Hypergraph cuts above the average

An r-cut of a k-uniform hypergraph H is a partition of the vertex set of H into r parts and the size of the cut is the number of edges which have a vertex in each part. A classical result of Edwards says that every m-edge graph has a 2-cut of size m/2 + Ω(√m), and this is best possible. That is, there exist cuts which exceed the expected size of a random cut by some multiple of the standard deviation. We study analogues of this and related results in hypergraphs. First, we observe that similarly to graphs, every m-edge k-uniform hypergraph has an r-cut whose size is Ω(√m) larger than the expected size of a random r-cut. Moreover, in the case where k = 3 and r = 2 this bound is best possible and is attained by Steiner triple systems. Surprisingly, for all other cases (that is, if k ≥ 4 or r ≥ 3), we show that every m-edge k-uniform hypergraph has an r-cut whose size is Ω(m^(5/9)) larger than the expected size of a random r-cut. This is a significant difference in behaviour, since the amount by which the size of the largest cut exceeds the expected size of a random cut is now considerably larger than the standard deviation

Hypergraph cuts above the average

An r-cut of a k-uniform hypergraph H is a partition of the vertex set of H into r parts and the size of the cut is the number of edges which have a vertex in each part. A classical result of Edwards says that every m-edge graph has a 2-cut of size m/2 + Ω(√m), and this is best possible. That is, there exist cuts which exceed the expected size of a random cut by some multiple of the standard deviation. We study analogues of this and related results in hypergraphs. First, we observe that similarly to graphs, every m-edge k-uniform hypergraph has an r-cut whose size is Ω(√m) larger than the expected size of a random r-cut. Moreover, in the case where k = 3 and r = 2 this bound is best possible and is attained by Steiner triple systems. Surprisingly, for all other cases (that is, if k ≥ 4 or r ≥ 3), we show that every m-edge k-uniform hypergraph has an r-cut whose size is Ω(m^(5/9)) larger than the expected size of a random r-cut. This is a significant difference in behaviour, since the amount by which the size of the largest cut exceeds the expected size of a random cut is now considerably larger than the standard deviation

D-branes at Toric Singularities: Model Building, Yukawa Couplings and Flavour Physics

We discuss general properties of D-brane model building at toric singularities. Using dimer techniques to obtain the gauge theory from the structure of the singularity, we extract results on the matter sector and superpotential of the corresponding gauge theory. We show that the number of families in toric phases is always less than or equal to three, with a unique exception being the zeroth Hirzebruch surface. With the physical input of three generations we find that the lightest family of quarks is massless and the masses of the other two can be hierarchically separated. We compute the CKM matrix for explicit models in this setting and find the singularities possess sufficient structure to allow for realistic mixing between generations and CP violation.Comment: 55 pages, v2: typos corrected, minor comments adde

Combined Effects of Botulinum Toxin Injection and Hind Limb Unloading on Bone and Muscle

Bone receives mechanical stimulation from two primary sources, muscle contractions and external gravitational loading; but the relative contribution of each source to skeletal health is not fully understood. Understanding the most effective loading for maintaining bone health has important clinical implications for prescribing physical activity for the treatment or prevention of osteoporosis. Therefore, we investigated the relative effects of muscle paralysis and reduced gravitational loading on changes in muscle mass, bone mineral density, and microarchitecture. Adult female C57Bl/6J mice (n = 10/group) underwent one of the following: unilateral botulinum toxin (BTX) injection of the hind limb, hind limb unloading (HLU), both unilateral BTX injection and HLU, or no intervention. BTX and HLU each led to significant muscle and bone loss. The effect of BTX was diminished when combined with HLU, though generally the leg that received the combined intervention (HLU+BTX) had the most detrimental changes in bone and muscle. We found an indirect effect of BTX affecting the uninjected (contralateral) leg that led to significant decreases in bone mineral density and deficits in muscle mass and bone architecture relative to the untreated controls; the magnitude of this indirect BTX effect was comparable to the direct effect of BTX treatment and HLU. Thus, while it was difficult to definitively conclude whether muscle force or external gravitational loading contributes more to bone maintenance, it appears that BTX-induced muscle paralysis is more detrimental to muscle and bone than HLU.National Institutes of Health (U.S.) (H R21 AR057522)United States. National Aeronautics and Space Administration (NNX10AE39G)National Space Biomedical Research Institute (NASA NCC 9-58)United States. National Aeronautics and Space Administration (NASA-Jenkins predoctoral fellowship)Northrop Grumman Corporation (Aerospace Systems PhD Training Fellowship

