Graph presentations for moments of noncentral Wishart distributions and their applications

We provide formulas for the moments of the real and complex noncentral Wishart distributions of general degrees. The obtained formulas for the real and complex cases are described in terms of the undirected and directed graphs, respectively. By considering degenerate cases, we give explicit formulas for the moments of bivariate chi-square distributions and $2\times 2$ Wishart distributions by enumerating the graphs. Noting that the Laguerre polynomials can be considered to be moments of a noncentral chi-square distributions formally, we demonstrate a combinatorial interpretation of the coefficients of the Laguerre polynomials

Electron and Ion Heating during Magnetic Reconnection in Weakly Collisional Plasmas

Gyrokinetic simulations of magnetic reconnection are presented to investigate plasma heating for strongly magnetized, weakly collisional plasmas. For a low plasma beta case, parallel and perpendicular phase mixing strongly enhance energy dissipation yielding electron heating. Heating occurs for a long time period after a dynamical process of magnetic reconnection ended. For a higher beta case, the ratio of ion to electron dissipation rate increases, suggesting that ion heating (via phase-mixing) may become an important dissipation channel in high beta plasmas.Comment: 9 pages, 3 figures, accepted for publication in JPSJ Suppl. [Proceedings of the 12th Asia Pacific Physics Conference

Fundamental Study of the Fill-in Minimization Problem

In this paper the fill-in minimization problem which arises at the application of the sparse matrix method for a large sparse set of linear equations is discussed from the graph-theoretic viewpoint and also through the numerical experiments. Therefore, this investigation consists of two parts, and in the former part the author shows, at first, that the elimination process of a sparse matrix is equivalently replaced to the vertex eliminations for a graph obtained from the matrix, and by use of some concepts in the theory of graph he proves that the vertex elimination process for the minimum fill-in is equivalent to the vertex eliminations for vertices in each subgraph which is obtained by the appropriate dissection of whole graph, and that there are only two types of vertex eliminations through the process. This results in the proposal of a new model of the vertex elimination process. The latter part of this investigation is used for the verification of the results from the theoretic investigation. Through the numerical experiments he concludes that the new model of the vertex elimination process is valid, at least, for a graph like a regular finite element mesh. Furthermore, he shows that this model coincides with Nested Dissection Method which can give the minimum value of fill-in, at present

Relationship between Estimated Glomerular Filtration Rate (eGFR) and Metabolic Syndrome in Japanese

We investigated the link between renal function as evaluated by estimated glomerular filtration rate (eGFR) and metabolic syndrome in Japanese. A total of 11,711 Japanese subjects, aged 20-79 years, were recruited in a cross-sectional clinical investigation. From this group, we further investigated the data on 1,576 subjects. eGFR was calculated using serum creatinine (Cr), age and sex. The diagnosis of metabolic syndrome was based on the Japanese criteria. In the first analysis, 288 men (7.8%) and 498 women (6.2%) were diagnosed with reduced eGFR (<60ml/min). eGFR was not correlated with anthropometric, body composition parameters in either sex. In the second analysis, in subjects without medications, 132 men (20.8%) and 15 women (1.6%) were diagnosed with metabolic syndrome. eGFR was lower in men with abdominal obesity and in women with hypertension was than in those without. Among Japanese not taking medications, lower eGFR may be a characteristic of men with abdominal obesity and of women with hypertension