Organisation and Dynamics in Complex Networks
Reference no.: EE1
Supervisor: Professor Ernesto Estrada
Date advertised: 13th November 2008
Please contact Professor Ernesto Estrada for further information.
The study of complex networks has become an important interdisciplinary field of research in XXI century. Its impact in biology, society, technology and ecology is expected to be a tremendous revolution. Complex networks are graphs in which nodes represent entities of the complex systems and links represent the interactions between these entities.
In particular we are interested in the study of global and local topological properties of these networks. Our interest is in developing graph-theoretic and statistical-mechanics concepts which permits to understand the organization and function of complex networks.
PhD work in this field would involve the study of linear algebra and graph theory (discrete mathematics) as well as some elements of statistical physics and computation.
Mathematical Study of Protein Structure and Function
Reference no.: EE2
Supervisor: Professor Ernesto Estrada
Date advertised: 13th November 2008
Please contact Professor Ernesto Estrada for further information.
Proteins are the real battle horses of living organisms. They realise functions as diverse and important as the enzymatic digestion of foods and the immunological responses to external agents. The function of proteins depends very much on their three-dimensional structure, eg their folding and packing.
In particular we are interested in the use of discrete mathematics techniques, such as graph theory and discrete geometry, in combination with experimental data available to characterize protein structure and function. Protein structures can also be represented as complex networks of interacting amino acids. Then, they can be represented as complex networks, which can be investigated to know how the topological structure of proteins determines their three dimensional structures, in particular their packing and folding.
PhD work in this field would involve the study of linear algebra and graph theory (discrete mathematics) as well as some elements of discrete geometry and computation.
Metric and Topological Properties of Networks
Reference no.: EE3
Supervisor: Professor Ernesto Estrada
Date advertised: 10th February 2010
Please contact Professor Ernesto Estrada for further information.
The study of complex networks has become an important interdisciplinary field of research in XXI century. Its impact in biology, society, technology and ecology is expected to be a tremendous revolution. Complex networks are graphs in which nodes represent entities of the complex systems and links represent the interactions between these entities.
In particular we are interested in algorithmic approaches to topological properties of networks related to their planarity. On the other hand, we are interested in the mathematical properties of new metrics for networks. The best known metric in use is the shortest-path distance. It has become very popular due to the discovery of small-world phenomenon in networks. However, there is another metric, known as resistance distance which display many interesting features completely unexplored in complex networks. We are interested in studying mathematical properties of this metric in complex networks, its relation with the spectrum of the Laplacian matrix, vibrational modes in networks and Markov chains.
PhD work in this field would involve the study of linear algebra and graph theory (discrete mathematics).