Filtrations on the knot contact homology of transverse knots

We construct a new invariant of transverse links in the standard contact structure on R^3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link. Here the knot contact homology of a link in R^3 is the Legendrian contact homology DGA of its conormal lift into the unit cotangent bundle S^*R^3 of R^3, and the filtrations are constructed by counting intersections of the holomorphic disks of the DGA differential with two conormal lifts of the contact structure. We also present a combinatorial formula for the filtered DGA in terms of braid representatives of transverse links and apply it to show that the new invariant is independent of previously known invariants of transverse links.Comment: 23 pages, v2: minor corrections suggested by refere

Data catalog series for space science and applications flight missions. Volume 4A: Descriptions of meteorological and terrestrial applications spacecraft and investigations

The National Space Science Data Center (NSSDC) provides data from and information about space science and applications flight investigations in support of additional studies beyond those performed as the principal part of any flight mission. The Earth-orbiting spacecraft for investigations of the earth and its atmosphere is discussed. Geodetic tracking data are included in this category. The principal subject areas presented are meteorology and earth resources survey, and the spacecraft selection is made according to those subjects. All experiments on board the spacecraft are described. No attempt is made to reference investigations that are related to the above disciplines, but that are described in other volumes of this series

Evidential-EM Algorithm Applied to Progressively Censored Observations

Evidential-EM (E2M) algorithm is an effective approach for computing maximum likelihood estimations under finite mixture models, especially when there is uncertain information about data. In this paper we present an extension of the E2M method in a particular case of incom-plete data, where the loss of information is due to both mixture models and censored observations. The prior uncertain information is expressed by belief functions, while the pseudo-likelihood function is derived based on imprecise observations and prior knowledge. Then E2M method is evoked to maximize the generalized likelihood function to obtain the optimal estimation of parameters. Numerical examples show that the proposed method could effectively integrate the uncertain prior infor-mation with the current imprecise knowledge conveyed by the observed data

Dynamical stability of entanglement between spin ensembles

We study the dynamical stability of the entanglement between the two spin ensembles in the presence of an environment. For a comparative study, we consider the two cases: a single spin ensemble, and two ensembles linearly coupled to a bath, respectively. In both circumstances, we assume the validity of the Markovian approximation for the bath. We examine the robustness of the state by means of the growth of the linear entropy which gives a measure of the purity of the system. We find out macroscopic entangled states of two spin ensembles can stably exist in a common bath. This result may be very useful to generate and detect macroscopic entanglement in a common noisy environment and even a stable macroscopic memory.Comment: 4 pages, 1 figur

Aperture Supervision for Monocular Depth Estimation

We present a novel method to train machine learning algorithms to estimate scene depths from a single image, by using the information provided by a camera's aperture as supervision. Prior works use a depth sensor's outputs or images of the same scene from alternate viewpoints as supervision, while our method instead uses images from the same viewpoint taken with a varying camera aperture. To enable learning algorithms to use aperture effects as supervision, we introduce two differentiable aperture rendering functions that use the input image and predicted depths to simulate the depth-of-field effects caused by real camera apertures. We train a monocular depth estimation network end-to-end to predict the scene depths that best explain these finite aperture images as defocus-blurred renderings of the input all-in-focus image.Comment: To appear at CVPR 2018 (updated to camera ready version

Time domain add-drop multiplexing scheme enhanced using a saw-tooth pulse shaper

We experimentally demonstrate the use of saw-tooth optical pulses, which are shaped using a fiber Bragg grating, to achieve robust and high performance time-domain add-drop multiplexing in a scheme based on cross-phase (XPM) modulation in an optical fiber, with subsequent offset filtering. As compared to the use of more conventional pulse shapes, such as Gaussian pulses of a similar pulse width, the purpose-shaped saw-tooth pulses allow higher extinction ratios for the add and drop windows and significant improvements in the receiver sensitivity for the dropped and added channels

Gmunu: Paralleled, grid-adaptive, general-relativistic magnetohydrodynamics in curvilinear geometries in dynamical spacetimes

We present an update of the General-relativistic multigrid numerical (Gmunu) code, a parallelized, multi-dimensional curvilinear, general relativistic magnetohydrodynamics code with an efficient non-linear cell-centred multigrid (CCMG) elliptic solver, which is fully coupled with an efficient block-based adaptive mesh refinement modules. Currently, Gmunu is able to solve the elliptic metric equations in the conformally flat condition (CFC) approximation with the multigrid approach and the equations of ideal general-relativistic magnetohydrodynamics by means of high-resolution shock-capturing finite volume method with reference-metric formularise multi-dimensionally in cartesian, cylindrical or spherical geometries. To guarantee the absence of magnetic monopoles during the evolution, we have developed an elliptical divergence cleaning method by using multigrid solver. In this paper, we present the methodology, full evolution equations and implementation details of our code Gmunu and its properties and performance in some benchmarking and challenging relativistic magnetohydrodynamics problems