On generating Sobolev orthogonal polynomials

Sobolev orthogonal polynomials are polynomials orthogonal with respect to a Sobolev inner product, an inner product in which derivatives of the polynomials appear. They satisfy a long recurrence relation that can be represented by a Hessenberg matrix. The problem of generating a finite sequence of Sobolev orthogonal polynomials can be reformulated as a matrix problem. That is, a Hessenberg inverse eigenvalue problem, where the Hessenberg matrix of recurrences is generated from certain known spectral information. Via the connection to Krylov subspaces we show that the required spectral information is the Jordan matrix containing the eigenvalues of the Hessenberg matrix and the normalized first entries of its eigenvectors. Using a suitable quadrature rule the Sobolev inner product is discretized and the resulting quadrature nodes form the Jordan matrix and associated quadrature weights are the first entries of the eigenvectors. We propose two new numerical procedures to compute Sobolev orthonormal polynomials based on solving the equivalent Hessenberg inverse eigenvalue problem.Comment: 24 pages, 5 figures, 2 table

Classification of Vegetation and Analysis of its Recent Trends at Camp Williams, Utah Using Remote Sensing and Geographic Information System Techniques

Current vegetation classes were generated from remotely sensed data to provide coarse-level information for an ecosystem management plan developed at Camp Williams, Utah. Vegetation trend from 1973 - 1993 was also examined via satellite imagery. The data set consisted of Landsat Multispectral Scanner (MSS) and Thematic Mapper (TM) images from July or August of 1973, 1975, 1980, 1988, and 1993. Two approaches were used to detect vegetation change. The first approach determined overall and cover type trend from standard digital image differencing of soil-adjusted vegetation index (SAVI) images. The second approach used an unsupervised classification of a composite SAVI image of all dates. The first approach defined areas of increase, decrease, and no significant change in SAVI and differences in trend for tree versus shrub cover types. The second approach resulted in an ecological classification that defined new environmental patterns based on vegetation trend

A ⋆\star-product solver with spectral accuracy for non-autonomous ordinary differential equations

A new method for solving non-autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called $\star$-algebra. This algebra is equipped with a product, the $\star$-product, which is the integral over the usual product of two bivariate distributions. Expanding the bivariate distributions in bases of Legendre polynomials leads to a discretization of the $\star$-product and this allows for the solution to be approximated by a vector that is obtained by solving a linear system of equations. The effectiveness of this approach is illustrated with numerical experiments

Affirmative acts: The need for American black theatre in the classroom

The purpose of this study is to reveal that racial inequality in American Theatre is still in existence: that while our country has gained some level of integration, several societal and artistic echelons evidence a remaining tendency towards discrimination--a separatist sense of culture that unfortunately informs elementary and secondary classrooms all across the United States as well as still exists in the general arts

To be or not to be... secreted as exosomes, a balance finely tuned by the mechanisms of biogenesis

International audienceThe release of extracellular vesicles such as exosomes provides an attractive intercellular communication pathway. Exosomes are 30-150 nm membrane vesicles that originate in endosomal compartment and act as intercellular mediators in both physiological and pathological context. Despite of the growing interest in exosome functions, the mechanisms responsible for their biogenesis and secretion are still not completely understood. This knowledge is yet capital as it controls the composition, and hence the function, and the secretion of exosomes. Exosomes are produced as intraluminal vesicles (ILVs) in very dynamic endosomal organelles that undergo various maturation processes in order to form multivesicular endosomes. The function of multivesicular endosomes will notably be balanced between exosome secretion and lysosomal degradation. In this review, we present and discuss each intracellular trafficking pathways that have been reported or proposed to regulate exosomes biogenesis with a particular focus on the importance of endosomal dynamics in the sorting of protein cargoes to exosomes and the secretion of multivesicular endosomes. A global picture reveals several key mechanisms that act mainly at crossroads of endosomal pathways acting as regulatory checkpoints of exosome biogenesis. Summary Points

