We consider a Markovian model, proposed by Littlewood, to assess the reliability of a modular software. Speci cally , we are interested in the asymptotic properties of the corresponding failure point process. We focus on its time-stationary version and on its behavior when reliability growth takes place. We prove the convergence in distribution of the failure point process to a Poisson process. Additionally, we provide a convergence rate using the distance in variation. This is heavily based on a similar result of Kabanov, Liptser and Shiryayev, for a doubly-stochastic Poisson process where the intensity is governed by a Markov process.
We have studied the leptonic decay ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, via the decay channel ${\ensuremath{\tau}}^{+}\ensuremath{\rightarrow}{e}^{+}{\ensuremath{\nu}}_{e}{\overline{\ensuremath{\nu}}}_{\ensuremath{\tau}}$, using a sample of tagged ${D}_{s}^{+}$ decays collected near the ${D}_{s}^{*\ifmmode\pm\else\textpm\fi{}}{D}_{s}^{\ensuremath{\mp}}$ peak production energy in ${e}^{+}{e}^{\ensuremath{-}}$ collisions with the CLEO-c detector. We obtain $\mathcal{B}({D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})=(5.30\ifmmode\pm\else\textpm\fi{}0.47\ifmmode\pm\else\textpm\fi{}0.22)%$ and determine the decay constant ${f}_{{D}_{s}}=(252.5\ifmmode\pm\else\textpm\fi{}11.1\ifmmode\pm\else\textpm\fi{}5.2)\text{ }\text{ }\mathrm{MeV}$, where the first uncertainties are statistical and the second are systematic.
We replicated Exp. 1 of Frank, Goldwater, Griffiths, & Tenenbaum (2010): Modeling human performance in statistical word segmentation, Cognition, 117(2), 107-125, as part of a multi-year project to replicate eery published adult statistical word segmentation study. With some minor differences likely associated with a higher sample size, we largely replicate the main conclusion that longer sentence length increases word segmentation difficulty.
Dependability evaluation is a basic component in the assessment of the quality of repairable systems. We develop a model taking simultaneously into account the occurrence of failures and repairs, together with the observation of user-defined success events. The model is built from a Markovian description of the behavior of the system. We obtain the distribution function of the joint number of observed failures and of delivered services on a fixed mission period of the system. In particular, the marginal distribution of the number of failures can be directly related to the distribution of the Markovian arrival process extensively used in queueing theory. We give both the analytical expressions of the considered distributions and the algorithmic solutions for their evaluation. An asymptotic analysis is also provided.
Analyzing 600/pb of e+e- collisions at 4170 MeV center-of-mass energy with the CLEO-c detector, we measure the branching fraction B(Ds+ -> tau+ nu)=(5.52\pm 0.57\pm 0.21)% using the tau+ -> rho^+ anti-nu decay mode. Combining with other CLEO measurements of B(Ds+ -> tau+ nu) we determine the pseudoscalar decay constant fDs = (259.7\pm 7.8\pm 3.4) MeV consistent with the value obtained from our Ds+ -> mu+ nu measurement of (257.6\pm 10.3\pm 4.3) MeV. Combining these measurements we find a value of fDs=(259.0 \pm 6.2\pm 3.0) MeV, that differs from the most accurate prediction based on unquenched lattice gauge theory of (241\pm 3) MeV by 2.4 standard deviations. We also present the first measurements of B(Ds+ -> K0 pi+ pi0)=(1.00\pm0.18\pm 0.04)%, and B(Ds+ -> pi+ pi0 pi0)=(0.65\pm0.13\pm 0.03)%, and measure a new value for B(Ds+ -> eta rho+)=(8.9\pm0.6\pm0.5)%.
G. Bonvicini, D. Cinabro, A. Lincoln, M. J. Smith, P. Zhou, J. Zhu, P. Naik, J. Rademacker, D. M. Asner, K. W. Edwards, J. Reed, A. N. Robichaud, G. Tatishvili, E. J. White, R. A. Briere, H. Vogel, P. U. E. Onyisi, J. L. Rosner, J. P. Alexander, D. G. Cassel, R. Ehrlich, L. Fields, R. S. Galik, L. Gibbons, S. W. Gray, D. L. Hartill, B. K. Heltsley, J. M. Hunt, D. L. Kreinick, V. E. Kuznetsov, J. Ledoux, H. Mahlke-Kruger, J. R. Patterson, D. Peterson, D. Riley, A. Ryd, A. J. Sadoff, X. Shi, S. Stroiney, W. M. Sun, J. Yelton, P. Rubin, N. Lowrey, S. Mehrabyan, M. Selen, J. Wiss, M. Kornicer, R. E. Mitchell, M. R. Shepherd, C. M. Tarbert, D. Besson, T. K. Pedlar, J. Xavier, D. Cronin-Hennessy, K. Y. Gao, J. Hietala, R. Poling, P. Zweber, S. Dobbs, Z. Metreveli, K. K. Seth, B. J. Y. Tan, A. Tomaradze, S. Brisbane, J. Libby, L. Martin, A. Powell, P. Spradlin, C. Thomas, G. Wilkinson, H. Mendez, J. Y. Ge, D. H. Miller, I. P. J. Shipsey, B. Xin, G. S. Adams, D. Hu, B. Moziak, J. Napolitano, K. M. Ecklund, J. Insler, H. Muramatsu, C. S. Park, E. H. Thorndike, F. Yang, M. Artuso, S. Blusk, S. Khalil, R. Mountain, K. Randrianarivony, T. Skwarnicki, J. C. Wang, L. M. Zhang, and C. Collaboration
This paper proposes additional material to the main statements of [HL13] which are are recalled in Section~2. In particular an application of [Theorem~2.2,HL13] to Renewal Markov Processes is provided in Section~4 and a detailed checking of the assumptions of [Theorem~2.2,HL13] for the joint distribution of local times of a finite jump process is reported in Section~5. A uniform version of [Theorem~2.2,HL13] with respect to a compact set of transition matrices is given in Section~6 (see [Remark 2.4,HL13]). The basic material on the semigroup of Fourier matrices and the spectral approach used in [HL13] is recalled in Section~3 in order to obtain a good understanding of the properties involved in this uniform version.
