A Simple Proof of the Alternation Theorem

A simple proof of the alternation theorem for minimax FIR filter design is presented in this paper. It requires no background on mathematical optimization theory, and is based on easily understood properties of filters with equiripple behavior. The method is similar to the classical counting argument used in early mathematics literature. The contribution here is a simplified presentation which directly uses filter design language

An isogeometric analysis for elliptic homogenization problems

A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational expenses while using traditional finite element methods. The isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in this paper is regarded as an alternative approach to the standard Finite Element Heterogeneous Multiscale Method (FE-HMM) which is currently an effective framework to solve these problems. The method utilizes non-uniform rational B-splines (NURBS) in both macro and micro levels instead of standard Lagrange basis. Beside the ability to describe exactly the geometry, it tremendously facilitates high-order macroscopic/microscopic discretizations thanks to the flexibility of refinement and degree elevation with an arbitrary continuity level provided by NURBS basis functions. A priori error estimates of the discretization error coming from macro and micro meshes and optimal micro refinement strategies for macro/micro NURBS basis functions of arbitrary orders are derived. Numerical results show the excellent performance of the proposed method

A new root-knot nematode, Meloidogyne moensi n. sp. (Nematoda : Meloidogynidae), parasitizing Robusta coffee from Western Highlands, Vietnam

A new root-knot nematode, parasitizing Robusta coffee in Dak Lak Province, Western Highlands of Vietnam, is described as Meloidogyne moensi n. sp. Morphological and molecular analyses demonstrated that this species differs clearly from other previously described root-knot nematodes. Morphologically, the new species is characterized by a swollen body of females with a small posterior protuberance that elongated from ovoid to saccate; perineal patterns with smooth striae, continuous and low dorsal arch; lateral lines marked as a faint space or linear depression at junction of the dorsal and ventral striate; distinct phasmids; perivulval region free of striae; visible and wide tail terminus surrounding by concentric circles of striae; medial lips of females in dumbbell-shaped and slightly raised above lateral lips; female stylet is normally straight with posteriorly sloping stylet knobs; lip region of second stage juvenile (J2) is not annulated; medial lips and labial disc of J2 formed dumbbell shape; lateral lips are large and triangular; tail of J2 is conoid with rounded unstriated tail tip; distinct phasmids and hyaline; dilated rectum. Meloidogyne moensi n. sp. is most similar to M. africana, M. ottersoni by prominent posterior protuberance. Results of molecular analysis of rDNA sequences including the D2-D3 expansion regions of 28S rDNA, COI, and partial COII/16S rRNA of mitochondrial DNA support for the new species status

MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM

We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) = \sum_{j \ge 1} y_j \, \phi_j$ with $y_j \sim \mathcal{N}(0,1)$ and a given sequence of functions $\{\phi_j\}_{j \ge 1}$. We use the MDFEM to approximate the expected value of a linear functional of the solution of the PDE which is an infinite-dimensional integral over the parameter space. The proposed algorithm uses the multivariate decomposition method to compute the infinite-dimensional integral by a decomposition into finite-dimensional integrals, which we resolve using quasi-Monte Carlo methods, and for which we use the finite element method to solve different instances of the PDE. We develop higher-order quasi-Monte Carlo rules for integration over the finite-dimensional Euclidean space with respect to the Gaussian distribution by use of a truncation strategy. By linear transformations of interlaced polynomial lattice rules from the unit cube to a multivariate box of the Euclidean space we achieve higher-order convergence rates for functions belonging to a class of anchored Gaussian Sobolev spaces while taking into account the truncation error. Under appropriate conditions, the MDFEM achieves higher-order convergence rates in term of error versus cost, i.e., to achieve an accuracy of $O(\epsilon)$ the computational cost is $O(\epsilon^{-1/\lambda-d'/\lambda}) = O(\epsilon^{-(p^* + d'/\tau)/(1-p^*)})$ where $\epsilon^{-1/\lambda}$ and $\epsilon^{-d'/\lambda}$ are respectively the cost of the quasi-Monte Carlo cubature and the finite element approximations, with $d' = d \, (1+\delta')$ for some $\delta' \ge 0$ and $d$ the physical dimension, and $0 < p^* \le (2 + d'/\tau)^{-1}$ is a parameter representing the sparsity of $\{\phi_j\}_{j \ge 1}$.Comment: 48 page

