RESEARCH

Study of Complex Systems at Different Size-Scales

Our research is directed to understand the structure and functioning of complex systems at different size-scales. Our philosophy is that it is more important to understand the organizational principles of such systems on the basis of their connectivity than understanding the role of their individual components. Then, we consider an integration of complex systems through the use of a common representation by means of graphs.  

Research Areas

1. Complex Interaction Networks

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. In particular we study global and local topological properties of these networks. Our interest is in developing statistical-mechanics concepts which permits to understand the organization and function of complex networks. At the global scale we study properties such as expansibility, topological and functional bottlenecks, organization of clusters, global communicability, “clumpiness” of nodes in a network, returnability, etc. We are also working in developing new mathematical approaches based of graph spectral theory to characterize the topology and dynamics of these networks.

Human Protein Interaction Network (PIN)

2. Biomoelecular Systems

We use techniques of discrete mathematics, such as graph theory and discrete geometry, in combination with quantum mechanics and statistical mechanics to characterize protein structure and function. These studies help us to understand the global folding characteristics of proteins and how they influence protein function. Protein structures can also be represented as complex networks of interacting amino acids. Then, they can be represented as complex networks, which we can investigate to know how the topological structure of proteins determines their three dimensional structures, in particular their packing and folding.  

3. Mathematical Chemistry

We have developed several approaches, e.g., TOPS-MODE (Topological Sub-Structural Molecular Design) and generalized topological indices to predict several pharmacological, ADME, toxicological and environmental properties of organic molecules like drugs, health care products, cosmetics, and so forth. The main objective of these methods is to reduce or completely eliminate in some situations, the number of animals in experiments. Other fields of research include, but are not limited to, the generation of algebraic invariants to represent molecular structures, the generalization of graph theoretic invariants, the study of spectral properties of molecular graphs and the elaboration of a theory combining the use of graph theory, quantum mechanics and statistical mechanics to understand the molecular structure.