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1. Celestial operator products of gluons and gravitons

   https://doi.org/10.1142/9789811210679_0020  

   Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew; Ye Yuan, Ellis (October 2019, ArXivorg)

   null (Ed.)

   The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents. 

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2. Improved Lower Bounds for 3-Query Matching Vector Codes

   https://doi.org/10.4230/LIPIcs.ITCS.2025.2  

   Aggarwal, Divesh; Dutta, Pranjal; Li, Zeyong; Obremski, Maciej; Saraogi, Sidhant (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Meka, Raghu (Ed.)

   A Matching Vector (MV) family modulo a positive integer m ≥ 2 is a pair of ordered lists U = (u_1, ⋯, u_K) and V = (v_1, ⋯, v_K) where u_i, v_j ∈ ℤ_m^n with the following property: for any i ∈ [K], the inner product ⟨u_i, v_i⟩ = 0 mod m, and for any i ≠ j, ⟨u_i, v_j⟩ ≠ 0 mod m. An MV family is called r-restricted if inner products ⟨u_i, v_j⟩, for all i,j, take at most r different values. The r-restricted MV families are extremely important since the only known construction of constant-query subexponential locally decodable codes (LDCs) are based on them. Such LDCs constructed via matching vector families are called matching vector codes. Let MV(m,n) (respectively MV(m, n, r)) denote the largest K such that there exists an MV family (respectively r-restricted MV family) of size K in ℤ_m^n. Such a MV family can be transformed in a black-box manner to a good r-query locally decodable code taking messages of length K to codewords of length N = m^n. For small prime m, an almost tight bound MV(m,n) ≤ O(m^{n/2}) was first shown by Dvir, Gopalan, Yekhanin (FOCS'10, SICOMP'11), while for general m, the same paper established an upper bound of O(m^{n-1+o_m(1)}), with o_m(1) denoting a function that goes to zero when m grows. For any arbitrary constant r ≥ 3 and composite m, the best upper bound till date on MV(m,n,r) is O(m^{n/2}), is due to Bhowmick, Dvir and Lovett (STOC'13, SICOMP'14).In a breakthrough work, Alrabiah, Guruswami, Kothari and Manohar (STOC'23) implicitly improve this bound for 3-restricted families to MV(m, n, 3) ≤ O(m^{n/3}). In this work, we present an upper bound for r = 3 where MV(m,n,3) ≤ m^{n/6 +O(log n)}, and as a result, any 3-query matching vector code must have codeword length of N ≥ K^{6-o(1)}. 

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3. AdS bulk locality from sharp CFT bounds

   https://doi.org/10.1007/JHEP11(2021)164  

   Caron-Huot, Simon; Mazáč, Dalimil; Rastelli, Leonardo; Simmons-Duffin, David (November 2021, Journal of High Energy Physics)

   A bstract It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆ gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆ gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆ gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS 4 naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT. 

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4. Some binomial formulas for non-commuting operators

   https://doi.org/10.1090/conm/733/14743  

   Kuchment, Peter; Lvin, Sergey (January 2019, Contemporary mathematics - American Mathematical Society)

   Let D and U be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomialtype identities for D and U assuming that either their commutator [D,U] or the second commutator [D, [D,U]] is proportional to U. Operators D = d/dx (differentiation) and U- multiplication by eλx or by sin λx are basic examples, for which some of these relations appeared unexpectedly as byproducts of an authors’ medical imaging research [2–5]. 

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5. PLAQUE: Automated Predicate Learning at Query Time

   https://doi.org/10.1145/3639301  

   Lin, Yiming; Mehrotra, Sharad (March 2024, Proceedings of the ACM on Management of Data)

   Predicate pushing down is a key optimization used to speed up query processing. Much of the existing practice is restricted to pushing predicates explicitly listed in the query. In this paper, we consider the challenge of learning predicates during query execution which are then exploited to accelerate execution. Prior related approaches with a similar goal are restricted (e.g., learn only from only join columns or from specific data statistics). We significantly expand the realm of predicates that can be learned from different query operators (aggregations, joins, grouping, etc.) and develop a system, entitled PLAQUE, that learns such predicates during query execution. Comprehensive evaluations on both synthetic and real datasets demonstrate that the learned predicate approach adopted by PLAQUE can significantly accelerate query execution by up to 33x, and this improvement increases to up to 100x when User-Defined Functions (UDFs) are utilized in queries. 

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