Abstract:
We show a uniqueness theorem for charged dipole rotating black rings in the bosonic sector of five-dimensional minimal supergravity, generalizing our previous work [arXiv:0901.4724] on the uniqueness of charged rotating black holes with topologically spherical horizon in the same theory. More precisely, assuming the existence of two commuting axial Killing vector fields, we prove that an asymptotically flat, stationary charged rotating black hole with non-degenerate connected event horizon of cross-section topology S^1XS^2 in the five-dimensional Einstein-Maxwell-Chern-Simons theory-if exists-is characterized by the mass, charge, two independent angular momenta, dipole charge, and the rod structure. As anticipated, the necessity of specifying dipole charge-which is not a conserved charge-is the new, distinguished ingredient that highlights difference between the present theorem and the corresponding theorem for vacuum case, as well as difference from the case of topologically spherical horizon within the same minimal supergravity. We also consider a similar boundary value problem for other topologically non-trivial black holes within the same theory, and find that generalizing the present uniqueness results to include black lenses-provided there exists such a solution in the theory-would not appear to be straightforward.

Abstract:
We show uniqueness theorems for Kaluza-Klein black holes in the bosonic sector of five-dimensional minimal supergravity. More precisely, under the assumptions of the existence of two commuting axial isometries and a non-degenerate connected event horizon of the cross section topology S^3, or lens space, we prove that a stationary charged rotating Kaluza-Klein black hole in five-dimensional minimal supergravity is uniquely characterized by its mass, two independent angular momenta, electric charge, magnetic flux and nut charge, provided that there does not exist any nuts in the domain of outer communication. We also show that under the assumptions of the same symmetry, same asymptotics and the horizon cross section of S^1\times S^2, a black ring within the same theory---if exists---is uniquely determined by its dipole charge and rod structure besides the charges and magnetic flux.

Abstract:
For square contingency tables with ordered categories, the present paper considers two kinds of weak marginal homogeneity and gives measures to represent the degree of departure from weak marginal homogeneity. The proposed measures lie between –1 to 1. When the marginal cumulative logistic model or the extended marginal homogeneity model holds, the proposed measures represent the degree of departure from marginal homogeneity. Using these measures, three kinds of unaided distance vision data are analyzed.

For square contingency tables with ordered categories, the present paper gives several theorems that the symmetry model holds if and only if the generalized linear diagonals-parameter symmetry model for cell probabilities and for cumulative probabilities and the mean nonequality model of row and column variables hold. It also shows the orthogonality of statistic for testing goodness-of-fit of the symmetry model. An example is given.

Abstract:
For square contingency tables with ordered categories, this article proposes new models, which are the extension of Tomizawa’s [1] diagonal exponent symmetry model. Also it gives the decomposition of proposed model, and shows the orthogonality of the test statistics for decomposed models. Examples are given and the simulation studies based on the bivariate normal distribution are also given.

For two-way contingency tables with ordered categories, the present paper gives a theorem that the independence model holds if and only if the logit uniform association model holds and equality of concordance and discordance for all pairs of adjacent rows and all dichotomous collapsing of the columns holds. Using the theorem, we analyze the cross-classification of duodenal ulcer patients according to operation and dumping severity.

Abstract:
For multi-way tables with ordered
categories, the present paper gives a decomposition of the point-symmetry model
into the ordinal quasi point-symmetry and equality of point-symmetric marginal
moments. The ordinal quasi point-symmetry model indicates asymmetry for cell
probabilities with respect to the center point in the table.

Abstract:
The purpose of this paper is to propose a new model of asymmetry for
square contingency tables with ordered categories. The new model may be appropriate
for a square contingency table if it is reasonable to assume an underlying
bivariate t-distribution with different marginal variances having any degrees
of freedom. As the degrees of freedom becomes larger, the proposed model
approaches the extended linear diagonals-parameter symmetry model, which may be
appropriate for a square table if it is reasonable to assume an underlying
bivariate normal distribution. The simulation study based on bivariate
t-distribution is given. An example is given.

Abstract:
nalysis of tooth decay data in Japan using asymmetric statistical models Methodology (682) Total Article Views Authors: Yamamoto K, Tomizawa S Published Date November 2012 Volume 2012:2 Pages 61 - 64 DOI: http://dx.doi.org/10.2147/OAMS.S35009 Received: 14 June 2012 Accepted: 12 September 2012 Published: 19 November 2012 Kouji Yamamoto,1 Sadao Tomizawa2 1Department of Medical Innovation, Osaka University Hospital, Osaka, 2Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan Background: The aim of the present paper was to develop two new asymmetry probability models to analyze data for tooth decay from 363 women and 349 men aged 18–39 years who visited a dental clinic in Sapporo City, Japan, from 2001 to 2005. Methods: We analyzed the probability relationship between grade of upper and lower tooth decay for men and women using the two new models, and tested goodness-of-fit for the models. Results: The probability that a woman's (man's) grade of lower tooth decay is i (i = 1,2) and her (his) grade of upper tooth decay is j(>i), (j = 2,3) is estimated to be at most 13.52 (10.23) times higher than the probability that the woman's (man's) grade of upper tooth decay is i and grade of lower tooth decay is j. Conclusion: From the data on tooth decay, decay of the upper teeth is worse than of the lower teeth in women and men, and the tendency becomes stronger as the numbers of decayed upper and lower teeth increase.

Abstract:
Kouji Yamamoto,1 Sadao Tomizawa21Department of Medical Innovation, Osaka University Hospital, Osaka, 2Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, JapanBackground: The aim of the present paper was to develop two new asymmetry probability models to analyze data for tooth decay from 363 women and 349 men aged 18–39 years who visited a dental clinic in Sapporo City, Japan, from 2001 to 2005.Methods: We analyzed the probability relationship between grade of upper and lower tooth decay for men and women using the two new models, and tested goodness-of-fit for the models.Results: The probability that a woman's (man's) grade of lower tooth decay is i (i = 1,2) and her (his) grade of upper tooth decay is j(>i), (j = 2,3) is estimated to be at most 13.52 (10.23) times higher than the probability that the woman's (man's) grade of upper tooth decay is i and grade of lower tooth decay is j.Conclusion: From the data on tooth decay, decay of the upper teeth is worse than of the lower teeth in women and men, and the tendency becomes stronger as the numbers of decayed upper and lower teeth increase.Keywords: distance-proportional symmetry, asymmetry, square contingency table, teeth