Universal macroscopic background formation in surface super-roughening

We study a class of super-rough growth models whose structure factor satisfies the Family-Vicsek scaling. We demonstrate that a macroscopic background spontaneously develops in the local surface profile, which dominates the scaling of the local surface width and the height-difference. The shape of the macroscopic background takes a form of a finite-order polynomial whose order is decided from the value of the global roughness exponent. Once the macroscopic background is subtracted, the width of the resulting local surface profile satisfies the Family-Vicsek scaling. We show that this feature is universal to all super-rough growth models, and we also discuss the difference between the macroscopic background formation and the pattern formation in other models.Comment: 5 pages, LaTex, 1 figure, minor correction

Scalable approximate FRNN-OWA classification

Fuzzy Rough Nearest Neighbour classification with Ordered Weighted Averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbour search. In practice, the query time complexity of exact nearest neighbour search algorithms in more than a handful of dimensions is near-linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbours returned by Hierarchical Navigable Small Worlds (HNSW), a recent approximative nearest neighbour search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW, and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster

Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient

This paper addresses a multi-scale finite element method for second order linear elliptic equations with arbitrarily rough coefficient. We propose a local oversampling method to construct basis functions that have optimal local approximation property. Our methodology is based on the compactness of the solution operator restricted on local regions of the spatial domain, and does not depend on any scale-separation or periodicity assumption of the coefficient. We focus on a special type of basis functions that are harmonic on each element and have optimal approximation property. We first reduce our problem to approximating the trace of the solution space on each edge of the underlying mesh, and then achieve this goal through the singular value decomposition of an oversampling operator. Rigorous error estimates can be obtained through thresholding in constructing the basis functions. Numerical results for several problems with multiple spatial scales and high contrast inclusions are presented to demonstrate the compactness of the local solution space and the capacity of our method in identifying and exploiting this compact structure to achieve computational savings

Wavelet feature extraction and genetic algorithm for biomarker detection in colorectal cancer data

Biomarkers which predict patient’s survival can play an important role in medical diagnosis and treatment. How to select the significant biomarkers from hundreds of protein markers is a key step in survival analysis. In this paper a novel method is proposed to detect the prognostic biomarkers ofsurvival in colorectal cancer patients using wavelet analysis, genetic algorithm, and Bayes classifier. One dimensional discrete wavelet transform (DWT) is normally used to reduce the dimensionality of biomedical data. In this study one dimensional continuous wavelet transform (CWT) was proposed to extract the features of colorectal cancer data. One dimensional CWT has no ability to reduce dimensionality of data, but captures the missing features of DWT, and is complementary part of DWT. Genetic algorithm was performed on extracted wavelet coefficients to select the optimized features, using Bayes classifier to build its fitness function. The corresponding protein markers were located based on the position of optimized features. Kaplan-Meier curve and Cox regression model 2 were used to evaluate the performance of selected biomarkers. Experiments were conducted on colorectal cancer dataset and several significant biomarkers were detected. A new protein biomarker CD46 was found to significantly associate with survival time

Impact of Selected Infrared Wavelengths Treatment on Inactivation of Microbes on Rough Rice

Formation of harmful microbes and their associated mycotoxins on rough rice during storage present negative socioeconomic impacts to producers and consumers. The objective for this study was to investigate the impact of treating rough rice with selected infrared (IR) wavelengths at different IR intensities and heating durations, followed by a tempering step for further inactivation of microbes (mold and bacteria) on the grain. Freshly-harvested long-grain, hybrid, rough rice (XL 745) with initial moisture content (IMC) of 18.4% wet basis (w.b.) was used. Two-hundred grams (200 g) of the samples were treated at different IR wavelengths (λ) which were 3.2, 4.5, and 5.8 μm for 10, 20 and 30 seconds (s) at product-to-emitter gaps of 110, 275, 440 mm. This was then followed by tempering the grain; putting them in air-tight jars and held at a constant temperature of 60 oC for 4 hours (h). The inoculated Petrifilm plates for mold and bacterial analyses were incubated at 25oC for 120 h and 35oC for 48 h respectively. . The samples treated at wavelength 3.2 μm (product-to-emitter gap 110 mm) for 30 s showed the highest reduction in mold and bacterial load; approximately 3.11 and 1.09 log reduction in the mold and bacterial loads, respectively. Tempering treatment further reduced the microbial load at each IR treatment condition. Molds showed more susceptibility to the IR decontamination than bacteria population. This study provides useful information on the effectiveness of IR heating and tempering on microbial inactivation on rough rice

Laboratory studies of the roughness and suspended load of alluvial streams

This report describes research work done under Contract No. DA-25-075-eng-3866 with the U. S. Army, Corps of Engineers, Missouri River Division, Omaha, during the period 1954-1957, on problems of suspended load transport in alluvial streams. A total of 94 experimental runs were made in two laboratory flumes charged with fine sand of several size distributions. Special attention was given to the variation of the friction factor caused by the changing bed configuration and the damping effect of suspended sediment. The relationship between the sediment transportation rate and the hydraulic variables was also investigated. Most of the runs (General Studies, Chap. V) were made with the bed of the flume completely covered with loose sand but some special runs (Special Studies, Chap. VII) were made with the sand bed chemically solidified in place to prevent sediment transport while preserving the bed configuration previously generated by a natural flow of the same velocity with loose sand. The principal laboratory results are as follows: 1. The friction factor f for a stream with a movable sand bed may vary several fold, being highest at low or medium flow velocities and lowest at high velocity. 2. The principal cause of the variation in f is the appearance of dunes at low or medium velocities and disappearance at high velocities. 3. A secondary cause for the reduction in f for high sediment transport rates is the damping effect of the suspended sediment on the turbulence, and the concomitant reduction in the turbulent diffusion coefficients. The maximum observed reduction due directly to the sediment load was only about 28 percent. 4. The discharge and sediment transportation rate are not unique functions of depth and slope because of the variable roughness. Slope (or shear) must probably be considered a dependent variable for alluvial streams because several equilibrium flows can yield the same slope and shear stress. The laboratory data are compared with similar data for natural streams, and the most promising existing analyses for roughness and sediment load are discussed in the light of the present findings. In addition, a critical review of early and recent literature on the resistance of sediment-laden streams is presented in Chapter II