On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

We study the solutions of the sixth Painlev\'e equation with a logarithmic asymptotic behavior at a critical point. We compute the monodromy group associated to the solutions by the method of monodromy preserving deformations and we characterize the asymptotic behavior in terms of the monodromy itself.Comment: LaTeX with 8 figure

Model building by coset space dimensional reduction in ten-dimensions with direct product gauge symmetry

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and gauge group is a direct product of two Lie groups. We list up candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space,we find fermion and scalar representations of $G_{\mathrm{GUT}} \times U(1)$ with $G_{\mathrm{GUT}}=SU(5), SO(10)$ and $E_6$ which accomodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with a different dimension for $G_{\mathrm{GUT}}=SO(10)$ and $E_6$ models.Comment: 14 pages; added local report number, added refferenc

Possible solution to the 7^7Li problem by the long lived stau

Modification of standard big-bang nucleosynthesis is considered in the minimal supersymmetric standard model to resolve the excessive theoretical prediction of the abundance of primordial lithium 7. We focus on the stau as a next-lightest superparticle, which is long lived due to its small mass difference with the lightest superparticle. It provides a number of additional decay processes of $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$. A particularly important process is the internal conversion in the stau-nucleus bound state, which destroys the $\mathrm{^{7}Li}$ and $\mathrm{^{7}Be}$ effectively. We show that the modification can lead to a prediction consistent with the observed abundance of $\mathrm{^{7}Li}$.Comment: 6 pages, 5 figure

Movable algebraic singularities of second-order ordinary differential equations

Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a (generally branched) solution with leading order behaviour proportional to (z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic at z_0 and a_N(z_0)\ne 0. We consider the subclass of equations for which each possible leading order term of this form corresponds to a one-parameter family of solutions represented near z_0 by a Laurent series in fractional powers of z-z_0. For this class of equations we show that the only movable singularities that can be reached by analytic continuation along finite-length curves are of the algebraic type just described. This work generalizes previous results of S. Shimomura. The only other possible kind of movable singularity that might occur is an accumulation point of algebraic singularities that can be reached by analytic continuation along infinitely long paths ending at a finite point in the complex plane. This behaviour cannot occur for constant coefficient equations in the class considered. However, an example of R. A. Smith shows that such singularities do occur in solutions of a simple autonomous second-order differential equation outside the class we consider here

A meta-learning configuration framework for graph-based similarity search indexes

Similarity searches retrieve elements in a dataset with similar characteristics to the input query element. Recent works show that graph-based methods have outperformed others in the literature, such as tree-based and hash-based methods. However, graphs are highly parameter-sensitive for indexing and searching, which usually demands extra time for finding a suitable trade-off for specific user requirements. Current approaches to select parameters rely on observing published experimental results or Grid Search procedures. While the former has no guarantees that good settings for a dataset will also perform well on a different one, the latter is computationally expensive and limited to a small range of values. In this work, we propose a meta-learning-based recommender framework capable of providing a suitable graph configuration according to the characteristics of the input dataset. We present two instantiations of the framework: a global instantiation that uses the whole meta-database to train meta-models and a dataset-similarity-based instantiation that relies on clustering to generate meta-models tailored to datasets with similar characteristics. We also developed generic and tuned versions of the instantiations. The generic versions can satisfy user requirements in orders of magnitude faster than the traditional Grid Search. The tuned versions provide more accurate predictions at a higher cost. Our results show that the tuned methods outperform the Grid Search for most cases, providing recommendations close to the optimal one and being a suitable alternative, particularly for more challenging datasets

Muonium as a shallow center in GaN

A paramagnetic muonium (Mu) state with an extremely small hyperfine parameter was observed for the first time in single-crystalline GaN below 25 K. It has a highly anisotropic hyperfine structure with axial symmetry along the [0001] direction, suggesting that it is located either at a nitrogen-antibonding or a bond-centered site oriented parallel to the c-axis. Its small ionization energy (=< 14 meV) and small hyperfine parameter (--10^{-4} times the vacuum value) indicate that muonium in one of its possible sites produces a shallow state, raising the possibility that the analogous hydrogen center could be a source of n-type conductivity in as-grown GaN.Comment: 4 figures, to be published in Phys. Rev. Letter

Electronic structure of the muonium center as a shallow donor in ZnO

The electronic structure and the location of muonium centers (Mu) in single-crystalline ZnO were determined for the first time. Two species of Mu centers with extremely small hyperfine parameters have been observed below 40 K. Both Mu centers have an axial-symmetric hyperfine structure along with a [0001] axis, indicating that they are located at the AB_{O,//} and BC_{//} sites. It is inferred from their small ionization energy (~6 meV and 50 meV) and hyperfine parameters (~10^{-4} times the vacuum value) that these centers behave as shallow donors, strongly suggesting that hydrogen is one of the primary origins of n type conductivity in as-grown ZnO.Comment: 4 pages, 4 figures, submitted to PR