Ein lösbarkeitskriterium für ein mehrstufen – mehrsorten – transportproblem

A variant for checking a solvability eriterion for multilevel multisort transportation problem is given.     

Optimization of Direct Blue 71 sorption by organic rich-compost following multilevel multifactor experimental design

Removal of a troublesome textile dye, Direct Blue 71 (DB71) from water by a food waste compost was assessed in the current study. Since compost dye sorption is a multi-factor process influenced by mass, pH, concentration, temperature, contact time, and salinity, the cumulative influence of all parameters on DB71 removal was examined following an optimal multilevel multifactor experimental design. The process had to be presented using both linear and interaction terms, according to the variables analysis: Dye sorption = –0.050Mass + 0.122Conc–0.114pH + 0.132Time – 0.074Temp + 0.056Sal + 0.103Mass × Conc + 0.226 Mass × pH – 0.257Mass × Time – 0.112Mass × Temp – 0.041Mass × Sal + 0.008Conc × pH + 0.100Conc × Time + 0.089Conc × Temp + 0.167Conc × Sal – 0.245pH × Time – 0.231pH × Temp – 0.123pH × Sal + 0.358Tim × Temp + 0.355Tim × Sal – 0.045Temp × Sal (R² = 0.9241)Salinity and pH were positively correlated with concentration, and contact time with temperature and salinity, to get better dye uptake. The optimal conditions for dye removal were the following: solid:liquid ratio 1:375, pH 3.0, initial dye concentration 400 mg L^?1, contact time 240 min, salinity 0.6 M NaCl, temperature 50 °C. At the optimum combination of factors, equilibrium sorption isotherm and sorption kinetics were studied. Kinetic analysis indicated high sorption rate 4.0 mg g^?1 min^?1 while 28% of maximum capacity was reached within the first 10 min of interaction. Sorption isotherm has L2-shape which reflected surface saturation at high solute concentration with low competition with solvent molecules, with a maximum sorption capacity of 95.4 mg g^?1. In column experiments performed at bed depth 5.1–12.8 cm, flow rate 1.0–2.0 mL min^?1 and influent concentration 10–20 mg L^?1, sorption capacity was 19.6 mg g^?1, which represents 21% of the maximum capacity at equilibrium conditions. IR analysis of dye-loaded-compost confirmed the contribution of hydrophobic-hydrophobic forces in the sorption process.     

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.     

等离子体放电中的滞后,分岔和多次上跳现象

滞后现象很早就在放电管的伏安曲线上被发现。近年来的研究发现,这种非线性现象存在于多种等离子体放电过程中并伴随着一些不稳定性出现,Knorr利用简单的突变模型对这种现象作了定性的描述。王海达等改进了Knorr的简单模型,以便对他们观察到的三稳现象作唯象的解释。我们在实验中仔细观察了放电伏安特性随气压的变化,发现随着气压的升高,伏安特性逐渐由单稳过渡到简单的滞后,随机分岔、然后再演变成二次上跳、三次三跳。     

CBS constants for multilevel splitting of graph-Laplacian and application to preconditioning of discontinuous Galerkin systems

The goal of this work is to derive and justify a multilevel preconditioner of optimal arithmetic complexity for symmetric interior penalty discontinuous Galerkin finite element approximations of second order elliptic problems. Our approach is based on the following simple idea given in [R.D. Lazarov, P.S. Vassilevski, L.T. Zikatanov, Multilevel preconditioning of second order elliptic discontinuous Galerkin problems, Preprint, 2005]. The finite element space of piece-wise polynomials, discontinuous on the partition , is projected onto the space of piece-wise constant functions on the same partition that constitutes the largest space in the multilevel method. The discontinuous Galerkin finite element system on this space is associated to the so-called “graph-Laplacian”. In 2-D this is a sparse M-matrix with -1 as off diagonal entries and nonnegative row sums. Under the assumption that the finest partition is a result of multilevel refinement of a given coarse mesh, we develop the concept of hierarchical splitting of the unknowns. Then using local analysis we derive estimates for the constants in the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality, which are uniform with respect to the levels. This measure of the angle between the spaces of the splitting was used by Axelsson and Vassilevski in [Algebraic multilevel preconditioning methods II, SIAM J. Numer. Anal. 27 (1990) 1569–1590] to construct an algebraic multilevel iteration (AMLI) for finite element systems. The main contribution in this paper is a construction of a splitting that produces new estimates for the CBS constant for graph-Laplacian. As a result we have a preconditioner for the system of the discontinuous Galerkin finite element method of optimal arithmetic complexity.     

A Cross-Entropy Approach to the Estimation of Generalized Linear Multilevel Models

In this article, we use the cross-entropy method for noisy optimization for fitting generalized linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to the benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the article, the method is used to model the probability of firm exits in the healthcare industry in Italy. Supplemental materials are available online.     

Structure dependent sampling in compressed sensing: Theoretical guarantees for tight frames

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame. By dividing the sampling coefficients into levels, our main result will describe how the amount of subsampling in each level is determined by the local coherences between the sampling and sparsifying operators and the localized level sparsities – the sparsity in each level under the sparsifying operator.     

Asymptotic robustness of the normal theory likelihood ratio statistic for two-level covariance structure models

Data in social and behavioral sciences are often hierarchically organized. Special statistical procedures have been developed to analyze such data while taking into account the resulting dependence of observations. Most of these developments require a multivariate normality distribution assumption. It is important to know whether normal theory-based inference can still be valid when applied to nonnormal hierarchical data sets. Using an analytical approach for balanced data and numerical illustrations for unbalanced data, this paper shows that the likelihood ratio statistic based on the normality assumption is asymptotically robust for many nonnormal distributions. The result extends the scope of asymptotic robustness theory that has been established in different contexts.     

Dual multilevel optimization

We study the structure of dual optimization problems associated with linear constraints, bounds on the variables, and separable cost. We show how the separability of the dual cost function is related to the sparsity structure of the linear equations. As a result, techniques for ordering sparse matrices based on nested dissection or graph partitioning can be used to decompose a dual optimization problem into independent subproblems that could be solved in parallel. The performance of a multilevel implementation of the Dual Active Set algorithm is compared with CPLEX Simplex and Barrier codes using Netlib linear programming test problems.