A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications, published as 'Online first', January 201

Spatial, temporal, and demographic patterns in prevalence of smoking tobacco use and attributable disease burden in 204 countries and territories, 1990-2019 : a systematic analysis from the Global Burden of Disease Study 2019

Background: Ending the global tobacco epidemic is a defining challenge in global health. Timely and comprehensive estimates of the prevalence of smoking tobacco use and attributable disease burden are needed to guide tobacco control efforts nationally and globally. Methods: We estimated the prevalence of smoking tobacco use and attributable disease burden for 204 countries and territories, by age and sex, from 1990 to 2019 as part of the Global Burden of Diseases, Injuries, and Risk Factors Study. We modelled multiple smoking-related indicators from 3625 nationally representative surveys. We completed systematic reviews and did Bayesian meta-regressions for 36 causally linked health outcomes to estimate non-linear dose-response risk curves for current and former smokers. We used a direct estimation approach to estimate attributable burden, providing more comprehensive estimates of the health effects of smoking than previously available. Findings: Globally in 2019, 1.14 billion (95% uncertainty interval 1.13-1.16) individuals were current smokers, who consumed 7.41 trillion (7.11-7.74) cigarette-equivalents of tobacco in 2019. Although prevalence of smoking had decreased significantly since 1990 among both males (27.5% [26. 5-28.5] reduction) and females (37.7% [35.4-39.9] reduction) aged 15 years and older, population growth has led to a significant increase in the total number of smokers from 0.99 billion (0.98-1.00) in 1990. Globally in 2019, smoking tobacco use accounted for 7.69 million (7.16-8.20) deaths and 200 million (185-214) disability-adjusted life-years, and was the leading risk factor for death among males (20.2% [19.3-21.1] of male deaths). 6.68 million [86.9%] of 7.69 million deaths attributable to smoking tobacco use were among current smokers. Interpretation: In the absence of intervention, the annual toll of 7.69 million deaths and 200 million disability-adjusted life-years attributable to smoking will increase over the coming decades. Substantial progress in reducing the prevalence of smoking tobacco use has been observed in countries from all regions and at all stages of development, but a large implementation gap remains for tobacco control. Countries have a dear and urgent opportunity to pass strong, evidence-based policies to accelerate reductions in the prevalence of smoking and reap massive health benefits for their citizens

Longitudinal retinal changes in MOGAD

OBJECTIVE: Patients with myelin oligodendrocyte glycoprotein antibody (MOG-IgG) associated disease (MOGAD) suffer from severe optic neuritis (ON) leading to retinal neuro-axonal loss, which can be quantified by optical coherence tomography (OCT). We assessed whether ON-independent retinal atrophy can be detected in MOGAD. METHODS: Eighty MOGAD patients and 139 healthy controls (HC) were included. OCT data was acquired with 1) Spectralis spectral domain OCT (MOGAD (N=66) and HC (N=103)) and 2) Cirrus HD-OCT (MOGAD (N=14) and HC (N=36)). Macular combined ganglion cell and inner plexiform layer (GCIPL) and peripapillary retinal nerve fibre layer (pRNFL) were quantified. RESULTS: At baseline, GCIPL and pRNFL were lower in MOGAD eyes with a history of ON (MOGAD-ON) compared with MOGAD eyes without a history of ON (MOGAD-NON) and HC (p12 months ago (p<0.001). The overall MOGAD cohort did not exhibit faster GCIPL thinning compared with HC. INTERPRETATION: Our study suggests the absence of attack-independent retinal damage in MOGAD. Yet, ongoing neuroaxonal damage or oedema resolution seems to occur for up to 12 months after ON, which is longer than what has been reported with other ON forms. These findings support that the pathomechanisms underlying optic nerve involvement and the evolution of OCT retinal changes after ON is distinct in MOGAD. This article is protected by copyright. All rights reserved

The OSCAR-MP consensus criteria for quality assessment of retinal optical coherence tomography angiography

