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Research

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Publications since 2000

Scholarly Books

  1. Wang J., Tan A. and Tian T. (ed) Next generation of microarray bioinformatics, Humana Press and Springer, 2012.

Scholarly Book Chapters

  1. Wang J, Davidson B and Tian T., Systems biology studies of gene network and cell signalling pathway in cancer research. in Bioinformatics for Diagnosis, Prognosis and Treatment of Complex Diseases, Shen B. ed. Springer, 109-130, 2014.
  2. Wang J and Tian T., Effective methods for inferring genetic regulation from microarray gene expressio data, in Next generation of microarray bioinformatics, Wang J. et al. ed., Humana Press and Springer, 235-246. 2012.
  3. Tian T., Stochastic modelling of genetic regulatory networks, in Applied statistics for Biological Networks, M. Dehmer (ed), 13-37, Wiley-VCH, 2011
  4. Burrage K., Burrage P.M., Hamilton N. and Tian T., Computer-intensive simulations for cellular models, in Parallel Computing in Bioinformatics and Computational Biology, A.Y. Zomaya ed, Wiley, 79-119, 2006.
  5. Burrage K. and Tian T., Poisson Runge-Kutta methods for chemical reaction systems, in Advances in Scientific Computing and Applicati ons, Y. Lu W. Sun and T. Tang eds, Science Press, Beijing/New York, 82-96, 2004.

