My research begins in the field of Mathematical Logic and its application to effectively computable functions and artificial intelligence for making business decisions, at the Complutense University of Madrid and in collaboration with F.Y.C.S.A., a subsidiary company of I.T.T. When I move to Seville to cover a teaching position at the University of Seville, I start my research in Chaos and Bifurcations of Dynamical Systems. A few years later I change research group and I focus on Discrete Mathematics, especially Extremal Graph Theory. I write my doctoral thesis in the field of Graph Drawing, again using techniques inherited from Logic and Computational Complexity Theory. These techniques are extended in the doctoral thesis that I direct next, finding a class of formulas whose satisfiability can be obtained in polynomial time and that encompasses all previously discovered classes with this property. In 2004, I start collaborating in graph problems applied to Quantum Mechanics, trying to solve the Peres Conjecture. While working on Discrete Mathematics problems, this new line is extended to several problems of quantum contextuality, obtaining very good results, publishing in leading journals (e.g. Physics Reviews Letter). In recent years, without abandoning research in Discrete Mathematics and quantum contextuality problems, I specialized in applying Graph Theory to other fields, including Neuroscience (genealogy of neurons in the eye of the drophilla fly), Chemistry (geometric graphs for the study of buckyespheres and fullerenes) and Architecture / Construction Engineering. I have also devoted much of my research to the study of applications of directed hypergraphs to fuzzy logic programming problems, with the group at the University of Cadiz led by Prof. Jesús Medina. It is worth mentioning the research carried out with the Fractal Dynamics of Consciousness: from Theory to Clinical Implementation group that produced a seminal article in PLoS of Computational Biology, a collaboration that is still active looking for other interesting results on applications of graph theory to electroencephalograms with intracranial stimulation in order to distinguish between patients with or without consciousness (e.g., in the case of prolonged comas or new anesthetics). We are also applying the same or similar techniques to the study of population growth problems in Ecology.
My research begins in the field of Mathematical Logic and its application to effectively computable functions and artificial intelligence for making business decisions, at the Complutense University of Madrid and in collaboration with F.Y.C.S.A., a subsidiary company of I.T.T. When I move to Seville to cover a teaching position at the University of Seville, I start my research in Chaos and Bifurcations of Dynamical Systems. A few years later I change research group and I focus on Discrete Mathematics, especially Extremal Graph Theory. I write my doctoral thesis in the field of Graph Drawing, again using techniques inherited from Logic and Computational Complexity Theory. These techniques are extended in the doctoral thesis that I direct next, finding a class of formulas whose satisfiability can be obtained in polynomial time and that encompasses all previously discovered classes with this property. In 2004, I start collaborating in graph problems applied to Quantum Mechanics, trying to solve the Peres Conjecture. While working on Discrete Mathematics problems, this new line is extended to several problems of quantum contextuality, obtaining very good results, publishing in leading journals (e.g. Physics Reviews Letter). In recent years, without abandoning research in Discrete Mathematics and quantum contextuality problems, I specialized in applying Graph Theory to other fields, including Neuroscience (genealogy of neurons in the eye of the drophilla fly), Chemistry (geometric graphs for the study of buckyespheres and fullerenes) and Architecture / Construction Engineering. I have also devoted much of my research to the study of applications of directed hypergraphs to fuzzy logic programming problems, with the group at the University of Cadiz led by Prof. Jesús Medina. It is worth mentioning the research carried out with the Fractal Dynamics of Consciousness: from Theory to Clinical Implementation group that produced a seminal article in PLoS of Computational Biology, a collaboration that is still active looking for other interesting results on applications of graph theory to electroencephalograms with intracranial stimulation in order to distinguish between patients with or without consciousness (e.g., in the case of prolonged comas or new anesthetics). We are also applying the same or similar techniques to the study of population growth problems in Ecology.
