Let m > 2 be an integer, let C2m denote the cycle of length 2m on the set of vertices [−m,m) = {−m,−m+ 1, . . . ,m− 2,m− 1}, and let G = G(m, d) denote the graph on the set of vertices [−m,m), in which two vertices are adjacent iff they are adjacent in one coordinate of C2m and equal in all others. This graph can be viewed as the graph of the d-dimensional torus. We prove that one can delete a ...

Saturation mutagenesis is a powerful technique for engineering proteins, metabolic pathways and genomes. In spite of its numerous applications, creating high-quality saturation mutagenesis libraries remains a challenge, as various experimental parameters influence in a complex manner the resulting diversity. We explore from the economical perspective various aspects of saturation mutagenesis li...

Reliability of large-scale hardware and software systems often depends on the correctness of the underlying structured data. Examples of structured data include heap-allocated linked data structures, files, and program states in software, and netlists and simulator states for modeling hardware. In this paper, we focus on automatically transforming structured data to make it satisfy certain prop...

Ubiquitination is a post-translational modification pathway involved in myriad cellular regulation and disease pathways. The Ub (ubiquitin) transfer cascade requires three enzyme activities: a Ub-activating (E1) enzyme, a Ub-conjugating (E2) enzyme, and a Ub ligase (E3). Because the E2 is responsible both for E3 selection and substrate modification, E2s function at the heart of the Ub transfer ...