Gauss–Seidel Estimation of Generalized Linear Mixed Models With Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) are often fit by computational procedures such as penalized quasi-likelihood (PQL). Special cases of GLMMs are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints make it difficult to apply these iterative procedures to datasets having a very large number of records.

We propose a computationally efficient strategy based on the Gauss–Seidel algorithm that iteratively fits submodels of the GLMM to collapsed versions of the data. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status, and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. For Poisson and binomial regression models, the Gauss–Seidel approach is found to substantially outperform existing methods in terms of maximum analyzable sample size. Remarkably, for both models, the average time per iteration and the total time until convergence of the Gauss–Seidel procedure are less than 0.3% of the corresponding times for the IWLS algorithm. Platform-independent pseudo-code for fitting GLMS, as well as the source code used to generate and analyze the datasets in the simulation studies, are available online as supplemental materials.     

大斯托克斯位移远红光至近红外荧光探针用于检测肝损伤过程中过氧化亚硝酸盐的动态变化

肝损伤是影响公众健康的重大问题之一, 已经引起了人们越来越多的关注. 而过表达的过氧化亚硝酸盐(ONOO^?)在肝损伤等疾病的发病机制中起着重要作用, 被认为是一种与早期肝损伤密切相关的生物活性分子. 因此, 为了探究ONOO^?在肝损伤过程中的作用, 开发可以实现肝损伤过程中ONOO^?高选择性和实时检测的分析方法具有重要意义. 本文报道了一种具有大斯托克斯位移的远红光至近红外(FR-NIR)ONOO^?荧光探针. 由于该探针具有大的斯托克斯位移, 可以有效消除光谱重叠和自吸收的干扰, 从而显著提高成像的信噪比. 此外, 该探针对ONOO^?具有高的灵敏度(检出限为25.8 nmol/L)和良好的选择性, 被成功用于药物诱导肝损伤过程中ONOO^?信号的成像检测.     

Heavy tails for an alternative stochastic perpetuity model

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten–Goldie setting but involve a logarithmic term.     

Meyniel's conjecture holds for random d‐regular graphs

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant C, the cop number of every connected graph G is at most . In a separate paper, we showed that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph. The result was obtained by showing that the conjecture holds for a general class of graphs with some specific expansion‐type properties. In this paper, this deterministic result is used to show that the conjecture holds asymptotically almost surely for random d‐regular graphs when d = d(n) ≥ 3.     

Parallel Schwarz alternating methods for anisotropic diffusion of speckled medical images

This paper deals with ultrasound medical image processing, particularly to filter the noise while preserving the edges and structures of information. The mathematical processing consists in solving by a numerical way a nonlinear evolutive boundary value problem. Several numerical semi-implicit time marching schemes are considered and analyzed. At each time step, parallel synchronous or asynchronous Schwarz alternating methods are used to solve the linear system and its convergence is studied. Lastly, the results of sequential and parallel simulations are presented.      

Cis-Trans Isomerism in Square Planar [TeX 2 (stu) 2 ] Complexes (X = Br − , I − ) with Bulky Substituted Thiourea (stu) Ligands. Syntheses and Structures of Four New Tellurium(II) Complexes

The complexes were synthesised by adding a hot solution of the appropriate substituted thiourea in MeOH (Br m complexes) or DMF (I m complexes) to a solution of TeO 2 dissolved in hot conc. HCl. The structures of the resulting four-coordinate square planar complexes, cis -[TeBr 2 {( i PrNH) 2 CS} 2 ] ( 1 ), cis -[TeBr 2 {( i BuNH) 2 CS} 2 ] ( 2 ), trans -[TeI 2 {( i PrNH) 2 CS} 2 ] ( 3 ), and trans -[TeI 2 {( i BuNH) 2 CS} 2 ] ( 4 ), were studied by means of X-ray crystallographic methods. The average Te-S bond length in 1 and 2 is 2.5364 Å. The corresponding average Te-Br bond length is 2.9639 Å, reflecting the stronger trans influences of the two thioureas as compared to that of bromide. In 3 and 4 where there is no trans influence affecting the Te-ligand bonds, the average Te-S and Te-I bond lengths are 2.6926 and 2.9761 Å respectively. Tetraalkyl- or arylsubstituted thioureas alone as well as bulky disubstituted thioureas together with I m ligands seem to favor formation of trans complexes.     

Synthesis of β,β′-edge fused, π-extended porphyrins and their applications in the dye-sensitized solar cells

Four π-extended, β,β′ aromatic ring fused porphyrins including mono- and opp-dibenzoporphyrins bearing two carboxyl groups at only one fused benzo group were synthesized. The optical results by UV–vis spectroscopy indicate that when compared with the absorption spectra of monobenzoporphyrins, greater light-harvesting capabilities can be realized for opp-dibenzoporphyrins with two benzo group at the opposite β,β′ positions of the porphyrin. The photovoltaic properties of these π-extended porphyrins were examined for the first time and the highest conversion efficiency of 1.62% was realized for opp-dibenzoporphyrin 8a-sensitized solar cell, which is ∼60% higher than that of monobenzoporphyrin 4a based solar cell indicating the effect of an extra aromatic π conjugation on the light-harvesting capabilities of π-extended porphyrins. Subsequent DFT calculation results supported our results obtained in the optical and photovoltaic studies.     

利用游戏化教学促进“微粒观”建构*——以“原子的结构”第一课时为例

分析了初中化学微粒观的教学内容和“原子的结构”的相关教学设计,针对学生“微粒观”建构存在的难题,提出利用反馈机制,采用“寓教于乐”的游戏化教学设计,并进行实践效果访谈。不仅完成了本课时的教学目标,也让学生对化学的兴趣更加浓厚。     

Superb thermal stability purple-blue phosphor through synergistic effect of emission compensation and nonradiative transition restriction of Eu2+

Phosphors with outstanding luminescence thermal stability are desirable for high-power phosphor-converted light-emitting diode (pc-LED) lightings. High structural rigidity and large bandgap of phosphor hosts are helpful to suppress nonradiative relaxation of optical centers and realize excellent thermal stability. Unfortunately, few host materials simultaneously possess aforementioned structural features. Herein, we confirm that Sr₃(PO₄)₂ (SPO) phosphate possesses high structural rigidity (Debye temperature, Θ_D = 559 K) and large bandgap (E_g = 8.313 eV) by density functional theory calculations. As expected, Eu²⁺-doped SPO purple-blue phosphors show extraordinary thermal stability. At 150/300 °C, SPO:5%Eu²⁺ presents emission loss of only 4%/8% and a predicated ultrahigh thermal quenching temperature of 973 °C. The most strikingly discoveries here are that thermal-induced emission compensation appears within two distinct Eu²⁺ sites of SPO host. The outstanding thermal stability, on one hand, is attributed to rigid structure and large bandgap of host that inhibits nonradiative relaxation of Eu²⁺ and on the other hand, the emission self-compensation of Eu²⁺. Benefiting from synergistic effect of emission compensation and nonradiative transition restriction of Eu²⁺, as-prepared SPO:5%Eu²⁺ purple-blue phosphor not only presents superior thermal stability but also high internal quantum efficiency of 95.1% and excellent hydrolysis resistant. Some advanced applications are explored including white LED lighting and wide-color-gamut display. Our work provides in-deep insights into structure-property relationships of thermally stable phosphors.