Applications of Some Elliptic Equations in Riemannian Manifolds

Let $(M^{n+1}, g)$ be a compact Riemannian manifold with smooth boundary B and nonnegative Bakry-Emery Ricci curvature. In this paper, we use the solvability of some elliptic equations to prove some estimates of the weighted mean curvature and some related rigidity theorems. As their applications, we obtain some lower bound estimate of the first nonzero eigenvalue of the drifting Laplacian acting on functions on B and some corresponding rigidity theorems

Risk and Predictability of Singapore’s Direct Residential Real Estate Market

This study explores the topic of the predictability of direct real estate prices in the short-run and the risks facing investors via a case study. Two models are estimated using heteroscedastic and autocorrelation robust ML method. Possible structural shifts of the models are examined. The one assuming that the model captures all the economic influences produces slightly better in-sample fitting. The other model assumes that there could be some important information which is not publicly available. Such information can nevertheless be extracted using Kalman filter. The latter has smaller forecast error in general. We found that a rational speculative bubble is an important predictor of short-run price movement, especially when the market is volatile and noisy. Rental is the only fundamental variable which has any important role to play in the short-run price generating process. Further more, the influence of rental is significant only when the market is inactive. Based on the study, we argue that the risk facing market participants comes not from the rational speculative bubble given its predictability, but primarily from unpredictable local policy shifts.Risk; information; rational bubble; Kalman filter

Massively Parallel Ray Tracing Algorithm Using GPU

Ray tracing is a technique for generating an image by tracing the path of light through pixels in an image plane and simulating the effects of high-quality global illumination at a heavy computational cost. Because of the high computation complexity, it can't reach the requirement of real-time rendering. The emergence of many-core architectures, makes it possible to reduce significantly the running time of ray tracing algorithm by employing the powerful ability of floating point computation. In this paper, a new GPU implementation and optimization of the ray tracing to accelerate the rendering process is presented

Randomized Algorithms for Tracking Distributed Count, Frequencies, and Ranks

We show that randomization can lead to significant improvements for a few fundamental problems in distributed tracking. Our basis is the {\em count-tracking} problem, where there are $k$ players, each holding a counter $n_i$ that gets incremented over time, and the goal is to track an \eps-approximation of their sum $n=\sum_i n_i$ continuously at all times, using minimum communication. While the deterministic communication complexity of the problem is \Theta(k/\eps \cdot \log N), where $N$ is the final value of $n$ when the tracking finishes, we show that with randomization, the communication cost can be reduced to \Theta(\sqrt{k}/\eps \cdot \log N). Our algorithm is simple and uses only O(1) space at each player, while the lower bound holds even assuming each player has infinite computing power. Then, we extend our techniques to two related distributed tracking problems: {\em frequency-tracking} and {\em rank-tracking}, and obtain similar improvements over previous deterministic algorithms. Both problems are of central importance in large data monitoring and analysis, and have been extensively studied in the literature.Comment: 19 pages, 1 figur

A practical approach to managing patients with HCV infection.

Hepatitis C virus (HCV) infection is a major worldwide public health concern. It is a common cause of chronic liver disease and hepatocellular carcinoma. HCV antibody and HCV RNA testing are available diagnostic studies that offer high degree of accuracy. Current standard therapy includes a combination of pegylated interferon and ribavirin. Response rate is approximately 40% for genotype 1 and 80% for genotypes 2 and 3, respectively. Successful treatment can stop the progression of chronic liver disease, reduce the need for liver transplantation, and possibly decrease the risk for Hepatocellular carcinoma (HCC). Evaluating for potential treatment candidacy is an important initial step in the management of chronic HCV infection as not all individuals may need or qualify for the treatment. Understanding the natural history, the different diagnostic modalities, the current therapeutic options and, the treatment response and adverse effect profiles can help the practitioners better manage chronic HCV infection