Hypersurfaces with constant anisotropic mean curvatures

We apply the evolution method to present a new proof of the Alexandrov type theorem for constant anisotropic mean curvature hypersurfaces in the Euclidean space $\mathbb{R}^{n+1}$.Comment: 9 page

Detecting Blackholes and Volcanoes in Directed Networks

In this paper, we formulate a novel problem for finding blackhole and volcano patterns in a large directed graph. Specifically, a blackhole pattern is a group which is made of a set of nodes in a way such that there are only inlinks to this group from the rest nodes in the graph. In contrast, a volcano pattern is a group which only has outlinks to the rest nodes in the graph. Both patterns can be observed in real world. For instance, in a trading network, a blackhole pattern may represent a group of traders who are manipulating the market. In the paper, we first prove that the blackhole mining problem is a dual problem of finding volcanoes. Therefore, we focus on finding the blackhole patterns. Along this line, we design two pruning schemes to guide the blackhole finding process. In the first pruning scheme, we strategically prune the search space based on a set of pattern-size-independent pruning rules and develop an iBlackhole algorithm. The second pruning scheme follows a divide-and-conquer strategy to further exploit the pruning results from the first pruning scheme. Indeed, a target directed graphs can be divided into several disconnected subgraphs by the first pruning scheme, and thus the blackhole finding can be conducted in each disconnected subgraph rather than in a large graph. Based on these two pruning schemes, we also develop an iBlackhole-DC algorithm. Finally, experimental results on real-world data show that the iBlackhole-DC algorithm can be several orders of magnitude faster than the iBlackhole algorithm, which has a huge computational advantage over a brute-force method.Comment: 18 page

Compositional Tuning of Structural Stability of Lithiated Cubic Titania via a Vacancy-Filling Mechanism under High Pressure

Experimental and theoretical studies on the compositional dependence of stability and compressibility in lithiated cubic titania are presented. The crystalline-to-amorphous phase transition pressure increases monotonically with Li concentration (from ∼17.5  GPa for delithiated to no phase transition for fully lithiated cubic titania up to 60 GPa). The associated enhancement in structural stability is postulated to arise from a vacancy filling mechanism in which an applied pressure drives interstitial Li ions to vacancy sites in the oxide interior. The results are of significance for understanding mechanisms of structural response of metal oxide electrode materials at high pressures as well as emerging energy storage technologies utilizing such materials

Morphing Switched-Capacitor Converters with Variable Conversion Ratio

High-voltage-gain and wide-input-range dc-dc converters are widely used in various electronics and industrial products such as portable devices, telecommunication, automotive, and aerospace systems. The two-stage converter is a widely adopted architecture for such applications, and it is proven to have a higher efficiency as compared with that of the single-stage converter. This paper presents a modular-cell-based morphing switched-capacitor (SC) converter for application as a front-end converter of the two-stage converter. The conversion ratio of this converter is flexible and variable and can be freely extended by increasing more SC modules. The varying conversion ratio is achieved through the morphing of the converter's structure corresponding to the amplitude of the input voltage. This converter is light and compact, and is highly efficient over a very wide range of input voltage and load conditions. Experimental work on a 25-W, 6-30-V input, 3.5-8.5-V output prototype, is performed. For a single SC module, the efficiency over the entire input voltage range is higher than 98%. Applied into the two-stage converter, the overall efficiency achievable over the entire operating range is 80% including the driver's loss