Zooming from Global to Local: A Multiscale RBF Approach

Because physical phenomena on Earth's surface occur on many different length scales, it makes sense when seeking an efficient approximation to start with a crude global approximation, and then make a sequence of corrections on finer and finer scales. It also makes sense eventually to seek fine scale features locally, rather than globally. In the present work, we start with a global multiscale radial basis function (RBF) approximation, based on a sequence of point sets with decreasing mesh norm, and a sequence of (spherical) radial basis functions with proportionally decreasing scale centered at the points. We then prove that we can "zoom in" on a region of particular interest, by carrying out further stages of multiscale refinement on a local region. The proof combines multiscale techniques for the sphere from Le Gia, Sloan and Wendland, SIAM J. Numer. Anal. 48 (2010) and Applied Comp. Harm. Anal. 32 (2012), with those for a bounded region in $\mathbb{R}^d$ from Wendland, Numer. Math. 116 (2012). The zooming in process can be continued indefinitely, since the condition numbers of matrices at the different scales remain bounded. A numerical example illustrates the process

Effect of the plastic hinge and boundary conditions on the impact behavior of reinforced concrete beams

This study numerically investigates the effect of the plastic hinge and boundary conditions on the behavior of reinforced concrete (RC) beams under slow-impact-velocity events. Numerical models are developed by using LS-Dyna and verified against experimental results. The effect of different factors including the impact velocity, projectile weight, and concrete strength on the impact behavior of RC beams is examined. The numerical results have shown that the effect of boundary condition is marginal on the impact force but significant on the displacement and damage of relatively long beams. Determining the structural stiffness of a beam in an equivalent single degree of freedom model for predicting the impact load should consider the plastic hinge formation and stationary location. And this model is not necessarily suitable for predicting the peak beam response since it is independent of the boundary conditions when the impact velocity is fast. The negative bending moment of the simply-supported beam occurs with a large magnitude which needs to be taken into account in the design. The residual displacement is more sensitive to the boundary conditions than the peak displacement. Varying concrete strength from 20 MPa to 100 MPa does not noticeably change the impact force and displacement but significantly affects the failure mode of the beam

Gender Patterns in Vietnam's Child Mortality

We analyze child mortality in Vietnam focusing on gender aspects. Contrary to several other countries in the region, mortality rates for boys are substantially larger than for girls. A large rural-urban mortality difference exists, but much more so for boys than for girls. A higher education level of the mother reduces mortality risk, but the effect is stronger for girls than for boys.child mortality, gender differences, hazard rate, frailty model

Development of a novel forward dynamic programming method for weather routing

This paper presents a novel forward dynamic programming method for weather routing to minimise ship fuel consumption during a voyage. Compared with traditional weather routing methods which only optimise the ship's heading, while the engine power or propeller rotation speed is set as a constant throughout the voyage, this new method considers both the ship power settings and heading controls. A float state technique is used to reduce the iterations required during optimisation and thus save computation time. This new method could lead to quasiglobal optimal routing in comparison with the traditional weather routing methods

Effect of crumb rubber on mechanical properties of multi-phase syntactic foams

Syntactic foam is a lightweight and strong material which can be used in marine and aeronautical applications. However, the brittleness of the material limits its application to a broader range. Adding crumb rubber to the syntactic foam can increase its energy absorption capacity. The effect of crumb rubber on the fracture toughness and energy absorption capacity of 2-phase and 3-phase syntactic foam is evaluated under both static and impact loads. The experimental results have shown that the fracture toughness of the 2-phase rubberized syntactic foam increased by 8% while an increase of 22% of its fracture energy was observed. Under quasi-static loads, the 3-phase rubberized syntactic foam showed decreases in the compressive strength and elastic modulus but an increase in the energy absorption capacity as compared to the syntactic foam without crumb rubber. In addition, the impact energy absorption of the 3-phase rubberized syntactic foam increased by 24% as compared to that of the 3-phase syntactic foam without crumb rubber

Suppression of monocyte and neutrophil function by recombinant IL-2

Little IS known about the influence of IL-2 on phagocytes. We now describe the effects of human recombinant IL-2 on human neutrophil and monocyte functions related to mobility, phagocytosis, glucose uptake, respiration and degranulation. Neutrophil adherence and hexose monophosphate shunt activities were both suppressed after incubation with IL-2. IL-2 had no effect on neutrophil migration, phagocytosis, deoxyglucose uptake or degranulation, ionocytes demonstrated a greater sensitivity to IL-2 with suppression of monocyte adherence, random and stimulated migration, glucose uptake and hexose monophosphate shunt activity, even after addition of phorbol myristate acetate. Monocyte phagocytosis and degranulation were not affected. All of the effects observed were dose-dependent within a biologically active range for IL-2. These studies suggest that IL-2 may have an important down-regulatory role across a broad range of monocyte functions including movement, deoxyglucose uptake and respiration. However, its role in regulation of neutrophil function is limited to adherence and respiration. IL-2 may be a more versatile cytokine than has previously been appreciated

Some Numerical Invariants Related to Central Embedding Problems

AbstractFor every central embedding problem three numerical invariants which give information about its solvability are defined. Furthermore, in the number field case universal estimates for these invariants are given

Removing the mask -- reconstructing a scalar field on the sphere from a masked field

The paper analyses a spectral approach to reconstructing %the image of a scalar field on the sphere, given only information about a masked version of the field together with precise information about the (smooth) mask. The theory is developed for a general mask, and later specialized to the case of an axially symmetric mask. Numerical experiments are given for the case of an axial mask motivated by the cosmic microwave background, assuming that the underlying field is a realization of a Gaussian random field with an artificial angular power spectrum of moderate degree ($\ell \le 100$). The recovery is highly satisfactory in the absence of noise and even in the presence of moderate noise

Fast and Efficient Compressive Sensing using Structurally Random Matrices

This paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we pre-randomize a sensing signal by scrambling its samples or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the transform coefficients as the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical sensing performance comparable with that of completely random sensing matrices. Numerical simulation results verify the validity of the theory as well as illustrate the promising potentials of the proposed sensing framework