Research/Scholarly/Creative Works

Journal Articles

• Godsoe W., Murray R. and Iritani R. (2023) Species interactions and diversity: a unified framework using Hill numbers. Oikos 2023(3) http://dx.doi.org/10.1111/oik.09282.

• Laufer B., Docherty PD., Murray R., Krueger-Ziolek S., Jalal NA., Hoeflinger F., Rupitsch SJ., Reindl L. and Moeller K. (2023) Sensor Selection for Tidal Volume Determination via Linear Regression—Impact of Lasso versus Ridge Regression. Sensors 23(17) http://dx.doi.org/10.3390/s23177407.

• Lam N., Murray R., Docherty PD., Te Morenga L. and Chase JG. (2022) The Effects of Additional Local-Mixing Compartments in the DISST Model-Based Assessment of Insulin Sensitivity. Journal of Diabetes Science and Technology 16(5): 1196-1207. http://dx.doi.org/10.1177/19322968211021602.

• Lam NN., Docherty PD. and Murray R. (2022) Practical identifiability of parametrised models: A review of benefits and limitations of various approaches. Mathematics and Computers in Simulation 199: 202-216. http://dx.doi.org/10.1016/j.matcom.2022.03.020.

• Gallardo P., Murray R. and Krumdieck S. (2021) A sequential optimization-simulation approach for planning the transition to the low carbon freight system with case study in the North Island of New Zealand. Energies 14(11) http://dx.doi.org/10.3390/en14113339.

• Laufer B., Docherty PD., Murray R., Jalal NA., Hoeflinger F., Reindl L. and Moeller K. (2021) Optimal Sensor Location in a Smart-Shirt to Measure Accurate Tidal Volumes during Abdominal and Thoracic Respiration. Current Directions in Biomedical Engineering 7(2): 574-577. http://dx.doi.org/10.1515/cdbme-2021-2146.

• Lam N., Docherty PD., Murray R., Chase JG. and Morenga LT. (2020) Using the Adapted Levenberg-Marquardt method to determine the validity of ignoring insulin and glucose data that is affected by mixing. IFAC-PapersOnLine 53(2): 16341-16346. http://dx.doi.org/10.1016/j.ifacol.2020.12.661.

• Laufer B., Murray R., Docherty PD., Krueger-Ziolek S., Hoeflinger F., Reindl L. and Moeller K. (2020) A Minimal Set of Sensors in a Smart-Shirt to Obtain Respiratory Parameters. IFAC-PapersOnLine 53(2): 16293-16298. http://dx.doi.org/10.1016/j.ifacol.2020.12.627.

• Poole M., Murray R., Davidson SM. and Docherty PD. (2019) The quadratic dimensional reduction method for parameter identification. Communications in Nonlinear Science and Numerical Simulation 73: 425-436. http://dx.doi.org/10.1016/j.cnsns.2019.03.001.

• Froyland G., Gonzalez-Tokman C. and Murray RDA. (2018) Quenched stochastic stability for eventually expanding-on-average random interval map cocycles. Ergodic Theory and Dynamical Systems 39(10): 2769-2792. http://dx.doi.org/10.1017/etds.2017.143.

• Mohd MH., Murray R., Plank MJ. and Godsoe W. (2018) Effects of different dispersal patterns on the presence-absence of multiple species. Communications in Nonlinear Science and Numerical Simulation 56: 115-130. http://dx.doi.org/10.1016/j.cnsns.2017.07.029.

• Davidson SM., Docherty PD. and Murray R. (2017) The dimensional reduction method for identification of parameters that trade-off due to similar model roles. Mathematical Biosciences 285: 119-127. http://dx.doi.org/10.1016/j.mbs.2017.01.003.

• Davidson SM., Docherty PD., Kretschmer J. and Murray R. (2017) The Novel Dimensional Reduction Method and Tikhonov Regularisation in Parameter Identification of Non-Linear Ill-Posed Problems. IFAC-PapersOnLine 50(1): 5474-5479. http://dx.doi.org/10.1016/j.ifacol.2017.08.1085.

• Mohd MH., Murray R., Plank MJ. and Godsoe W. (2017) Effects of biotic interactions and dispersal on the presence-absence of multiple species. Chaos, Solitons and Fractals 99: 185-194. http://dx.doi.org/10.1016/j.chaos.2017.04.012.

• Gray RAL., Docherty PD., Fisk LM. and Murray R. (2016) A modified approach to objective surface generation within the Gauss-Newton parameter identification to ignore outlier data points. Biomedical Signal Processing and Control 30: 162-169. http://dx.doi.org/10.1016/j.bspc.2016.06.009.

