current projects

Learning of general Metric Spaces 

Joint work with Pablo Groisman (UBA) and Sebastian Zaninovich (UBA)

In this project we put forth a theoretical framework for inferring general metric spaces, drawing upon two key elements: 1) the general theory of metric measure spaces and the Gromov-weak topology, and 2) convergence results from sample Fermat distances (e.g., Groisman et al., 2022).

phase-type distributions and inhomogeneous coalescent processes

Joint work with Arno Siri-Jégousse (IIMAS - UNAM), Lizbeth Peñaloza (UMAR), and Matthias Stenruecken (Univ. of Chicago)

In this project, we leverage the simplicity and effectiveness of phase-type distributions to investigate the time to the most recent common ancestor in population models characterized by temporal inhomogeneity. Specifically, we focus on populations whose total size evolves deterministically over time.

stochastic control and restless bandits

Joint work with Matthieu Johnckeere (LAAS- CNRS) and Maaike Verloop (IRIT-ENSEEIHT)

In this project we investigate Markov processes whose dynamics can be decomposed into fast and slow components. We have derived a theoretical result that involves averaging the fast dynamics at equilibrium. This is aimed at facilitating the fluid limit characterization of the entire system, a technique widely employed in the stability analysis of various models, including restless bandits.

preprints and published

Self-similarity: a new perspective in population genetics

https://arxiv.org/abs/2405.10193

Joint work with Arno Siri-Jégousse (IIMAS - UNAM)

We introduce, for the first time, the notion of measure-valued self-similar Markov processes. By extending the well-known Lamperti transformation for self-similar Markov processes to the infinite-dimensional setting, we generalize the celebrated work of Birkner et al. (2005) in mathematical population genetics. Our results only scratch the surface of the potential power of the interplay between population genetics and the theory of self-similar Markov processes. This project constitutes a first, yet important, step in the development of this new research program.

branching random walks with selection

https://arxiv.org/abs/2301.07762

Joint work with Emmanuel Shcertzer (Univ. of Vienna)

In this project, we investigated a stochastic model of a biological population under the influence of natural selection. Our findings revealed two intriguing phenomena in this model: 1) contrary to common understanding, increasing the strength of selection can increase the genetic variability within the population, and 2) we identified a novel phase transition in traveling waves, which we term the shift from pulled to semi-pulled waves.

A broader class of netural population models

https://arxiv.org/abs/2212.02154

Joint work with Arno Siri-Jégousse (IIMAS - UNAM)

In this project we examined the genealogies of a broad class of neutral population models that includes the well-known Cannings' models. Departing from the standard assumption of symmetry in offspring distributions in Cannings' models, we introduced a less restrictive condition of non-heritability of reproductive success. This adjustment provides a more precise mathematical framework for studying neutral biological populations. Additionally, our framework enabled us to analyze the genealogy of a new exponential model. Despite its built-in fitness inheritance mechanism, this model fits within our neutrality setting. 

Site frequency spectrum of the bolthausen-sznitman coalescent

https://alea.impa.br/articles/v18/18-53.pdf

Joint work with Arno Siri-Jégousse (IIMAS - UNAM) and Götz Kersting (Goethe Univ.)

In this project we characterized the Site Frequency Spectrum (SFS) of the Bolthausen-Sznitman coalescent. The SFS is a statistic based on the genetic diversity present in a biological population that is  frequently used in Population Genetics for the inference of its evolutionary past. The Bolthausen-Sznitman coalescent is a stochastic model for the genealogy of a population that has been recently proposed as a new null model for populations that are under selective pressure.

Metassembler: merging and optimizing de novo genome assemblies

https://genomebiology.biomedcentral.com/articles/10.1186/s13059-015-0764-4

https://sourceforge.net/projects/metassembler/

Joint work with Michael Schatz (Johns Hopkins University, CSHL)

In this project, we designed and implemented a software package for the "de novo" assembly of genomes. The main heuristic of this software is to combine the assemblies produced using multiple (possibly different) algorithms into a single superior sequence by identifying and merging the best sequence stretches from each of them.

De novo assemblies of rice genomes

https://genomebiology.biomedcentral.com/articles/10.1186/s13059-014-0506-z

Large collaborative effort together with Michael Schatz (Johns Hopkins University, CSHL)

The aim of this project was to characterize the genome of novel strains of rice. I contributed to the bioinformatics component by using computational tools to identify and compare the coding regions of the newly assembled sequences. 

human genomics: barcoding each nucleotide

https://www.pnas.org/doi/full/10.1073/pnas.1112567108

Large collaborative effort together with Rafael Palacios (UNAM)

The aim of this project was to barcode each nucleotide in the human genome based on its genomic context. Our findings revealed that a genomic context of 50 nucleotides is sufficient to uniquely identify 92% of the nucleotides in the human genome. My role in this project involved contributing to discussions that determined the direction of our research.