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In this paper, we present CPL-Sync, a certifiably correct algorithm to solve planar pose graph optimization (PGO) using the complex number representation. We formulate planar PGO as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to complex semidefinite programming (SDP). Furthermore, we simplify the corresponding semidefinite programming to Riemannian staircase optimization (RSO) on complex oblique manifolds that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through comparisons with existing methods as well as applications on planar PGO in simultaneous localization and mapping (SLAM), which indicates that the proposed algorithm is more efficient and capable of solving planar PGO certifiably. The C++ code for CPL-Sync is available at https://github. com/fantaosha/CPL- Sync. 

Many mobile applications (i.e., apps) include UI widgets to use or collect users’ sensitive data. Thus, to identify suspicious sensitive data usage such as UI-permission mis- match, it is crucial to understand the intentions of UI widgets. However, many UI widgets leverage icons of specific shapes (object icons) and icons embedded with text (text icons) to express their intentions, posing challenges for existing detection techniques that analyze only textual data to identify sensitive UI widgets. In this work, we propose a novel app analysis frame- work, ICONINTENT, that synergistically combines program analysis and icon classification to identify sensitive UI widgets in Android apps. ICONINTENT automatically associates UI widgets and icons via static analysis on app’s UI layout files and code, and then adapts computer vision techniques to classify the associated icons into eight categories of sensitive data. Our evaluations of ICONINTENT on 150 apps from Google Play show that ICONINTENT can detect 248 sensitive UI widgets in 97 apps, achieving a precision of 82.4%. When combined with SUPOR, the state-of-the-art sensitive UI widget identification technique based on text analysis, SUPOR +ICONINTENT can detect 487 sensitive UI widgets (101.2% improvement over SU- POR only), and reduces suspicious permissions to be inspected by 50.7% (129.4% improvement over SUPOR only).