Covariant phase space with null boundaries

By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one, we find that the key requirement in Harlow-Wu's algorithm fails to be met in the whole covariant phase space. Instead, it can be satisfied in its submanifold with the null boundaries given by the expansion free and shear free hypersurfaces in Einstein's gravity, which can be regarded as the origin of the non-triviality of null boundaries in terms of Wald-Zoupas's prescription. But nevertheless, by sticking to the variational principle as our guiding principle and adapting Harlow-Wu's algorithm to the aforementioned submanifold, we successfully reproduce the Hamiltonians obtained previously by Wald-Zoupas' prescription, where not only are we endowed with the expansion free and shear free null boundary as the natural stand point for the definition of the Hamiltonian in the whole covariant phase space, but also led naturally to the correct boundary term for such a definition.Comment: version to appear in Communications in Theoretical Physic

Riemannian kernel based Nystr\"om method for approximate infinite-dimensional covariance descriptors with application to image set classification

In the domain of pattern recognition, using the CovDs (Covariance Descriptors) to represent data and taking the metrics of the resulting Riemannian manifold into account have been widely adopted for the task of image set classification. Recently, it has been proven that infinite-dimensional CovDs are more discriminative than their low-dimensional counterparts. However, the form of infinite-dimensional CovDs is implicit and the computational load is high. We propose a novel framework for representing image sets by approximating infinite-dimensional CovDs in the paradigm of the Nystr\"om method based on a Riemannian kernel. We start by modeling the images via CovDs, which lie on the Riemannian manifold spanned by SPD (Symmetric Positive Definite) matrices. We then extend the Nystr\"om method to the SPD manifold and obtain the approximations of CovDs in RKHS (Reproducing Kernel Hilbert Space). Finally, we approximate infinite-dimensional CovDs via these approximations. Empirically, we apply our framework to the task of image set classification. The experimental results obtained on three benchmark datasets show that our proposed approximate infinite-dimensional CovDs outperform the original CovDs.Comment: 6 pages, 3 figures, International Conference on Pattern Recognition 201

Optimal Control Strategies in an Alcoholism Model

This paper presents a deterministic SATQ-type mathematical model (including susceptible, alcoholism, treating, and quitting compartments) for the spread of alcoholism with two control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, existence and stability are analyzed. The optimal control strategies are derived by proposing an objective functional and using Pontryagin’s Maximum Principle. Numerical simulations are also conducted in the analytic results

Accelerating Spatial Data Processing with MapReduce

Abstract—MapReduce is a key-value based programming model and an associated implementation for processing large data sets. It has been adopted in various scenarios and seems promising. However, when spatial computation is expressed straightforward by this key-value based model, difficulties arise due to unfit features and performance degradation. In this paper, we present methods as follows: 1) a splitting method for balancing workload, 2) pending file structure and redundant data partition dealing with relation between spatial objects, 3) a strip-based two-direction plane sweep-ing algorithm for computation accelerating. Based on these methods, ANN(All nearest neighbors) query and astronomical cross-certification are developed. Performance evaluation shows that the MapReduce-based spatial applications outperform the traditional one on DBMS

Unexpected versatile electrical transport behaviors of ferromagnetic nickel films

Perpendicular magnetic anisotropy (PMA) of magnets is paramount for electrically controlled spintronics due to their intrinsic potentials for higher memory density, scalability, thermal stability and endurance, surpassing an in-plane magnetic anisotropy (IMA). Nickel film is a long-lived fundamental element ferromagnet, yet its electrical transport behavior associated with magnetism has not been comprehensively studied, hindering corresponding spintronic applications exploiting nickel-based compounds. Here, we systematically investigate the highly versatile magnetism and corresponding transport behavior of nickel films. As the thickness reduces within the general thickness regime of a magnet layer for a memory device, the hardness of nickel films' ferromagnetic loop of anomalous Hall effect increases and then decreases, reflecting the magnetic transitions from IMA to PMA and back to IMA. Additionally, the square ferromagnetic loop changes from a hard to a soft one at rising temperatures, indicating a shift from PMA to IMA. Furthermore, we observe a butterfly magnetoresistance resulting from the anisotropic magnetoresistance effect, which evolves in conjunction with the thickness and temperature-dependent magnetic transformations as a complementary support. Our findings unveil the rich magnetic dynamics and most importantly settle down the most useful guiding information for current-driven spintronic applications based on nickel film: The hysteresis loop is squarest for the ~8 nm-thick nickel film, of highest hardness with Rxyr/Rxys~1 and minimum Hs-Hc, up to 125 K; otherwise, extra care should be taken for a different thickness or at a higher temperature.Comment: 9 pages, 5 figures, accepted by Journal of Physics: Condensed Matte