Refereed Journal Articles

  1. Q Wu, F Jiang, T Tian (2015) Sensitivity and Robustness Analysis for Stochastic Model of Nanog Gene Regulatory Network. International Journal of Bifurcation and Chaos 25 (07), 1540009.
  2. W Zhang, T Tian, X Zou. (2015) Negative feedback contributes to the stochastic expression of the interferon-beta gene in virus-triggered type I interferon signaling pathways. Mathematical biosciences 265, 12-27.
  3. Wu F., Yin G. and Tian T. (2014) Gene regulatory networks driven byintrinsic noise with two-time scales:a stochastic averaging approach, Front Math China, 9(4):947-963, 2014.
  4. Sun S., Klebaner F. and Tian T. (2014) A new model of time scheme for progression process of colorectal cancer, BMC Systems Biology, 8(S3):S2, 2014.
  5. Wu Q, Smith-Miles K and Tian T. (2014) Approximate Bayesian computation schemes for parameter inference of discrete stochastic models using simulated likelihood density, BMC Bioinformatics, 15(S12):S3, 2014.
  6. Tian T., Zhou Y., Wu Y. and Ge X. (2014) Estimation of parameters in mean-reverting stochastic systems, Mathematical Problems in Engineering, ID 317059, 2014.
  7. Tian T. and Harding, A., How the topology of MAP modules facilitates Eukaryotic evolution, Cell Cycle, 13(15): 2379-2390, 2014.
  8. Tian T. and Smith-Miles K., Mathematical modeling of GATA-switching for regulating the differentiation of hematopoietic stem cell, BMC Systems Biology, 8(S1):S8, 2014.
  9. Deng Z. and Tian T., A continuous optimization approach for inferring parameters in mathematical models of regulatory networks, BMC Bioinformatics, 15:286, 2014.
  10. Tian T. Simplified stochastic models with time delay for studying the degradation process of mRNA molecules, International Journal of Data Mining and Bioinformatics, 10(1):18-32, 2014.
  11. Wu Q., Smith-Miles K., Zhou T. and Tian T., Stochastic modelling of chemical events with multi-step reactions using a simplified two-variable model, BMC Systems Biology, 7(S4): S14, 2013.
  12. Tian T. and Wu F. Robustness Analysis of the PI3K/AKT Cell Signaling Module, Journal of Medical and Bioengineering, 2(2): 93-97, 2013.
  13. Tian T. Chemical memory reactions induced bursting dynamics in gene expression, PLoS One, 8(1): e52029, 2013.
  14. Zong X., Wu F. and Tian T., Stability and stochastic stabilization of numerical solutions of regime-switching jump diffusion systems, Journal of Difference Equations and Applications, 19(11): 1733-1757. 2013.
  15. Tian T. and Song J., Mathematical modelling of the MAP kinase pathway based on proteomics dataset, PLoS ONE, 7(8):e42230, 2012.
  16. Duff C., Smith-Miles K., Lopes L. and Tian T., Mathematical models of stem cell differentiation: the PU.1 - Gata-1 interaction, Journal of Mathematical Biology, 64(3), 449-468, 2012.
  17. Li W., Luo X., Hill N.A., Ogden R.W., Tian T., Smythe A., Majeed A.W. and Bird N., Cross-bridge apparent rate constants of human gallbladder smooth muscle, Journal of Muscle Research and Cell Motility, 32(3), 209-220, 2011.
  18. Tian T., Olson S., Whitacre J.M. and Harding A., The origins of cancer robustness and evolvability, Integrative Biology, 3(1):17-30, 2011.
  19. Qiao M., Qi H., Liu A. and Tian T., Analysis of Stability and Permanence for a HBV Model with Impulsive Releasing Immune Factor, Chinese Annals of Mathematics, Series A, 32:173-184, 2011.
    The English translation of this paper was published in Chinese Journal of Contemporary Mathematics, vol.31(2): 149-162, 2011.
  20. Tian T., Plowman S., Parton R.G., Kloog Y. and Hancock J.F., Mathematical modelling of K-Ras nanocluster formation on the plasma membrane, Biophysical Journal, 99 (2), 534-543, 2010.
  21. Qiao M., Qi H. and Tian T., Steady state solution and stability of an age-structured MSIQR epidemic model, Intelligent Information Management, 2 (5), 316-324, 2010.
  22. Wang J. and Tian T., Quantitative model for inferring dynamic regulation of the tumour suppressor gene p53, BMC Bioinformatics , 11(1), 36, 2010.
  23. Tian T., Stochastic models for inferring genetic regulation from microarray gene expression data, BioSystems , 99(3), 192-200, 2010.
  24. Tian T., Effective stochastic simulation methods for chemical reaction systems, Journal of Numerical Mathematics and Stochastics, 1(1):85-101, 2009
  25. Shalom-Feuerstein R., Plowman S.J., Rotblat B., Ariotti N., Tian T., Hancock J.F. and Kloog Y., K-ras nanoclustering is subverted by overexpression of the scaffold protein galectin-3. Cancer Res., 68, 6608-6616, 2008.
  26. Tian T., Harding A., Inder K., Plowman S., Parton R.G. and Hancock J.F., Plasma membrane nano-clusters generate high-fidelity Ras signal transduction, Nature Cell Biology, 9, 905-914, 2007.
  27. Tian T., Xu S., Gao J. and Burrage K., Simulated maximum likelihood method for estimating kinetic rates in genetic regulation, Bioinformatics, 23, 84-91, 2007.
  28. Tian T., Burrage K., Burrage P.M. and Carletti M., Stochastic Delay Differential Equations for Genetic Regulatory Networks, J. of Comput. and Appl. Maths., 205, 696-707, 2007.
  29. Tian T and Burrage K., Stochastic models for regulatory networks of the genetic toggle switch, Proceedings of the National Academy of Sciences (USA), 103, 8372-8377, 2006.
  30. Barrio M., Burrage K., Leier A. and Tian T., Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation, PLoS Computational Biology, 2, 1017-1039 (e117), 2006.
  31. Tian T and Burrage K., An efficient stepsize selection procedure for discrete simulation of biochemical reaction system, ANZIAM J. 48, C1022-C1040, 2006
  32. Harding A., Tian T., Westbury E., Frische E. and Hancock J.F., Subcellular localization determines MAP kinase signal output, Current Biology, 15: 869-873, 2005.
  33. Tian T. and Burrage K., Binomial leap methods for simulating stochastic chemical kinetics, Journal of Chemical Physics 121, 10356-10364, 2004.
  34. Tian T. and Burrage K., Bistability and switching in the lysis/lysogeny genetic regulatory network of Bacteriophage lambda, Journal of Theoretical Biololy, 227, 229-237, 2004.
  35. Burrage K., Tian T. and Burrage P.M., A multi-scaled approach for simulating chemical reaction systems, Progress in Biophysics and Molecular Biology, 85, 217-234, 2004.
  36. Burrage K., Burrage P.M. and Tian T., Numerical Methods for Strong Solutions of Stochastic Differential Equations: an Overview, Proceedings of the Royal Society of London. Series A 460, 373-402, 2004.
  37. Tian T., Robustness of mathematical models for biological systems, ANZIAM J. 45(C), 565-577, 2004
  38. Tian T., Burrage K. and Volker R., Stochastic modelling and simulations for solute transport in porous media, ANZIAM J. 45(C), 551-564, 2004.
  39. Burrage K. and Tian T., Implicit stochastic Runge-Kutta methods for stochastic differential equations, BIT 44, 21-39, 2004.
  40. Tian T and K. Burrage, Accuracy issues of Monte-Carlo methods for valuing American options, ANZIAM J. 44(E) ppC739--C758, 2003.
  41. Tian T. and Burrage K., Two-stage stochastic Runge-Kutta methods for stochastic differential equations, BIT, 42 (2002), 625-643.
  42. Burrage K. and Tian T., Predictor-corrector methods of Runge-Kutta type for stochastic differential equations, SIAM Numer. Anal., 40 (4), 1516-1537, 2002.
  43. Tian T. and Burrage K., Implicit Taylor methods for stiff stochastic differential equations, Applied Numer. Maths., 38 (2001), 167-185.
  44. Burrage K. and Tian T., Stiffly Accurate Runge-Kutta Methods for stiff Stochastic Differential Equations, Comput. Phys. Commun., 142, 186-190, 2001.
  45. Burrage K. and Tian T., The composite Euler method for solving stiff stochastic differential equations, J. of Comput. and Appl. Maths., 131, 407-426, 2001.
  46. Burrage K. and Tian T., A note on the stability properties of the Euler methods for solving stochastic differential equations, New Zealand J. of Maths., 29, 115-127. (Special issue for the retirement of Professor John Butcher), 2000.
  47. Burrage K. and Tian T., Parallel half-block methods for initial value problems, Applied Numer. Math., 32, 255-271, 2000.

