# Giang Thu Nguyen

## exploring mathematics, three theorems at a time

My current research interests are stochastic differential equations, Markov-modulated Brownian motion, stochastic fluid flows, matrix-analytic methods, branching processes, and the Hamiltonian cycle problem.

Publications

###### Book

[38] V. S. Borkar, V. Ejov, J. A. Filar and G. T. Nguyen. Hamiltonian cycle problem and Markov chains.

In International Series in Operations Research & Management Science, Springer, 2012. [Buy it on Amazon]

###### Submitted Papers

[37] G. T. Nguyen and O. Peralta. Rate of strong convergence to solutions of regime-switching stochastic differential equations. [arXiv:2101.03250]

[36] A. Lewis, N. Bean, and G. T. Nguyen. Estimation of Markovian-regime-switching models with independent regimes. [arXiv:1906.07957]

[35] A. Lewis, N. Bean, and G. T. Nguyen. Bayesian estimation of a Markovian regime-switching model for the South Australian wholesale electricity market.

[34] G. T. Nguyen and F. Poloni. Componentwise accurate Brownian motion computations using Cyclic Reduction. [arXiv:1605.01482]

###### Refereed Papers

[33] G. Latouche, G. T. Nguyen and O. Peralta. Strong convergence to two-dimensional alternating Brownian motion processes. To appear in Stochastic Models. [arXiv:1910.06495]

[32] N. Bean, G. T. Nguyen, B. F. Nielsen, O. Peralta. RAP-modulated fluid processes: First passages and the stationary distribution. To appear in Stochastic Processes and Applications.

[31] N. Bean, A. H. Lewis, M. M. O'Reilly, G. T. Nguyen, V. Sunkara. A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes. To appear.

###### [30] G. T. Nguyen and O. Peralta. Rate of strong convergence to Markov-modulated Brownian motion. To appear in Journal of Applied Probability, 2021 [arXiv: 1908.11075]

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###### [29] A. Hamilton, G. T. Nguyen and M. Roughan. Counting Candy Crush configurations. Discrete Applied Mathematics, 295:47-46, 2021 [arXiv: 1908.09996]

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###### [27] A. M. Austin, M. J.J. Douglass, G. T. Nguyen, L. Cunningham, H. Le, Y. Hu,

###### and S. N. Penfold. Individualized selection of left-sided breast cancer patients for proton therapy based on cost-effectiveness. Journal of Medical Radiation Sciences, 63(1): 44-51, 2021

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###### [28] G. T. Nguyen and O. Peralta. An explicit solution to the Skorokhod embedding problem for double exponential increments. Statistics and Probability Letters, 165:108867, 2020 [arXiv:2002.00361]

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###### [26] A. M. Austin, M. J.J. Douglass, G. T. Nguyen and S. N. Penfold. Patient selection for proton therapy: A radiobiological fuzzy Markov model incorporating robust plan analysis. Australasian Physical and Engineering Sciences in Medicine, 2020, https://doi.org/10.1007/s13246-020-00849-4.

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###### [25] A. Austin, M. J. J. Douglass, G. T. Nguyen, R. Dalfsen, H. Le, P. Gorayski,, H. Tee, M. Penniment, and S. N. Penfold. Cost-effectiveness of proton therapy in treating base of skull chordoma. Australasian Physical and Engineering Sciences in Medicine, 42(4):1091-1098, 2019.

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###### [24] P. Mathews, C. Gray, L. Mitchell, G. T. Nguyen, N. G. Bean. SMERC: Social media event response clustering using textual and temporal information.

###### BSMDMA2018: The 2018 International Workshop on Big Social Data Management and Analysis, at IEEE BigData 2018. [arXiv:1811.0506]

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###### [23] A. M. Austin, M. J.J. Douglass, G. T. Nguyen, S. N. Penfold. A radiobiological Markov simulation tool for aiding decision making in proton therapy referral.

###### 37th Meeting of the European-Society-for-Radiotherapy-and-Oncology (ESTRO), Radio Therapy and Oncology, Elsevier 127: S1079-S1080, 2018.

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###### [22] N. Bean, G. T. Nguyen, and F. Poloni. Doubling Algorithms for Stationary Distributions of Fluid Queues: A Probabilistic Interpretation.

###### Performance Evaluation, 125, 1-20, 2018. [arXiv:1801.05981]

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###### [21] G. Latouche and G. T. Nguyen. Analysis of fluid flow models. Queueing Models and Service Management, 1(2), 1-29, 2018. [arXiv:1802.04355]

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[20] A. M. Austin, M. J.J. Douglass, G. T. Nguyen, S. N. Penfold. A radiobiological Markov simulation tool for aiding decision making in proton therapy referral.

Physica Medica, 44, 72-92. 2017 [Article]

[19] G. Latouche and G. T. Nguyen. Slowing time: Markov-modulated Brownian motion with a sticky boundary.

Stochastic Models, 33(2), 297-321. 2017 [arXiv:1508.00922] [Article]

[18] P. Mathews, L. Mitchell, G. T. Nguyen, N. G. Bean. The nature and origin of heavy tails in retweet activity.

MSM2017: 8th International Workshop on Modelling Social Media: Machine Learning and AI for Modelling and Analysing Social Media, April 2017, Perth, Australia. [arXiv: 1703.05545]

[17] G. Latouche and G. T. Nguyen. Feedback control: two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundaries.

Performance Evaluation, 106, 30-49. 2016. [arXiv:1603.01945]

[16] G. Latouche and G. T. Nguyen. The morphing of fluid queues into Markov-modulated Brownian motion.

Stochastic Systems, 5(1), 62-86, 2015. [arXiv:1311.3359]

[15] G. Latouche and G. T. Nguyen. Fluid approach to two-sided Markov-modulated Brownian motion.

