Observational constraints on decaying vacuum dark energy model

The decaying vacuum model (DV), treating dark energy as a varying vacuum, has been studied well recently. The vacuum energy decays linearly with the Hubble parameter in the late-times, $\rho_\Lambda(t) \propto H(t)$, and produces the additional matter component. We constrain the parameters of the DV model using the recent data-sets from supernovae, gamma-ray bursts, baryon acoustic oscillations, CMB, the Hubble rate and x-rays in galaxy clusters. It is found that the best fit of matter density contrast $\Omega_m$ in the DV model is much lager than that in $\Lambda$CDM model. We give the confidence contours in the $\Omega_m-h$ plane up to $3\sigma$ confidence level. Besides, the normalized likelihoods of $\Omega_m$ and $h$ are presented, respectively. %Comment: 7 pages, 3 figures, accepted by European Physical Journal

Completely positive maps within the framework of direct-sum decomposition of state space

We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They includes not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.Comment: 7 pages, no figur

The Quantum Dynamics of Heterotic Vortex Strings

We study the quantum dynamics of vortex strings in N=1 SQCD with U(N_c) gauge group and N_f=N_c quarks. The classical worldsheet of the string has N=(0,2) supersymmetry, but this is broken by quantum effects. We show how the pattern of supersymmetry breaking and restoration on the worldsheet captures the quantum dynamics of the underlying 4d theory. We also find qualitative matching of the meson spectrum in 4d and the spectrum on the worldsheet.Comment: 13 page

MALA-within-Gibbs samplers for high-dimensional distributions with sparse conditional structure

Markov chain Monte Carlo (MCMC) samplers are numerical methods for drawing samples from a given target probability distribution. We discuss one particular MCMC sampler, the MALA-within-Gibbs sampler, from the theoretical and practical perspectives. We first show that the acceptance ratio and step size of this sampler are independent of the overall problem dimension when (i) the target distribution has sparse conditional structure, and (ii) this structure is reflected in the partial updating strategy of MALA-within-Gibbs. If, in addition, the target density is blockwise log-concave, then the sampler's convergence rate is independent of dimension. From a practical perspective, we expect that MALA-within-Gibbs is useful for solving high-dimensional Bayesian inference problems where the posterior exhibits sparse conditional structure at least approximately. In this context, a partitioning of the state that correctly reflects the sparse conditional structure must be found, and we illustrate this process in two numerical examples. We also discuss trade-offs between the block size used for partial updating and computational requirements that may increase with the number of blocks

Sudden jumps and plateaus in the quench dynamics of a Bloch state

We take a one-dimensional tight binding chain with periodic boundary condition and put a particle in an arbitrary Bloch state, then quench it by suddenly changing the potential of an arbitrary site. In the ensuing time evolution, the probability density of the wave function at an arbitrary site \emph{jumps indefinitely between plateaus}. This phenomenon adds to a former one in which the survival probability of the particle in the initial Bloch state shows \emph{cusps} periodically, which was found in the same scenario [Zhang J. M. and Yang H.-T., EPL, \textbf{114} (2016) 60001]. The plateaus support the scattering wave picture of the quench dynamics of the Bloch state. Underlying the cusps and jumps is the exactly solvable, nonanalytic dynamics of a Luttinger-like model, based on which, the locations of the jumps and the heights of the plateaus are accurately predicted.Comment: final versio

Cosmic age, Statefinder and OmOm diagnostics in the decaying vacuum cosmology

As an extension of $\Lambda$CDM, the decaying vacuum model (DV) describes the dark energy as a varying vacuum whose energy density decays linearly with the Hubble parameter in the late-times, $\rho_\Lambda(t) \propto H(t)$, and produces the matter component. We examine the high-$z$ cosmic age problem in the DV model, and compare it with $\Lambda$CDM and the Yang-Mills condensate (YMC) dark energy model. Without employing a dynamical scalar field for dark energy, these three models share a similar behavior of late-time evolution. It is found that the DV model, like YMC, can accommodate the high-$z$ quasar APM 08279+5255, thus greatly alleviates the high-$z$ cosmic age problem. We also calculate the Statefinder $(r,s)$ and the {\it Om} diagnostics in the model. It is found that the evolutionary trajectories of $r(z)$ and $s(z)$ in the DV model are similar to those in the kinessence model, but are distinguished from those in $\Lambda$CDM and YMC. The ${\it Om}(z)$ in DV has a negative slope and its height depends on the matter fraction, while YMC has a rather flat ${\it Om}(z)$, whose magnitude depends sensitively on the coupling.Comment: 12 pages, 4 figures, with some correction

Random design analysis of ridge regression

This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis provides sharp results on the ``out-of-sample'' prediction error, as opposed to the ``in-sample'' (fixed design) error. The analysis also reveals the effect of errors in the estimated covariance structure, as well as the effect of modeling errors, neither of which effects are present in the fixed design setting. The proofs of the main results are based on a simple decomposition lemma combined with concentration inequalities for random vectors and matrices