AI-enabled evaluation of genome-wide association relevance and polygenic risk score prediction in Alzheimer's disease.

GWAS focuses on significance loosing false positives; machine learning probes sub-significant features relying on predictivity. Yet, these are far from orthogonal. We sought to explore how these inform each other in sub-genome-wide significant situations to define relevance for predictive features.

Simplicial complex entropy for time series analysis.

The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods have been proposed to evaluate their irregularity. However, for some types of dynamics such as stochastic and chaotic, new approaches are required that can provide a better characterization of them.

Signal enrichment with strain-level resolution in metagenomes using topological data analysis.

Background: A metagenome is a collection of genomes, usually in a micro-environment, and sequencing a metagenomic sample en masse is a powerful means for investigating the community of the constituent microorganisms. One of the challenges is in distinguishing between similar organisms due to rampant multiple possible assignments of sequencing reads, resulting in false positive identifications. We map the problem to a topological data analysis (TDA) framework that extracts information from the geometric structure of data.

Self-organized criticality and pattern emergence through the lens of tropical geometry.

Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC.