Main

Dr. Sergey Melnik

Department of Mathematics and Statistics,

University of Limerick, Ireland

Telephone: +353 61 233264

Office: A-2015f, Main building, UL.

Email: sergey-dot-melnik-at-ul-dot-ie

I am a postdoctoral research fellow at the University of Limerick and a member of the group of Prof. J.P. Gleeson and MACSI. I have previously held an IRCSET-Marie Curie Research Fellowship at the University of Oxford. Prior to that I have held a postdoctoral position at the University of Limerick. I received PhD in Physics (2008, University College Cork, Ireland) and the joint MSc/BSc in Computer Science & Mathematics (2003, Nayanova University, Samara, Russia).

My Google Scholar, ResearcherID and LinkedIn profiles.

News

• [Nov. 2017] Our paper "Exact analytical solution of irreversible binary dynamics on networks" has just appeared on arXiv:1711.02721. In this paper, we introduce a set of recursive equations for the exact calculation of cascade dynamics on networks. Our code is also available here.

• [Feb. 2017] Our paper "A framework for analyzing contagion in assortative banking networks" has just been published in PLoS ONE 12(2): e0170579 (2017). In this paper, we introduce a probabilistic framework to study default cascades in (dis)assortative directed interbank networks.

• [Sept. 2016] I won 1st prize in the HackOn(Data) Data Science / Machine Learning workshop exercises and challenges, competing with over 200 participants. http://hackondata.com/#participants

• [July 2016] Our paper "Double cascade model of financial crises" has just been published in Int. J. Theor. Appl. Fin. 19,1650041 (2016). In this paper, we introduce a financial network model that combines the default and liquidity stress mechanisms and demonstrates that the level of defaults in a financial network is negatively related to the strength of bank liquidity hoarding.

• [June 2016] Our paper "Emergence of coexisting percolating clusters in networks" has just been published in Phys. Rev. E 93, 062308 (2016). In this paper, we show that multiple coexisting percolating clusters can emerge in networks, contrary to the common assumption that at most one percolating cluster can exist.

• [Apr. 2016] Our new paper "Simple and accurate analytical calculation of shortest path lengths" has just appeared on arXiv:1604.05521. In this paper, we propose a simple method that allows one to accurately predict the distribution of shortest path lengths on synthetic or real-world networks using their degree distribution, or joint degree-degree distribution. Compared to some other analytical methods, our approach is simpler and yields more accurate results.

• [March 2016] Our new paper "The limitations of discrete-time approaches to continuous-time contagion dynamics" has just appeared on arXiv:1603.01132. In this paper, we show that discrete-time approaches should be used with care when analysing continuous-time systems as they can lead, for example, to incorrect prediction of epidemic threshold. Simulation code written in C++ is available online.

• [May 2015] Our new paper "Network cloning unfolds the effect of clustering on dynamical processes" has been published in Phys. Rev. E 91, 052807 (2015). In this paper, we introduce a technique which we call "L-cloning" , which is a great framework for the analysis of the effects of short loops on dynamics operating on networks.

• [Oct. 2014] Our new paper "Analytical solution for a class of network dynamics with mechanical and financial applications" with P. Krejčí, H. Lamba, and D. Rachinskii has been published in Phys. Rev. E 90, 032822 (2014).

• [Aug. 2014] MATLAB code for generating L-cloned networks introduced in our recent paper by Faqeeh et al. "Network cloning unfolds the effect of clustering on dynamical processes" [arXiv:1408.1294] can be downloaded here.

• [Nov. 2013] Octave/MATLAB code for generating modular networks with heterogeneous correlations (the so-called Piikk-networks introduced in Melnik et al., Chaos 24, 023106 (2014) [see also arXiv:1207.1809v2]) is now available for download from here.

Papers

• 1. [Get PDF] [Get CODE] E. Laurence, J.-G. Young, S. Melnik and L. J. Dubé, "Exact analytical solution of irreversible binary dynamics on networks", [arXiv:1711.02721] (2017).

  2. [Get PDF] S. Melnik and J. P. Gleeson, "Simple and accurate analytical calculation of shortest path lengths", [arXiv:1604.05521] (2016).

  3. [Get PDF] A. Faqeeh, S. Melnik, P. Colomer-de-Simón, and J. P. Gleeson, "Emergence of coexisting percolating clusters in networks", [arXiv:1508.05590] (2016).

  4. [Get PDF] T. R. Hurd, D. Cellai, H. Cheng, S. Melnik, and Q. Shao, "Illiquidity and Insolvency: a Double Cascade Model of Financial Crises" [arXiv:1310.6873] (2016).

  5. [Get PDF] P. G. Fennell, S. Melnik, and J. P. Gleeson, "The limitations of discrete-time approaches to continuous-time contagion dynamics", [arXiv:1603.01132] (2016).

  6. [Get PDF] A. Faqeeh, S. Melnik, and J. P. Gleeson, "Network cloning unfolds the effect of clustering on dynamical processes", Phys. Rev. E 91, 052807 (2015). [arXiv:1408.1294] MATLAB code for L-cloning is here.

  7. [Get PDF] P. Krejčí, H. Lamba, S. Melnik, and D. Rachinskii, "Kurzweil integral representation of interacting Prandtl-Ishlinskii operators", Discrete. Contin. Dyn. Syst. B 20, 2949 (2015).

  8. [Get PDF] S. Melnik, M. A. Porter, P. J. Mucha, and J. P. Gleeson, "Dynamics on modular networks with heterogeneous correlations", Chaos 24, 023106 (2014). [arXiv:1207.1809v2] MATLAB code and examples are here.