Queueing Systems, 80(1-2), 105-125, 2015. [arXiv:1403.2522]

[14] G. T. Nguyen and F. Poloni. Componentwise accurate fluid queue computations using doubling algorithms.

Numerische Mathematik, 130(4), 763-792, 2015. [arXiv:1406.7301]

[13] Hautphenne, G. Latouche, and G. T. Nguyen. On the nature of Phase-Type Poisson distributions.

Annals of Actuarial Science, 8(1): 79-98, 2014.

[12] S. Hautphenne, G. Latouche, and G. T. Nguyen. Extinction probabilities of branching processes with countably infinitely many types.

Advances in Applied Probability, 45(4): 1068-1082, 2013.

[11] S. Hautphenne, G. Latouche, and G. T. Nguyen. Markovian trees subject to catastrophes: Do they survive forever?

Matrix-Analytic Methods in Stochastic Models, Latouche, G.; Ramaswami, V.; Sethuraman, J.; Sigman, K.; Squillante, M.S.; Yao, D. (Eds.).

Springer Proceedings in Mathematics & Statistics, 27: 87-106, 2013. [Article]

[10] G. Latouche, G. T. Nguyen and Z. Palmowski. Two-dimensional fluid queues with temporary assistance.

Matrix- Analytic Methods in Stochastic Models, Latouche, G.; Ramaswami, V.; Sethuraman, J.; Sigman, K.; Squillante, M.S.; Yao, D. (Eds.).

Springer Proceedings in Mathematics & Statistics, 27: 187--207, 2013. [Article]

[9] V. Ejov, N. Litvak, G. T. Nguyen and P. G. Taylor. Proof of the Hamiltonicity–Trace conjecture for singularly perturbed Markov chains.

Journal of Applied Probability, 48(4): 901–910, 2011. [Article]

[8] G. Latouche, G. T. Nguyen and P. G. Taylor. Queues with boundary assistance and the many effects of truncations.

Queueing Systems, 69(2): 175–197, 2011. [Article]

[7] G. Latouche, G. T. Nguyen, and Z. Palmowski. Two-buffer fluid models with multiple ON-OFF inputs and threshold assistance.

VALUETOOLS’11: Proceedings of the 5th ICST Workshop on Tools for Solving Markov Chains, 2011.

[6] J. A. Filar, M. Haythorpe and G. T. Nguyen. A conjecture on the prevalence of cubic bridge graphs.

Discussiones Mathematicae Graph Theory, 30(1): 175–179, 2010. [Article]

[5] V. Ejov, J. A. Filar, M. Haythorpe and G. T. Nguyen. Refined MDP–based branch–and–fixed algorithm for the Hamiltonian cycle problem.

Mathematics of Operations Research, 34(3): 758–768, 2009. [Article]

[4] V. Ejov, S. Friedland and G. T. Nguyen. A note on cubic graphs, generating functions and multi-filar structures.

Linear Algebra and its Applications, 431(8): 1367–1379, 2009. [Article]

[3] V. Ejov and G. T. Nguyen. Consistent behavior of certain perturbed determinants induced by graphs.

Linear Algebra and its Applications, 431(5-7): 543–552, 2009. [Article]

[2] P. Kilby, D. Lun and G. T. Nguyen. Multipoint-to-multipoint network communication.

Proceedings of the 2009 Mathematics and Statistics in Industry Study Group, 109–125, 2009. [Article]

[1] V. Ejov, J. A. Filar, W. Murray and G. T. Nguyen. Determinants and longest cycles of graphs.

SIAM Journal on Discrete Mathematics, 22(3): 1215–1225, 2008. [Article]

Consulting Report

R. C. Cope, G. T. Nguyen, N. G. Bean, and J. V. Ross, Review of forecast accuracy metrics for the Australian Energy Market Operator, The University of Adelaide, Australia, 2019. [Report]

###### Theses

Hamiltonian cycle problem, Markov decision processes and graph spectra. PhD Thesis, University of South Australia, 2009.

Investigating the Hamiltonian cycle problem using Markov decision processes. Honours Thesis, University of South Australia, 2005.

##### Collaborators

Nigel Bean, The University of Adelaide

Vivek Borkar, Indian Institute of Technology Bombay

Vladimir Ejov, Flinders University

Ali Eshragh, The University of Newcastle

Jerzy Filar, The University of Queensland

Shmuel Friedland, University of Illinois

Adam Hamilton, The University of Adelaide

Sophie Hautphenne, The University of Melbourne

Michael Haythorpe, Flinders University

Guy Latouche, Université libre de Bruxelles

Angus Lewis, The University of Adelaide

Nelly Litvak, University of Twente

Desmond Lun, Rutgers

Lewis Mitchell, The University of Adelaide

Zbigniew Palmowski, University of Wroclaw

Oscar Peralta, The University of Adelaide

Federico Poloni, University of Pisa

Matt Roughan, The University of Adelaide

Vikram Sunkara, Freie Universitat Berlin

Peter Taylor, The University of Melbourne

Walter Murray, Stanford University

##### Other mathematicians

Soren Asmussen, Aarhus University

Kostya Borovkov, University of Melbourne

Jim Dai, Georgia Institute of Technology & Cornell

Ton Dieker, Georgia Institute of Technology

Bronwyn Hajek, University of South Australia

Masakiyo Miyazawa, Tokyo University of Science

Brendan McKay, ANU

Yoni Narazathy, University of Queensland

Phil Pollett, University of Queensland

V. Ramaswami, AT&T

Leonardo Rojas-Nandayapa, University of Queensland

Matt Roughan, University of Adelaide

Lesley Ward, University of South Australia

Bert Zwart, CWI