On Curvature Pinching for Submanifolds with Parallel Normalized Mean Curvature Vector

In this note, we investigate the pinching problem for oriented compact submanifolds of dimension n with parallel normalized mean curvature vector in a space form Fn+p(c). We first prove a codimension reduction theorem for submanifolds under lower Ricci curvature bounds. Moreover, if the submanifolds have constant normalized scalar curvature R≥c, we obtain a classification theorem for submanifolds under lower Ricci curvature bounds. It should be emphasized that our Ricci pinching conditions are sharp for even n and p=2

PEDroid: Automatically Extracting Patches from Android App Updates

Identifying and analyzing code patches is a common practice to not only understand existing bugs but also help find and fix similar bugs in new projects. Most patch analysis techniques aim at open-source projects, in which the differentials of source code are easily identified, and some extra information such as code commit logs could be leveraged to help find and locate patches. The task, however, becomes challenging when source code as well as development logs are lacking. A typical scenario is to discover patches in an updated Android app, which requires bytecode-level analysis. In this paper, we propose an approach to automatically identify and extract patches from updated Android apps by comparing the updated versions and their predecessors. Given two Android apps (original and updated versions), our approach first identifies identical and modified methods by similarity comparison through code features and app structures. Then, it compares these modified methods with their original implementations in the original app, and detects whether a patch is applied to the modified method by analyzing the difference in internal semantics. We implemented PEDroid, a prototype patch extraction tool against Android apps, and evaluated it with a set of popular open-source apps and a set of real-world apps from different Android vendors. PEDroid identifies 28 of the 36 known patches in the former, and successfully analyzes 568 real-world app updates in the latter, among which 94.37% of updates could be completed within 20 minutes

PEDroid: Automatically Extracting Patches from Android App Updates (Artifact)

We propose an approach to automatically identify and extract patches from updated Android apps by comparing the updated versions and their predecessors. PEDroid, a prototype patch extraction tool against Android apps, consists of two phases: differential analysis and patch identification. We evaluated it with a set of popular open-source apps to demonstrate its effectiveness. PEDroid achieves a recall of 92% in differential analysis and successfully identifies 28 of 36 patches in patch identification. We also provide specific guidance on reproducing the experimental results