. 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]
  33. 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). [journal site]
  34. 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). [journal site]
  35. 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). [journal site]
  36. 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]
  37. 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). [journal site]
  38. D.B. Killough and R. Edwards. Bifurcations in Glass networks. International Journal of Bifurcation and Chaos 15:395-423 (2005). [journal site]
  39. 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). [journal site]
  40. 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). [journal site]
  41. M.S. Titcombe, R. Edwards and A. Beuter. Mathematical modelling of parkinsonian tremor. Nonlinear Studies 11:363-384 (2004). [journal site]
  42. 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]
  43. 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]
  44. 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]
  45. K. Kappler, R. Edwards and L. Glass. Dynamics in high dimensional model gene networks, Signal Processing, 83:789-798 (2003).[journal site]
  46. 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]
  47. A. Beuter and R. Edwards. Kinetic tremor during tracking movements in patients with Parkinson's disease, Parkinsonism and Related Disorders, 8:361-368 (2002). [journal site]
  48. A. Beuter and R. Edwards. Caractérisation et discrimination du tremblement cinétique dans la maladie de Parkinson, Revue Neurologique, 158:338-340 (2002). [journal site]
  49. R. Edwards. Chaos in neural and gene networks with hard switching, Differential Equations and Dynamical Systems, 9:187-220 (2001). [preprint]
  50. R. Edwards, H. T. Siegelmann, K. Aziza and L. Glass. Symbolic dynamics and computation in model gene networks, Chaos, 11:160-169 (2001). [journal site]
  51. R. Edwards. Analysis of continuous-time switching networks, Physica D, 146:165-199 (2000). [journal site]
  52. R. Edwards and L. Glass. Combinatorial explosion in model gene networks, Chaos, 10:691-704 (2000). [journal site]
  53. 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). [journal site]
  54. A. Beuter, R. Edwards and A. Boucher. Physiological tremor: Does handedness make a difference?, International Journal of Neuroscience, 101:9-19 (2000). [journal site]
  55. 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]
  56. R. Edwards, A. Beuter and L. Glass. Parkinsonian tremor and simplification in network dynamics, Bulletin of Mathematical Biology, 61:157-177 (1999). [journal site]
  57. 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). [journal site]
  58. 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]
  59. 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). [journal site (yes, it's actually there - see pp.207-211)]
  60. 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). [journal site]
  61. 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) [preprint].
  62. 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).
  63. 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, 80:50-63 (1999). [journal site]
  64. 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, 80:64-79 (1999). [journal site]
  65. A. Beuter and R. Edwards. Tremor in Cree subjects exposed to methylmercury: A preliminary study, Neurotoxicology and Teratology, 20:581-589 (1998). [journal site]
  66. R. Edwards and A. Beuter. Sensitivity and specificity of a portable system measuring postural tremor, Neurotoxicology and Teratology, 19:95-104 (1997). [journal site]
  67. 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). [journal site]
  68. R. Edwards. Stable patterns in spatially discrete reaction-diffusion equations, Dynamic Systems and Applications, 5:245-262 (1996) [preprint].
  69. R. Edwards. Approximation of neural network dynamics by reaction-diffusion equations, Mathematical Methods in the Applied Sciences, 19:651-677 (1996). [journal site]
Conference articles:
  1. E. Bossolini, R. Edwards, P.A. Glendinning, M.R. Jeffrey, S. Webber. Regularization by external variables, in: A. Colombo, M. Jeffrey, J. Lázaro, J. Olm (eds.), Extended Abstracts Spring 2016: Nonsmooth Systems. Trends in Mathematics, vol. 8 (Birkhäuser, 2017), pp.19-24. [online]
  2. R. Edwards and A. Maignan. DEM-systems: A new type of adaptive system. Exploratory Papers of Automata 2016, 22nd International Workshop on Cellular Autmomata and Discrete Complex Systems, Zurich, June 2016. [conference site]
  3. R. Edwards, A. Hill, M. Jacquier. Analysis of transient damped oscillations in gene regulatory networks, in: MTNS 2014: 21st International Symposium on Mathematical Theory of Networks and Systems (Proceedings of the MTNS 2014 conference, Groningen, July 2014). [online]
  4. R. Edwards, A. Maignan. Complex self-reproducing systems, in: A. Sanayei, I. Zelinka and O.E. Rossler (eds.), ISCS 2013: Interdisciplinary Symposium on Complex Systems, Springer, New York (2014), pp.65-76. (Proceedings of the ISCS 2013 conference, Prague, September 2013). [online]
  5. P. Boissy, S. Briere, M. Hamel, M. Jog, M. Speechley, A. Karelis, J. Frank, C. Vincent, R. Edwards, C. Duval. Wireless inertial measurement unit with GPS (WIMU-GPS) --- Wearable monitoring platform for ecological assessment of lifespace and mobility in aging and disease, in: Proceedings of the 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Boston, USA., August-September 2011, pp.5815-5819. [online]
  6. F. Rahimi, C. Duval, Ma. Jog, C. Bee, A. South, Mo. Jog, R. Edwards, P. Boissy. Capturing whole-body mobility of patients with Parkinson disease using inertial motion sensors: expected challenges and rewards, in: Proceedings of the 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Boston, USA., August-September 2011, pp.5833-5838. [online]
  7. A. Beuter and R. Edwards. Is tremor in Parkinson's disease a simplification in network dynamics?, in: A.M. Graybiel, M.R. DeLong, S.T. Kitai (eds.), The Basal Ganglia VI, Plenum, New York (2003), pp.51-60. (Proceedings of the 6th triennial meeting of the IBAGS, Oct. 1998.)
  8. R. Edwards. Chaos in a continuous-time Boolean network, in: Proceedings of the 3rd International Conference on Dynamic Systems and Applications, Atlanta, May 1999, Dynamic Publishing (2001), pp.185-192.
  9. 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, in: 3rd PIMS Industrial Problem Solving Workshop, Victoria, B.C., June 1999, PIMS (2000), pp.83-93. [online]
  10. 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 (ISEK, 1998), pp.110-111. [online]

Book chapters:

  1. R. Edwards and L. Collins. Modelling L2 vocabulary learning, in: Vocabulary knowledge: Human ratings and automated measures, S. Jarvis and M. Daller (eds.), Amsterdam: John Benjamin's, 2013, pp.157-184. [online]
  2. 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. [online]
  3. 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. [Springer site]

Introduction to special issue:

  1. A. Beuter, R. Edwards and D. Mottet. Insights from mathematical approaches to complex dynamics of physiological systems. Nonlinear Studies 11:301-303 (2004). [journal site]

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Last updated: 24 Oct. 2017