Abstract This paper introduces two logic frameworks for the study of SIR (Susceptible-Infected-Recovered) and SIRS compartmental epidemic models, one based on Linear Temporal Logic and the other on Computation Tree Logic. We provide a short literature overview on compartmental models and other related works using logics, and then define our logics with their respective axiomatizations, and demonstrate their soundness and completeness proofs.

Abstract This paper introduces a logic with a class of social network models that is based on standard Linear Temporal Logic, which allows for leveraging the power of existing model checkers for the analysis of social networks. We provide a short literature overview, and then define our logic and its axiomatization, present some simple motivational examples of both models and formulas and show its soundness and completeness via a translation into propositional formulas. Lastly, we discuss model checking, time complexity analysis and a Susceptible–Infectious–Recovered model variation for infectious diseases.

Advances in de novo synthesis of DNA and computational gene design methods make possible the customization of genes by direct manipulation of features such as codon bias and mRNA secondary structure. Codon context is another feature significantly affecting mRNA translational efficiency, but existing methods and tools for evaluating and designing novel optimized protein coding sequences utilize untested heuristics and do not provide quantifiable guarantees on design quality. In this study we examine statistical properties of codon context measures in an effort to better understand the phenomenon. We analyze the computational complexity of codon context optimization and design exact and efficient heuristic gene recoding algorithms under reasonable constraint models. We also present a web-based tool for evaluating codon context bias in the appropriate context.