Constructing and sampling partite, 3-uniform hypergraphs with given degree sequence.

Partite, 3-uniform hypergraphs are 3-uniform hypergraphs in which each hyperedge contains exactly one point from each of the 3 disjoint vertex classes. We consider the degree sequence problem of partite, 3-uniform hypergraphs, that is, to decide if such a hypergraph with prescribed degree sequences exists. We prove that this decision problem is NP-complete in general, and give a polynomial running time algorithm for third almost-regular degree sequences, that is, when each degree in one of the vertex classes is k or k - 1 for some fixed k, and there is no restriction for the other two vertex classes.

Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs.

Since 1997 a considerable effort has been spent on the study of the swap (switch) Markov chains on graphic degree sequences. All of these results assume some kind of regularity in the corresponding degree sequences. Recently, Greenhill and Sfragara published a breakthrough paper about irregular normal and directed degree sequences for which rapid mixing of the swap Markov chain is proved.

Oral administration of pyrophosphate inhibits connective tissue calcification.

Various disorders including pseudoxanthoma elasticum (PXE) and generalized arterial calcification of infancy (GACI), which are caused by inactivating mutations in and , respectively, present with extensive tissue calcification due to reduced plasma pyrophosphate (PPi). However, it has always been assumed that the bioavailability of orally administered PPi is negligible. Here, we demonstrate increased PPi concentration in the circulation of humans after oral PPi administration.