Calculation of Higher-Order Derivatives of a Modified Ising Model of Gene Interaction Networks
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- Project Offer-Number:
- UROP International
- Computational Engineering Science
- Organisation unit:
- Joint Research Center for Computational Biomedicine (JRC-Combine)/ AICES
- Language Skills:
- English knowledge is mandatory
- Computer Skills:
- Python/ Matlab or C++
The Ising model is one of the simplest and most frequently studied models of phase transitions and cooperative phenomena in statistical mechanics [Ising (1925)]. Traditionally, Ising models have been studied in homogeneous structures such as the lattice up to three-dimensions. Recently, phase transitions using Ising model has been studied in more complicated topologies such as small-world and scale-free networks [Aleksiejuk(2002), Bianconi(2002), Pekalski(2001), Dorogovstev(2002)]. A gene regulatory network has been known to exhibit a scale-free topology wherein genes are nodes involved in a particular regulatory function, controlling expression levels of other genes and that of their resultant proteins. From our work, we know that Ising model of a gene regulatory network with states exhibiting a binary random variable exhibits phase transition of first order as inferred from the order parameter of such a system [J.Krishnan et al. To be Published].
The objective of this project is to compute higher order derivatives of a modified Ising model of gene interaction networks including free energy and heat capacity; make inferences on critical exponents of the system and compare to the spin glass properties of a conventional Ising model.
Interested candidate must have a background in Physics or Computer Science.