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   https://doi.org/10.1007/s00209-024-03512-w  

   Baudier, Florent P; Braga, Bruno M; Farah, Ilijas; Vignati, Alessandro; Willett, Rufus (July 2024, Mathematische Zeitschrift)

   We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if the uniform Roe algebras over metric spaces that are coarse unions of expanders graphs are isomorphic, then the metric spaces must be bijectively coarsely equivalent. 

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2. Newtonian Equivalence Principles

   Teh, Nicholas; Read, James (February 2022, Erkenntnis)

   The equivalence principle has constituted one of the cornerstones of discussions in the foundations of spacetime theories over the past century. However, up to this point the principle has been considered overwhelmingly only within the context of relativistic physics. In this article, we demonstrate that the principle has much broader, super-theoretic significance: to do so, we present a unified framework for understanding the principle in its various guises, applicable to both relativistic and Newtonian contexts. We thereby deepen significantly our understanding of the role played by the equivalence principle in a broad class of spacetime theories. 

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3. Strong Equivalence and Program Structure in Arguing Essential Equivalence between Logic Programs

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   LIERLER, YULIYA (May 2022, Theory and Practice of Logic Programming)

   Abstract Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially different answer set programs exist for a given problem. Sometimes these encodings may display significantly different performance. Uncovering precise formal links between these programs is often important and yet far from trivial. This paper presents formal results carefully relating a number of interesting program rewritings. It also provides the proof of correctness of system projector concerned with automatic program rewritings for the sake of efficiency. 

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4. Testing equivalence of clustering

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   Gao, Chao; Ma, Zongming (February 2022, The Annals of Statistics)
5. Equivalence relations and determinacy

   https://doi.org/10.1142/S0219061322500039  

   Crone, Logan; Fishman, Lior; Jackson, Stephen (April 2022, Journal of Mathematical Logic)

   We introduce the notion of [Formula: see text]-determinacy for [Formula: see text] a pointclass and [Formula: see text] an equivalence relation on a Polish space [Formula: see text]. A case of particular interest is the case when [Formula: see text] is the (left) shift-action of [Formula: see text] on [Formula: see text] where [Formula: see text] or [Formula: see text]. We show that for all shift actions by countable groups [Formula: see text], and any “reasonable” pointclass [Formula: see text], that [Formula: see text]-determinacy implies [Formula: see text]-determinacy. We also prove a corresponding result when [Formula: see text] is a subshift of finite type of the shift map on [Formula: see text]. 

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