NBLDA: Negative Binomial Linear Discriminant Analysis for RNA-Seq Data

RNA-sequencing (RNA-Seq) has become a powerful technology to characterize gene expression profiles because it is more accurate and comprehensive than microarrays. Although statistical methods that have been developed for microarray data can be applied to RNA-Seq data, they are not ideal due to the discrete nature of RNA-Seq data. The Poisson distribution and negative binomial distribution are commonly used to model count data. Recently, Witten (2011) proposed a Poisson linear discriminant analysis for RNA-Seq data. The Poisson assumption may not be as appropriate as negative binomial distribution when biological replicates are available and in the presence of overdispersion (i.e., when the variance is larger than the mean). However, it is more complicated to model negative binomial variables because they involve a dispersion parameter that needs to be estimated. In this paper, we propose a negative binomial linear discriminant analysis for RNA-Seq data. By Bayes' rule, we construct the classifier by fitting a negative binomial model, and propose some plug-in rules to estimate the unknown parameters in the classifier. The relationship between the negative binomial classifier and the Poisson classifier is explored, with a numerical investigation of the impact of dispersion on the discriminant score. Simulation results show the superiority of our proposed method. We also analyze four real RNA-Seq data sets to demonstrate the advantage of our method in real-world applications

Response of piles subjected to progressive soil movement

Model tests were conducted to investigate the behavior of vertically loaded, free head piles undergoing lateral soil movement using an experimental apparatus developed in house. This paper presents ten new tests on an instrumented model pile in dry sand, which provide the profiles of bending moment, shear force and pile deflection along the pile, the development of maximum bending moment Mmax, maximum shear force Tmax, and pile deflection y0 at the ground surface with soil movement. The tests reveal the effects of axial load P (at pile head), the distance between the tested pile and source of free soil movement Sb, sliding depths, and angle of soil movement (via loading angle) on the pile response. For instance, the axial loading P leads to extra bending moment and deflection in the passive pile; the Mmax reduces with increase in Sb; and the Mmax is proportional to the angle of soil movement. The elastic solution by Guo and Qin [Guo, W. D., Qin, H. Y., 2010, Thrust and Bending Moment of Rigid Piles Subjected to Moving Soil, Can. Geotech. J., Vol. 47, No. 2, pp. 180-196] was used to predict the development of Mmax and Tmax observed in the current tests, a boundary element analysis, and an in situ pile test, respectively. It provides satisfactory predictions for all cases against the measured data

Reinterpretation of Velocity-Dependent Atomic Friction: Influence of the Inherent Instrumental Noise in Friction Force Microscopes

We have applied both the master equation method and harmonic transition state theory to interpret the velocity-dependent friction behavior observed in atomic friction experiments. To understand the discrepancy between attempt frequencies measured in atomic force microscopy experiments and those estimated by theoretical models, both thermal noise and instrumental noise are introduced into the model. It is found that the experimentally observed low attempt frequency and the transition point at low velocity regimes can be interpreted in terms of the instrumental noise inherent in atomic force microscopy. In contrast to previous models, this model also predicts (1) the existence of a two-slope curve of velocity dependence and (2) the decrease of critical velocity with temperature, which provides clues for further experimental verification of the influence of instrumental noise in friction measurements

Effects of Increasing Concentrations of Corn Dried Distiller’s Grains with Solubles on the Egg Production and Internal Quality of Eggs

Four diets were formulated to contain 0, 17, 35 or 50% corn DDGS. A total of 240 54-week-old single-comb White Leghorn laying hens were assigned to one of four dietary treatments and fed for a 24-week experimental period. Two sets of the experimental diets were formulated and each diet was fed for 12 weeks. Egg production, feed consumption, egg component, yolk color, Haugh unit during storage times, and shell breaking strength were measured. Egg production, egg weight, egg mass, feed intake, and feed efficiency were adversely affected by the highest level of DDGS in the diet (50%) during the first 12-week period. Once diets were reformulated to include an increased concentration of both lysine and methionine, differences among the dietary treatments were reduced, as the performance of the 50% DDGS diets was greatly improved. Over the last 6 weeks of study, no differences in egg production, egg weight and feed intake among the DDGS treatments were found. DDGS diets positively affected the internal quality of eggs during storage. Improved yolk color and Haugh unit were observed as the dietary DDGS levels increased, but the increase in Haugh unit was significant only when the DDGS level was 50%. Shell weight percentage was increased in 50% DDGS diet. It was suggested that up to 50% of DDGS could be included in the layer’s diet without affecting egg weight, feed intake, egg mass, fee efficiency, and egg production as long as digestible amino acids were sufficient in DDGS-added diets

Recurrent Chunking Mechanisms for Long-Text Machine Reading Comprehension

In this paper, we study machine reading comprehension (MRC) on long texts, where a model takes as inputs a lengthy document and a question and then extracts a text span from the document as an answer. State-of-the-art models tend to use a pretrained transformer model (e.g., BERT) to encode the joint contextual information of document and question. However, these transformer-based models can only take a fixed-length (e.g., 512) text as its input. To deal with even longer text inputs, previous approaches usually chunk them into equally-spaced segments and predict answers based on each segment independently without considering the information from other segments. As a result, they may form segments that fail to cover the correct answer span or retain insufficient contexts around it, which significantly degrades the performance. Moreover, they are less capable of answering questions that need cross-segment information. We propose to let a model learn to chunk in a more flexible way via reinforcement learning: a model can decide the next segment that it wants to process in either direction. We also employ recurrent mechanisms to enable information to flow across segments. Experiments on three MRC datasets -- CoQA, QuAC, and TriviaQA -- demonstrate the effectiveness of our proposed recurrent chunking mechanisms: we can obtain segments that are more likely to contain complete answers and at the same time provide sufficient contexts around the ground truth answers for better predictions

Fabrication and Characterization of In Situ Synthesized SiC/Al Composites by Combustion Synthesis and Hot Press Consolidation Method

The in situ SiC/Al composites were fabricated in Al-Si-C systems with different Si/C mass ratios and holding time by the method of combustion synthesis and hot press consolidation. The influences of Si/C mass ratio and holding time on the phase constitution, microstructure, and hardness of the composites were investigated. The results indicate that the increase of Si/C mass ratio leads to more uniform size distribution of the SiC particles in the Al matrix. Moreover, by improving the Si/C mass ratio from 4 : 1 to 5 : 1, the maximum size of SiC particle was reduced from 4.1 μm to 2.0 μm. Meanwhile, the percentage of submicroparticles was increased from 22% to 63%, and the average hardness value of the composites was increased by 13%. In addition, when the holding time is set to be fifteen minutes, the Al4C3 phase did not exist in the composites because of its total reactions with Si atoms to form SiC particles, and the average hardness value was 73.8 HB