A nonstandard finite difference method for solving a mathematical model of HIV-TB co-infection

We design and analyze an unconditionally convergent nonstandard finite-difference method to study transmission dynamics of a mathematical model of HIV-TB co-infection. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves positivity of the solution which is one of the essential requirements when modelling epidemic diseases. Furthermore, we show that the numerical method is unconditionally stable. Competitive numerical results confirming theoretical investigations are provided. Comparisons are also made with other conventional approaches that are routinely used to solve these types of problems.     

半监督度量学习内蕴最速下降算法的收敛性分析

主要研究对称正定矩阵群上的内蕴最速下降算法的收敛性问题.首先针对一个可转化为对称正定矩阵群上无约束优化问题的半监督度量学习模型,提出对称正定矩阵群上一种自适应变步长的内蕴最速下降算法.然后利用李群上的光滑函数在任意一点处带积分余项的泰勒展开式,证明所提算法在对称正定矩阵群上是线性收敛的.最后通过在分类问题中的数值实验说明算法的有效性.     

Sharp oscillation and nonoscillation tests for linear difference equations

We consider difference equations with a single delay term and obtain sufficient conditions for both oscillation and nonoscillation. Moreover, our nonoscillation theorem improves the affirmative answer to Ladas’ corrected conjecture given by Tang and Yu in [Comput. Math. Appl. 38(11–12) (1999), pp. 229–237]. We also present a detailed discussion with examples to emphasize the significance and the sharpness of the new results.     

Efficient Computation of the Joint Sample Frequency Spectra for Multiple Populations

A wide range of studies in population genetics have employed the sample frequency spectrum (SFS), a summary statistic which describes the distribution of mutant alleles at a polymorphic site in a sample of DNA sequences and provides a highly efficient dimensional reduction of large-scale population genomic variation data. Recently, there has been much interest in analyzing the joint SFS data from multiple populations to infer parameters of complex demographic histories, including variable population sizes, population split times, migration rates, admixture proportions, and so on. SFS-based inference methods require accurate computation of the expected SFS under a given demographic model. Although much methodological progress has been made, existing methods suffer from numerical instability and high computational complexity when multiple populations are involved and the sample size is large. In this article, we present new analytic formulas and algorithms that enable accurate, efficient computation of the expected joint SFS for thousands of individuals sampled from hundreds of populations related by a complex demographic model with arbitrary population size histories (including piecewise-exponential growth). Our results are implemented in a new software package called momi (MOran Models for Inference). Through an empirical study, we demonstrate our improvements to numerical stability and computational complexity.     

New upper bounds for online strip packing

In this paper, we consider the online strip packing problem, in which a list of online rectangles has to be packed without overlap or rotation into one or more strips of width 1 and infinite height so as to minimize the required height of the packing. By analyzing a two-phase shelf algorithm, we derive a new upper bound 6.4786 on the competitive ratio for online one strip packing. This result improves the best known upper bound of 6.6623. We also extend this algorithm to online multiple strips packing and present some numeric upper bounds on their competitive ratios which are better than the previous bounds.     

Plasmonic Pollen Grain Nanostructures: A Three-Dimensional Surface-Enhanced Raman Scattering (SERS)-Active Substrate

A new route has been developed to design plasmonic pollen grain-like nanostructures (PGNSs) as surface-enhanced Raman scattering (SERS)-active substrate. The nanostructures consisting of silver (Ag) and gold (Au) nanoparticles along with zinc oxide (ZnO) nanoclusters as spacers were found highly SERS-active. The morphology of PGNSs and those obtained in the intermediate stage along with each elemental evolution has been investigated by a high-resolution field emission scanning electron microscopy. The optical band gaps and crystal structure have been identified by UV-vis absorption and X-ray powder diffraction (XRD) measurements, respectively. For PGNSs specimen, three distinct absorption bands related to constituent elements Ag, Au, and ZnO were observed, whereas XRD peaks confirmed the existence of Ag, Au, and ZnO within the composition of PGNSs. SERS-activity of PGNSs was confirmed using Rhodamine 6G (R6G) as Raman-active dyes. Air-cooled solid-state laser kits of 532 nm were used as excitation sources in SERS measurements. SERS enhancement factor was estimated for PGNSs specimen and was found as high as 3.5×10⁶. Finite difference time domain analysis was carried out to correlate the electromagnetic (EM) near-field distributions with the experiment results achieved under this investigation. EM near-field distributions at different planes were extracted for s-, p- and 45° of incident polarizations. EM near-field distributions for such nanostructures as well as current density distributions under different circumstances were demonstrated and plausible scenarios were elucidated given SERS enhancements. Such generic fabrication route as well as correlated investigation is not only indispensable to realize the potential of SERS applications but also unveil the underneath plasmonic characteristics of complex SERS-active nanostructures.     

Combination of RSM and NSGA-II algorithm for optimization and prediction of thermal conductivity and viscosity of bioglycol/water mixture containing SiO2 nanoparticles

The fluids containing nanoparticles have enhanced thermo-physical characteristics in comparison with conventional fluids without nanoparticles. Thermal conductivity and viscosity are thermo-physical properties that strongly determine heat transfer and momentum. In this study, the response surface method was firstly used to derive an equation for the thermal conductivity and another one for the viscosity of bioglycol/water mixture (20:80) containing silicon dioxide nanoparticles as a function of temperature as well as the volume fraction of silicon dioxide. Then, NSGA-II algorithm was used for the optimization and maximizing thermal conductivity and minimizing the nanofluid viscosity. Different fronts were implemented and 20th iteration number was selected as Pareto front. The highest thermal conductivity (0.576 W/m.K) and the lowest viscosity (0.61 mPa.s) were obtained at temperature on volume concentration of (80 °C and 2%) and (80 °C without nanoparticle) respectively. It was concluded that the optimum thermal conductivity and viscosity of nanofluid could be obtained at maximum temperature (80 °C) or a temperature close to this temperature. An increase in the volume fraction of silicon dioxide led to the enhancement of thermal conductivity but the solution viscosity was also increased. Therefore, the optimum point should be selected based on the system requirement.