We show that for all sufficiently large d, the uniform proper 3-coloring model (in physics called the 3-state antiferromagnetic Potts model at zero temperature) on Zd admits multiple maximal-entropy Gibbs measures. This is a consequence of the following combinatorial result: if a proper 3-coloring is chosen uniformly from a box in Zd, conditioned on color 0 being given to all the vertices on th...

conclusions the established method has an acceptable performance in quantifying yb-1. in addition, serum yb-1 may aid in the diagnosis of hcc. results the developed method was linear to 150 μg/l of yb-1 with a minimum detection limit of 0.01 μg/l. the average recoveries were between 93.9% and 109.0%. the mean intra- and inter-assay coefficients of variation (cvs) were 4.0-4.8% and 8.2-10.2%, re...

We propose using the black-box α-divergence [1] as a flexible alternative to variational inference in deep generative models. By simply switching the objective function from the variational free-energy to the black-box α-divergence objective we are able to learn better generative models, which is demonstrated by a considerable improvement of the test log-likelihood in several preliminary experi...

Small nucleolar RNAs (snoRNAs) play important roles in ribosomal RNA metabolism. In Saccharomyces cerevisiae, box C/D snoRNAs are synthesized from excised introns, polycistronic precursors, or independent transcription units. Previous studies have shown that only a few independently transcribed box C/D snoRNAs are processed at their 5' end. Here we describe 12 additional independently transcrib...

1. Introduction. In recent years more and more attention has been paid in mathematical papers to fractal functions and to fractal sets. There are various definitions of those objects. We assume that a compact set K ∈ R d+1 is fractal, by definition, if its box (entropy) dimension dim b (K) = j for j = 0, 1,. .. , d + 1 and 0 < dim b (K) < d + 1. At the same time the function f : I d → R d , I =...