New algorithms for numerical assessment of nonlinear integro-differential equations of second-order using Haar wavelets

This paper deals with the extended design for Fredholm and Volterra integral equations and design for Fredholm and Volterra integro-differential equations of first-order to second-order nonlinear Fredholm and second-order nonlinear Volterra integro-differential equations having square integrable kernels. This approach utilizes the inherent dynamics of the Haar wavelet. The Haar wavelet is used to provide a single platform for the proposed method. The method is tested on problems from literature, and numerical results are compared with existing methods. The numerical results indicate that the accuracy of the method is reasonably high, even on a coarse grid

An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems: a computational study

An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\cal N})$ operations where ${\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties

Global, regional, and national age-specific progress towards the 2020 milestones of the WHO End TB Strategy: a systematic analysis for the Global Burden of Disease Study 2021

Background Global evaluations of the progress towards the WHO End TB Strategy 2020 interim milestones on mortality (35% reduction) and incidence (20% reduction) have not been age specific. We aimed to assess global, regional, and national-level burdens of and trends in tuberculosis and its risk factors across five separate age groups, from 1990 to 2021, and to report on age-specific progress between 2015 and 2020. Methods We used the Global Burden of Diseases, Injuries, and Risk Factors Study 2021 (GBD 2021) analytical framework to compute age-specific tuberculosis mortality and incidence estimates for 204 countries and territories (1990–2021 inclusive). We quantified tuberculosis mortality among individuals without HIV co-infection using 22 603 site-years of vital registration data, 1718 site-years of verbal autopsy data, 825 site-years of sample-based vital registration data, 680 site-years of mortality surveillance data, and 9 site-years of minimally invasive tissue sample (MITS) diagnoses data as inputs into the Cause of Death Ensemble modelling platform. Age-specific HIV and tuberculosis deaths were established with a population attributable fraction approach. We analysed all available population-based data sources, including prevalence surveys, annual case notifications, tuberculin surveys, and tuberculosis mortality, in DisMod-MR 2.1 to produce internally consistent age-specific estimates of tuberculosis incidence, prevalence, and mortality. We also estimated age-specific tuberculosis mortality without HIV co-infection that is attributable to the independent and combined effects of three risk factors (smoking, alcohol use, and diabetes). As a secondary analysis, we examined the potential impact of the COVID-19 pandemic on tuberculosis mortality without HIV co-infection by comparing expected tuberculosis deaths, modelled with trends in tuberculosis deaths from 2015 to 2019 in vital registration data, with observed tuberculosis deaths in 2020 and 2021 for countries with available cause-specific mortality data. Findings We estimated 9·40 million (95% uncertainty interval [UI] 8·36 to 10·5) tuberculosis incident cases and 1·35 million (1·23 to 1·52) deaths due to tuberculosis in 2021. At the global level, the all-age tuberculosis incidence rate declined by 6·26% (5·27 to 7·25) between 2015 and 2020 (the WHO End TB strategy evaluation period). 15 of 204 countries achieved a 20% decrease in all-age tuberculosis incidence between 2015 and 2020, eight of which were in western sub-Saharan Africa. When stratified by age, global tuberculosis incidence rates decreased by 16·5% (14·8 to 18·4) in children younger than 5 years, 16·2% (14·2 to 17·9) in those aged 5–14 years, 6·29% (5·05 to 7·70) in those aged 15–49 years, 5·72% (4·02 to 7·39) in those aged 50–69 years, and 8·48% (6·74 to 10·4) in those aged 70 years and older, from 2015 to 2020. Global tuberculosis deaths decreased by 11·9% (5·77 to 17·0) from 2015 to 2020. 17 countries attained a 35% reduction in deaths due to tuberculosis between 2015 and 2020, most of which were in eastern Europe (six countries) and central Europe (four countries). There was variable progress by age: a 35·3% (26·7 to 41·7) decrease in tuberculosis deaths in children younger than 5 years, a 29·5% (25·5 to 34·1) decrease in those aged 5–14 years, a 15·2% (10·0 to 20·2) decrease in those aged 15–49 years, a 7·97% (0·472 to 14·1) decrease in those aged 50–69 years, and a 3·29% (–5·56 to 9·07) decrease in those aged 70 years and older. Removing the combined effects of the three attributable risk factors would have reduced the number of all-age tuberculosis deaths from 1·39 million (1·28 to 1·54) to 1·00 million (0·703 to 1·23) in 2020, representing a 36·5% (21·5 to 54·8) reduction in tuberculosis deaths compared to those observed in 2015. 41 countries were included in our analysis of the impact of the COVID-19 pandemic on tuberculosis deaths without HIV co-infection in 2020, and 20 countries were included in the analysis for 2021. In 2020, 50 900 (95% CI 49 700 to 52 400) deaths were expected across all ages, compared to an observed 45 500 deaths, corresponding to 5340 (4070 to 6920) fewer deaths; in 2021, 39 600 (38 300 to 41 100) deaths were expected across all ages compared to an observed 39 000 deaths, corresponding to 657 (–713 to 2180) fewer deaths. Interpretation Despite accelerated progress in reducing the global burden of tuberculosis in the past decade, the world did not attain the first interim milestones of the WHO End TB Strategy in 2020. The pace of decline has been unequal with respect to age, with older adults (ie, those aged >50 years) having the slowest progress. As countries refine their national tuberculosis programmes and recalibrate for achieving the 2035 targets, they could consider learning from the strategies of countries that achieved the 2020 milestones, as well as consider targeted interventions to improve outcomes in older age groups

Stochastic numerical treatment for solving Falkner–Skan equations using feedforward neural networks

In this article, the artificial intelligence techniques have been used for the solution of Falkner–Skan (FS) equations based on neural networks optimized with three methods including active set technique, sequential quadratic programming and genetic algorithms (GA) hybridization. Log-sigmoid activation function is used in artificial neural network architecture. The proposed techniques are applied to a number of cases for Falkner–Skan problems, and results were compared with GA hybrid results in all cases and were found accurate. The level of accuracy is examined through statistical analyses based on a sufficiently large number of independent runs

Optimum initialization of South Asian seasonal forecast using climatological relevant singular vectors

Designing an efficient seasonal forecasting system is ensuring that the uncertainty in the initial conditions is sampled optimally. Perturbation in the initial condition and the methodology used for sampling perturbation optimally plays a key role in the improvement of the current seasonal climate forecast. In this study the error growth properties of initial perturbation are investigated using climatically relevant singular vectors (CSVs). The Community Climate System Model version 4 (CCSM4) is used as a simulation tool to examine the growth of optimal perturbations with different lead times over the South Asian Monsoon region. It is found that reliable set of CSVs can be estimated by running an ensemble of model forecasts. Amplification of the optimal perturbations occurs for more than 1 month and possibly up to 6 months. The results show the growth rates of the singular vectors are very sensitive to the variable of perturbation, number of perturbations and the error norm. When the SV is used as an initial perturbation, the forecast skill of key atmospheric variables over South Asian Monsoon region is significantly improved. Further, it is demonstrated that the predictions with the singular vector have a more reliable ensemble spread, suggesting a potential merit for a probabilistic forecast. The promising results reported here should hopefully encourage further investigation of the methodology at different timescales.Non UBCUnreviewedAuthor affiliation: University of Northern British ColumbiaOthe