arXiv subjects

Carlos Martinez

Publications and source records attributed to Carlos Martinez.

4 recordsLinked to original sources

arXiv2025

Mixing time and isoperimetry in random geometric graphs

In this paper we study the mixing time of the simple random walk on the giant component of supercritical $d$-dimensional random geometric graphs generated by the unit intensity Poisson Point Process in a $d$-dimensional cube of volume $n$. With $r_g$ denoting the threshold for having a giant component, we show that for every $\epsilon > 0$ and any $r \ge (1+\epsilon)r_g$, the mixing time of the giant component is with high probability $\Theta(n^{2/d}/r^{2})$, thereby closing a gap in the literature. The main tool is an isoperimetric inequality which holds, w.h.p., for any large enough vertex set, a result which we believe is of independent interest. Our analysis also implies that the relaxation time is of the same order.

math.PR↗

arXiv2025

Benchmarking Waitlist Mortality Prediction in Heart Transplantation Through Time-to-Event Modeling using New Longitudinal UNOS Dataset

Decisions about managing patients on the heart transplant waitlist are currently made by committees of doctors who consider multiple factors, but the process remains largely ad-hoc. With the growing volume of longitudinal patient, donor, and organ data collected by the United Network for Organ Sharing (UNOS) since 2018, there is increasing interest in analytical approaches to support clinical decision-making at the time of organ availability. In this study, we benchmark machine learning models that leverage longitudinal waitlist history data for time-dependent, time-to-event modeling of waitlist mortality. We train on 23,807 patient records with 77 variables and evaluate both survival prediction and discrimination at a 1-year horizon. Our best model achieves a C-Index of 0.94 and AUROC of 0.89, significantly outperforming previous models. Key predictors align with known risk factors while also revealing novel associations. Our findings can support urgency assessment and policy refinement in heart transplant decision making.

stat.AP↗

arXiv2019

Estimation of Gaussian directed acyclic graphs using partial ordering information with an application to dairy cattle data

Estimating a directed acyclic graph (DAG) from observational data represents a canonical learning problem and has generated a lot of interest in recent years. Research has focused mostly on the following two cases: when no information regarding the ordering of the nodes in the DAG is available, and when a domain-specific complete ordering of the nodes is available. In this paper, motivated by a recent application in dairy science, we develop a method for DAG estimation for the middle scenario, where partition based partial ordering of the nodes is known based on domain specific knowledge.We develop an efficient algorithm that solves the posited problem, coined Partition-DAG. Through extensive simulations using the DREAM3 Yeast data, we illustrate that Partition-DAG effectively incorporates the partial ordering information to improve both speed and accuracy. We then illustrate the usefulness of Partition-DAG by applying it to recently collected dairy cattle data, and inferring relationships between various variables involved in dairy agroecosystems.

stat.AP↗

arXiv2007

Complex Hybrid Inflation and Baryogenesis

We propose a hybrid inflation model with a complex waterfall field which contains an interaction term that breaks the U(1) global symmetry associated to the waterfall field charge. We show that the asymmetric evolution of the real and imaginary parts of the complex field during the phase transition at the end of inflation translates into a charge asymmetry. The latter strongly depends on the vev of the waterfall field, which is well constrained by diverse cosmological observations.

hep-ph↗