Ernesto Estrada
Professor of Complexity Sciences

Research

Study of Complex Systems at Different Size-Scales

Complex 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 I concentrate on the study of global and local topological properties of these networks. I am interested in developing statistical-mechanics concepts which permits to understand the organization and function of such networks. At the global scale I am going beyond the studies of “small-worldness” and “scale-freeness” to account for topological characteristics such as expansibility, topological and functional bottlenecks, organization of clusters, global communicability, “clumpiness” of nodes in a network, returnability, etc. I am interested in developing new mathematical approaches based of graph spectral theory. The relationship between these mathematical techniques and statistical physics has been already investigated by myself.

Human Protein Interaction Network (PIN)

Meaning of the links in a PIN

Biomolecular Systems

My objective here is to 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. By exploring the topological properties of such networks from the point of view of several graph spectral techniques I investigate how the topological structure of proteins determines their three dimensional structures, in particular their packing and folding.

Mathematical Chemistry

I have developed several approaches, e.g., TOPS-MODE (Topological Sub-Structural Molecular Design), generalized topological indices, etc., to understand and 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 and quantum mechanics to understand the molecular structure.

Highlights