• Mohd MH., Murray R., Plank MJ. and Godsoe W. (2016) Effects of dispersal and stochasticity on the presence–absence of multiple species. Ecological Modelling 342: 49-59. http://dx.doi.org/10.1016/j.ecolmodel.2016.09.026.

• Godsoe W., Murray R. and Plank MJ. (2015) Information on biotic interactions improves transferability of distribution models. American Naturalist 185(2): 281-290. http://dx.doi.org/10.1086/679440.

• Godsoe W., Murray R. and Plank MJ. (2015) The effect of competition on species' distributions depends on coexistence, rather than scale alone. Ecography 38(11): 1071-1079. http://dx.doi.org/10.1111/ecog.01134.

• Bose C. and Murray R. (2014) First hyperbolic times for intermittent maps with unbounded derivative. Dynamical Systems: An International Journal 29(3): 352-368. http://dx.doi.org/10.1080/14689367.2014.902038.

• Bose C. and Murray R. (2014) Maximum Entropy Estimates for Risk-Neutral Probability Measures with Non-Strictly-Convex Data. Journal of Optimisation Theory and Applications 161(1): 285-307. http://dx.doi.org/10.1007/s10957-013-0349-x.

• Bose C., Froyland G., González-Tokman C. and Murray R. (2014) Ulam's Method for Lasota-Yorke Maps with Holes. SIAM Journal on Applied Dynamical Systems 13(2): 1010-1032. http://dx.doi.org/10.1137/130917533.

• Bose C. and Murray R. (2013) Polynomial decay of correlations in the generalized baker's transformation. International Journal of Bifurcation and Chaos 23(8) 1350130 http://dx.doi.org/10.1142/S0218127413501307.

• Froyland G., Murray R. and Stancevic O. (2011) Spectral degeneracy and escape dynamics for intermittent maps with a hole. Nonlinearity 24: 2435-2463. http://dx.doi.org/10.1088/0951-7715/24/9/003.

• Murray R. (2010) Ulam's method for some non-uniformly expanding maps. Discrete and Continuous Dynamical Systems 26(3): 1007-1018. http://dx.doi.org/10.3934/dcds.2010.26.1007.

• Bose CJ. and Murray R. (2007) Duality and the Computation of Approximate Invariant Densities for Nonsingular Transformations. SIAM Journal on Optimization 18(2): 691-709. http://dx.doi.org/10.1137/060658163.

• Froyland G., Murray R. and Terhesiu D. (2007) Efficient computation of topological entropy, pressure, conformal measures, and equilibrium states in one dimension. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76(3): 36702. http://dx.doi.org/10.1103/PhysRevE.76.036702.

• Bose CJ. and Murray R. (2006) Dynamical conditions for convergence of a maximum entropy method for Frobenius-Perron operator equations. Applied Mathematics and Computation 182(1): 210-212. http://dx.doi.org/10.1016/j.amc.2006.01.089.

• Bose CJ. and Murray R. (2006) Minimum 'energy' approximations of invariant measures for nonsingular transformations. Discrete and Continuous Dynamical Systems 14(3): 597-615. http://dx.doi.org/10.3934/dcds.2006.14.597.

• Domijan M., Murray R. and Sneyd J. (2006) Dynamical Probing of the Mechanisms Underlying Calcium Oscillations. Journal of Nonlinear Science 16(5): 483-506. http://dx.doi.org/10.1007/s00332-005-0744-z.

• Murray R. (2004) Optimal partition choice for invariant measure approximation for one-dimensional maps. Nonliinearity 17(5): 1623-1644. http://dx.doi.org/10.1088/0951-7715/17/5/004.

• Bose C. and Murray R. (2001) The exact rate of approximation in Ulam's method. Discrete and Continuous Dynamical Systems 7(1): 219-235. http://dx.doi.org/10.3934/dcds.2001.7.219.

• Murray R. (2001) Existence, mixing and approximation of invariant densities for expanding maps on R^r. Nonlinear Analysis: Theory, Methods and Applications 45(1): 37-72. http://dx.doi.org/10.1016/S0362-546X(99)00329-6.

• Santoboni G., Murray R. and Bishop S. (2000) Roundoff-induced phenomena and diffusion processes: the ``premature'' synchronisation of coupled maps. Physics Letters A 271 271(5-6): 358-367. http://dx.doi.org/10.1016/S0375-9601(00)00381-9.

• Keane M., Murray R. and Young LS. (1998) Computing invariant measures for expanding circle maps. Nonliinearity 11: 27-46. http://dx.doi.org/10.1088/0951-7715/11/1/004.

• Murray R. (1998) Approximation error for invariant density calculations. Discrete & Continuous Dynamical Systems 4(3): 535-557. http://dx.doi.org/10.3934/dcds.1998.4.535.

