Improved estimation of duality gap in binary quadratic programming using a weighted distance measure

We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights can be computed by solving a semidefinite programming problem. We further establish a necessary and sufficient condition under which the weighted distance measure gives a strictly tighter estimation of the duality gap than the existing estimations.     

Exponential probabilistic inequalities

We extend the mapping properties of martingale transforms, decoupling inequalities, differential subordination, and the Stein inequalities to exponential Orlicz spaces.     

Improved measurement of electron antineutrinodisappearance at Daya Bay

We report an improved measurement of the neutrino mixing angle θ₁₃ from the Daya Bay Reactor Neutrino Experiment. We exclude a zero value for sin² θ₁₃ with a significance of 7.7 standard deviations. Electron antineutrinos from six reactors of 2.9 GW_th were detected in six antineutrino detectors deployed in two near （flux-weighted baselines of 470 m and 576 m） and one far （1648 m） underground experimental halls. Using 139 days of data, 28909 （205308） electron antineutrino candidates were detected at the far hall （near halls）. The ratio of the observed to the expected number of antineutrinos assuming no oscillations at the far hall is 0.944±0.007（stat.）±0.003（syst.）. An analysis of the relative rates in six detectors finds sin² θ₁₃ =0.089±0.010（stat.）±0.005（syst.） in a three-neutrino framework.     

The d-very ampleness of adjoint line bundles on quasi-elliptic surfaces

In this paper, we give a numerical criterion of Reider-type for the d-very ampleness of the adjoint line bundles on quasi-elliptic surfaces, and meanwhile we give a new proof of the vanishing theorem on quasi-elliptic surfaces emailed from Langer and show that it is the optimal version.     

A class of random field memory models for mortality forecasting

This article proposes a parsimonious alternative approach for modeling the stochastic dynamics of mortality rates. Instead of the commonly used factor-based decomposition framework, we consider modeling mortality improvements using a random field specification with a given causal structure. Such a class of models introduces dependencies among adjacent cohorts aiming at capturing, among others, the cohort effects and cross generations correlations. It also describes the conditional heteroskedasticity of mortality. The proposed model is a generalization of the now widely used AR-ARCH models for random processes. For such a class of models, we propose an estimation procedure for the parameters. Formally, we use the quasi-maximum likelihood estimator (QMLE) and show its statistical consistency and the asymptotic normality of the estimated parameters. The framework being general, we investigate and illustrate a simple variant, called the three-level memory model, in order to fully understand and assess the effectiveness of the approach for modeling mortality dynamics.     

On the kačanov method for a quasi-newtonian flow problem 1

The Ka?anov method is an iteration method for solving nonlinear Problems. In this paper, we apply the Ka?anov method to solve the problem of quasi-Newtonian flow obeying the Carreau law. The emphasis of the paper is the derivation of a posteriori error estimate for Ka?anov iterates. A numerical example shows the efficiency of the error estimate.     

Un problème de confinement pour une coque membranaire linéairement élastique de type elliptique

We identify, and rigorously justify by an asymptotic analysis, the variational inequalities of the two-dimensional problem satisfied by the displacement field of a linearly elastic membrane shell of elliptic type subjected to a confinement condition inside a half-space. This type of condition substantially differs from the Signorini condition usually imposed on the “lower face” of the shell.     

Robust sparse phase retrieval made easy

In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise. In addition, the proposed strategy is fairly general, allowing for a large number of new measurement constructions and recovery algorithms to be designed with minimal effort.     

Equivalent Conditions for Local Error Bounds

In this paper we present two classes of equivalent conditions for local error bounds in finite dimensional spaces. We formulate conditions of the first class by using subderivatives, subdifferentials and strong slopes for nearby points outside the referenced set, and show that these conditions actually characterize a uniform version of the local error bound property. We demonstrate this uniformity for the max function of a finite collection of smooth functions, and as a consequence we show that quasinormality constraint qualifications guarantee the existence of local error bounds. We further present the second class of equivalent conditions for local error bounds by using the various limits defined on the boundary of the referenced set. In presenting these conditions, we exploit the variational geometry of the referenced set in a systematic way and unify some existing results in the literature.