Cycle decompositions in k-uniform hypergraphs

We show that k-uniform hypergraphs on n vertices whose codegree is at least (2/3+o(1))n can be decomposed into tight cycles, subject to the trivial divisibility conditions. As a corollary, we show those graphs contain tight Euler tours as well. In passing, we also investigate decompositions into tight paths.In addition, we also prove an alternative condition for building absorbers for edge-decompositions of arbitrary k-uniform hypergraphs, which should be of independent interest

Cycle decompositions in k-uniform hypergraphs

We show that k-uniform hypergraphs on n vertices whose codegree is at least (2/3+o(1))n can be decomposed into tight cycles, subject to the trivial divisibility conditions. As a corollary, we show those graphs contain tight Euler tours as well. In passing, we also investigate decompositions into tight paths.In addition, we also prove an alternative condition for building absorbers for edge-decompositions of arbitrary k-uniform hypergraphs, which should be of independent interest

A general bound for the induced poset saturation problem

For a fixed poset P, a family F of subsets of [n] is induced P-saturated if F does not contain an induced copy of P, but for every subset S of [n] such that S ∉ F, then P is an induced subposet of F ∪ {S}. The size of the smallest such family F is denoted by sat* (n, P). Keszegh, Lemons, Martin, Pálvölgyi and Patkós [Journal of Combinatorial Theory Series A, 2021] proved that there is a dichotomy of behaviour for this parameter: given any poset P, either sat* (n, P) = O(1) or sat* (n, P) ≥  log2n. We improve this general result showing that either sat* (n, P) = O(1) or sat* (n, P) ≥ 2√n-2. Our proof makes use of a Turán-type result for digraphs. Curiously, it remains open as to whether our result is essentially best possible or not. On the one hand, a conjecture of Ivan states that for the so-called diamond poset ◊ we have sat* (n, ◊) = Θ(√n); so if true this conjecture implies our result is tight up to a multiplicative constant. On the other hand, a conjecture of Keszegh, Lemons, Martin, Pálvölgyi and Patkós states that given any poset P, either sat* (n, P)= O(1) or sat* (n, P) ≥ n + 1. We prove that this latter conjecture is true for a certain class of posets P. <br/

Cold atoms meet lattice gauge theory

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more ‘accessible’ and easier to manipulate for experimentalists, but this ‘substitution’ also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or Z2 Bose–Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz–Hubbard ladder, or Gross–Neveu–Wilson and Wilson–Hubbard models. This article is not a general review of the rapidly growing field—it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue ‘Quantum technologies in particle physics’

The arthritis-associated HLA-B*27:05 allele forms more cell surface B27 dimer and free heavy chain ligands for KIR3DL2 than HLA-B*27:09

Objectives. HLA-B*27:05 is associated with AS whereas HLA-B*27:09 is not associated. We hypothesized that different interactions with KIR immune receptors could contribute to the difference in disease association between HLA-B*27:05 and HLAB*27:09. Thus, the objective of this study was to compare the formation of β2m-free heavy chain (FHC) including B27 dimers (B272) by HLA-B*27:05 and HLA-B*27:09 and their binding to KIR immunoreceptors. Methods. We studied the formation of HLA-B*27:05 and HLA-B*27:09 heterotrimers and FHC forms including dimers in vitro and in transfected cells. We investigated HLA-B*27:05 and HLA-B*27:09 binding to KIR3DL1, KIR3DL2 and LILRB2 by FACS staining with class I tetramers and by quantifying interactions with KIR3DL2CD3ε-reporter cells and KIR3DL2-expressing NK cells. We also measured KIR expression on peripheral blood NK and CD4 T cells from 18 HLA-B*27:05 AS patients, 8 HLA-B27 negative and 12 HLA-B*27:05+ and HLA-B*27:09+ healthy controls by FACS staining. Results. HLA-B*27:09 formed less B272 and FHC than HLA-B*27:05. HLA-B*27:05-expressing cells stimulated KIR3DL2CD3ε-reporter T cells more effectively. Cells expressing HLA-B*27:05 promoted KIR3DL2+ NK cell survival more strongly than HLA-B*27:09. HLA-B*27:05 and HLA-B*27:09 dimer tetramers stained KIR3DL1, KIR3DL2 and LILRB2 equivalently. Increased proportions of NK and CD4 T cells expressed KIR3DL2 in HLA-B*27:05+ AS patients compared with HLA-B*27:05+, HLA-B*27:09+ and HLA-B27− healthy controls. Conclusion. Differences in the formation of FHC ligands for KIR3DL2 by HLA-B*27:05 and HLA-B*27:09 could contribute to the differential association of these alleles with A