SL(2,C) gravity on noncommutative space with Poisson structure

The Einstein's gravity theory can be formulated as an SL(2,C) gauge theory in terms of spinor notations. In this paper, we consider a noncommutative space with the Poisson structure and construct an SL(2,C) formulation of gravity on such a space. Using the covariant coordinate technique, we build a gauge invariant action in which, according to the Seiberg-Witten map, the physical degrees of freedom are expressed in terms of their commutative counterparts up to the first order in noncommutative parameters.Comment: 12 pages, no figures; v2: 13 pages, clarifications and references added; v3: clarifications added; v4: more clarifications and references added, final version to appear in Phys. Rev.

A Robust Stepwise Clustering Approach to Detect Individual Trees in Temperate Hardwood Plantations Using Airborne LiDAR Data

Precise tree inventory plays a critical role in sustainable forest planting, restoration, and management. LiDAR-based individual tree detection algorithms often focus on finding individual treetops to discern tree positions. However, deliquescent tree forms (broad, flattened crowns) in deciduous forests can make these algorithms ineffective. In this study, we propose a stepwise tree detection approach, by first identifying individual trees using horizontal point density and then analyzing their vertical structure profiles. We first project LiDAR data onto a 2D horizontal plane and apply mean shift clustering to generate candidate tree clusters. Next, we apply a series of structure analyses on the vertical phase, to overcome local variations in crown size and tree density. This study demonstrates that the horizontal point density of LiDAR data provides critical information to locate and isolate individual trees in temperate hardwood plantations with varied densities, while vertical structure profiles can identify spreading branches and reconstruct deliquescent crowns. One challenge of applying mean shift clustering is training a dynamic search kernel to identify trees of different sizes, which usually requires a large number of field measurements. The stepwise approach proposed in this study demonstrated robustness when using a constant kernel in clustering, making it an efficient tool for large-scale analysis. This stepwise approach was designed for quantifying temperate hardwood plantation inventories using relatively low-density airborne LiDAR, and it has potential applications for monitoring large-scale plantation forests. Further research is needed to adapt this method to natural stands with diverse tree ages and structures

Constraints on Unparticle Interactions from Invisible Decays of Z, Quarkonia and Neutrinos

Unparticles (\U) interact weakly with particles. The direct signature of unparticles will be in the form of missing energy. We study constraints on unparticle interactions using totally invisible decay modes of $Z$, vector quarkonia $V$ and neutrinos. The constraints on the unparticle interaction scale \Lambda_\U are very sensitive to the dimension d_\U of the unparticles. From invisible $Z$ and $V$ decays, we find that with d_\U close to 1 for vector \U, the unparticle scale \Lambda_\U can be more than $10^4$ TeV, and for d_\U around 2, the scale can be lower than one TeV. From invisible neutrino decays, we find that if d_\U is close to 3/2, the scale can be more than the Planck mass, but with d_\U around 2 the scale can be as low as a few hundred GeV. We also study the possibility of using V (Z)\to \gamma + \U to constrain unparticle interactions, and find that present data give weak constraints.Comment: 12 pages, 4 figures, version to appear in JHEP

U(2,2) gravity on noncommutative space with symplectic structure

The classical Einstein's gravity can be reformulated from the constrained U(2,2) gauge theory on the ordinary (commutative) four-dimensional spacetime. Here we consider a noncommutative manifold with a symplectic structure and construct a U(2,2) gauge theory on such a manifold by using the covariant coordinate method. Then we use the Seiberg-Witten map to express noncommutative quantities in terms of their commutative counterparts up to the first-order in noncommutative parameters. After imposing constraints we obtain a noncommutative gravity theory described by the Lagrangian with up to nonvanishing first order corrections in noncommutative parameters. This result coincides with our previous one obtained for the noncommutative SL(2,C) gravity.Comment: 13 pages, no figures; v2: 14 pages, clarifications and references added; v3: 16 pages, title changed, clarifications and references added; v4: 17 pages, clarifications added, this final version accepted by Physical Review