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

Neural population representation hypothesis of visual flow and its illusory after effect in the brain: psychophysics, neurophysiology and computational approaches

The neural representation of motion aftereffects induced by various visual flows (translational, rotational, motion-in-depth, and translational transparent flows) was studied under the hypothesis that the imbalances in discharge activities would occur in favor in the direction opposite to the adapting stimulation in the monkey MST cells (cells in the medial superior temporal area) which can discriminate the mode (i.e., translational, rotational, or motion-in-depth) of the given flow. In single-unit recording experiments conducted on anaesthetized monkeys, we found that the rate of spontaneous discharge and the sensitivity to a test stimulus moving in the preferred direction decreased after receiving an adapting stimulation moving in the preferred direction, whereas they increased after receiving an adapting stimulation moving in the null direction. To consistently explain the bidirectional perception of a transparent visual flow and its unidirectional motion aftereffect by the same hypothesis, we need to assume the existence of two subtypes of MST D cells which show directionally selective responses to a translational flow: component cells and integration cells. Our physiological investigation revealed that the MST D cells could be divided into two types: one responded to a transparent flow by two peaks at the instances when the direction of one of the component flow matched the preferred direction of the cell, and the other responded by a single peak at the instance when the direction of the integrated motion matched the preferred direction. In psychophysical experiments on human subjects, we found evidence for the existence of component and integration representations in the human brain. To explain the different motion perceptions, i.e., two transparent flows during presentation of the flows and a single flow in the opposite direction to the integrated flows after stopping the flow stimuli, we suggest that the pattern-discrimination system can select the motion representation that is consistent with the perception of the pattern from two motion representations. We discuss the computational aspects related to the integration of component motion fields

特発性正常圧水頭症における心周期のADC変化の解析

取得学位 : 博士(保健学), 学位授与番号 : 医博甲第2250 号, 学位授与年月日 : 平成24年3月22日, 学位授与大学 : 金沢大学, 審査結果の報告日 : 平成24年2月23

What variables were associated with the inducibility of ventricular fibrillation during electrophysiologic stimulation test in patients without apparent organic heart disease?

SummaryObjectiveThe purpose of our study was to determine what variables were associated with ventricular fibrillation (VF) induced during electrophysiological stimulation test in patients without apparent organic heart disease.MethodsOur study evaluated 77 patients (51±15 years) who underwent electrophysiological stimulation test, signal averaging, and Na+ channel-blocker challenge test (pilsicainide test). The subjects were divided into two groups, the Brugada group and non-Brugada group. Further, the patients were divided into three subgroups on the base of symptoms (8, 7 symptomatic; 9, 13 syncope; 28, 12 asymptomatic group; in the Brugada and non-Brugada groups, respectively). Multivariate analyses evaluated the association between baseline clinical factors and the induction of VF.ResultsThe inducibility of VF was significantly (p<0.0001) higher in the Brugada group (n=33, 73%) than the non-Brugada group (n=4, 13%). The multivariate analysis demonstrated that symptoms (odds ratio (OR) 31.6; 95% confidence interval (CI): 2.3–430.6; p<0.01), type 1 electrocardiogram after pilsicainide test (OR 21.3; CI: 1.7–272.2; p<0.02), and syncope (OR 13.5; CI: 1.2–158.8; p<0.05) were strongly associated with the inducibility of VF, but not with family history, type 1 electrocardiogram in control, positive in late potential, maxΔST elevation (≧200μV) after pilsicainide test.ConclusionsThe symptoms, syncope, and type 1 electrocardiogram after pilsicainide test were independently associated with the electrophysiological substrate of VF in patients without apparent heart disease