The log-convexity of the poly-Cauchy numbers

In 2013, Komatsu introduced the poly-Cauchy numbers, which generalize Cauchy numbers. Several generalizations of poly-Cauchy numbers have been considered since then. One particular type of generalizations is that of multiparameter-poly-Cauchy numbers. In this paper, we study the log-convexity of the multiparameter-poly-Cauchy numbers of the first kind and of the second kind. In addition, we also discuss the log-behavior of multiparameter-poly-Cauchy numbers

Understanding for flavor physics in the lepton sector

In this paper, we give a model for understanding flavor physics in the lepton sector--mass hierarchy among different generations and neutrino mixing pattern. The model is constructed in the framework of supersymmetry, with a family symmetry $S4*U(1)$. There are two right-handed neutrinos introduced for seesaw mechanism, while some standard model(SM) gauge group singlet fields are included which transforms non-trivially under family symmetry. In the model, each order of contributions are suppressed by $\delta \sim 0.1$ compared to the previous one. In order to reproduce the mass hierarchy, $m_\tau$ and $\sqrt{\Delta m_{atm}^2}$, $m_\mu$ and $\sqrt{\Delta m_{sol}^2}$ are obtained at leading-order(LO) and next-to-leading-order(NLO) respectively, while electron can only get its mass through next-to-next-to-next-to-leading-order(NNNLO) contributions. For neutrino mixing angels, $\theta_{12}, \theta_{23}, \theta_{13}$ are $45^\circ, 45^\circ, 0$ i.e. Bi-maximal mixing pattern as first approximation, while higher order contributions can make them consistent with experimental results. As corrections for $\theta_{12}$ and $\theta_{13}$ originate from the same contribution, there is a relation predicted for them $\sin{\theta_{13}}=\displaystyle \frac{1-\tan{\theta_{12}}}{1+\tan{\theta_{12}}}$. Besides, deviation from $\displaystyle \frac{\pi}{4}$ for $\theta_{23}$ should have been as large as deviation from 0 for $\theta_{13}$ if it were not the former is suppressed by a factor 4 compared to the latter.Comment: version to appear in Phys. Rev.

The Qphyl System: a web-based interactive system for phylogenetic analysis

Phylogenetic tree reconstruction is a prominent problem in computational biology. Currently, all computational methods have their limitations and work well only for simple problems of small size. No existing method can guarantee that trees constructed for real-world problems are true phylogenetic trees for large and complex problems mainly because the existing computational models are not very biologically realistic. It has become a serious issue for many important real-life applications which often desire accurate results from phylogenetic analysis. Thus, it is very crucial to effectively incorporate multi-disciplinary analyses and synthesize results from various sources when answering real-life questions. In this thesis, a novel web-based phylogeny reconstruction system with a real-time interactive environment, called Qphyl (short for quartet-based phylogenetic analysis) is introduced. The Qphyl system uses a new interactive approach to enable biologists to greatly improve the final results through effectively dynamic interaction with the computation, e.g., to move the computation back and forth to different stages so users can check the intermediate results, compare results from different methods and carry out certain manual refinements using their biological domain-specific knowledge in the decision making on how a tree should be reconstructed. Currently the alpha version of this web-based interactive system has been released and accessible through the URL: http://ww-test.it.usyd.edu.au/sogrid/qphyl/

On the four-zero texture of quark mass matrices and its stability

We carry out a new study of quark mass matrices $M^{}_{\rm u}$ (up-type) and $M^{}_{\rm d}$ (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations.Comment: 33 pages, 4 figures, minor comments added, version to appear in Nucl. Phys.