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   Cheng, Qing; Shen, Jie (June 2022, SIAM Journal on Numerical Analysis)
2. A new Lagrange multiplier approach for constructing structure preserving schemes, I. Positivity preserving

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3. Building a Privacy-Preserving Smart Camera System

   https://doi.org/10.2478/popets-2022-0034  

   Beugin, Yohan; Burke, Quinn; Hoak, Blaine; Sheatsley, Ryan; Pauley, Eric; Tan, Gang; Hussain, Syed Rafiul; McDaniel, Patrick (March 2022, Proceedings on Privacy Enhancing Technologies)

   Abstract Millions of consumers depend on smart camera systems to remotely monitor their homes and businesses. However, the architecture and design of popular commercial systems require users to relinquish control of their data to untrusted third parties, such as service providers (e.g., the cloud). Third parties therefore can (and in some instances have) access the video footage without the users’ knowledge or consent—violating the core tenet of user privacy. In this paper, we present CaCTUs , a privacy-preserving smart Camera system Controlled Totally by Users. CaCTUs returns control to the user ; the root of trust begins with the user and is maintained through a series of cryptographic protocols, designed to support popular features, such as sharing, deleting, and viewing videos live. We show that the system can support live streaming with a latency of 2 s at a frame rate of 10 fps and a resolution of 480 p. In so doing, we demonstrate that it is feasible to implement a performant smart-camera system that leverages the convenience of a cloud-based model while retaining the ability to control access to (private) data. 

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4. A Nullspace Property for Subspace-Preserving Recovery

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5. A Local Algorithm for Structure-Preserving Graph Cut

   https://doi.org/10.1145/3097983.3098015  

   Zhou, Dawei; Zhang, Si; Yildirim, Mehmet Yigit; Alcorn, Scott; Tong, Hanghang; Davulcu, Hasan; He, Jingrui (August 2017, KDD)

   Nowadays, large-scale graph data is being generated in a variety of real-world applications, from social networks to co-authorship networks, from protein-protein interaction networks to road traffic networks. Many existing works on graph mining focus on the vertices and edges, with the first-order Markov chain as the underlying model. They fail to explore the high-order network structures, which are of key importance in many high impact domains. For example, in bank customer personally identifiable information (PII) networks, the star structures often correspond to a set of synthetic identities; in financial transaction networks, the loop structures may indicate the existence of money laundering. In this paper, we focus on mining user-specified high-order network structures and aim to find a structure-rich subgraph which does not break many such structures by separating the subgraph from the rest. A key challenge associated with finding a structure-rich subgraph is the prohibitive computational cost. To address this problem, inspired by the family of local graph clustering algorithms for efficiently identifying a low-conductance cut without exploring the entire graph, we propose to generalize the key idea to model high-order network structures. In particular, we start with a generic definition of high-order conductance, and define the high-order diffusion core, which is based on a high-order random walk induced by user-specified high-order network structure. Then we propose a novel High-Order Structure-Preserving LOcal Cut (HOSPLOC) algorithm, which runs in polylogarithmic time with respect to the number of edges in the graph. It starts with a seed vertex and iteratively explores its neighborhood until a subgraph with a small high-order conductance is found. Furthermore, we analyze its performance in terms of both effectiveness and efficiency. The experimental results on both synthetic graphs and real graphs demonstrate the effectiveness and efficiency of our proposed HOSPLOC algorithm. 

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