BACKGROUND AND OBJECTIVES: Optical coherence tomography angiography (OCTA) is a noninvasive high-resolution imaging technique for assessing the retinal vasculature and is increasingly used in various ophthalmologic, neuro-ophthalmologic, and neurologic diseases. To date, there are no validated consensus criteria for quality control (QC) of OCTA. Our study aimed to develop criteria for OCTA quality assessment. METHODS: To establish criteria through (1) extensive literature review on OCTA artifacts and image quality to generate standardized and easy-to-apply OCTA QC criteria, (2) application of OCTA QC criteria to evaluate interrater agreement, (3) identification of reasons for interrater disagreement, revision of OCTA QC criteria, development of OCTA QC scoring guide and training set, and (4) validation of QC criteria in an international, interdisciplinary multicenter study. RESULTS: We identified 7 major aspects that affect OCTA quality: (O) obvious problems, (S) signal strength, (C) centration, (A) algorithm failure, (R) retinal pathology, (M) motion artifacts, and (P) projection artifacts. Seven independent raters applied the OSCAR-MP criteria to a set of 40 OCTA scans from people with MS, Sjogren syndrome, and uveitis and healthy individuals. The interrater kappa was substantial (? 0.67). Projection artifacts were the main reason for interrater disagreement. Because artifacts can affect only parts of OCTA images, we agreed that prior definition of a specific region of interest (ROI) is crucial for subsequent OCTA quality assessment. To enhance artifact recognition and interrater agreement on reduced image quality, we designed a scoring guide and OCTA training set. Using these educational tools, 23 raters from 14 different centers reached an almost perfect agreement (? 0.92) for the rejection of poor-quality OCTA images using the OSCAR-MP criteria. DISCUSSION: We propose a 3-step approach for standardized quality control: (1) To define a specific ROI, (2) to assess the occurrence of OCTA artifacts according to the OSCAR-MP criteria, and (3) to evaluate OCTA quality based on the occurrence of different artifacts within the ROI. OSCAR-MP OCTA QC criteria achieved high interrater agreement in an international multicenter study and is a promising QC protocol for application in the context of future clinical trials and studies

Spatial, temporal, and demographic patterns in prevalence of smoking tobacco use and attributable disease burden in 204 countries and territories, 1990-2019 : a systematic analysis from the Global Burden of Disease Study 2019

Background Ending the global tobacco epidemic is a defining challenge in global health. Timely and comprehensive estimates of the prevalence of smoking tobacco use and attributable disease burden are needed to guide tobacco control efforts nationally and globally. Methods We estimated the prevalence of smoking tobacco use and attributable disease burden for 204 countries and territories, by age and sex, from 1990 to 2019 as part of the Global Burden of Diseases, Injuries, and Risk Factors Study. We modelled multiple smoking-related indicators from 3625 nationally representative surveys. We completed systematic reviews and did Bayesian meta-regressions for 36 causally linked health outcomes to estimate non-linear dose-response risk curves for current and former smokers. We used a direct estimation approach to estimate attributable burden, providing more comprehensive estimates of the health effects of smoking than previously available. Findings Globally in 2019, 1.14 billion (95% uncertainty interval 1.13-1.16) individuals were current smokers, who consumed 7.41 trillion (7.11-7.74) cigarette-equivalents of tobacco in 2019. Although prevalence of smoking had decreased significantly since 1990 among both males (27.5% [26. 5-28.5] reduction) and females (37.7% [35.4-39.9] reduction) aged 15 years and older, population growth has led to a significant increase in the total number of smokers from 0.99 billion (0.98-1.00) in 1990. Globally in 2019, smoking tobacco use accounted for 7.69 million (7.16-8.20) deaths and 200 million (185-214) disability-adjusted life-years, and was the leading risk factor for death among males (20.2% [19.3-21.1] of male deaths). 6.68 million [86.9%] of 7.69 million deaths attributable to smoking tobacco use were among current smokers. Interpretation In the absence of intervention, the annual toll of 7.69 million deaths and 200 million disability-adjusted life-years attributable to smoking will increase over the coming decades. Substantial progress in reducing the prevalence of smoking tobacco use has been observed in countries from all regions and at all stages of development, but a large implementation gap remains for tobacco control. Countries have a dear and urgent opportunity to pass strong, evidence-based policies to accelerate reductions in the prevalence of smoking and reap massive health benefits for their citizens. Copyright (C) 2021 The Author(s). Published by Elsevier Ltd.Peer reviewe

Measurement of the azimuthal anisotropy of Y(1S) and Y(2S) mesons in PbPb collisions at √S^{S}NN = 5.02 TeV

