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1. Complexity of stability

   https://doi.org/10.1016/j.jcss.2021.07.001  

   Frei, Fabian; Hemaspaandra, Edith; Rothe, Jörg (February 2022, Journal of Computer and System Sciences)
2. Stability of Nanobubbles

   https://doi.org/10.1089/ees.2018.0203  

   Meegoda, Jay N.; Aluthgun Hewage, Shaini; Batagoda, Janitha H. (November 2018, Environmental Engineering Science)
3. Complexity of Stability

   https://doi.org/10.4230/LIPIcs.ISAAC.2020.19  

   Frei, F; Hemaspaandra, E; Rothe, J (January 2021, 31st International Symposium on Algorithms and Computation (ISAAC))

   null (Ed.)

   Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the chromatic number of a graph (i.e., the smallest number of colors needed to color all vertices such that no two adjacent vertices are of the same color) can be applied in solving practical tasks as diverse as pattern matching, scheduling jobs to machines, allocating registers in compiler optimization, and even solving Sudoku puzzles. Typically, however, the underlying graphs are subject to (often minor) changes. To make these applications of graph parameters robust, it is important to know which graphs are stable for them in the sense that adding or deleting single edges or vertices does not change them. We initiate the study of stability of graphs for such parameters in terms of their computational complexity. We show that, for various central graph parameters, the problem of determining whether or not a given graph is stable is complete for $$\Phi_2^p$$, a well-known complexity class in the second level of the polynomial hierarchy, which is also known as “parallel access to NP.” 

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4. Finite generation for valuations computing stability thresholds and applications to K-stability

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   Liu, Yuchen; Xu, Chenyang; Zhuang, Ziquan (September 2022, Annals of Mathematics)
5. A non-Archimedean approach to K-stability, II: Divisorial stability and openness

   https://doi.org/10.1515/crelle-2023-0062  

   Boucksom, Sébastien; Jonsson, Mattias (October 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   To any projective pair (X,B) equipped with an ample Q-line bundle L (or even any ample numerical class), we attach a new invariant $$\beta(\mu)$$, defined on convex combinations $$\mu$$ of divisorial valuations on X , viewed as point masses on the Berkovich analytification of X . The construction is based on non-Archimedean pluripotential theory, and extends the Dervan–Legendre invariant for a single valuation – itself specializing to Li and Fujita’s valuative invariant in the Fano case, which detects K-stability. Using our $$\beta$$-invariant, we define divisorial (semi)stability, and show that divisorial semistability implies (X,B) is sublc (i.e. its log discrepancy function is non-negative), and that divisorial stability is an open condition with respect to the polarization L. We also show that divisorial stability implies uniform K-stability in the usual sense of (ample) test configurations, and that it is equivalent to uniform K-stability with respect to all norms/filtrations on the section ring of (X,L), as considered by Chi Li. 

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