We analyze the computational complexity of various rolling cube puzzles.

A partial orthomorphism of a group G (with additive notation) is an injection π : S → G for some S ⊆ G such that π(x) − x 6= π(y) − y for all distinct x, y ∈ S. We refer to |S| as the size of π, and if S = G, then π is an orthomorphism. Despite receiving a fair amount of attention in the research literature, many basic questions remain concerning the number of orthomorphisms of a given group, a...

Research so far has provided little evidence that benthic biogeochemical cycling is affected by ocean acidification under realistic climate change scenarios. We measured nutrient exchange and sediment community oxygen consumption (SCOC) rates to estimate nitrification in natural coastal permeable and fine sandy sediments under pre-phytoplankton bloom and bloom conditions. Ocean acidification, a...

OBJECTIVE To assess the contraceptive efficacy, user acceptability, cycle control, and tolerability of a combined contraceptive vaginal ring for up to 13 cycles. MATERIALS AND METHODS Healthy women coming to the OPD for contraceptive advice were enrolled in this one-year study. Each ring was used for three weeks followed by a one-week ring-free period. RESULTS A total of 184 women started t...

Background: Common treatment for infertile couples is the use of controlled ovulation hyperstimulation (COH) with intrauterine inseminations (IUI). IUI is used in cases such as ovulatory dysfunction, cervical factor infertility, male subfertility, and unexplained infertility. In this study, we evaluated the relationship between IUI outcome and special causes of infertility. Methods: This was a...

In this paper, we study pattern matching conditions in the cycle structures of permutations. We develop methods to find the joint distribution of the number of cycles and the number of cycle descents over the set of permutations in the symmetric group Sn which have no cycle occurrences or no consecutive cycle occurrences of a given pattern or set of patterns. Our methods also allow us to refine...

The hierarchical hypercube network is suitable for massively parallel systems. The number of links in the hierarchical hypercube network forms a compromise between those of the hypercube and the cube-connected cycles. Recently, some interesting properties of the hierarchical hypercube network were investigated. Since the hierarchical hypercube is bipartite. A bipartite graph is bipancyclic if i...

[This corrects the article DOI: 10.1371/journal.pone.0152611.].

Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 4. Assume that the intersection numbers of Γ satisfy ai = 0 for 0 ≤ i ≤ D − 1 and aD 6= 0. We show that Γ is a polygon, a folded cube, or an Odd graph.