Zn3(C6H14N2)3[B6P12O39(OH)12] · (C6H14N2)[HPO4]: A Chiral Borophosphate – Triethylenediammonium Hydrogenphosphate Composite

A novel borophosphate, Zn₃(C₆H₁₄N₂)₃[B₆P₁₂O₃₉(OH)₁₂] · (C₆H₁₄N₂)[HPO₄] has been synthesised under mild hydrothermal conditions at T = 165 °C. The chiral crystal structure was determined by single crystal X‐ray diffraction data (trigonal, R3 (no. 146), Z = 3, a = 2089.55(4) pm, c = 1237.03(4) pm, V = 4677.5(2) · 10⁶ pm³, R₁ = 0.066, wR₂ = 0.164 for 5100 observed reflections). The title compound can be considered as an ordered composite of the two different and neutral structures which fit into each other: An open framework of composition Zn₃(C₆H₁₄N₂)₃[B₆P₁₂O₃₉(OH)₁₂] and columns of composition (C₆H₁₄N₂)[HPO₄]. The framework structure is formed by mixed octahedral‐tetrahedral secondary building units, in a three‐dimensional arrangement reflecting a hierarchical derivative of the NbO structure type. The underlying NbO topology is illustrated with the help of Periodic Nodal Surfaces. The composite nature of the compound is resolved in the spatial segregation of two frameworks with a separating surface.     

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.     

Finding an efficient solution to linear bilevel programming problem: An effective approach

Multilevel programming is developed to solve the decentralized problem in which decision makers (DMs) are often arranged within a hierarchical administrative structure. The linear bilevel programming (BLP) problem, i.e., a special case of multilevel programming problems with a two level structure, is a set of nested linear optimization problems over polyhedral set of constraints. Two DMs are located at the different hierarchical levels, both controlling one set of decision variables independently, with different and perhaps conflicting objective functions. One of the interesting features of the linear BLP problem is that its solution may not be Paretooptimal. There may exist a feasible solution where one or both levels may increase their objective values without decreasing the objective value of any level. The result from such a system may be economically inadmissible. If the decision makers of the two levels are willing to find an efficient compromise solution, we propose a solution procedure which can generate effcient solutions, without finding the optimal solution in advance. When the near-optimal solution of the BLP problem is used as the reference point for finding the efficient solution, the result can be easily found during the decision process.     

Cluster Analysis of Gene Expression Data

The expression levels of many thousands of genes can be measured simultaneously by DNA microarrays (chips). This novel experimental tool has revolutionized research in molecular biology and generated considerable excitement. A typical experiment uses a few tens of such chips, each dedicated to a single sample—such as tissue extracted from a particular tumor. The results of such an experiment contain several hundred thousand numbers, that come in the form of a table, of several thousand rows (one for each gene) and 50–100 columns (one for each sample). We developed a clustering methodology to mine such data. In this review I provide a very basic introduction to the subject, aimed at a physics audience with no prior knowledge of either gene expression or clustering methods. I explain what genes are, what is gene expression and how it is measured by DNA chips. Next I explain what is meant by clustering and how we analyze the massive amounts of data from such experiments, and present results obtained from analysis of data from colon cancer, brain tumors and breast cancer.     

Nearest q-Flat to m Points

Recently, Bradley and Mangasarian studied the problem of finding the nearest plane to m given points in ⁿ in the least square sense. They showed that the problem reduces to finding the least eigenvalue and associated eigenvector of a certain n×n symmetric positive-semidefinite matrix. We extend this result to the general problem of finding the nearest q-flat to m points, with 0qn–1.     

Approximate importance sampling Monte Carlo for data assimilation

Importance sampling Monte Carlo offers powerful approaches to approximating Bayesian updating in sequential problems. Specific classes of such approaches are known as particle filters. These procedures rely on the simulation of samples or ensembles of the unknown quantities and the calculation of associated weights for the ensemble members. As time evolves and/or when applied in high-dimensional settings, such as those of interest in many data assimilation problems, these weights typically display undesirable features. The key difficulty involves a collapse toward approximate distributions concentrating virtually all of their probability on an implausibly few ensemble members.

After reviewing ensembling, Monte Carlo, importance sampling and particle filters, we present some approximations intended to moderate the problem of collapsing weights. The motivations for these suggestions are combinations of (i) the idea that key dynamical behavior in many systems actually takes place on a low dimensional manifold, and (ii) notions of statistical dimension reduction. We illustrate our suggestions in a problem of inference for ocean surface winds and atmospheric pressure. Real observational data are used.     

Preparation of hybrid film with superhydrophobic surfaces based on irregularly structure by emulsion polymerization

A superhydrophobic surface originated from quincunx-shape composite particles was obtained by utilizing the encapsulation and graft of silica particles to control the surface chemistry and morphology of the hybrid film. The composite particles make the surface of film form a composite interface with irregular binary structure to trap air between the substrate surface and the liquid droplets which plays an essential role in obtaining high water contact angle and low water contact angle hysteresis. The water contact angle on the hybrid film is determined to be 154 ± 2° and the contact angle hysteresis is less than 5°. This is expected to be a simple and practical method for preparing self-cleaning hydrophobic surfaces on large area.     

The k-means range algorithm for personalized data clustering in e-commerce

This paper describes the k-means range algorithm, a combination of the partitional k-means clustering algorithm with a well known spatial data structure, namely the range tree, which allows fast range searches. It offers a real-time solution for the development of distributed interactive decision aids in e-commerce since it allows the consumer to model his preferences along multiple dimensions, search for product information, and then produce the data clusters of the products retrieved to enhance his purchase decisions. This paper also discusses the implications and advantages of this approach in the development of on-line shopping environments and consumer decision aids in traditional and mobile e-commerce applications.     

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.     

基于对象多属性差异的灰色发展聚类方法及应用

在现实决策问题中,决策对象在不同时期行为状态和所属类型往往呈现一定的发展规律,而现有聚类方法难以充分挖掘聚类对象的发展信息、对象间的关系信息和发展属性的差异信息。为有效处理此类问题,考虑到研究对象的发展趋势、发展行为和发展绝对量与增长量的属性差异,采用GM(1,1)和灰色定权聚类方法,构建了基于对象多属性差异的灰色发展聚类方法,并以我国区域高新技术产业化聚类评估问题为例验证了模型的有效性与合理性。结果表明,所构建模型能够有效描述研究对象呈现发展趋势或未来行为,并实现对研究对象的有效聚类。