  9. [Get PDF] P. Krejčí, H. Lamba, S. Melnik, and D. Rachinskii, "Analytical solution for a class of network dynamics with mechanical and financial applications", Phys. Rev. E 90, 032822 (2014). [arXiv:1309.4050]

  10. [Get PDF] S. Melnik, J. A. Ward, J. P. Gleeson, and M. A. Porter, "Multi-stage complex contagions", Chaos 23, 013124 (2013). [arXiv:1111.1596v2]

  11. [Get PDF] J. P. Gleeson, S. Melnik, J. A. Ward, M. A. Porter, and P. J. Mucha, "Accuracy of mean-field theory for dynamics on real-world networks", Phys. Rev. E 85, 026106, (2012). [arXiv:1011.3710v3]

1. [Get PDF] A. Hackett, S. Melnik, and J. P. Gleeson, "Cascades on a class of clustered random networks", Phys. Rev. E 83, 056107, (2011). [arXiv:1012.3651v2]

   1. [Get PDF] A. Hackett, J. P. Gleeson, and S. Melnik, "Site percolation in clustered random networks", Int. J. Comp. Syst. Sci. 1, 25-30 (2011).

   2. [Get PDF] S. Melnik, A. Hackett, M. A. Porter, P. J. Mucha, and J. P. Gleeson, "The unreasonable effectiveness of tree-based theory for networks with clustering", Phys. Rev. E 83, 036112 (2011).

   3. [Get PDF] J. P. Gleeson, S. Melnik, and A. Hackett, "How clustering affects the bond percolation threshold in complex networks", Phys. Rev. E 81, 066114 (2010).

   4. [Get PDF] J. P. Gleeson and S. Melnik, "Analytical results for bond percolation and k-core sizes on clustered networks", Phys. Rev. E 80, 046121 (2009). [arXiv:0811.4511v2]

   5. [Get PDF] S. Melnik, O. Rasskazov, and G. Huyet, "A Route to Robust Double Pulse Excitability in Optically Injected Semiconductor Lasers", J. Phys. Conf. Ser. 138, 012014 (2008).

   6. [Get PDF] D. Goulding, S. Melnik, D. Curtin, T. Piwonski, J. Houlihan, J. P. Gleeson and G. Huyet, "Kramers' Law for a Bistable System with Time-Delayed Noise", Phys. Rev. E. 76, 031128 (2007).

   7. [Get PDF] D. Goulding, S. P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J. G. McInerney, D. Rachinskii, and G. Huyet, "Excitability in a Quantum Dot Semiconductor Laser with Optical Injection", Phys. Rev. Lett. 98, 153903 (2007).

   8. [Get PDF] S. Melnik, G. Huyet, A.V. Uskov, "The Linewidth Enhancement Factor Alpha of Quantum Dot Semiconductor Lasers", Opt. Express 14, 2950-2955 (2006).

Research Interests

• • Machine Learning

  • Data Science

  • Social network analysis

  • Dynamics on networks

  • Parallel computations

  • Bifurcation analysis

Education

• • 2003-2008: PhD in Physics, University College Cork, Ireland. Thesis title: "Nonlinear and stochastic dynamics of semiconductor laser systems"

  • 1999-2003: BSc & MSc (with 1st honours) in Computer Science and Mathematics, Nayanova University, Samara, Russia.

Awards & Funding

• • 2016 $500: 1st prize at HackOnData.com Data Science exercises and challenges competition.

  • 2015 €6,000: New Foundations award from the Irish Research Council.

  • 2014 €6,000: New Foundations award from the Irish Research Council.

  • 2010 €220,000: INSPIRE: IRCSET-Marie Curie Postdoctoral Fellowship. Awarded to two mathematicians in Ireland.

  • 2010 €200: Prize in the Best Paper Awards at ECCS'10: European Conference on Complex Systems, September 13-17, 2010, Lisbon, Portugal.

  • 2010 €800: The only Irish-based researcher selected to attend the competitive 3-week long Santa Fe Insititute's Complex Systems Summer School in NM, USA. Received financial support from ERA-Complexity, Ireland.

  • 2009 €8,000: Short Term Travel Fellowship from Science Foundation Ireland to support a 3-month research visit to the group of Prof. Mason A. Porter at the University of Oxford, UK.

Teaching

• • Spring 2014: Science Mathematics II (MA4602), Lecturer. Department of Mathematics & Statistics, University of Limerick, Ireland.

  • Fall 2011: Mathematical Biology and Ecology (B8a), Class Tutor, managed two teaching assistants. Mathematical Institute, University of Oxford, UK.

  • Spring 2006: Numerical Methods and Programming (AM2032), Tutor. Department of Applied Mathematics, University College Cork, Ireland.

  • Fall 2004 - Spring 2006: Introductory Physics I (PY1052) & II (PY1053), Practical demonstrator. Physics Department, University College Cork, Ireland.

  • Fall 2003 - Spring 2004: Manager of Physics Helpdesk, Physics Department, University College Cork, Ireland.

Work Experience

• • 01/2012 - present: Research Fellow, Department of Mathematics & Statistics, University of Limerick.

  • 09/2010 - 01/2012: IRCSET-Marie Curie Research Fellow, OCIAM, Mathematical Institute, University of Oxford.

  • 03/2008 - 09/2010: Postdoctoral researcher, Department of Mathematics and Statistics, University of Limerick, Ireland.

  • 10/2003 - 03/2008: PhD Studies

  • 06/2002 - 07/2003: Software Engineer, Institute of Industrial Automation, Samara, Russia.

  • 01/1998 - 07/2003: Computer System Administrator, Audit Company "Kornaud-S", Samara, Russia

Computer Skills

• • MATLAB, Python, R, C/C++, Java, Distributed computations, Spark, Scala, Map/Reduce, Bash, Perl, Mathematica, AUTO, XPPAUT, Mathcad, Pascal, Assembler.

  • Linux and Windows-based computer systems administration.