Equivariance and Invariance for Optimal Designs in Generalized Linear Models Exemplified by a Class of Gamma Models

The main intention of the present work is to outline the concept of equivariance and invariance in the design of experiments for generalized linear models and to demonstrate its usefulness. In contrast with linear models, pairs of transformations have to be employed for generalized linear models. These transformations act simultaneously on the experimental settings and on the location parameters in the linear component. Then, the concept of equivariance provides a tool to transfer locally optimal designs from one experimental region to another when the nominal values of the parameters are changed accordingly. The stronger concept of invariance requires a whole group of equivariant transformations. It can be used to characterize optimal designs which reflect the symmetries resulting from the group actions. The general concepts are illustrated by models with gamma distributed response and a canonical link. There, for a given transformation of the experimental settings, the transformation of the parameters is not unique and may be chosen to be nonlinear in order to fully exploit the model structure. In this case, we can derive invariant maximin efficient designs for the D- and the IMSE-criterion.

The Effects of Different Slurry Concentrations and Wire Speeds for Swinging and Non-Swinging Wire-Saw Machining

Slurry concentration and wire speed affect the yield and machining quality of ceramics (Al2O3) that are produced using wire-saw machining (WSM). This study determines the effect of slurry concentration and wire speed on the material removal rate (MRR), the machined surface roughness (SR), the kerf width, the wire wear and the flatness for swinging and non-swinging WSM. The experiments show that swinging WSM results in a higher machining efficiency than non-swinging WSM. WSM with swinging also achieves a peak MRR at a medium slurry concentration (25 wt%) and a higher wire speed (5.6 m/s) using the cutting conditions for the experimental region. However, slurry concentration and wire speed have no significant effect on the machined SR, the kerf width, the wire wear or the flatness for WSM with swinging mode.

A Refinement of the Conjecture on the Pseudo Component Transformation of the Lattice Points in the Simplex

We consider mixture experiments in which the proportions of the components must be non-negative and their sum must equal one. Thus, the experimental region for a mixture of components is a simplex. Li and Zhang (2017) made the conjecture that the pseudo component transformation of the lattice points in the simplex has a special property. In this paper, we show that this conjecture is not true in general. Furthermore, we refine this conjecture and prove the refined conjecture.

Types of housing estate – German nomenclature and systematics on the example of Wałbrzych agglomeration settlements

The term housing estate ( Wohnsiedlung, osiedle mieszkaniowe) appeared in the press and professional literature at the beginning of 20th century. Analysis of the German terms, initially of a cultural and geographical nature, used then in the emerging professional architecture-related language, reveals what factors were considered to be the most important in deciding on the characteristic traits of the housing development. In most cases, the nomenclature and typology were based on experience from Berlin and the largest German cities. The local specificity based on research into the characteristics of an ‘experimental’ region (i.e. the developing Wałbrzych (Waldenburg) agglomeration) may highlight not only issues related to the perception of the terms of housing estate types but also their design solutions, and in some cases, also the origins of new architectural concepts.

BAYESIAN APPROACH TO THE D-OPTIMAL FOR MIXTURE EXPERIMENTAL DESIGN

A mixture experiment is a special case of response surface methodology in which the value of the components are proportions. In case there are constraints on the proportions, the experimental region can be not a simplex. The classical designs such as a simplex-lattice design or a simplex-centroid design, in some cases, cannot fit to the problem. In this case, optimal design come up as a solution. A D-optimal design is seeking a design in which minimizing the covariance of the model parameter. Some model parameters are important and some of them are less important. As the priority of the parameters, the prior information of parameters is needed in advance. This brings to a Bayesian D-optimal design. This research was focus on a baking experiment in which consisted of three ingredients with lower bounds on the proportion of the ingredients. The assumption model was a quadratic model. Due to the priority of the model parameters, the Bayesian D-optimal design was used to solve the problem. A point-exchange algorithm was developed to find the optimal design. Nineteen candidates is used to choose twelve design points. It found that the potential term is feasible to the actual model and design points represent overall points in the design area.

Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes

Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the run sizes. In this paper, we propose a new method for constructing SLHDs with arbitrary run sizes, and a new combined space-filling measurement describing the space-filling property for both the whole design and its slices. Furthermore, we develop general algorithms to search for the optimal SLHD with arbitrary run sizes under the proposed measurement. Examples are presented to illustrate that effectiveness of the proposed methods.

Response of Bio-priming in okra for vegetable production

The field experiment was conducted at District Seed Farm, Bidhan Chandra Krishi Viswavidyalaya, Kalyani, Nadia, West Bengal in summer season of 2011 and 2012. Pre-sowing bio-priming was done with Trichoderma viride and Pseudomonas fluorescens with an un-primed control to assess the trend of okra varieties viz., Lalu, Arka Anamika, Ramya, Satsira, Lady Luck,Debpusa Jhar,Japani Jhar and Barsha Laxmi due to bio-priming of seeds towards vegetable production Significant variation among the varieties was noted for all the characters studied. Okra variety Lalu gave highest vegetable yield per plant in both years and it was statistically at par with Arka Anamika. Vegetable yield per plant was increased by 4.33 to 20.08% in first year and 3.68 to 19.60% in second year with T. viride as compared to P. fluorescens and un-primed control. Individual varieties indicated that vegetable yield per plant was maximum with Lalu when priming was made with both the bio-inoculants followed by Arka Anamika during both years. Hence, Lalu and Arka Anamika may be recommended for experimental region for higher yield and pre-sowing seed bio-priming may be recommended with both T.viride and P. fluorescens for enhanced vegetable yield of okra.

The public committed effective dose caused by consumption of foods & foodstuffs in Ninh Thuan

Based on the data set about radionuclides concentration in foods and foodstuffs obtained from the implementation of the National Projects on “Investigation on radionuclides and toxic elements concentration in the main kinds of foods & foodstuffs of Vietnam” and “Assessment of Marine Environmental Radioactivity Status for two selected sites of Nuclear Power Plant in the near future at Ninh Thuan Province”, a calculation software of the International Commission for Radiological Protection (ICRP), the public committed effective doses (for adult only) caused by consumption of main foods & foodstuffs in the studied experimental region were estimated. In general, the committed effective doses for adult public caused by the daily intake of radionuclides of U, 232Th, 210Pb, 210Po, 226Ra, 40K, 90Sr, 137Cs and 239,240Pu are: 7.9´10-5, 4.1´10-6, 1.1´10-2, 1.7´10-1, 1.4´10-3, 1.2´10-1, 2.32´10-4, 1.9´10-4, 2.7´10-9 (mSv/year), respectively, and the contribution of U, Th series, 40K and artificial radionuclides are 61.3%, 38.6% and 0.1%, respectively.