Chapters

• Bose C. and Murray R. (2014) Numerical approximation of conditionally invariant measures via Maximum Entropy. In Bahsoun W; Bose C; Froyland G (Ed.), Ergodic theory, open dynamics, and coherent structures. Springer Proceedings in Mathematics & Statistics, Vol 70: 81-104. New York: Springer-Verlag. http://dx.doi.org/10.1007/978-1-4939-0419-8_5.

Conference Contributions - Published

• Gallardo Ocampo P., Murray R., Bishop D. and Krumdieck S. (2020) A freight distribution exercise. In.

• Gallardo Ocampo P., Bishop D., Murray R. and Krumdieck S. (2019) New Zealand transition engineering retro-analysis. In.

• Gallardo Ocampo P., Leon P., Murray R. and Krumdieck S. (2018) Geographic economic accessibility (GEA) for freight transport. In.

• Santoboni G., Murray R. and Bishop S. (2001) A simple use of the diffusion approximation for treating roundoff-induced problems in coupled maps with an invariant subset. In Proceedings of Space-Time Chaos: Characterization, Control and Synchronization: 223-232.

• Murray R. (1997) Invariant measures and stochastic discretisations of dynamical systems. In Proceedings of 15th IMACS World Congress on Scientific Computation.

Conference Contributions - Other

• Laufer B., Murray R., Docherty PD., Krüger-Ziolek S., Höflinger F., Reindl L. and Möller K. (2020) Anzahl und Position von Sensoren in einem Smart-Shirt zur Bestimmung von Tidalvolumina. Lübeck, Deutschland: Automatisierungstechnische Verfahren für die Medizin AUTOMED, 2-3 Mar 2020.

• Fee CJ., Newberry F., Gordon A., Wilson P., Moyers-Gonzales M., Murray R., Huber T. and Dimartino S. (2016) Optimization of porous bed geometric features to maximize adsorption of proteins and passage of suspended solids in a 3D-printed adsorption column. Philadelphia, PA, USA: PREP Symposium 2016, 18-21 Jul 2016.

• Fee CJ., Newberry F., Gordon A., Wilson PL., Moyers-Gonzalez M., Murray R., Huber T. and Dimartino S. (2016) 3D-printed chromatography columns for downstream capture of proteins in the presence of suspended cells. Phuket, Thailand: 2nd Bioprocess Asia Conference, 5-8 Dec 2016.

• Froyland G., De Jong J., Moyers-Gonzales M., Roberts B., Wilson PL. and Murray R. (2016) Vortices in a street canyon. Orlando, FL, USA: The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 1-5 Jul 2016.

• Goodman M., David T., Docherty PD. and Murray R. (2016) Calcium Dynamics in Coupled Cellular Reaction Diffusion Equations. Queenstown, New Zealand: 34th Australasian Winter Conference on Brain Research, 27-31 Aug 2016.

• Goodman M., David T., Docherty PD. and Murray R. (2016) Homogenisation Theory Applied to Coupled Mammalian Cells. Christchurch, New Zealand: Health Research Society of Canterbury: Christchurch Hospitals' Grand Rounds series 2016, 27-27 May 2016.

• Goodman M., Murray R., Docherty PD. and David T. (2016) Homogenisation Theory with Coupled Cellular Reaction Diffusion Equations. Boston, MA, USA: SIAM Conference on the Life Sciences 2016, 11-14 Jul 2016.

• Asuncion J., Krumdieck S., Rendall S., Page S. and Murray R. (2013) Geographic Energy Adaptive Potential of Farmers' Market System as Compared with Conventional Supermarket System. Washington DC, USA: Transportation Research Board 92nd Annual Meeting, 13-17 Jan 2013.

• Asuncion J., Page S., Murray R. and Krumdieck S. (2012) Analysis of the truck trip generation characteristics of supermarkets and convenience stores. Rotorua, New Zealand: IPENZ Transportation Group Conference, 18-21 Mar 2012.

• Asuncion J., Rendall S., Murray R. and Krumdieck S. (2012) New Zealand intermodal freight network and the potential for mode shifting. Rotorua, New Zealand: IPENZ Transportation Group Conference, 18-21 Mar 2012.

Reports

• Martin G., Anthony G., Brown J., Dalrymple M., Ell F., Greenwood S., Higgins J., Hunter J., Murray R. and Roskruge M. (2021) Pāngarau Mathematics and Tauanga Statistics in Aotearoa New Zealand. In Pāngarau Mathematics and Tauanga Statistics in Aotearoa New Zealand - Advice on refreshing the English-medium Mathematics and Statistics learning area of the New Zealand Curriculum, Royal Society Te Apārangi. Commissioned by Ministry of Education. 56 pp.

