Analysis of moving least squares approximation revisited

In this article the error estimation of the moving least squares approximation is provided for functions in fractional order Sobolev spaces. The analysis presented in this paper extends the previous estimations and explains some unnoticed mathematical details. An application to Galerkin method for partial differential equations is also supplied.Comment: Journal of Computational and Applied Mathematics, 2015 Journal of Computational and Applied Mathematic

Error and Stability Estimates of the Least-Squares Variational Kernel-Based Methods for Second Order PDEs

We consider the least-squares variational kernel-based methods for numerical solution of partial differential equations. Indeed, we focus on least-squares principles to develop meshfree methods to find the numerical solution of a general second order ADN elliptic boundary value problem in domain $\Omega \subset \mathbb{R}^d$ under Dirichlet boundary conditions. Most notably, in these principles it is not assumed that differential operator is self-adjoint or positive definite as it would have to be in the Rayleigh-Ritz setting. However, the new scheme leads to a symmetric and positive definite algebraic system allowing us to circumvent the compatibility conditions arising in standard and mixed-Galerkin methods. In particular, the resulting method does not require certain subspaces satisfying any boundary condition. The trial space for discretization is provided via standard kernels that reproduce $H^\tau(\Omega)$, $\tau>d/2$, as their native spaces. Therefore, the smoothness of the approximation functions can be arbitrary increased without any additional task. The solvability of the scheme is proved and the error estimates are derived for functions in appropriate Sobolev spaces. For the weighted discrete least-squares principles, we show that the optimal rate of convergence in $L^2(\Omega)$ is accessible. Furthermore, for $d \le 3$, the proposed method has optimal rate of convergence in $H^k(\Omega)$ whenever $k \le \tau$. The condition number of the final linear system is approximated in terms of discterization quality. Finally, the results of some computational experiments support the theoretical error bounds.Comment: This paper includes 29 pages, 1 figure and 2 table

An overview of VANET vehicular networks

Today, with the development of intercity and metropolitan roadways and with various cars moving in various directions, there is a greater need than ever for a network to coordinate commutes. Nowadays, people spend a lot of time in their vehicles. Smart automobiles have developed to make that time safer, more effective, more fun, pollution-free, and affordable. However, maintaining the optimum use of resources and addressing rising needs continues to be a challenge given the popularity of vehicle users and the growing diversity of requests for various services. As a result, VANET will require modernized working practices in the future. Modern intelligent transportation management and driver assistance systems are created using cutting-edge communication technology. Vehicular Ad-hoc networks promise to increase transportation effectiveness, accident prevention, and pedestrian comfort by allowing automobiles and road infrastructure to communicate entertainment and traffic information. By constructing thorough frameworks, workflow patterns, and update procedures, including block-chain, artificial intelligence, and SDN (Software Defined Networking), this paper addresses VANET-related technologies, future advances, and related challenges. An overview of the VANET upgrade solution is given in this document in order to handle potential future problems

An Optimized Multi-Layer Resource Management in Mobile Edge Computing Networks: A Joint Computation Offloading and Caching Solution

Nowadays, data caching is being used as a high-speed data storage layer in mobile edge computing networks employing flow control methodologies at an exponential rate. This study shows how to discover the best architecture for backhaul networks with caching capability using a distributed offloading technique. This article used a continuous power flow analysis to achieve the optimum load constraints, wherein the power of macro base stations with various caching capacities is supplied by either an intelligent grid network or renewable energy systems. This work proposes ubiquitous connectivity between users at the cell edge and offloading the macro cells so as to provide features the macro cell itself cannot cope with, such as extreme changes in the required user data rate and energy efficiency. The offloading framework is then reformed into a neural weighted framework that considers convergence and Lyapunov instability requirements of mobile-edge computing under Karush Kuhn Tucker optimization restrictions in order to get accurate solutions. The cell-layer performance is analyzed in the boundary and in the center point of the cells. The analytical and simulation results show that the suggested method outperforms other energy-saving techniques. Also, compared to other solutions studied in the literature, the proposed approach shows a two to three times increase in both the throughput of the cell edge users and the aggregate throughput per cluster

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4% (62.3 (55.1–70.8) million) to 6.4% (58.3 (47.6–70.7) million), but is predicted to remain above the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025. Prevalence of overweight increased from 5.2% (30 (22.8–38.5) million) in 2000 to 6.0% (55.5 (44.8–67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic

Adolescent transport and unintentional injuries: a systematic analysis using the Global Burden of Disease Study 2019

Background: Globally, transport and unintentional injuries persist as leading preventable causes of mortality and morbidity for adolescents. We sought to report comprehensive trends in injury-related mortality and morbidity for adolescents aged 10–24 years during the past three decades. Methods: Using the Global Burden of Disease, Injuries, and Risk Factors 2019 Study, we analysed mortality and disability-adjusted life-years (DALYs) attributed to transport and unintentional injuries for adolescents in 204 countries. Burden is reported in absolute numbers and age-standardised rates per 100 000 population by sex, age group (10–14, 15–19, and 20–24 years), and sociodemographic index (SDI) with 95% uncertainty intervals (UIs). We report percentage changes in deaths and DALYs between 1990 and 2019. Findings: In 2019, 369 061 deaths (of which 214 337 [58%] were transport related) and 31·1 million DALYs (of which 16·2 million [52%] were transport related) among adolescents aged 10–24 years were caused by transport and unintentional injuries combined. If compared with other causes, transport and unintentional injuries combined accounted for 25% of deaths and 14% of DALYs in 2019, and showed little improvement from 1990 when such injuries accounted for 26% of adolescent deaths and 17% of adolescent DALYs. Throughout adolescence, transport and unintentional injury fatality rates increased by age group. The unintentional injury burden was higher among males than females for all injury types, except for injuries related to fire, heat, and hot substances, or to adverse effects of medical treatment. From 1990 to 2019, global mortality rates declined by 34·4% (from 17·5 to 11·5 per 100 000) for transport injuries, and by 47·7% (from 15·9 to 8·3 per 100 000) for unintentional injuries. However, in low-SDI nations the absolute number of deaths increased (by 80·5% to 42 774 for transport injuries and by 39·4% to 31 961 for unintentional injuries). In the high-SDI quintile in 2010–19, the rate per 100 000 of transport injury DALYs was reduced by 16·7%, from 838 in 2010 to 699 in 2019. This was a substantially slower pace of reduction compared with the 48·5% reduction between 1990 and 2010, from 1626 per 100 000 in 1990 to 838 per 100 000 in 2010. Between 2010 and 2019, the rate of unintentional injury DALYs per 100 000 also remained largely unchanged in high-SDI countries (555 in 2010 vs 554 in 2019; 0·2% reduction). The number and rate of adolescent deaths and DALYs owing to environmental heat and cold exposure increased for the high-SDI quintile during 2010–19. Interpretation: As other causes of mortality are addressed, inadequate progress in reducing transport and unintentional injury mortality as a proportion of adolescent deaths becomes apparent. The relative shift in the burden of injury from high-SDI countries to low and low–middle-SDI countries necessitates focused action, including global donor, government, and industry investment in injury prevention. The persisting burden of DALYs related to transport and unintentional injuries indicates a need to prioritise innovative measures for the primary prevention of adolescent injury. Funding: Bill &amp; Melinda Gates Foundation