GPU Acceleration of Partial Differential Equation Solvers

Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

Vaccination and All Cause Child Mortality 1985-2011: Global Evidence from the Demographic and Health Surveys

Based on models with calibrated parameters for infection, case fatality rates, and vaccine efficacy, basic childhood vaccinations have been estimated to be highly cost effective. We estimate the association of vaccination with mortality directly from survey data. Using 149 cross-sectional Demographic and Health Surveys, we determine the relationship between vaccination coverage and under five mortality at the survey cluster level. Our data include approximately one million children in 68,490 clusters in 62 countries. We consider the childhood measles, Bacille Calmette-Guérin (BCG), Diphtheria-Pertussis-Tetanus (DPT), Polio, and maternal tetanus vaccinations. Using modified Poisson regression to estimate the relative risk of child mortality in each cluster, we also adjust for selection bias caused by the vaccination status of dead children not being reported. Childhood vaccination, and in particular measles and tetanus vaccination, is associated with substantial reductions in childhood mortality. We estimate that children in clusters with complete vaccination coverage have relative risk of mortality 0.73 (95% Confidence Interval: 0.68, 0.77) that of children in a cluster with no vaccination. While widely used, basic vaccines still have coverage rates well below 100% in many countries, and our results emphasize the effectiveness of increasing their coverage rates in order to reduce child mortality.

Joint Optimization of Area Spectral Efficiency and Delay over PPP Interfered Ad-Hoc Networks

To evaluate the performance of the co-channel transmission based communication, we propose a new metric for area spectral efficiency (ASE) of interference limited ad-hoc network by assuming that the nodes are randomly distributed according to a Poisson point processes (PPP). We introduce a utility function, U = ASE/delay and derive the optimal ALOHA transmission probability p and the SIR threshold τ that jointly maximize the ASE and minimize the local delay. Finally, numerical results have been conducted to confirm that the joint optimization based on the U metric achieves a significant performance gain compared to conventional systems.

A Tractable Approach to Uplink Spectral Efficiency of Two-Tier Massive MIMO Cellular HetNets

This letter investigates the uplink spectral efficiency (SE) of a two-tier cellular network, where massive multiple-input multiple-output macro base stations are overlaid with dense small cells. Macro user equipments (MUEs) and small cells with single user equipment uniformly scattered are modeled as two independent homogeneous Poisson point processes. By applying stochastic geometry, we analyze the SE of the multiuser uplink at a macro base station that employs a zero-forcing detector and we obtain a novel lower bound as well as its approximation. According to the simple and near-exact analytical expression, we observe that the ideal way to improve the SE is by increasing the MUE density and the base station antennas synchronously rather than increasing them individually. Furthermore, a large value of path loss exponent has a positive effect on the SE due to the reduced aggregated interference.

Scaled Heavy-Ball Acceleration of the Richardson-Lucy Algorithm for 3D Microscopy Image Restoration

The Richardson–Lucy algorithm is one of the most important in image deconvolution. However, a drawback is its slow convergence. A significant acceleration was obtained using the technique proposed by Biggs and Andrews (BA), which is implemented in the deconvlucy function of the image processing MATLAB toolbox. The BA method was developed heuristically with no proof of convergence. In this paper, we introduce the heavy-ball (H-B) method for Poisson data optimization and extend it to a scaled H-B method, which includes the BA method as a special case. The method has a proof of the convergence rateof O(K^2), where k is the number of iterations. We demonstrate the superior convergence performance, by a speedup factor off ive, of the scaled H-B method on both synthetic and real 3D images.