Towards a Systematic Construction of Realistic D-brane Models on a del Pezzo Singularity

A systematic approach is followed in order to identify realistic D-brane models at toric del Pezzo singularities. Requiring quark and lepton spectrum and Yukawas from D3 branes and massless hypercharge, we are led to Pati-Salam extensions of the Standard Model. Hierarchies of masses, flavour mixings and control of couplings select higher order del Pezzo singularities, minimising the Higgs sector prefers toric del Pezzos with dP3 providing the most successful compromise. Then a supersymmetric local string model is presented with the following properties at low energies: (i) the MSSM spectrum plus a local B-L gauge field or additional Higgs fields depending on the breaking pattern, (ii) a realistic hierarchy of quark and lepton masses and (iii) realistic flavour mixing between quark and lepton families with computable CKM and PMNS matrices, and CP violation consistent with observations. In this construction, kinetic terms are diagonal and under calculational control suppressing standard FCNC contributions. Proton decay operators of dimension 4, 5, 6 are suppressed, and gauge couplings can unify depending on the breaking scales from string scales at energies in the range 10^{12}-10^{16} GeV, consistent with TeV soft-masses from moduli mediated supersymmetry breaking. The GUT scale model corresponds to D3 branes at dP3 with two copies of the Pati-Salam gauge symmetry SU(4)\timesSU(2)R\timesSU(2)L. D-brane instantons generate a non-vanishing mu-term. Right handed sneutrinos can break the B-L symmetry and induce a see-saw mechanism of neutrino masses and R-parity violating operators with observable low-energy implications.Comment: 27 pages plus 5 appendices (42 pages total), 9 figures. v3: equation refs and citation correcte

Inborn Errors of Immunity on the Island of Ireland - a Cross-Jurisdictional UKPID/ESID Registry Report

The epidemiology of inborn errors of immunity (IEI) in the Republic of Ireland was first published in 2005 but has not been updated since. IEI prevalence data from Northern Ireland was last published in 2018. Using data from the United Kingdom Primary Immune Deficiency (UKPID) and European Society for Immunodeficiencies (ESID) registries, we reviewed all registered cases of IEI affecting adult patients ≥ 18 years of age from the two largest immunology specialist centres in Northern Ireland and the Republic of Ireland, respectively and calculated the combined minimum adult prevalence of IEI on the island of Ireland for the first time. We also recorded data pertaining to presenting symptoms of IEI, diagnostic delay, immunoglobulin data, and genetic testing, as well as briefly reporting data pertaining to secondary immunodeficiency in both countries. As of 1 May 2020, we identified a minimum adult IEI prevalence in Ireland of 8.85/100,000 population

Inborn Errors of Immunity on the Island of Ireland - a Cross-Jurisdictional UKPID/ESID Registry Report

Correction; Early Access:The epidemiology of inborn errors of immunity (IEI) in the Republic of Ireland was first published in 2005 but has not been updated since. IEI prevalence data from Northern Ireland was last published in 2018. Using data from the United Kingdom Primary Immune Deficiency (UKPID) and European Society for Immunodeficiencies (ESID) registries, we reviewed all registered cases of IEI affecting adult patients >= 18 years of age from the two largest immunology specialist centres in Northern Ireland and the Republic of Ireland, respectively and calculated the combined minimum adult prevalence of IEI on the island of Ireland for the first time. We also recorded data pertaining to presenting symptoms of IEI, diagnostic delay, immunoglobulin data, and genetic testing, as well as briefly reporting data pertaining to secondary immunodeficiency in both countries. As of 1 May 2020, we identified a minimum adult IEI prevalence in Ireland of 8.85/100,000 population.Peer reviewe

MicroRNA profiling of the bovine alveolar macrophage response to Mycobacterium bovis infection suggests pathogen survival is enhanced by microRNA regulation of endocytosis and lysosome trafficking

