On the efficiency of bootstrap method into the analysis contingency table

The bootstrap method is a computer intensive statistical method that is widely used in performing nonparametric inference. Categorical data analysis, in particular the analysis of contingency tables, is commonly used in applied field. This work considers nonparametric bootstrap tests for the analysis of contingency tables. There are only a few research papers which exploit this field. The p-values of tests in contingency tables are discrete and should be uniformly distributed under the null hypothesis. The results of this article show that corresponding bootstrap versions work better than the standard tests. Properties of the proposed tests are illustrated and discussed using Monte Carlo simulations. This article concludes with an analytical example that examines the performance of the proposed tests and the confidence interval of the association coefficient.     

Nonsmooth nonnegative matrix factorization (nsNMF)

We propose a novel nonnegative matrix factorization model that aims at finding localized, part-based, representations of nonnegative multivariate data items. Unlike the classical nonnegative matrix factorization (NMF) technique, this new model, denoted "nonsmooth nonnegative matrix factorization" (nsNMF), corresponds to the optimization of an unambiguous cost function designed to explicitly represent sparseness, in the form of nonsmoothness, which is controlled by a single parameter. In general, this method produces a set of basis and encoding vectors that are not only capable of representing the original data, but they also extract highly focalized patterns, which generally lend themselves to improved interpretability. The properties of this new method are illustrated with several data sets. Comparisons to previously published methods show that the new nsNMF method has some advantages in keeping faithfulness to the data in the achieving a high degree of sparseness for both the estimated basis and the encoding vectors and in better interpretability of the factors.     

Stochastic Models for Pad Structure and Pad Conditioning Used in Chemical-Mechanical Polishing

Stochastic models are presented for the structure and conditioning of pads used in chemical-mechanical polishing of wafers. First the one-dimensional distribution function of surface depth in the case of a conditioned solid pad is described. Then, for characterizing the structure of a foamed pad, the theory of random closed sets is applied. An important distributional characteristic of a random closed set, the linear contact distribution function, yields the contribution to surface depth resulting from pores. As a special example the Boolean model is considered. This leads to a formula that describes the variability of the surface of a conditioned foamed pad after a certain time. Simulations and experimental data show a good agreement between theory and reality.     

Influence of particle elasticity in shear testers

Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft particle molecular dynamics simulations (Particle Flow Code, PFC) for elastic particles and contact dynamics simulations (CD) for the limit of perfectly rigid particles. As soon as the system dilates to form shear bands, it relaxes the elastic strains so that one finds the same stresses for rigid respectively elastic particles in steady state flow. The principal stresses in steady state flow are determined. They are proportional to each other, giving rise to an effective macroscopic friction coefficient which is about 10% smaller than the microscopic friction coefficient between the grains.     

Physiological cost of energy-equivalent noise exposures with a rating level of 85 dB(A):: Hearing threshold shifts associated with energetically negligible continuous and impulse noise

In industry continuous or impulse noise does not occur exclusively; rather it is a combination of both. If low-level continuous noise or impulse noise (below 120 dB) is added to an already existing high-level continuous noise this often numerically causes no essential increase in the rating level. Yet, it cannot be expected that also aural strain of these exposures is always negligible. Therefore, in a cross-over test series, ten male subjects (Ss) were exposed to white noise of 94 dB(A) for 1 h (TS I), energy-equivalent to an 8 h-rating level L_Ard of 85 dB(A). In a second test series (TS II) the same exposure was combined with 900 energetically negligible 5-ms impulses with a noise level of 113 dB(A) which increased the rating level by only 0.4 dB. The noise exposure of TS I and TS II was followed by an idealized resting phase in a soundproof cabin. In a third test series (TS III) the continuous noise of 94 dB(A) / 1 h was followed by 3 h of white noise at 70 dB(A). Such an additional load increases the L_Ard by merely 0.1 dB to 85.1 dB(A). In all three test series, the noise-induced temporary threshold shift (TTS₂) and its restitution were measured. The continuous noise exposure of 94 dB(A) for 1 h was associated with a TTS₂ of around 20 dB which disappeared completely after about 2 h. The additional impulse noise caused a small increase in the TTS₂ and a prolongation of the restitution time. The maximum mean temporary threshold shift for the group increased only slightly (from 22.5 to 25.9 dB, which nevertheless can be statistically proven at a significance level of p 0.99). Yet, more importantly, the restitution time increased from 126 to 175 min, i. e. 3 h, which can be statistically proven at a significance level of p0.95. The TTS₂-values of TS III did not differ significantly from those resulting from TS I. That was expected as the conditions up to that point in time were identical. But due to the additional subsequent exposure, the mean restitution time increased considerably from 126 min up to 240 min (4 h). The mean total physiological cost represented by the integrated restitution temporary threshold shift (IRTTS) increased in TS II by approximately 40% and in TS III even by 140%.

Relevance to industry

The results of the study show that levels of noise which have no influence on the rating level which traditionally is calculated according to the energy-equivalence principle are often of great importance, as they can lead to considerably prolonged restitution times. Therefore, the purely energy-equivalent determination of the rating level of both impulse noise and low sound levels can lead to an underestimation of latent problems so that over time a reversible TTS can evolve into a permanent threshold shift. The results are also of importance for the acoustic design of break rooms for noise-exposed workers. There should be conditions that allow an undisturbed restitution of hearing.     

High-intensity x-ray diffraction apparatus for pressures up to 100 kilobars and temperatures down to 1.5 K

A high-pressure diamond anvil pressure technique for x-ray structure investigations at temperatures down to 1.5 K is described. An energy dispersive method in conjunction with a newly developed conical x-ray shutter brings maximum intensity to the adjacent germanium detector. Superconductivity is detected by use of a SQUID. The 4096-channel analyzer data are evaluated on-line by a computer. The precision of the lattice parameter determination is discussed.