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

The contribution of T2 relaxation time to diffusion MRI quantification and its clinical implications: a hypothesis

Considering liver as the reference, that both fast diffusion (PF) and slow diffusion (Dslow) of the spleen are much underestimated is likely due to the MRI properties of the spleen such as the much longer T2 relaxation time. It is possible that longer T2 relaxation time partially mitigates the signal decay effect of various gradients on diffusion weighted image. This phenomenon will not be limited to the spleen. Most liver tumors have a longer T2 relaxation time than their native normal tissue and this is considered to be associated with oedema. On the other hand, most tumors are measured with lower MRI diffusion (despite being oedematous). The reason why malignant tumors have lower diffusion value [apparent diffusion coefficient (ADC) and Dslow] are poorly understood but has been proposed to be related to a combination of higher cellularity, tissue disorganization, and increased extracellular space tortuosity. These explanations may be true, but it is also possible to that many tumors have MRI properties similar to the spleen such as longer T2 (relative to the liver) and these MRI properties may also contribute to the lower MRI measured ADC and Dslow . In other words, if we could hypothetically plant a piece of spleen tissue in the liver, MRI would recognize this planted spleen tissue as being similar to a tumor and measure it to have lower diffusion than the liver