Adaptation of K-means-type algorithms to the Grassmann manifold, An

2019 Spring.Includes bibliographical references.The Grassmann manifold provides a robust framework for analysis of high-dimensional data through the use of subspaces. Treating data as subspaces allows for separability between data classes that is not otherwise achieved in Euclidean space, particularly with the use of the smallest principal angle pseudometric. Clustering algorithms focus on identifying similarities within data and highlighting the underlying structure. To exploit the properties of the Grassmannian for unsupervised data analysis, two variations of the popular K-means algorithm are adapted to perform clustering directly on the manifold. We provide the theoretical foundations needed for computations on the Grassmann manifold and detailed derivations of the key equations. Both algorithms are then thoroughly tested on toy data and two benchmark data sets from machine learning: the MNIST handwritten digit database and the AVIRIS Indian Pines hyperspectral data. Performance of algorithms is tested on manifolds of varying dimension. Unsupervised classification results on the benchmark data are compared to those currently found in the literature

k-simplex volume optimizing projection algorithms for high-dimensional data sets

2021 Spring.Includes bibliographical references.Many applications produce data sets that contain hundreds or thousands of features, and consequently sit in very high dimensional space. It is desirable for purposes of analysis to reduce the dimension in a way that preserves certain important properties. Previous work has established conditions necessary for projecting data into lower dimensions while preserving pairwise distances up to some tolerance threshold, and algorithms have been developed to do so optimally. However, although similar criteria for projecting data into lower dimensions while preserving k-simplex volumes has been established, there are currently no algorithms seeking to optimally preserve such embedded volumes. In this work, two new algorithms are developed and tested: one which seeks to optimize the smallest projected k-simplex volume, and another which optimizes the average projected k-simplex volume

Not Available

Not Available16S rDNA analysis of archaea indicates dominance of Methanobacterium and high abundance of Methanomassiliicoccaceae in rumen of Nili-Ravi buffalo.Not Availabl

Runway Scheduling Using Generalized Dynamic Programming

A generalized dynamic programming method for finding a set of pareto optimal solutions for a runway scheduling problem is introduced. The algorithm generates a set of runway flight sequences that are optimal for both runway throughput and delay. Realistic time-based operational constraints are considered, including miles-in-trail separation, runway crossings, and wake vortex separation. The authors also model divergent runway takeoff operations to allow for reduced wake vortex separation. A modeled Dallas/Fort Worth International airport and three baseline heuristics are used to illustrate preliminary benefits of using the generalized dynamic programming method. Simulated traffic levels ranged from 10 aircraft to 30 aircraft with each test case spanning 15 minutes. The optimal solution shows a 40-70 percent decrease in the expected delay per aircraft over the baseline schedulers. Computational results suggest that the algorithm is promising for real-time application with an average computation time of 4.5 seconds. For even faster computation times, two heuristics are developed. As compared to the optimal, the heuristics are within 5 % of the expected delay per aircraft and 1 % of the expected number of runway operations per hour and can be 1000x faster

Quantitative comparisons of select cultured and uncultured microbial populations in the rumen of cattle fed different diets

<p>Abstract</p> <p>Background</p> <p>The number and diversity of uncultured ruminal bacterial and archaeal species revealed by 16S rRNA gene (<it>rrs</it>) sequences greatly exceeds that of cultured bacteria and archaea. However, the significance of uncultured microbes remains undetermined. The objective of this study was to assess the numeric importance of select uncultured bacteria and cultured bacteria and the impact of diets and microenvironments within cow rumen in a comparative manner.</p> <p>Results</p> <p>Liquid and adherent fractions were obtained from the rumen of Jersey cattle fed hay alone and Holstein cattle fed hay plus grain. The populations of cultured and uncultured bacteria present in each fraction were quantified using specific real-time PCR assays. The population of total bacteria was similar between fractions or diets, while total archaea was numerically higher in the hay-fed Jersey cattle than in the hay-grain-fed Holstein cattle. The population of the genus <it>Prevotella</it> was about one log smaller than that of total bacteria. The populations of <it>Fibrobacter succinogenes</it>, <it>Ruminococcus flavefaciens</it>, the genus <it>Butyrivibrio</it>, and <it>R. albus</it> was at least one log smaller than that of genus <it>Prevotella</it>. Four of the six uncultured bacteria quantified were as abundant as <it>F. succinogenes</it>, <it>R. flavefaciens</it> and the genus <it>Butyrivibrio</it>. In addition, the populations of several uncultured bacteria were significantly higher in the adherent fractions than in the liquid fractions. These uncultured bacteria may be associated with fiber degradation.</p> <p>Conclusions</p> <p>Some uncultured bacteria are as abundant as those of major cultured bacteria in the rumen. Uncultured bacteria may have important contribution to ruminal fermentation. Population dynamic studies of uncultured bacteria in a comparative manner can help reveal their ecological features and importance to rumen functions.</p

Investigation of bacterial diversity in the feces of cattle fed different diets1

The objective of this study is to investigate individual animal variation of bovine fecal microbiota including as affected by diets. Fecal samples were collected from 426 cattle fed 1 of 3 diets typically fed to feedlot cattle: 1) 143 steers fed finishing diet (83% dry-rolled corn, 13% corn silage, and 4% supplement), 2) 147 steers fed late growing diet (66% dry-rolled corn, 26% corn silage, and 8% supplement), and 3) 136 heifers fed early growing diet (70% corn silage and 30% alfalfa haylage). Bacterial 16S rRNA gene amplicons were determined from individual fecal samples using next-generation pyrosequencing technology. A total of 2,149,008 16S rRNA gene sequences from 333 cattle with at least 2,000 sequences were analyzed. Firmicutes and Bacteroidetes were dominant phyla in all fecal samples. At the genus level, Oscillibacter, Turicibacter, Roseburia, Fecalibacterium, Coprococcus, Clostridium, Prevotella, and Succinivibrio were represented by more than 1% of total sequences. However, numerous sequences could not be assigned to a known genus. Dominant unclassified groups were unclassified Ruminococcaceae and unclassified Lachnospiraceae that could be classified to a family but not to a genus. These dominant genera and unclassified groups differed (P \u3c 0.001) with diets. A total of 176,692 operational taxonomic units (OTU) were identified in combination across all the 333 cattle. Only 2,359 OTU were shared across 3 diet groups. UniFrac analysis showed that bacterial communities in cattle feces were greatly affected by dietary differences. This study indicates that the community structure of fecal microbiota in cattle is greatly affected by diet, particularly between forage- and concentrate-based diets