Rare tau decays at Belle

We report results of a search for tau lepton decays strongly suppressed in the Standard Model based on the world-largest data sample accumulated with the Belle detector at the KEKB asymmetric-energy e+e- collider. The decays include: lepton flavor and lepton number violating tau decays into a lepton (e or mu) and two charged mesons (K or pi) as well as lepton and baryon number violating tau decays into a Lambda and a charged meson (K or pi). The sensitivity to the branching fractions is significantly improved compared to our previous results and reaches O(10^{-8}).Comment: 4 pages, 3 figures. contribution to the EPS-HEP2011, July 21-27, 2011, Grenoble, Rhone-Alpes, Franc

Asymptotic vanishing of homogeneous components of multigraded modules and its applications

In this article, we give a condition on the vanishing of finitely many homogeneous components which must imply the asymptotic vanishing for multigraded modules. We apply our result to multi-Rees algebras of ideals. As a consequence, we obtain a result on normality of monomial ideals, which extends and improves the results of Reid-Roberts-Vitulli, Singla, and Sarkar-Verma.Comment: 21 pages, to appear in J. Algebr

Search for lepton-flavor-violating tau decay and lepton-number-violation B decay at Belle

We report on the recent results of searches for lepton-flavor-violating tau decays as well as lepton-number-violating B decays with the world-highest data samples accumulated at the Belle.Comment: 4 pages. Proceedings for 35th International Conference of High Energy Physics - ICHEP2010, July 22-28, 2010, Paris Franc

Explosive percolation in thresholded networks

Explosive percolation in a network is a phase transition where a large portion of nodes becomes connected with an addition of a small number of edges. Although extensively studied in random network models and reconstructed real networks, explosive percolation has not been observed in a more realistic scenario where a network is generated by thresholding a similarity matrix describing between-node associations. In this report, I examine construction schemes of such thresholded networks, and demonstrate that explosive percolation can be observed by introducing edges in a particular order

A formula for the associated Buchsbaum-Rim multiplicities of a direct sum of cyclic modules

In this article, we compute the Buchsbaum-Rim function of two variables associated to a direct sum of cyclic modules and give a formula for the last positive associated Buchsbaum-Rim multiplicity in terms of the ordinary Hilbert-Samuel multiplicity of an ideal. This is a generalization of a formula for the last positive Buchsbaum-Rim multiplicity given by Kirby and Rees.Comment: 10 pages, to appear in JPA

Crystalline spin-orbit interaction and the Zeeman splitting in Pb1−x_{1-x}Snx_xTe

The ratio of the Zeeman splitting to the cyclotron energy ($M=\Delta E_Z / \hbar \omega_c$), which characterizes the relative strength of the spin-orbit interaction in crystals, is examined for the narrow gap IV-VI semiconductors PbTe, SnTe, and their alloy Pb$_{1-x}$Sn$_x$Te on the basis of the multiband $k\cdot p$ theory. The inverse mass $\alpha$, the g-factor $g$, and $M$ are calculated numerically by employing the relativistic empirical tight-binding band calculation. On the other hand, a simple but exact formula of $M$ is obtained for the six-band model based on the group theoretical analysis. It is shown that $M1$ for SnTe, which are interpreted in terms of the relevance of the interband couplings due to the crystalline spin-orbit interaction. It is clarified both analytically and numerically that $M=1$ just at the band inversion point, where the transition from trivial to nontrivial topological crystalline insulator occurs. By using this property, one can detect the transition point only with the bulk measurements. It is also proposed that $M$ is useful to evaluate quantitatively a degree of the Dirac electrons in solids.Comment: 9 pages, 3 figure

A Note on the Buchsbaum-Rim multiplicity of a parameter module

In this article we prove that the Buchsbaum-Rim multiplicity $e(F/N)$ of a parameter module $N$ in a free module $F=A^r$ is bounded above by the colength $\ell_A(F/N)$. Moreover, we prove that once the equality $\ell_A(F/N)=e(F/N)$ holds true for some parameter module $N$ in $F$, then the base ring $A$ is Cohen-Macaulay.Comment: 9 pages, to appear in Proceedings of the AM

A Note on the Buchsbaum-Rim function of a parameter module

In this article, we prove that the Buchsbaum-Rim function $\ell_A(\S_{\nu+1}(F)/N^{\nu+1})$ of a parameter module $N$ in $F$ is bounded above by $e(F/N) \binom{\nu+d+r-1}{d+r-1}$ for every integer $\nu \geq 0$. Moreover, it turns out that the base ring $A$ is Cohen-Macaulay once the equality holds for some integer $\nu$. As a direct consequence, we observe that the first Buchsbaum-Rim coefficient $e_1(F/N)$ of a parameter module $N$ is always non-positive.Comment: 11 page

Degree distributions in mesoscopic and macroscopic functional brain networks

We investigated the degree distribution of brain networks extracted from functional magnetic resonance imaging of the human brain. In particular, the distributions are compared between macroscopic brain networks using region-based nodes and mesoscopic brain networks using voxel-based nodes. We found that the distribution from these networks follow the same family of distributions and represent a continuum of exponentially truncated power law distributions

Tau lepton physics at Belle

We report the recent results of a search for lepton-flavor-violating tau decays and a search for CP violation in tau to nu Ks pi using a large data sample accumulated with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. The sensitivity to these modes is significantly improved compared to previous experiments.Comment: 7 pages, proceedings for DISCRETE1