phd science
Alejandro H. Wences
Alejandro Hernandez Wences
__________________________________________________________
mathematician
Postdoc in Probability and Theoretical Machine Learning at CIMI - LAAS - CNRS, Toulouse, France.
Currently looking for a new position to start in 2025.
My Career Drivers and Interests are:
Curiosity
Purpose and Meaning
Analytical Problem Solving
Multidisciplinarity
Programming and Data Analysis
Research interests
self-similarity in POPULATION GENETICS
The study of stochastic processes inspired by biology, such as branching and coalescing processes, serves a dual purpose: informing biological research and providing formal analytical tools. The novel perspective of self-similarity within this context allows for the exploration of more complex models.
INFERENCE OF METRIC SPACES
The application of Fermat's principle of light within a probability framework for inferring forms and structures from data contributes to the development of machine learning algorithms.
STOCHASTIC OPTIMAL CONTROL
The study of Markov decision processes and their optimal policies by leveraging fluid limits and averaging over fast-evolving variables. This research finds applications in telecommunications, machine learning, robotics, and more.
A brief overview of my career
I have always been fascinated by both the theoretical and applied aspects of the Probability and Statistics field. I began my career in Computational Biology, where I developed a software package (in C++, Python, and R) for analyzing extensive datasets of DNA sequences with the goal of building up entire genomic sequences from a vast array of small pieces. In this period, I developed skills in collecting and analyzing large datasets, in the development of software packages, in working with parallel computing, and in testing and comparing scientific methods and results.
Subsequently, during my MSc and PhD studies in Mathematics, I delved deeply into the theoretical aspects of Stochastic Processes, Probability, and Statistics. I gained extensive experience in mathematical modeling and its applications to real-world problems, particularly in the field of Mathematical Population Genetics. During this stage, I gained experience in collaborative work, in exploring and learning entirely new fields (and in incorporating them into my prior knowledge), in analytical problem-solving, and in presenting complex ideas in a simple way. I also had the opportunity to teach undergraduate courses where I gained experience in managing a small team of educators and in formulating, organizing, and teaching new courses.
In parallel to my PhD studies, I did freelance voluntary work at an NGO (Partners in Health Mexico), where I developed an R-Shiny application with the aims of collecting medical data offline in uncommunicated rural areas, and of computing relevant indicators and presenting them to decision-makers. I also developed a second R-Shiny application with the aim of informing diagnostics and treatment options for a particular disease using Bayesian decision analysis.
Currently, during my Postdoc position and alongside my ongoing research in population genetics, I am engaged in two main endeavors. On one hand, I am developing mathematical tools for Machine Learning applications, specifically focusing on clustering algorithms. This involves inferring general metric spaces from distance matrices using Fermat's principle of light in a probabilistic framework. On the other hand, I am also studying Stochastic Control Systems, employing fluid limits and averaging principles to analyze systems with fast-evolving variables.
CONTACT
https://www.researchgate.net/profile/Alejandro-Hernandez-Wences-2