Difference of Facial Achromatic Numbers between Two Triangular Embeddings of a Graph

A facial $3$-complete $k$-coloring of a triangulation $G$ on a surface is a vertex $k$-coloring such that every triple of $k$-colors appears on the boundary of some face of $G$. The facial $3$-achromatic number $\psi_3(G)$ of $G$ is the maximum integer $k$ such that $G$ has a facial $3$-complete $k$-coloring. This notion is an expansion of the complete coloring, that is, a proper vertex coloring of a graph such that every pair of colors appears on the ends of some edge. For two triangulations $G$ and $G\u27$ on a surface, $\psi_3(G)$ may not be equal to $\psi_3(G\u27)$ even if $G$ is isomorphic to $G\u27$ as graphs. Hence, it would be interesting to see how large the difference between $\psi_3(G)$ and $\psi_3(G\u27)$ can be. We shall show that an upper bound for such difference in terms of the genus of the surface

Facial Achromatic Number of Triangulations with Given Guarding Number

A (not necessarily proper) $k$-coloring $c : V(G) \rightarrow \{1,2,\dots,k\}$ of a graph $G$ on a surface is a {\em facial $t$-complete $k$-coloring} if every $t$-tuple of colors appears on the boundary of some face of $G$. The maximum number $k$ such that $G$ has a facial $t$-complete $k$-coloring is called a {\em facial $t$-achromatic number} of $G$, denoted by $\psi_t(G)$. In this paper, we investigate the relation between the facial 3-achromatic number and guarding number of triangulations on a surface, where a {\em guarding number} of a graph $G$ embedded on a surface, denoted by \gd(G), is the smallest size of its {\em guarding set} which is a generalized concept of guards in the art gallery problem. We show that for any graph $G$ embedded on a surface, \psi_{\Delta(G^*)}(G) \leq \gd(G) + \Delta(G^*) - 1, where $\Delta(G^*)$ is the largest face size of $G$. Furthermore, we investigate sufficient conditions for a triangulation $G$ on a surface to satisfy \psi_{3}(G) = \gd(G) + 2. In particular, we prove that every triangulation $G$ on the sphere with \gd(G) = 2 satisfies the above equality and that for one with guarding number $3$, it also satisfies the above equality with sufficiently large number of vertices

Facial achromatic number of triangulations on the sphere (Women in Mathematics)

A graph consists of a set of vertices and a set of edges. A coloring of a graph is an assigning of colors to the vertices such that any adjacent vertices receive different colors. In particular, a coloring is called complete if every pair of colors appear on some edge. In this talk, we expand complete colorings of graphs to those of graphs embedded on surfaces and consider such colorings of even triangulations on the sphere

子宮体癌におけるCOX-2発現の役割 : 宿主免疫と患者予後への影響

取得学位 : 博士（医学）, 学位授与番号 : 医博甲第1689号, 学位授与年月日 : 平成17年3月22日, 学位授与大学 : 金沢大

In vitro evaluation method for screening of candidate prebiotic foods

AbstractThe aim of this work was to develop a simple and rapid in vitro evaluation method for screening and discovery of uncharacterised and untapped prebiotic foods. Using a NMR-based metabolomic approach coupled with multivariate statistical analysis, the metabolic profiles generated by intestinal microbiota after in vitro incubation with feces were examined. The viscous substances of Japanese bunching onion (JBOVS) were identified as one of the candidate prebiotic foods by this in vitro screening method. The JBOVS were primarily composed of sugar components, especially fructose-based carbohydrates. Our results suggested that ingestion of JBOVS contributed to lactate and acetate production by the intestinal microbiota, and were accompanied by an increase in the Lactobacillus murinus and Bacteroidetes sp. populations in the intestine and fluctuation of the host-microbial co-metabolic process. Therefore, our approach should be useful as a rapid and simple screening tool for potential prebiotic foods

Expression of NLRP7(PYPAF3) protein in endometrial cancer tissues

Division of Immunology and Molecular Biolog

Phosphorylation of the RSRSP stretch is critical for splicing regulation by RNA-Binding Motif Protein 20 (RBM20) through nuclear localization

RBM20 is a major regulator of heart-specific alternative pre-mRNA splicing of TTN encoding a giant sarcomeric protein titin. Mutation in RBM20 is linked to autosomal-dominant familial dilated cardiomyopathy (DCM), yet most of the RBM20 missense mutations in familial and sporadic cases were mapped to an RSRSP stretch in an arginine/serine-rich region of which function remains unknown. In the present study, we identified an R634W missense mutation within the stretch and a G1031X nonsense mutation in cohorts of DCM patients. We demonstrate that the two serine residues in the RSRSP stretch are constitutively phosphorylated and mutations in the stretch disturb nuclear localization of RBM20. Rbm20 S637A knock-in mouse mimicking an S635A mutation reported in a familial case showed a remarkable effect on titin isoform expression like in a patient carrying the mutation. These results revealed the function of the RSRSP stretch as a critical part of a nuclear localization signal and offer the Rbm20 S637A mouse as a good model for in vivo study