Outward Influence and Cascade Size Estimation in Billion-scale Networks

Estimating cascade size and nodes' influence is a fundamental task in social, technological, and biological networks. Yet this task is extremely challenging due to the sheer size and the structural heterogeneity of networks. We investigate a new influence measure, termed outward influence (OI), defined as the (expected) number of nodes that a subset of nodes $S$ will activate, excluding the nodes in S. Thus, OI equals, the de facto standard measure, influence spread of S minus |S|. OI is not only more informative for nodes with small influence, but also, critical in designing new effective sampling and statistical estimation methods. Based on OI, we propose SIEA/SOIEA, novel methods to estimate influence spread/outward influence at scale and with rigorous theoretical guarantees. The proposed methods are built on two novel components 1) IICP an important sampling method for outward influence, and 2) RSA, a robust mean estimation method that minimize the number of samples through analyzing variance and range of random variables. Compared to the state-of-the art for influence estimation, SIEA is $\Omega(\log^4 n)$ times faster in theory and up to several orders of magnitude faster in practice. For the first time, influence of nodes in the networks of billions of edges can be estimated with high accuracy within a few minutes. Our comprehensive experiments on real-world networks also give evidence against the popular practice of using a fixed number, e.g. 10K or 20K, of samples to compute the "ground truth" for influence spread.Comment: 16 pages, SIGMETRICS 201

Importance Sketching of Influence Dynamics in Billion-scale Networks

The blooming availability of traces for social, biological, and communication networks opens up unprecedented opportunities in analyzing diffusion processes in networks. However, the sheer sizes of the nowadays networks raise serious challenges in computational efficiency and scalability. In this paper, we propose a new hyper-graph sketching framework for inflence dynamics in networks. The central of our sketching framework, called SKIS, is an efficient importance sampling algorithm that returns only non-singular reverse cascades in the network. Comparing to previously developed sketches like RIS and SKIM, our sketch significantly enhances estimation quality while substantially reducing processing time and memory-footprint. Further, we present general strategies of using SKIS to enhance existing algorithms for influence estimation and influence maximization which are motivated by practical applications like viral marketing. Using SKIS, we design high-quality influence oracle for seed sets with average estimation error up to 10x times smaller than those using RIS and 6x times smaller than SKIM. In addition, our influence maximization using SKIS substantially improves the quality of solutions for greedy algorithms. It achieves up to 10x times speed-up and 4x memory reduction for the fastest RIS-based DSSA algorithm, while maintaining the same theoretical guarantees.Comment: 12 pages, to appear in ICDM 2017 as a regular pape

Difference in quality of life and associated factors among the elderly in rural Vietnam

Background. In Vietnam today, many generations remain living together in a family. With escalating urbanization and population aging, mental health disorders and the quality of life (QoL) among the elderly are gradually presenting themselves as of great concern. The objective of this study was to examine gender differences in QoL and some associated factors among the elderly in rural Vietnam using the QoL scale of WHO (WHOQOL-BREF). Methods. A cross-sectional study using quantitative methods. Results and Conclusions. The proportion of the elderly men having higher level of QoL in physical health, psychological health and environment was higher than that of their women counterparts. Reversely, of those having medium and lower QoL, females made up a larger proportion than males. The overall QoL score in elderly men (75.32) was higher than that of women (72.32) and the same pattern was witnessed in all four domains of QoL. While higher QoL in elderly men was significantly correlated with 5 factors, aged ≥ 80 years, following Buddhism and Christianity, having better connection and without illness in the past 6 months, these among female counterparts are aged ≥ 80 years, completing secondary level or above, having medium and high socioeconomic status and without illness in the last 6 months. © 2017, Pacini Editore S.p.A. All rights reserved