Prof. James P.
Gleeson
(PhD, Applied Math, Caltech, 1999)
Department
of Mathematics and Statistics,
University
of Limerick, Ireland
Telephone: +353 61 202634 Fax: +353 61 334927
Email: james.gleeson@ul.ie
Office: B3051, Main Building, UL
Teaching:
·
Course director MSc
in Mathematical Modelling
·
MS6011: Advanced Methods I
·
MS4028: Stochastic
differential equations for finance
Research
I work on mathematical models for stochastic
dynamics, particularly on complex networks. As co-director of MACSI, I am also interested in applying
mathematical tools and techniques to solving real-world problems, in collaboration
with partners from industry, science and engineering. Our research is funded by
Science Foundation Ireland.
News:
·
A test version of MATLAB code for
solving the differential equations arising from the master equations, pair
approximations, and mean-field theories derived in [Gleeson JP, High-accuracy
approximation of binary-state dynamics on networks, Phys. Rev. Letters, 107, 068701 (2011)]
is now available for download from here. Comments
and bug reports are welcome.
·
Vacancies:
o Two
PhD studentships in Modelling of Stochastic Dynamics on Complex Networks,
funded by Science Foundation Ireland, to begin in Summer/Autumn 2012. Details
are available here or from the MACSI Vacancies page.
o Postdoctoral
fellowships in mathematical modelling and applied optimization, funded by
Science Foundation Ireland through the Sustainable
Electrical Energy Systems cluster. Details are available from the MACSI Vacancies page.
Recent
presentations:
·
Speaker at MAPCON12: Mathematical
Physics of Complex Networks, Dresden, Germany, 14-18 May 2012.
·
Invited speaker at Workshop
on Stochastic Dynamics in Mathematics, Physics and Engineering, Bielefeld,
Germany, 2-4 Nov 2011.
·
Invited speaker at 24th Marian Smoluchowski Symposium on Statistical Physics, Zakopane, Poland, 17-22 Sep 2011.
Research
areas and selected publications
·
Complex
networks: dynamics and structural models
We have developed
methods for analytically calculating the expected size of cascades on random networks,
and on networks with clustering (transitivity) [6,7].
Recently we extended these methods to a general class of binary-state dynamics
[2,3,1]. We have also investigated why mean-field
theory often works well, even on highly-clustered networks [4,5].
1. Durrett R,
Gleeson JP, Lloyd AL, Mucha PJ, Shi F, Sivakoff D, Socolar JES and
Varghese C, Graph fission in an evolving voter model, Proc.
Natl. Acad. Sci. USA, 109, 3682 (2012)
2. Gleeson
JP, High-accuracy approximation of binary-state dynamics on networks, Phys. Rev. Letters, 107, 068701 (2011); extended version
at arXiv:1104.1537
3.
Cellai D, Lawlor A, Dawson KA, Gleeson
JP, Tricritical point in heterogeneous k-core
percolation, Phys. Rev. Letters, 107, 175703 (2011); arXiv:1106.1565
4.
Gleeson JP, Melnik S, Ward J, Porter
MA, Mucha PJ, Accuracy of mean-field theory for
dynamics on real-world networks, Phys. Rev. E, 85, 026106
(2012); arXiv:1011.3710
5.
Melnik S, Hackett A,
Porter MA, Mucha PJ, Gleeson JP, The unreasonable
effectiveness of tree-based theory for networks with clustering, Phys. Rev. E, 83, 036112 (2011); arXiv:1001.1439
6.
Gleeson JP, Bond
percolation on a class of clustered random networks, Phys. Rev. E, 80, 036107 (2009), arXiv:0904.4292
7. Gleeson
JP, Cascades on correlated and modular random networks, Phys. Rev. E, 77, 046117 (2008); [PDF]
·
Systemic
risk models for contagion in banking networks
8. Hurd TR and Gleeson
JP, A framework for analyzing contagion in banking
networks, submitted; arXiv:1110.4312
9. Gleeson
JP, Hurd TR, Melnik S, Hackett A, Systemic risk in
banking networks without Monte Carlo simulation, submitted; PDF.
·
Mathematical
modelling
Noise in
electronic oscillators [10,11]; mixing, sorting and
diffusion in microfluidic devices
[12-15].
10. O’Doherty
F and Gleeson JP, Phase diffusion coefficient for oscillators perturbed by colored noise, IEEE Trans. Circuits and Systems II, 54,
435-439 (2007). [PDF]
11. Gleeson
JP and O’Doherty F, Non-Lorentzian spectral lineshapes near a Hopf
bifurcation, SIAM J. Appl. Math., 66, 1669-1688 (2006) [PDF]
12. Lanyon
YH et al., Fabrication of nanopore array electrodes
by focused ion beam milling, Anal. Chem., 79, 3048 (2007) [PDF]
13. Gleeson JP, Sancho JM, Lacasta AM, and Lindenberg K,
Analytical approach to sorting in periodic and random potentials, Phys. Rev. E,
73, 041102 (2006) [PDF]
14. Gleeson JP, Transient micromixing: Examples of laminar and chaotic stirring,
Phys. Fluids, 17, 100614 (2005) [PDF]
15. Gleeson JP, Roche OM, West J, and Gelb A, Modelling
annular micromixers, SIAM J. Appl. Math., 64,
1294-1310 (2004) [PDF]
Stochastic
Dynamics and Complex Systems (SDCS) homepage
Mathematics
and Statistics homepage