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1. Matter waves and clocks do not observe uniform gravitational fields

   https://doi.org/10.1088/1402-4896/ad340c  

   Asenbaum, Peter; Overstreet, Chris; Kasevich, Mark A (March 2024, Physica Scripta)

   Abstract In a uniform gravitational field, classical test objects fall universally. Any reference object or observer will fall in the same universal manner. Therefore, a uniform gravitational field cannot create dynamics between observers and classical test objects. The influence of a uniform gravitational field on matter waves and clocks, however, is described inconsistently throughout research and education. To illustrate, we discuss the behavior of a matter-wave interferometer and a clock redshift experiment in a uniform gravitational field. As a consistent formulation of the equivalence principle implies, a uniform gravitational field has no observable influence on these systems and is physically equivalent to the absence of gravity. 

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2. COHOMOLOGICAL OBSTRUCTIONS TO GROUP STABILITYWITH RESPECT TO THE OPERATOR NORM

   https://doi.org/10.59277/RRMPA.2024.471.485  

   DADARLAT, MARIUS (January 2024, Revue Roumaine Mathematiques Pures Appliquees)

   In this article, we survey recent results concerning non-stability of discrete groupswith respect to the operator norm. We focus on topological obstructions toperturbing almost representations of a discrete group Γ into unitary groups U(n)to true representations. Several natural notions of stability are discussed: localto-local stability, uniform-to-uniform stability, uniform-to-local stability, and C∗-stability. 

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3. A Uniform Error Bound for Stochastic Kriging: Properties and Implications on Simulation Experimental Design

   https://doi.org/10.1145/3682059  

   Chen, Xi; Zhang, Yutong; Xie, Guangrui; Zhang, Jingtao (July 2024, ACM Transactions on Modeling and Computer Simulation)

   In this work, we propose a method to construct a uniform error bound for the SK predictor. In investigating the asymptotic properties of the proposed uniform error bound, we examine the convergence rate of SK’s predictive variance under the supremum norm in both fixed and random design settings. Our analyses reveal that the large-sample properties of SK prediction depend on the design-point sampling scheme and the budget allocation scheme adopted. Appropriately controlling the order of noise variances through budget allocation is crucial for achieving a desirable convergence rate of SK’s approximation error, as quantified by the uniform error bound, and for maintaining SK’s numerical stability. Moreover, we investigate the impact of noise variance estimation on the uniform error bound’s performance theoretically and numerically. We demonstrate the superiority of the proposed uniform bound to the Bonferroni correction-based simultaneous confidence interval under various experimental settings through numerical evaluations. 

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4. Off‐Diagonal Ramsey Numbers for Slowly Growing Hypergraphs

   https://doi.org/10.1002/rsa.21284  

   Mattheus, Sam; Mubayi, Dhruv; Nie, Jiaxi; Verstraëte, Jacques (January 2025, Random Structures & Algorithms)

   ABSTRACT For ak‐uniform hypergraph and a positive integer , the Ramsey number denotes the minimum such that every ‐vertex ‐free ‐uniform hypergraph contains an independent set of vertices. A hypergraph isslowly growingif there is an ordering of its edges such that for each . We prove that if is fixed and is any non‐k‐partite slowly growing ‐uniform hypergraph, then for ,In particular, we deduce that the off‐diagonal Ramsey number is of order , where is the triple system . This is the only 3‐uniform Berge triangle for which the polynomial power of its off‐diagonal Ramsey number was not previously known. Our constructions use pseudorandom graphs and hypergraph containers. 

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5. Maximum packings of the λ-fold complete 3-uniform hypergraph with loose 3-cycles

   https://doi.org/10.7494/OpMath.2020.40.2.209  

   Bunge, Ryan C.; Collins, Dontez; Conko-Camel, Daryl; El-Zanati, Saad I.; Liebrecht, Rachel; Vasquez, Alexander (January 2020, Opuscula Mathematica)

   It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order \(v\) if and only if \(v \equiv 0, 1,\text{ or }2 (\operatorname{mod} 9)\). For all positive integers \(\lambda\) and \(v\), we find a maximum packing with loose 3-cycles of the \(\lambda\)-fold complete 3-uniform hypergraph of order \(v\). We show that, if \(v \geq 6\), such a packing has a leave of two or fewer edges. 

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