The second-order Fourier coefficients (υ$_{2}$) characterizing the azimuthal distributions of Υ(1S) and Υ(2S) mesons produced in PbPb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV are studied. The Υmesons are reconstructed in their dimuon decay channel, as measured by the CMS detector. The collected data set corresponds to an integrated luminosity of 1.7 nb$^{-1}$. The scalar product method is used to extract the υ$_{2}$ coefficients of the azimuthal distributions. Results are reported for the rapidity range |y| < 2.4, in the transverse momentum interval 0 < p$_{T}$ < 50 GeV/c, and in three centrality ranges of 10–30%, 30–50% and 50–90%. In contrast to the J/ψ mesons, the measured υ$_{2}$ values for the Υ mesons are found to be consistent with zero

Measurement of prompt D0^{0} and D‾\overline{D}0^{0} meson azimuthal anisotropy and search for strong electric fields in PbPb collisions at root SNN\sqrt{S_{NN}} = 5.02 TeV

The strong Coulomb field created in ultrarelativistic heavy ion collisions is expected to produce a rapiditydependent difference (Av2) in the second Fourier coefficient of the azimuthal distribution (elliptic flow, v2) between D0 (uc) and D0 (uc) mesons. Motivated by the search for evidence of this field, the CMS detector at the LHC is used to perform the first measurement of Av2. The rapidity-averaged value is found to be (Av2) = 0.001 ? 0.001 (stat)? 0.003 (syst) in PbPb collisions at ?sNN = 5.02 TeV. In addition, the influence of the collision geometry is explored by measuring the D0 and D0mesons v2 and triangular flow coefficient (v3) as functions of rapidity, transverse momentum (pT), and event centrality (a measure of the overlap of the two Pb nuclei). A clear centrality dependence of prompt D0 meson v2 values is observed, while the v3 is largely independent of centrality. These trends are consistent with expectations of flow driven by the initial-state geometry. ? 2021 The Author. Published by Elsevier B.V. This is an open access article under the CC BY licens

Performance of the CMS Level-1 trigger in proton-proton collisions at √s = 13 TeV

At the start of Run 2 in 2015, the LHC delivered proton-proton collisions at a center-of-mass energy of 13\TeV. During Run 2 (years 2015–2018) the LHC eventually reached a luminosity of 2.1× 10$^{34}$ cm$^{-2}$s$^{-1}$, almost three times that reached during Run 1 (2009–2013) and a factor of two larger than the LHC design value, leading to events with up to a mean of about 50 simultaneous inelastic proton-proton collisions per bunch crossing (pileup). The CMS Level-1 trigger was upgraded prior to 2016 to improve the selection of physics events in the challenging conditions posed by the second run of the LHC. This paper describes the performance of the CMS Level-1 trigger upgrade during the data taking period of 2016–2018. The upgraded trigger implements pattern recognition and boosted decision tree regression techniques for muon reconstruction, includes pileup subtraction for jets and energy sums, and incorporates pileup-dependent isolation requirements for electrons and tau leptons. In addition, the new trigger calculates high-level quantities such as the invariant mass of pairs of reconstructed particles. The upgrade reduces the trigger rate from background processes and improves the trigger efficiency for a wide variety of physics signals

Measurement of the Y(1S) pair production cross section and search for resonances decaying to Y(1S)μ⁺μ⁻ in proton-proton collisions at √s = 13 TeV

The fiducial cross section for Y(1S)pair production in proton-proton collisions at a center-of-mass energy of 13TeVin the region where both Y(1S)mesons have an absolute rapidity below 2.0 is measured to be 79 ± 11 (stat) ±6 (syst) ±3 (B)pbassuming the mesons are produced unpolarized. The last uncertainty corresponds to the uncertainty in the Y(1S)meson dimuon branching fraction. The measurement is performed in the final state with four muons using proton-proton collision data collected in 2016 by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9fb$^{-1}$. This process serves as a standard model reference in a search for narrow resonances decaying to Y(1S)μ$^{+}$μ$^{-}$ in the same final state. Such a resonance could indicate the existence of a tetraquark that is a bound state of two bquarks and two b̅ antiquarks. The tetraquark search is performed for masses in the vicinity of four times the bottom quark mass, between 17.5 and 19.5GeV, while a generic search for other resonances is performed for masses between 16.5 and 27GeV. No significant excess of events compatible with a narrow resonance is observed in the data. Limits on the production cross section times branching fraction to four muons via an intermediate Y(1S)resonance are set as a function of the resonance mass