A branch and cut algorithm for the hierarchical network design problem

The Hierarchical Network Design Problem consists of locating a minimum cost bi-level network on a graph. The higher level sub-network is a path visiting two or more nodes. The lower level sub-network is a forest connecting the remaining nodes to the path. We optimally solve the problem using an ad hoc branch and cut procedure. Relaxed versions of a base model are solved using an optimization package and, if binary variables have fractional values or if some of the relaxed constraints are violated in the solution, cutting planes are added. Once no more cuts can be added, branch and bound is used. The method for finding valid cutting planes is presented. Finally, we use different available test instances to compare the procedure with the best known published optimal procedure, with good results. In none of the instances we needed to apply branch and bound, but only the cutting planes.     

Vibration of an elastic plate under action of an incompressible fluid in case of N = 0 approximation of I. Vekua's hierarchical models

This article deals with the study of the interaction between an elastic plate with constant thickness and an incompressible fluid when the plate is approximated by the N?=?0 order term of Vekua's hierarchical model.     

Case Influence Analysis in Bayesian Inference

Abstract

We demonstrate how case influence analysis, commonly used in regression, can be applied to Bayesian hierarchical models. Draws from the joint posterior distribution of parameters are importance weighted to reflect the effect of deleting each observation in turn; the ensuing changes in the posterior distribution of each parameter are displayed graphically. The procedure is particularly useful when drawing a sample from the posterior distribution requires extensive calculations (as with a Markov Chain Monte Carlo sampler). The structure of hierarchical models, and other models with local dependence, makes the importance weights inexpensive to calculate with little additional programming. Some new alternative weighting schemes are described that extend the range of problems in which reweighting can be used to assess influence. Applications to a growth curve model and a complex hierarchical model for opinion data are described. Our focus on case influence on parameters is complementary to other work that measures influence by distances between posterior or predictive distributions.     

Statistical Computations on Biological Rhythms I: Dissecting Variable Cycles and Computing Signature Phases in Activity-Event Time Series

We propose a computational methodology to compute and extract circadian rhythmic patterns from an individual animal’s activity-event time series. This lengthy dataset, composed of a sequential event history, contains an unknown number of latent rhythmic cycles of varying duration and missing waveform information. Our computations aim at identifying the onset signature phase which individually indicates a sharp event intensity surge, where a subject-night ends and a brand new cycle’s subject-day begins, and collectively induces a linearity manifesting the individual circadian rhythmicity and information about the average period. Based on the induced linearity, the least squares criterion is employed to choose an optimal sequence of computed onset signature phases among a finite collection derived from the hierarchical factor segmentation (HFS) algorithm. The multiple levels of coding schemes in the HFS algorithm are designed to extract contrasting patterns of aggregation against sparsity of activity events along the entire temporal axis. This optimal sequence dissects the whole time series into a sequence of rhythmic cycles without model assumptions or ad hoc behavioral definitions regarding the missing waveform information. The performance of our methodology is favorably compared with two popular approaches based on the periodogram in a simulation study and in real data analyses. The computer code and data used in this article are available on the JCGS webpage.     

Evaluating and selecting the supplier in detergent production industry using hierarchical fuzzy TOPSIS

Supply chain management has increasingly attracted attention as a systematic approach to integrate the supply chain in order to planning and controlling the materials and information from suppliers to customers. One of the most important issues in supply chain management is selection of the appropriate supplier which has significant effect on purchasing cost decrease and increase in the organization’s competition ability. Selection of the best supplier is naturally complex with no definite structure, and dependent on the type of suppliers’ activity. In the process of decision making about suppliers and many qualitative and quantitative performance indicators such as quality, price, flexibility, and due date should be considered. Then, the supplier selection problem is a multi-criteria decision making problem where numerous methods have been proposed to solve this problem so far. In the current paper, four suppliers of imported raw material “Tripolyphosphate (TPP)” (primary material to produce the detergent powder with a case study in Iran) are evaluated based on 25 effective criteria using the hierarchical fuzzy TOPSIS (HFTOPSIS) approach.     

Error Bounds for Low-Rank Approximations of the First Exponential Integral Kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.     

氮化硼纳米管-纳米片分级结构的制备及光学和吸附特性

将五硼酸铵、 氨硼烷络合物和氧化镁混合, 球磨均匀后, 在1200 ℃及0.6 L/min流动氨气保护条件下退火6 h, 即可在氧化铝基片上收集到白色毛状产物. 采用X射线衍射(XRD), 红外光谱(FTIR)、 扫描电子显微镜(SEM)、 透射电子显微镜(TEM)、 拉曼光谱(Raman)、 紫外-可见吸收光谱(UV-Vis)和荧光光谱(PL)对产物进行了表征. 结果表明, 样品呈一维线状分级结构, 长度大于5 mm, 中间为竹节状空心结构, 内部管径为50~350 nm, 外径范围为200~800 nm. 分级结构表面负载了大量氮化硼(BN)纳米薄片, 单个薄片厚度约为13 nm. 薄片弯曲褶皱, 相互交织, 构成1个氮化硼片层, 其厚度约为50~200 nm. UV-Vis和PL光谱测试结果表明, 氮化硼纳米管(BNNT)分级结构在紫外光材料领域具有一定的应用潜力, 且对亚甲基蓝具有良好的吸附能力(7 min即可吸附71%, 107 min时可吸附96%). 对比实验结果表明, BNNT的生长机理遵循气-液-固相(VLS)模型, 而表面负载的超薄BN片的生长机理遵循气-固相(VS)模型.     

Facile assembly of mesoporous silica nanoparticles with hierarchical pore structure for CO2 capture

In the work, we propose an efficient one-pot approach for synthesis of a new type of mesoporous silica nanoparticles (MSNs). That can be successfully realized by using tetraethylorthosilicate (TEOS) and N-[3-(trimethoxysilyl)propyl]ethylenediamine (TSD) as the silica precursors and cetyltrimethylammonium bromide (CTAB) as the structure-directing agent through a facile assembly process. The as-synthesized MSNs possess a spherical morphology with about 230 nm, a relatively high surface area of 133 m²/g, and a hierarchical pore size distribution. When applied as the sorbents, the amine-functioned MSNs demonstrate the enhanced adsorption capacity for CO₂ capture (at 1 bar, 15 vol% CO₂, up to 80.5 mg/g at 75 °C), high selectivity, and good cycling durability, benefiting from the suitable modification of polyethyleneimine.