Leptonic Charm Decays

We review the recent experimental results on D and Ds meson leptonic decays from CLEO-c, Belle, and BABAR, which results in the decay constants f_D= (206.7 +- 8.9) MeV and f_Ds= (257.3 +- 5.3) MeV. The latter is an average obtained by the Heavy Flavor Averaging Group (HFAG). Comparisons with Lattice QCD (LQCD) calculations are discussed.Comment: Proceedings of CKM2010, the 6th International Workshop on the CKM Unitarity Triangle, University of Warwick, UK, 6-10 September 201

Exploring Algorithmic Limits of Matrix Rank Minimization under Affine Constraints

Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the nuclear norm, which acts as a convenient convex surrogate. While elegant theoretical conditions elucidate when this replacement is likely to be successful, they are highly restrictive and convex algorithms fail when the ambient rank is too high or when the constraint set is poorly structured. Non-convex alternatives fare somewhat better when carefully tuned; however, convergence to locally optimal solutions remains a continuing source of failure. Against this backdrop we derive a deceptively simple and parameter-free probabilistic PCA-like algorithm that is capable, over a wide battery of empirical tests, of successful recovery even at the theoretical limit where the number of measurements equal the degrees of freedom in the unknown low-rank matrix. Somewhat surprisingly, this is possible even when the affine constraint set is highly ill-conditioned. While proving general recovery guarantees remains evasive for non-convex algorithms, Bayesian-inspired or otherwise, we nonetheless show conditions whereby the underlying cost function has a unique stationary point located at the global optimum; no existing cost function we are aware of satisfies this same property. We conclude with a simple computer vision application involving image rectification and a standard collaborative filtering benchmark

The Kaon Form Factor in the Light-Cone Quark Model

The electromagnetic form factor of the kaon meson is calculated in the light-cone formalism of the relativistic constituent quark model. The calculated $K^+$ form factor is consistent with almost all of the available experimental data at low energy scale, while other properties of kaon could also be interrelated in this representation with reasonable parameters. Predictions of the form factors for the charged and neutral kaons at higher energy scale are also given, and we find non-zero $K^0$ form factor at $Q^2 \ne 0$ due to the mass difference between the strange and down quarks inside $K^0$.Comment: 12 latex pages, 2 figures, to appear in Eur.Phy.J.