Let G be a series-parallel graph with integer edge weights. A p-coloring of G is a mapping of vertices of G into Zp (ring of integers modulo p) so that the distance between colors of adjacent vertices u and v is at least the weight of the edge uv. We describe a quadratic time p-coloring algorithm where p is either twice the maximum edge weight or the largest possible sum of three weights of edg...

Cullin/RING ubiquitin ligases (CRL) comprise the largest subfamily of ubiquitin ligases. CRLs are involved in cell cycle regulation, DNA replication, DNA damage response (DDR), development, immune response, transcriptional regulation, circadian rhythm, viral infection, and protein quality control. One of the main functions of CRLs is to regulate the DDR, a fundamental signaling cascade that mai...

We describe a part of the lattice of subvarieties of left distributive left idempotent groupoids (i.e. those satisfying the identities x(yz) ≈ (xy)(xz) and (xx)y ≈ xy) modulo the lattice of subvarieties of left distributive idempotent groupoids. A free groupoid in a subvariety of LDLI groupoids satisfying an identity x ≈ x decomposes as the direct product of its largest idempotent factor and a ...