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The variant of a semigroup $S$ with respect to an element $a\in S$, denoted $S^a$, is the semigroup with underlying set $S$ and operation ⋆ defined by $x\star y=xay$ for $x,y\in S$. In this paper, we study variants ${{𝒯}}_X^a$ of the full transformation semigroup ${{𝒯}}_X$ on a finite set $X$. We explore the structure of ${{𝒯}}_X^a$ as well as its subsemigroups $\mathrm{\text{Reg}}({{𝒯}}_X^a)$ (consisting of all regular elements) and ${{ℰ}}_X^a$ (consisting of all products of idempotents), and the ideals of $\mathrm{\text{Reg}}({{𝒯}}_X^a)$. Among other results, we calculate the rank and idempotent rank (if applicable) of each semigroup, and (where possible) the number of (idempotent) generating sets of the minimal possible size.

This paper shows how a new theory of epidemics can be developed for viral pandemics in a globally interconnected world. The study of the in-host dynamics and, in parallel, the spatial diffusion of epidemics defines the goal of our work, which looks ahead to new mathematical tools to model epidemics beyond the traditional approach of population dynamics. The approach takes into account the evolutionary nature of the virus, which can generate pseudo-Darwinian mutations and selection, while learning the presence of the virus and activating adaptive immunity. The study of immune competition plays a key role in both the in-host dynamics and the contagion dynamics.

The influence of genetic variations on diseases or cellular processes is the main focus of many investigations, and results of biomedical studies are often only accessible through scientific publications. Automatic extraction of this information requires recognition of the gene names and the accompanying allelic variant information. In a previous work, the OSIRIS system for the detection of allelic variation in text based on a query expansion approach was communicated. Challenges associated with this system are the relatively low recall for variation mentions and gene name recognition. To tackle this challenge, we integrate the ProMiner system developed for the recognition and normalization of gene and protein names with a conditional random field (CRF)-based recognition of variation terms in biomedical text. Following the newly developed normalization of variation entities, we can link textual entities to Single Nucleotide Polymorphism database (dbSNP) entries. The performance of this novel approach is evaluated, and improved results in comparison to state-of-the-art systems are reported.

Precision medicine focuses on developing treatments and preventative strategies tailored to an individual’s genomic profile, lifestyle, and environmental context. The Precision Medicine sessions at the Pacific Symposium on Biocomputing (PSB) have consistently spotlighted progress in this domain. Our 2025 manuscript collection features algorithmic innovations that integrate data across scales and diverse data modalities, presenting novel techniques to derive clinically relevant insights from molecular datasets. These studies highlight recent advances in technology and analytics and their application toward realizing the potential of precision medicine to enhance human health outcomes and extend lifespan.