A three parameter family of probability distributions is constructed such that its Mellin transform defined over the same domain as 2D GMC on Riemann sphere with insertion points $(\alpha_1,\alpha_2,\alpha_3)$ and satisfies DOZZ formula in sense Kupiainen (Ann. Math. 191 (2020) 81 -- 166). The are products independent Fyodorov-Bouchaud powers Barnes beta types $(2, 1)$ 2).$ In special case $\al...

Crohn's disease and ulcerative colitis (the inflammatory bowel diseases) have a strong genetic component. Although over 20 putative susceptibility loci have been identified by individual genome scans, the majority of these loci have not been replicated. Many individual studies are at the lower limit of acceptable power for complex disease linkage analysis. Genome scan meta-analysis (GSMA), by u...

Let C be a smooth projective irreducible curve defined over a finite field Fq of q elements and characteristic p > 3 with function field K = Fq(C). Let E/K be a non-constant elliptic curve and φ : E → C its minimal regular model. For every P ∈ C, denote by deg(P ) = [κP : Fq] its degree and qP = q deg(P . If EP = φ (P ) is an elliptic curve over κP denote by t(EP ) = qP + 1 − #EP (κP ) the trac...

The hepatitis C virus (HCV) has been classified into six genotypes and more than 70 subtypes with distinct geographical and epidemiological distributions. While 18 genotype 2 subtypes have been proposed, only 5 have had their complete sequence determined. The aim of this study was to characterize HCV isolates from three patients from the Barcelona metropolitan area of Spain for whom commercial ...

For two given graphs G and H , the Ramsey number R(G, H) is the smallest positive integer p such that for every graph F on p vertices the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn, Fm), where Pn is a path on n vertices and Fm is the graph obtained from m disjoint triangles by identifying pr...

A detailed analysis of the constitutional chromosomal changes in two pediatric patients was performed using high resolution genetic analysis techniques, microarray comparative genomic hybridization (array CGH) and multiplex ligation-dependent probe amplification (MLPA) as well as FISH. The aim was to come to a more precise characterization of the genotype/phenotype relationship. Case 1 was a gi...

The expression of acute experimental autoimmune encephalomyelitis (EAE) in mice is controlled by several dominant genes, H-2 and histamine sensitization genes. SJL/J and SWR/J, which are H-2s and H-2q, respectively, are susceptible to EAE and sensitive to Bordetella pertussis histamine-sensitizing factor (HSF), which produces a vasoactive amine hypersensitivity. Other H-2s or H-2q strains such ...

Let G be a planar graph without 4-cycles and 5-cycles and with maximum degree ∆ ≥ 32. We prove that χ`(G ) ≤ ∆ + 3. For arbitrarily large maximum degree ∆, there exist planar graphs G∆ of girth 6 with χ(G 2 ∆) = ∆ + 2. Thus, our bound is within 1 of being optimal. Further, our bound comes from coloring greedily in a good order, so the bound immediately extends to online list-coloring. In additi...

Abstract. Zero-sum problems on abelian groups, subset sums in a field and covers of the integers by residue classes, are three different active topics initiated by P. Erdős more than 40 years ago and investigated by many researchers separately since then. In an earlier announcement [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author claimed some connections among these seeming...

Abstract. Zero-sum problems on abelian groups, subset sums in a field and covers of the integers by residue classes, are three different active topics initiated by P. Erdős and investigated by many researchers. In an earlier paper [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author announced some connections among these seemingly unrelated fascinating areas. In this paper we e...