Associate Professor, Deputy Head of Department
Department of Mathematics and Applied Mathematics at the University of Cape Town
Born: October 12, 1968 in Sydney, Australia
1990: B.Sc. in Physics, University of Athens, Greece.
1997: Ph.D. in Nonlinear Dynamical Systems, University of Athens, Greece. Ph.D. Thesis: Numerical and theoretical study of structures in the phase space of dynamical systems with two and three degrees of freedom.
2005: B.Sc. in Mathematics, University of Athens, Greece.
Jan. 2002 – Dec. 2003: University of Patras (Greece), Department of Mathematics, "Karatheodoris" postdoctoral fellow.
Sept. 2004 – June 2005: Technological Educational Institute of Messolonghi (Greece), Department of Applied Informatics in Management and Finance, Assistant Professor (annual contract).
Jan. 1999 – Dec. 2005: Academy of Athens (Greece), Research Center for Astronomy and Applied Mathematics, postdoctoral fellow.
Feb. 2006 – Jan. 2008: Observatory of Paris (France), Institut de Mécanique Céleste et de Calcul des Éphémérides, postdoctoral fellow (Marie Curie Intra-European Fellowship).
Feb. 2008 – June 2011: Max Planck Institute for the Physics of Complex Systems (Dresden, Germany), research fellow.
June 2000 – July 2005 and Oct. 2006 – July 2013: Hellenic Open University (Greece), School of Science and Technology, teaching staff (annual contracts).
July 2011 – Sept. 2013: Aristotle University of Thessaloniki (Greece), Physics Department, Assistant Professor.
Sept. 2013 – Dec. 2016: University of Cape Town (South Africa), Department of Mathematics and Applied Mathematics, Senior Lecturer.
Jan. 2017 – present: University of Cape Town (South Africa), Department of Mathematics and Applied Mathematics, Associate Professor.
Jan. 2017 – present: Deputy Head of Department.
International Journal of Bifurcation and Chaos (World Scientific).
Discrete Dynamics in Nature and Society (Hindawi Publishing Corporation).
Frontiers in Applied Mathematics and Statistics (Frontiers).
Punjab University Journal of Mathematics (Department of Mathematics, Punjab University).
Hillebrand M., Paterson-Jones G., Kalosakas G., Skokos C.
Distribution of Base Pair Alternations in a Periodic DNA Chain: Application of Pólya Counting to a Physical System
2018, vol. 23, no. 2, pp. 135-151
In modeling DNA chains, the number of alternations between Adenine–Thymine (AT) and Guanine–Cytosine (GC) base pairs can be considered as a measure of the heterogeneity of the chain, which in turn could affect its dynamics. A probability distribution function of the number of these alternations is derived for circular or periodic DNA. Since there are several symmetries to account for in the periodic chain, necklace counting methods are used. In particular, Pólya’s Enumeration Theorem is extended for the case of a group action that preserves partitioned necklaces. This, along with the treatment of generating functions as formal power series, allows for the direct calculation of the number of possible necklaces with a given number of AT base pairs, GC base pairs and alternations. The theoretically obtained probability distribution functions of the number of alternations are accurately reproduced by Monte Carlo simulations and fitted by Gaussians. The effect of the number of base pairs on the characteristics of these distributions is also discussed, as well as the effect of the ratios of the numbers of AT and GC base pairs.