The impact of the new Earth gravity models on the measurement of the Lense-Thirring effect

In this paper we use, in a preliminary way, the recently released EIGEN2 Earth gravity model, which is based on six months of data of CHAMP only, in order to reassess the systematic error due to the mismodelling in the even zonal harmonics of geopotential in the LAGEOS-LAGEOS II Lense-Thirring experiment involving the nodes of both the LAGEOS satellites and the perigee of LAGEOS II. The first results from the GGM01C Earth gravity model including the first GRACE data are very promising.Comment: LaTeX, 15 pages, no figures, 4 tables. To appear in General Relativity and Gravitatio

Forward-backward truncated Newton methods for convex composite optimization

This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the second one combines the global efficiency estimates of the corresponding first-order methods, while achieving fast asymptotic convergence rates. Furthermore, they are computationally attractive since each Newton iteration requires the approximate solution of a linear system of usually small dimension

Tight entropic uncertainty relations for systems with dimension three to five

We consider two (natural) families of observables $O_k$ for systems with dimension $d=3,4,5$: the spin observables $S_x$, $S_y$ and $S_z$, and the observables that have mutually unbiased bases as eigenstates. We derive tight entropic uncertainty relations for these families, in the form $\sum_kH(O_k)\geqslant\alpha_d$, where $H(O_k)$ is the Shannon entropy of the measurement outcomes of $O_k$ and $\alpha_d$ is a constant. We show that most of our bounds are stronger than previously known ones. We also give the form of the states that attain these inequalities

State independent uncertainty relations from eigenvalue minimization

We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based on finding the ground state of appropriate Hamiltonian operators, which can make use of the many known techniques developed to this aim. To demonstrate the simplicity of the method we analyze multiple instances, both previously known and novel, that involve two or more observables, both bounded and unbounded.Comment: 14 pages, 3 figure

Douglas-Rachford Splitting: Complexity Estimates and Accelerated Variants

We propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope (DRE), whose stationary points correspond to the solutions of the original (possibly nonsmooth) problem. By proving the equivalence between the Douglas-Rachford splitting method and a scaled gradient method applied to the DRE, results from smooth unconstrained optimization are employed to analyze convergence properties of DRS, to tune the method and to derive an accelerated version of it

Multipartite steering inequalities based on entropic uncertainty relations

We investigate quantum steering for multipartite systems by using entropic uncertainty relations. We introduce entropic steering inequalities whose violation certifies the presence of different classes of multipartite steering. These inequalities witness both steerable states and genuine multipartite steerable states. Furthermore, we study their detection power for several classes of states of a three-qubit system.Comment: 3 figure

From local to global deformation quantization of Poisson manifolds

We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a vector bundle with flat connection.Comment: 16 pages. Reference and dedication added. Sign corrected, remark on Poisson vector fields adde

Remote Tracking via Encoded Information for Nonlinear Systems

The problem addressed in this paper is to control a plant so as to have its output tracking (a family of) reference commands generated at a remote location and transmitted through a communication channel of finite capacity. The uncertainty due to the presence of the communication channel is counteracted by a suitable choice of the parameters of the regulator