The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

Measurement of the cross section of high transverse momentum Z→bb̄ production in proton–proton collisions at √s = 8 TeV with the ATLAS detector

This Letter reports the observation of a high transverse momentum Z→bb̄ signal in proton–proton collisions at √s=8 TeV and the measurement of its production cross section. The data analysed were collected in 2012 with the ATLAS detector at the LHC and correspond to an integrated luminosity of 19.5 fb−¹. The Z→bb̄ decay is reconstructed from a pair of b -tagged jets, clustered with the anti-ktkt jet algorithm with R=0.4R=0.4, that have low angular separation and form a dijet with pT>200 GeVpT>200 GeV. The signal yield is extracted from a fit to the dijet invariant mass distribution, with the dominant, multi-jet background mass shape estimated by employing a fully data-driven technique that reduces the dependence of the analysis on simulation. The fiducial cross section is determined to be σZ→bb¯fid=2.02±0.20 (stat.) ±0.25 (syst.)±0.06 (lumi.) pb=2.02±0.33 pb, in good agreement with next-to-leading-order theoretical predictions

Dairy foods, calcium, and risk of breast cancer overall and for subtypes defined by estrogen receptor status: a pooled analysis of 21 cohort studies

Background: Epidemiologic studies examining the relations between dairy product and calcium intakes and breast cancer have been inconclusive, especially for tumor subtypes. Objective: To evaluate the associations between intakes of specific dairy products and calcium and risk of breast cancer overall and for subtypes defined by estrogen receptor (ER) status. Method: We pooled the individual-level data of over 1 million women who were followed for a maximum of 8-20 years across studies. Associations were evaluated for dairy product and calcium intakes and risk of incident invasive breast cancer overall (n = 37,861 cases) and by subtypes defined by ER status. Study-specific multivariable hazard ratios (HRs) were estimated and then combined using random-effects models. Results: Overall, no clear association was observed between the consumption of specific dairy foods, dietary (from foods only) calcium, and total (from foods and supplements) calcium, and risk of overall breast cancer. Although each dairy product showed a null or very weak inverse association with risk of overall breast cancer (P, test for trend >0.05 for all), differences by ER status were suggested for yogurt and cottage/ricotta cheese with associations observed for ER-negative tumors only (pooled HR = 0.90, 95% CI: 0.83, 0.98 comparing >= 60 g/d with = 25 g/d with Conclusion: Our study shows that adult dairy or calcium consumption is unlikely to associate with a higher risk of breast cancer and that higher yogurt and cottage/ricotta cheese intakes were inversely associated with the risk of ER-negative breast cancer, a less hormonally dependent subtype with poor prognosis. Future studies on fermented dairy products, earlier life exposures, ER-negative breast cancer, and different racial/ethnic populations may further elucidate the relation

The Atacama Cosmology Telescope: A Catalog of >4000 Sunyaev–Zel’dovich Galaxy Clusters

We present a catalog of 4195 optically confirmed Sunyaev–Zel'dovich (SZ) selected galaxy clusters detected with signal-to-noise ratio >4 in 13,211 deg2 of sky surveyed by the Atacama Cosmology Telescope (ACT). Cluster candidates were selected by applying a multifrequency matched filter to 98 and 150 GHz maps constructed from ACT observations obtained from 2008 to 2018 and confirmed using deep, wide-area optical surveys. The clusters span the redshift range 0.04 1 clusters, and a total of 868 systems are new discoveries. Assuming an SZ signal versus mass-scaling relation calibrated from X-ray observations, the sample has a 90% completeness mass limit of M500c > 3.8 × 1014 M⊙, evaluated at z = 0.5, for clusters detected at signal-to-noise ratio >5 in maps filtered at an angular scale of 2farcm4. The survey has a large overlap with deep optical weak-lensing surveys that are being used to calibrate the SZ signal mass-scaling relation, such as the Dark Energy Survey (4566 deg2), the Hyper Suprime-Cam Subaru Strategic Program (469 deg2), and the Kilo Degree Survey (825 deg2). We highlight some noteworthy objects in the sample, including potentially projected systems, clusters with strong lensing features, clusters with active central galaxies or star formation, and systems of multiple clusters that may be physically associated. The cluster catalog will be a useful resource for future cosmological analyses and studying the evolution of the intracluster medium and galaxies in massive clusters over the past 10 Gyr

Measurement of the CKM angle γ in the B0→DK *0 channel using self-conjugate D→ KS0h+ h- decays

A model-independent study of CP violation in B-0 -> DK (*0) decays is presented using data corresponding to an integrated luminosity of 9 fb(-1) collected by the LHCb experiment at centre-of-mass energies of v s = 7, 8 and 13TeV. The CKM angle. is determined by examining the distributions of signal decays in phase-space bins of the self-conjugate D. K(S)(0)h(+) h(-) decays, where h = p, K. Observables related to CP violation are measured and the angle. is determined to be. = (49+22 -19).. Measurements of the amplitude ratio and strong-phase difference between the favoured and suppressed B-0 decays are also presented

Dual-baseline search for active-to-sterile neutrino oscillations in NOvA

We report a search for neutrino oscillations to sterile neutrinos under a model with three active and one sterile neutrinos (3 þ 1 model). This analysis uses the NOvA detectors exposed to the NuMI beam, running in neutrino mode. The data exposure, 13.6 × 1020 protons on target, doubles that previously analyzed by NOvA, and the analysis is the first to use νμ charged-current interactions in conjunction with neutralcurrent interactions. Neutrino samples in the near and far detectors are fitted simultaneously, enabling the search to be carried out over a Δm2 41 range extending 2 (3) orders of magnitude above (below) 1 eV2. NOvA finds no evidence for active-to-sterile neutrino oscillations under the 3 þ 1 model at 90% confidence level. New limits are reported in multiple regions of parameter space, excluding some regions currently allowed by IceCube at 90% confidence level. We additionally set the most stringent limits for anomalous ντ appearance for Δm2 41 ≤ 3 eV2

Characterising acute and chronic care needs: insights from the Global Burden of Disease Study 2019

Chronic care manages long-term, progressive conditions, while acute care addresses short-term conditions. Chronic conditions increasingly strain health systems, which are often unprepared for these demands. This study examines the burden of conditions requiring acute versus chronic care, including sequelae. Conditions and sequelae from the Global Burden of Diseases Study 2019 were classified into acute or chronic care categories. Data were analysed by age, sex, and socio-demographic index, presenting total numbers and contributions to burden metrics such as Disability-Adjusted Life Years (DALYs), Years Lived with Disability (YLD), and Years of Life Lost (YLL). Approximately 68% of DALYs were attributed to chronic care, while 27% were due to acute care. Chronic care needs increased with age, representing 86% of YLDs and 71% of YLLs, and accounting for 93% of YLDs from sequelae. These findings highlight that chronic care needs far exceed acute care needs globally, necessitating health systems to adapt accordingly