I was born in Mexico City, where I lived until 1997. I graduated from the College of Science at the National Autonomous University of Mexico (UNAM) in 1997. While at UNAM, I was a student/athlete. My course of study at UNAM was centered on mathematics, especially probability theory. To graduate from college, I wrote a thesis on martingales and gambling under the supervision of Prof. Luis Briseño Aguirre. As an athlete, I represented UNAM both nationally and internationally.
After I graduated, I started to do research in nonlinear dynamics with Dr. Manuel Falconi, also at UNAM While doing so, I was awarded a fellowship for academic excellence from the UNAM Foundation that allowed me to participate in a graduate exchange program between UNAM and the University of Arizona (UA) in Tucson. A few months following my arrival to the Mathematics Department in Tucson, I received an invitation to join the Ph.D. Program in Mathematics, which I graciously accepted. My initial interest in graduate school was on dynamical systems under random perturbations. Then I became aware of the connections between neurophysiology and dynamical systems through the work of Dr. Joceline Lega, who agreed to supervise my program of study. I initially studied coupled oscillators and dynamics of membrane potential in dendrites. For my dissertation in Mathematics I focused on the dynamics of molecular flux across membranes. In that work I developed generic expressions for transmembrane ionic transport and using bifurcation theory, established explicit connections between electrophysiological profiles in excitable cells and patterns of ion channel expression. While doing the preliminary research to begin my dissertation, I realized my fascination with dynamical systems extended beyond the models to the systems themselves. Desiring a deeper understanding, and hoping to develop a more integrative program of study, I joined the laboratory of John Hildebrand in the Division of Neurobiology at the Arizona Research Laboratories, where I studied integration and network properties of the olfactory system in the moth Manduca Sexta.
In the fall of 2002, I decided to also seek a Ph.D. in Physiological Sciences at the UA. Having no formal background in the biological sciences, I spent two years between the classroom and the laboratory educating myself in the foundations of biology. Soon after finishing the requisite courses, I joined the Division of Neural Systems Memory (NSMA) and Aging to work with Dr. Bruce McNaughton. While in NSMA, I designed and performed experiments based on electrophysiological recordings on freely behaving animals to study the emergence and reactivation of neural representations while learning, and during subsequent sleep and behavior. My research program in NSMA focused on developing an understanding of context-sensitive neural traces in the neurons of the rat ventral-tegmental area. For my dissertation in Physiological Sciences, I had the honor of working with Dr. Andrew Fuglevand from the Physiology Department. My dissertation research was about the relationship between nearly coincident spiking and common excitatory synaptic input in motor neurons. I successfully defended my dissertation in Physiological Sciences in August of 2008. In parallel, I worked with Dr. Joceline Lega from the Mathematics Department on a second PhD, this time in Mathematics, which was awarded to me in January of 2014.
In the fall of 2008, soon after obtaining my first PhD, I joined the Mathematical, Computational and Modeling Sciences Center (MCMSC) working as a postdoc under the supervision of Sharon Crook and Carlos Castillo-Chavez. My research during that postdoctoral training period focused on two projects: biophysics of neuronal excitability during development in holometabolous insects, and geometry underlying multiwave dynamics during pandemics. Part of my work at MCMSC also involved teaching courses, advising graduate students, and working with postdocs, some of which participate in the research groups mentioned above.
In August of 2010 I became a research scientist at the Evelyn F. McKnight Brain Institute at the University of Arizona. During that year, I was also appointed as Research Professor in Complex Adaptive Systems at ASU. Since then, I lead research efforts in mainly two different areas, mathematical physiology and mathematical epidemiology. The projects carried by the mathematical physiology research group I formed in ASU aimed to understand how learning, memory, and performance are dynamically linked, from physiological perspective. These projects combine dynamical systems, biophysical theory, and experiments, to study relationships between neuronal excitability, gene expression, and plasticity. The experiments involve simultaneous recordings from multiple neurons while animals (honey bees and rats) behave, learn, and sleep. I also lead a research group in mathematical epidemiology that studies the effects of different perturbations in transmission cause on the dynamics of epidemics. For instance, one of the projects studies the role played by local transport, social distancing, school closures, and vaccination, in mitigating pandemic outbreaks, assuming limited supplies are distributed over multiple regions, each having distribution capacity.
In the spring of 2011 I was recruited by the Institute for Interdisciplinary Research and Mathematics and Physics Department of the University of Puerto Rico in Cayey, where I set up a Biophysics, Neuroethology, and Nonlinear Dynamics Laboratory. My recruitment was funded in part by the NIH BRIC initiative from the Institute for Interdisciplinary Research. While in Puerto Rico, I co-established a research training program for undergraduates in the form of the Interdisciplinary Research Group in Science and Mathematics. I carried my academic activities in Puerto Rico from July of 2011, and until December of 2012.
I have been carrying out research in Mexico since December of 2012. I started as a Visiting Professor at the Institute of Mathematics in UNAM. I am currently a Professor in the Department of Mathematics at UNAM. There, I have a laboratory in which we study physiological systems combining mathematics, biophysics, and experiments using electrophysiological and optical recording techniques. I collaborate on projects with researchers at UNAM, the University of Arizona, Wilfrid Laurer University, Exeter University, and the University of Würzburg.