Christian Reidys

Weighted Homology of Bi-Structures over Certain Discrete Valuation Rings

Mathematics · 2021-03-31 · 9 citations

An RNA bi-structure is a pair of RNA secondary structures that are considered as arc-diagrams. We present a novel weighted homology theory for RNA bi-structures, which was obtained through the intersections of loops. The weighted homology of the intersection complex X features a new boundary operator and is formulated over a discrete valuation ring, R. We establish basic properties of the weighted complex and show how to deform it in order to eliminate any 3-simplices. We connect the simplicial…

Multiscale Feedback Loops in SARS-CoV-2 Viral Evolution

Journal of Computational Biology · 2020-12-04 · 8 citations

COVID-19 is an infectious disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The viral genome is considered to be relatively stable and the mutations that have been observed and reported thus far are mainly focused on the coding region. This article provides evidence that macrolevel pandemic dynamics, such as social distancing, modulate the genomic evolution of SARS-CoV-2. This view complements the prevalent paradigm that microlevel observables control macrolevel…

Developing a framework for tracking antimicrobial resistance gene movement in a persistent environmental reservoir

npj Antimicrobials and Resistance · 2024-12-30 · 7 citations

Mobile genetic elements are key to the global emergence of antibiotic resistance. We successfully reconstructed the complete bacterial genome and plasmid assemblies of isolates sharing the same blaKPC carbapenemase gene to understand evolution over time in six confined hospital drains over five years. From 82 isolates we identified 14 unique strains from 10 species with 113 blaKPC-carrying plasmids across 16 distinct replicon types. To assess dynamic gene movement, we introduced the ‘Composite-S…

On the Loop Homology of a Certain Complex of RNA Structures

Mathematics · 2021-07-24 · 4 citations

In this paper, we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence–structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. The loop complex of a τ-structure captures the intersections of loops in both secondary structures. We compute the loop homology of τ-structures. We show that only the zeroth, first and second homology…

Lipschitz continuity under toric equivalence for asynchronous Boolean networks

Chaos An Interdisciplinary Journal of Nonlinear Science · 2023-02-01 · 3 citations

Mathematical models rooted in network representations are becoming increasingly more common for capturing a broad range of phenomena. Boolean networks (BNs) represent a mathematical abstraction suited for establishing general theory applicable to such systems. A key thread in BN research is developing theory that connects the structure of the network and the local rules to phase space properties or so-called structure-to-function theory. While most theory for BNs has been developed for the synch…