Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page

A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

3D environment mapping using the Kinect V2 and path planning based on RRT algorithms

This paper describes a 3D path planning system that is able to provide a solution trajectory for the automatic control of a robot. The proposed system uses a point cloud obtained from the robot workspace, with a Kinect V2 sensor to identify the interest regions and the obstacles of the environment. Our proposal includes a collision-free path planner based on the Rapidly-exploring Random Trees variant (RRT*), for a safe and optimal navigation of robots in 3D spaces. Results on RGB-D segmentation and recognition, point cloud processing, and comparisons between different RRT* algorithms, are presented.Peer ReviewedPostprint (published version

Diabetes and Risk of Non-Hodgkin's Lymphoma

OBJECTIVE: To examine the epidemiologic association between diabetes and risk of non-Hodgkin's lymphoma (NHL). RESEARCH DESIGN AND METHODS: We searched MEDLINE for observational studies on the association between diabetes and NHL in adults using the keywords "diabetes" and "lymphoma." Prospective cohort studies that reported relative risks or standardized incidence ratios and case-control studies that reported odds ratios with 95% CIs were included. A random-effects model was used to combine results from the individual studies. RESULTS: A total of 15 manuscripts (reporting data from 5 prospective cohort and 11 case-control studies) met the inclusion criteria. Combining data from all studies, the risk ratio (RR) of developing NHL in patients with diabetes was 1.19 (95% CI 1.04–1.35). Based on prospective studies, patients with diabetes had an RR of developing NHL of 1.41 (1.07–1.88), without heterogeneity among studies (I2 = 34.3%; P > 0.10). Based on case-control studies, patients with diabetes had an RR of 1.12 (95% CI 0.95–1.31) of developing NHL compared with people without diabetes, with some heterogeneity among studies (I2 = 36.28%; P = 0.09). CONCLUSIONS: Diabetes is associated with a moderately increased risk of NHL, which is consistent with other reported associations between diabetes and malignancies. Future studies should focus on elucidating potential pathophysiologic links between diabetes and NHL.National Institutes of Health grants (R01-DK76092, R0179003, and R2178867

Optimal Capacity of the Blume-Emery-Griffiths perceptron

A Blume-Emery-Griffiths perceptron model is introduced and its optimal capacity is calculated within the replica-symmetric Gardner approach, as a function of the pattern activity and the imbedding stability parameter. The stability of the replica-symmetric approximation is studied via the analogue of the Almeida-Thouless line. A comparison is made with other three-state perceptrons.Comment: 10 pages, 8 figure