peer-reviewedMycobacterium bovis, the causative agent of bovine tuberculosis, a major problem for global agriculture, spreads via an airborne route and is taken up by alveolar macrophages (AM) in the lung. Here, we describe the first next-generation sequencing (RNA-seq) approach to temporally profile miRNA expression in primary bovine AMs post-infection with M. bovis. One, six, and forty miRNAs were identified as significantly differentially expressed at 2, 24 and 48 h post-infection, respectively. The differential expression of three miRNAs (bta-miR-142-5p, bta-miR-146a, and bta-miR-423-3p) was confirmed by RT-qPCR. Pathway analysis of the predicted mRNA targets of differentially expressed miRNAs suggests that these miRNAs preferentially target several pathways that are functionally relevant for mycobacterial pathogenesis, including endocytosis and lysosome trafficking, IL-1 signalling and the TGF-β pathway. Over-expression studies using a bovine macrophage cell-line (Bomac) reveal the targeting of two key genes in the innate immune response to M. bovis, IL-1 receptor-associated kinase 1 (IRAK1) and TGF-β receptor 2 (TGFBR2), by miR-146. Taken together, our study suggests that miRNAs play a key role in tuning the complex interplay between M. bovis survival strategies and the host immune response

Searching for dark matter in X-rays: how to check the dark matter origin of a spectral feature

A signal from decaying dark matter (DM) can be unambiguously distinguished from spectral features of astrophysical or instrumental origin by studying its spatial distribution. We demonstrate this approach by examining the recent claim of 0912.0552 regarding the possible DM origin of the 2.5 keV line in Chandra observations of the Milky Way satellite known as Willman 1. Our conservative strategy is to adopt a relatively large dark mass for Willman 1 and relatively small dark masses for the comparison objects. We analyze archival observations by XMM-Newton of M31 and Fornax dwarf spheroidal galaxy (dSph) and Chandra observations of Sculptor dSph. By performing a conservative analysis of X-ray spectra, we show the absence of a DM decay line with parameters consistent with those of 0912.0552. For M31, the observations of the regions between 10 and 20 kpc from the center, where the uncertainties in the DM distribution are minimal, make a strong exclusion at the level above 10sigma. The minimal estimate for the amount of DM in the central 40 kpc of M31 is provided by the model of 0912.4133, assuming the stellar disk's mass to light ratio ~8 and almost constant DM density within a core of 28 kpc. Even in this case one gets an exclusion at 5.7sigma from central region of M31 whereas modeling all processed data from M31 and Fornax produces more than 14sigma exclusion. Therefore, despite possible systematic uncertainties, we exclude the possibility that the spectral feature at ~2.5 keV found in 0912.0552 is a DM decay line. We conclude, however, that the search for DM decay line, although demanding prolonged observations of well-studied dSphs, M31 outskirts and other similar objects, is rather promising, as the nature of a possible signal can be checked. An (expected) non-observation of a DM decay signal in the planned observations of Willman 1 should not discourage further dedicated observations.Comment: 16 pages, 8 figures; journal version; analysis of additional data from M31 outskirts and comments on arXiv:1001.4055 are adde

Risk Analysis Index and Its Recalibrated Version Predict Postoperative Outcomes Better Than 5-Factor Modified Frailty Index in Traumatic Spinal Injury

Objective To assess the discriminative ability of the Risk Analysis Index-administrative (RAI-A) and its recalibrated version (RAI-Rev), compared to the 5-factor modified frailty index (mFI-5), in predicting postoperative outcomes in patients undergoing surgical intervention for traumatic spine injuries (TSIs). Methods The Current Procedural Terminology (CPT) and International Classification of Disease-9 (ICD-9) and ICD-10 codes were used to identify patients ≥ 18 years who underwent surgical intervention for TSI from National Surgical Quality Improvement Program (ACS-NSQIP) database 2015–2019 (n = 6,571). Multivariate analysis and receiver operating characteristic (ROC) curve analysis were conducted to evaluate the comparative discriminative ability of RAI-Rev, RAI-A, and mFI-5 for 30-day postoperative outcomes. Results Multivariate regression analysis showed that with all 3 frailty scores, increasing frailty tiers resulted in worse postoperative outcomes, and patients identified as frail and severely frail using RAI-Rev and RAI-A had the highest odds of poor outcomes. In the ROC curve/C-statistics analysis for prediction of 30-day mortality and morbidity, both RAI-Rev and RAI-A outperformed mFI-5, and for many outcomes, RAI-Rev showed better discriminative performance compared to RAI-A, including mortality (p = 0.0043, DeLong test), extended length of stay (p = 0.0042), readmission (p < 0.0001), reoperation (p = 0.0175), and nonhome discharge (p < 0.0001). Conclusion Both RAI-Rev and RAI-A performed better than mFI-5, and RAI-Rev was superior to RAI-A in predicting postoperative mortality and morbidity in TSI patients. RAI-based frailty indices can be used in preoperative risk assessment of spinal trauma patients