Application of Current Algebra in Three Pseudoscalar Meson Decays of τ\tau Lepton

The decays of $\tau \to 3\pi \nu$ and $\tau \to \pi K^{*} \nu, K\rho \nu$ are calculated using the hard pion and kaon current algebra and assuming the Axial-Vector meson dominance of the hadronic axial currents. Using the experimental data on their masses and widths, the $\tau$ decay branching ratios into these channels are calculated and found to be in a reasonable agreement with the experimental data. In particular, using the available Aleph data on the $3\pi$ spectrum, we determine the $A_1$ parameters, $m_A=1.24\pm 0.02 GeV$, $\Gamma _A=0.43\pm 0.02$ GeV; the hard current algebra calculation yields a $3\pi$ branching ratio of $19 \pm 3 \%$.Comment: 14 pages, Tex, 6 included figure

Constraining Universal Extra Dimensions through B decays

We analyze the exclusive rare $B \to K^{(*)} \ell^+ \ell^-$, $B \to K^{(*)} \nu \bar \nu$ and $B \to K^* \gamma$ decays in the Applequist-Cheng-Dobrescu model, an extension of the Standard Model in presence of universal extra dimensions. In the case of a single universal extra dimension, we study the dependence of several observables on the compactification parameter 1/R, and discuss whether the hadronic uncertainty due to the form factors obscures or not such a dependence. We find that, using present data, it is possible in many cases to put a sensible lower bound to 1/R, the most stringent one coming from $B \to K^* \gamma$.Comment: Invited talk at "Continuous Advances in QCD 2006", May 11-14 2006, Minneapolis (Minnesota). LaTex, 7 pages, 8 Figure

Latin cubes of even order with forbidden entries

We consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant $\gamma > 0$ such that if $n=2t$ and $A$ is a $3$-dimensional $n\times n\times n$ array where every cell contains at most $\gamma n$ symbols, and every symbol occurs at most $\gamma n$ times in every line of $A$, then $A$ is {\em avoidable}; that is, there is a Latin cube $L$ of order $n$ such that for every $1\leq i,j,k\leq n$, the symbol in position $(i,j,k)$ of $L$ does not appear in the corresponding cell of $A$.Comment: arXiv admin note: substantial text overlap with arXiv:1809.0239

K Means Segmentation of Alzheimers Disease in PET scan datasets: An implementation

The Positron Emission Tomography (PET) scan image requires expertise in the segmentation where clustering algorithm plays an important role in the automation process. The algorithm optimization is concluded based on the performance, quality and number of clusters extracted. This paper is proposed to study the commonly used K Means clustering algorithm and to discuss a brief list of toolboxes for reproducing and extending works presented in medical image analysis. This work is compiled using AForge .NET framework in windows environment and MATrix LABoratory (MATLAB 7.0.1)Comment: International Joint Conference on Advances in Signal Processing and Information Technology, SPIT201