Refereed conference papers

  1. Sun S., Klebaner F. and Tian T. A new mathematical model for inbreeding depression in Large populations, Proceedings of ISBRA 2014, Lecture Notes in Bioinformatics 8492, 310-321, Springer. 2014.
  2. Sun S., Klebaner F. and Tian T. A new mathematical model for progression of colorectal cancer, Proceedings of 2013 IEEE International Conference on Bioinformatics and Biomedicine (BIBM2013), 560-565, IEEE Press. 2013.
  3. Wu Q, Smith-Miles K and Tian T. Approximate Bayesian computation for estimating rate constants in biochemical reaction systems, Proceedings of 2013 IEEE International Conference on Bioinformatics and Biomedicine (BIBM2013), 416-421, IEEE Press, 2013.
  4. Wu Q, Smith-Miles K and Tian T. A two-variable model for stochastic modelling of chemical events with multi-step reactions, Proceedings of 2012 IEEE International Conference on Bioinformatics and Biomedicine (BIBM2012), 270-275, IEEE Press, 2012.
  5. Tian T. and Ge X., Calibration of stochastic differential equation models using implicit numerical methods and particle swarm optimization, Proceedings of 2012 International Conference on Modelling, Identification and Control, ICMIC 2012, 1049-1054, IEEE Press, 2012
  6. Tian T., Stochastic models for studying the degradation of mRNA molecules, Proceedings of 2011 IEEE International Conference on Bioinformatics and Biomedicine (BIBM2011). 167-172, IEEE Press, 2011.
  7. Tian T., Stochastic dynamics of a Hepatitis B virus transmission model, Proceedings of 2011 IEEE International Symposium on IT in Medicine and Education. 496-500, IEEE Press, 2011.
  8. Tian T., Estimation of kinetic rates of MAP kinase activation from experimental data, Proceedings of IJCBS 457-462, IEEE Press, 2009.
  9. Burrage K., Mac S. and Tian T., Accelerated leap methods for simulating discrete stochastic chemical kinetics, Proceedings of POSTA06, Lecture Notes in Control and Information Sciences 341, 359-366, 2006.
  10. Tian T. and Burrage K., A mathematical model for genetic regulation of the lactose operon, in Proceedings of the International Con ference on Computational Science and its Applications, Lecture Notes in Computer Science, 3481, 1245-1253, 2005.
  11. Tian T. and Burrage, K., Parallel implementation of stochastic simulations for large-scale cellular processes, Proceedings of the 8th International Conference on HPC-Asia, 621-626, IEEE Press, 2005.
  12. Burrage K. and Tian T., Effective simulation techniques for biological systems, in Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II (Proceedings of SPIE Volume: 5467), SPIE, 311-325, 2004.
  13. Tian, T. and Burrage, K., Stochastic neural network models for gene regulatory networks, Proceedings of the 2003 Congress on Evolutio nary Computation, 162-169, IEEE Press, 2003.
  14. Burrage, K., Burrage, P.M., Jeffrey, S., Pickett, T., Sidje, R. and Tian, T., A Grid Implementation of Chemical Kinetic Simulation Met hods in Genetic Regulation, Proceedings of APAC03 on Advanced Computing, Grid Applications and eResearch, 2003.
  15. Tian T., Numerical simulations of solute transport in porous media on parallel computers, Proceedings of the 5th international conference on High-Performance Computing in the Asia-Pacific Region, 2001.
  16. Burrage K., Burrage P.M. and Tian T., Numerical methods for solving stochastic differential equations on parallel computers, Proceedings of the 5th international conference on High-Performance Computing in the Asia-Pacific Region, 2001.
  17. Tian T. and Burrage K., Numerical simulations of a financial market model, Proceedings of the 3th operations research conference of the Australian society for operations research Queensland branch, E. Kozan and R.Beard ed., 168-179, Brisbane, 2000.