• Bose C., Froyland G., Gonzalez-Tokman C. and Murray R. (2011) New methods for analysing metastable structures in closed, open or non-autonomous dynamical systems.Commissioned by Banff International Research Station. 5pp.

Theses / Dissertations

• Murray R. (1997) Discrete approximation of invariant densities. United Kingdom. University of Cambridge.

Other

• Murray R. (2023) Review of "A Modern Introduction to Differential Equations." Third Edition. By Henry J. Ricardo. SIAM Review 65(3): 910-913. Society for Industrial and Applied Mathematics. http://dx.doi.org/10.1137/23N975764.

• Ackerley E. and Murray R. (2013) Progress on Improving Student Success in First-Year Mathematics at the University of Canterbury. The CULMS Newsletter 8: 7-10. [Print and Online].

• Murray R. (2006) Geon Ho Choe, Computational Ergodic Theory. Algorithms and Computation in Mathematics 13, 2005; 453pp. Newsletter of the New Zealand Mathematical Society 96: 28-29. Wellington: New Zealand Mathematical Society Inc.. [Book Review].

• Murray R. (1999) Book review: "B Kitchens. Symbolic dynamics: one-sided, two-sided and countable state Markov shifts, Springer-Verlag (1998).". UK Nonlinear News 16 [Electronic].

• Murray R. (1996) Stochastic discretisation: approximating invariant measures by noisy dynamics. An essay submitted for consideration for the J T Knight Prizes. .

Student Supervision

Displaying all items.

Current
• PhD - Hayashi S: Extending Control-Based Continuation Methods for Dynamical System Analysis
• PhD - Lam N: Advancing numerical evaluation of model identifiability in noisy data.
• PhD - MacDonald L: Optimization Methods with Applications to Large Scale Machine Learning Problems
Completed
• PhD - Asuncion J: The geographic adaptive potential of freight transportation and production system in the context of fuel and emission constraints (2013)
• PhD - Gallardo PO: Essential elements of the energy transition for freight movements in post-colonial countries: data mining, modelling tools and policy scenarios - with case study in Ecuador (2020)
• PhD - Goodman M: Homogenisation Theory Applied to Coupled Mammalian Cells (2018)
• PhD - Mohd M: Modelling the Presence-Absence of Multiple Species (2016)
• PhD - Santoboni G: Synchronisation of coupled chaotic systems (1999) (1998)
• PhD - Sinescu V: Construction of lattice rules for multiple integration based on a weighted discrepancy (2008)
• Masters - Bills R: A model of follicular development and ovulation in mammals (2000)
• Masters - Candy T: A study of Besov-Lipschitz and Triebel-Lizorkin spaces using non-smooth kernels (2008)
• Masters - Domijan M: Dynamical probing of mechanisms underlying Calcium oscillations (2005)
• Masters - Fletcher F: Optimising irrigation and on-farm water storage (2022)
• Masters - Hughes EH: Modelling wilding pines
• Masters - Litchfield B: Implementation of chaos based communication systems in real time (2017)
• Masters - Peters N: Dynamic mode decomposition and nonlinear PDEs (2023)
• Masters - Shek J: Homogenised models of smooth muscle and endothelial cells (2013)
• Masters - Sung J: Reconstructing distributions from option prices (2013)
• Masters - Papachristou P: 1998-Masters Project-Papachristou, Pandelis (1998)
• Honours - Di S: Metastability in open dynamical systems (2013)
• Honours - Domijan M: 2003-Honours-Domijan, Mirela (2003)
• Honours - Fisher K: Excitability in Random Dynamical Systems (2017)
• Honours - Frater F: Data driven analysis of dynamical systems via DMD (2020)
• Honours - Hayr A: 2003-Honours-Hayr, Alexandra (2004)
• Honours - Jeffreys B: Identification of coherent structures within a flow using the Ulam matrix method (2016)
• Honours - Kempe A: Bank failure in complex financial networks (2013)
• Honours - Mugford J: Coupled cell dynamics (2013)
• Honours - O'Keeffe F: Slow mixing in dynamical systems (2021)
• Honours - Robinson G: SIR models of the effectiveness of contact tracing for epidemic control at different infection prevalence (2021)
• Honours - Shepherd R: Adaptive dynamics and eco-evolution (2021)
• Honours - Williams J: L^2 quantization of area preserving maps (2011)
• Summer Student - Churcher K: Large-scale networks of nonlinear oscillators: parameter gradients, spatio-temporal decoherence and chaos. (2012)
• Summer Student - Newberry F: Geometry optimisation of porous media (2016)
• Summer Student - Roberts B: Coherent Structures in High Reynolds Number Flows (2016)

Editorial Work

• Journal of Computational Dynamics Associate Editor ( 2012 - 2023)

Research Groups