Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general. In this article, using the geometry of K_C orbits on the generalized flag variety G_C/P_C, we give a necessary and sufficient condition on the triple (g,k, p) such that the restriction X|_k always contains simple k-modules for any g-module $X$ lying in the parabolic BGG category O^p attached to a parabolic subalgebra p of g. Formulas are derived for the Gelfand-Kirillov dimension of any simple k-module occurring in a simple generalized Verma module of g. We then prove that the restriction X|_k is multiplicity-free for any generic g-module X \in O if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n), or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free for any symmetric pair (g, k) and any parabolic subalgebra p with abelian nilradical and for any generic g-module X \in O^p. Explicit branching laws are also presented.Comment: 31 pages, To appear in Transformation Group

Double inflation in supergravity and the primordial black hole formation

We study a double inflation model (a hybrid inflation + a new inflation) in supergravity and discuss the formation of primordial black holes (PBHs) with mass \sim 10^{-20}-10^{5}M_{\odot}. We find that in a wide range of parameter space, we obtain PBHs which amount to \Omega \simeq 1, i.e., PBH dark matter. Also, we find a set of inflation parameters which produces PBHs evaporating now. Those PBHs may be responsible for antiproton fluxes observed by the BESS experiment.Comment: 14 pages, 2 figures (RevTeX file

Visual Exploration System for Analyzing Trends in Annual Recruitment Using Time-varying Graphs

Annual recruitment data of new graduates are manually analyzed by human resources specialists (HR) in industries, which signifies the need to evaluate the recruitment strategy of HR specialists. Every year, different applicants send in job applications to companies. The relationships between applicants' attributes (e.g., English skill or academic credential) can be used to analyze the changes in recruitment trends across multiple years' data. However, most attributes are unnormalized and thus require thorough preprocessing. Such unnormalized data hinder the effective comparison of the relationship between applicants in the early stage of data analysis. Thus, a visual exploration system is highly needed to gain insight from the overview of the relationship between applicants across multiple years. In this study, we propose the Polarizing Attributes for Network Analysis of Correlation on Entities Association (Panacea) visualization system. The proposed system integrates a time-varying graph model and dynamic graph visualization for heterogeneous tabular data. Using this system, human resource specialists can interactively inspect the relationships between two attributes of prospective employees across multiple years. Further, we demonstrate the usability of Panacea with representative examples for finding hidden trends in real-world datasets and then describe HR specialists' feedback obtained throughout Panacea's development. The proposed Panacea system enables HR specialists to visually explore the annual recruitment of new graduates

Isocurvature Fluctuations of the M-theory Axion in a Hybrid Inflation Model

The M-theory, the strong-coupling heterotic string theory, presents various interesting new phenomenologies. The M-theory bulk axion is one of these. The decay constant in this context is estimated as $F_a\simeq 10^{16}$ GeV. Direct searches for the M-theory axion seem impossible because of the large decay constant. However, we point out that large isocurvature fluctuations of the M-theory axion are obtained in a hybrid inflation model, which will most likely be detectable in future satellite experiments on anisotropies of cosmic microwave background radiation.Comment: 14 pages (RevTeX file), the final version to appear in Prog. Theor. Phy

Disability Prevention Programs for Older People: Factors Associated with Medical and Nursing Care Costs

This study aimed to clarify factors associated with medical and nursing care costs for older people living in community and to suggest an effective disability prevention programs. Total of participants in this study was 83 individuals (29 men and 54 women; mean age 81.2 ± 6.3 years old) on November 1st – December 28th, 2014. This study compared the average medical and nursing care costs per month with national average for those aged ≥ 65 years old. Logistic regression test was conducted to examine its association with medical and nursing care costs. Those who had outing activities ≥ 3 times a week were approximately three times less likely to reduce medical and nursing care costs than those who had outing activities < 3 times a week despite three controlled covariates (OR = 3.23 and 95% CI = 1.03 – 10.42). Disability prevention programs that improve frequency of outing at least three times in a week may become a valid economic approach to older people who do not live in nursing home

Special functions associated to a certain fourth order differential equation

We develop a theory of "special functions" associated to a certain fourth order differential operator $\mathcal{D}_{\mu,\nu}$ on $\mathbb{R}$ depending on two parameters $\mu,\nu$. For integers $\mu,\nu\geq-1$ with $\mu+\nu\in2\mathbb{N}_0$ this operator extends to a self-adjoint operator on $L^2(\mathbb{R}_+,x^{\mu+\nu+1}dx)$ with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, $L^2$-norms, integral representations and various recurrence relations. This fourth order differential operator $\mathcal{D}_{\mu,\nu}$ arises as the radial part of the Casimir action in the Schr\"odinger model of the minimal representation of the group $O(p,q)$, and our "special functions" give $K$-finite vectors