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   https://doi.org/10.1515/crelle-2023-0016  

   Chen, Gao; Viaclovsky, Jeff; Zhang, Ruobing (May 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We develop a Fredholm theory for the Hodge Laplacian in weighted spaces on ALG ∗ manifolds in dimension four.We then give several applications of this theory.First, we show the existence of harmonic functions with prescribed asymptotics at infinity.A corollary of this is a non-existence result for ALG ∗ manifolds with non-negative Ricci curvature having group Γ = { e } \Gamma=\{e\} at infinity.Next, we prove a Hodge decomposition for the first de Rham cohomology group of an ALG ∗ manifold.A corollary of this is vanishing of the first Betti number for any ALG ∗ manifold with non-negative Ricci curvature.Another application of our analysis is to determine the optimal order of ALG ∗ gravitational instantons. 

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2. Remarks on a Mean Field Equation on S²

   https://doi.org/10.4208/jms.v54n1.21.04  

   Gui, Changfeng (May 2020, Journal of Mathematical Study)

   null (Ed.)
3. Scoring Cyber Vulnerabilities based on Their Impact on Organizational Goals ^*

   https://doi.org/10.1109/SIEDS52267.2021.9483741  

   Keskin, Omer; Gannon, Nick; Lopez, Brian; Tatar, Unal (April 2021, 2021 Systems and Information Engineering Design Symposium (SIEDS))

   Vulnerability Management, which is a vital part of risk and resiliency management efforts, is a continuous process of identifying, classifying, prioritizing, and removing vulnerabilities on devices that are likely to be used by attackers to compromise a network component. For effective and efficient vulnerability management, which requires extensive resources– such as time and personnel, vulnerabilities should be prioritized based on their criticality. One of the most common methods to prioritize vulnerabilities is the Common Vulnerability Scoring System (CVSS). However, in its severity score, the National Institute of Standards and Technology (NIST) only provides the base metric values that include exploitability and impact information for the known vulnerabilities and acknowledges the importance of temporal and environmental characteristics to have a more accurate vulnerability assessment. There is no established method to conduct the integration of these metrics. In this study, we created a testbed to assess the vulnerabilities by considering the functional dependencies between vulnerable assets, other assets, and business processes. The experiment results revealed that a vulnerability's severity significantly changes from its CVSS base score when the vulnerable asset's characteristics and role inside the organization are considered. 

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4. A 4H ⁺ /4e ^– Electron-Coupled-Proton Buffer Based on a Mononuclear Cu Complex

   https://doi.org/10.1021/jacs.2c05454  

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