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1. Lattice Hamiltonian for adjoint QCD2

   https://doi.org/10.1007/JHEP08(2024)009  

   Dempsey, Ross; Klebanov, Igor R; Pufu, Silviu S; Søgaard, Benjamin T (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We introduce a Hamiltonian lattice model for the (1 + 1)-dimensional SU(N_c) gauge theory coupled to one adjoint Majorana fermion of massm. The discretization of the continuum theory uses staggered Majorana fermions. We analyze the symmetries of the lattice model and find lattice analogs of the anomalies of the corresponding continuum theory. An important role is played by the lattice translation by one lattice site, which in the continuum limit involves a discrete axial transformation. On a lattice with periodic boundary conditions, the Hilbert space breaks up into sectors labeled by theN_c-alityp= 0, …N_c− 1. Our symmetry analysis implies various exact degeneracies in the spectrum of the lattice model. In particular, it shows that, form= 0 and evenN_c, the sectorspandp′ are degenerate if |p−p′| =N_c/2. In theN_c= 2 case, we explicitly construct the action of the Hamiltonian on a basis of gauge-invariant states, and we perform both a strong coupling expansion and exact diagonalization for lattices of up to 12 lattice sites. Upon extrapolation of these results, we find good agreement with the spectrum computed previously using discretized light-cone quantization. One of our new results is the first numerical calculation of the fermion bilinear condensate. 

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2. Neotypification for five names linked to Arenaria (Caryophyllaceae) for the endemic flora of Peru and Bolivia

   https://doi.org/10.3897/phytokeys.230.107263  

   Montesinos-Tubée, Daniel B; Iamonico, Duilio (August 2023, PhytoKeys)

   The namesArenaria mattfeldii,A. pallens,A. peruviana,A. pintaudii, andA. stuebelii(Caryophyllaceae, Arenarieae) from Peru and Bolivia were studied and neotypified based on specimens preserved at B and P. 

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3. Universal Algorithms for Clustering Problems

   https://doi.org/10.1145/3572840  

   Ganesh, Arun; Maggs, Bruce M; Panigrahi, Debmalya (April 2023, ACM Transactions on Algorithms)

   This article presentsuniversalalgorithms for clustering problems, including the widely studiedk-median,k-means, andk-center objectives. The input is a metric space containing allpotentialclient locations. The algorithm must selectkcluster centers such that they are a good solution foranysubset of clients that actually realize. Specifically, we aim for lowregret, defined as the maximum over all subsets of the difference between the cost of the algorithm’s solution and that of an optimal solution. A universal algorithm’s solutionSolfor a clustering problem is said to be an α , β-approximation if for all subsets of clientsC^′, it satisfiessol(C^′) ≤ α ċopt(C′) + β ċmr, whereopt(C′ is the cost of the optimal solution for clients (C′) andmris the minimum regret achievable by any solution. Our main results are universal algorithms for the standard clustering objectives ofk-median,k-means, andk-center that achieve (O(1),O(1))-approximations. These results are obtained via a novel framework for universal algorithms using linear programming (LP) relaxations. These results generalize to other ℓ_p-objectives and the setting where some subset of the clients arefixed. We also give hardness results showing that (α, β)-approximation is NP-hard if α or β is at most a certain constant, even for the widely studied special case of Euclidean metric spaces. This shows that in some sense, (O(1),O(1))-approximation is the strongest type of guarantee obtainable for universal clustering. 

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4. Black hole masses for 14 gravitationally lensed quasars

   https://doi.org/10.1051/0004-6361/202347078  

   Melo, A; Motta, V; Mejía-Restrepo, J; Assef, R J; Godoy, N; Mediavilla, E; Falco, E; Kochanek, C S; Ávila-Vera, F; Jerez, R (December 2023, Astronomy & Astrophysics)

   Aims.We have estimated black hole masses (M_BH) for 14 gravitationally lensed quasars using Balmer lines; we also provide estimates based on MgII and CIV emission lines for four and two of them, respectively. We compared these estimates to results obtained for other lensed quasars. Methods.We used spectroscopic data from the Large Binocular Telescope (LBT),Magellan, and the Very Large Telescope (VLT) to measure the full width at half maximum of the broad emission lines. Combined with the bolometric luminosity measured from the spectral energy distribution, we estimatedM_BHvalues and provide the uncertainties, including uncertainties from microlensing and variability. Results.We obtainedM_BHvalues using the single-epoch method from the Hαand/or Hβbroad emission lines for 14 lensed quasars, including the first-ever estimates for QJ0158−4325, HE0512−3329, and WFI2026−4536. The masses are typical of non-lensed quasars of similar luminosities, as are the implied Eddington ratios. We have thus increased the sample of lenses withM_BHestimates by 60%. 

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5. Proximity Gaps for Reed–Solomon Codes

   https://doi.org/10.1145/3614423  

   Ben-Sasson, Eli; Carmon, Dan; Ishai, Yuval; Kopparty, Swastik; Saraf, Shubhangi (August 2023, Journal of the ACM)

   A collection of sets displays aproximity gapwith respect to some property if for every set in the collection, either (i) all members areδ-close to the property in relative Hamming distance or (ii) only a tiny fraction of members areδ-close to the property. In particular, no set in the collection has roughly half of its membersδ-close to the property and the othersδ-far from it. We show that the collection of affine spaces displays a proximity gap with respect to Reed–Solomon (RS) codes, even over small fields, of size polynomial in the dimension of the code, and the gap applies to anyδsmaller than the Johnson/Guruswami–Sudan list-decoding bound of the RS code. We also show near-optimal gap results, over fields of (at least)linearsize in the RS code dimension, forδsmaller than the unique decoding radius. Concretely, ifδis smaller than half the minimal distance of an RS code\(V\subset {\mathbb {F}}_q^n \), every affine space is either entirelyδ-close to the code, or alternatively at most an (n/q)-fraction of it isδ-close to the code. Finally, we discuss several applications of our proximity gap results to distributed storage, multi-party cryptographic protocols, and concretely efficient proof systems. We prove the proximity gap results by analyzing the execution of classical algebraic decoding algorithms for Reed–Solomon codes (due to Berlekamp–Welch and Guruswami–Sudan) on aformal elementof an affine space. This involves working with Reed–Solomon codes whose base field is an (infinite) rational function field. Our proofs are obtained by developing an extension (to function fields) of a strategy of Arora and Sudan for analyzing low-degree tests. 

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