Algorithms for Modifying Recurrence Relations of Orthogonal Polynomial and Rational Functions when Changing the Discrete Inner Product

Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed. Moreover, also typically the inner product is changed to a discrete inner product, which is the finite sum of weighted functions evaluated in specific nodes. For particular applications it is beneficial to have an efficient procedure to update the recurrence relations when adding or removing nodes from the inner product. The construction of the recurrence relations is equivalent to computing a structured matrix (polynomial) or pencil (rational) having prescribed spectral properties. Hence the solution of this problem is often referred to as solving an Inverse Eigenvalue Problem. In Van Buggenhout et al. (2022) we proposed updating techniques to add nodes to the inner product while efficiently updating the recurrences. To complete this study we present in this article manners to efficiently downdate the recurrences when removing nodes from the inner product. The link between removing nodes and the QR algorithm to deflate eigenvalues is exploited to develop efficient algorithms. We will base ourselves on the perfect shift strategy and develop algorithms, both for the polynomial case and the rational function setting. Numerical experiments validate our approach.Comment: 45 pages, 19 figure

Nutrient requirements of lactococci in defined growth media

Many attempts have been made for the last six decades to design defined media for species of the lactococcus group. The general outcome of the studies suggests that this group is heterogeneous with respect to specific requirements for nutrients. Lactococcal species are limited in various metabolic pathways. Early attempts to trace the required nutrients were not always successful because of the poor quality of analysis and the presence of impurities in the medium components

Remote Sensing Of Rice-Based Irrigated Agriculture: A Review

The ‘Green Revolution’ in rice farming of the late 1960’s denotes the beginning of the extensive breeding programs that have led to the many improved rice varieties that are now planted on more than 60% of the world’s riceland (Khush, 1987). This revolution led to increases in yield potential of 2 to 3 times that of traditional varieties (Khush, 1987). Similar trends have also been seen in the Irrigation Areas and Districts of southern New South Wales (NSW) as the local breeding program has produced many improved varieties of rice adapted to local growing conditions since the 1960’s (Brennan et al., 1994). Increases in area of rice planted, rice quality, and paddy yield resulted (Brennan et al., 1994). Increased rice area, however, has led to the development of high water tables and risk of large tracts of land becoming salt-affected in southern NSW (Humphreys et al., 1994b). These concerns have led to various environmental regulations on rice in the region, culminating in 1994 when restrictions on rice area, soil suitability, and water consumption were fully enacted (Humphreys et al., 1994b). Strict environmental restrictions in combination with large areas of land make the management of this region a difficult task. Land managers require, among other things, a way of regulating water use, assessing or predicting crop area and productivity, and making management decisions in support of environmentally and economically sustainable agriculture. In the search for more time and cost effective methods for attaining these goals, while monitoring complex management situations, many have turned to remote sensing and Geographic Information System (GIS) technologies for assistance. The spectral information and spatial density of remote sensing data lends itself well to the measurement of large areas. Since the launch of LANDSAT-1 in 1972, this technology has been used extensively in agricultural systems for crop identification and area estimation, crop yield estimation and prediction, and crop damage assessment. The incorporation of remote sensing and GIS can also help integrate management practices and develop effective management plans. However, in order to take advantage of these tools, users must have an understanding of both what remote sensing is and what sensors are now available, and how the technology is being used in applied agricultural research. Accordingly, a description of both follows: first a description of the technology, and then how it is currently being applied. The applications of remote sensing relevant to this discussion can be separated into crop type identification; crop area measurement; crop yield; crop damage; water use/ moisture availability (ma) mapping; and water use efficiency monitoring/mapping. This report focuses on satellite remote sensing for broad-scale rice-based irrigation agricultural applications. It also discusses related regional GIS analyses that may or may not include remote sensing data, and briefly addresses other sources of finer-scale remote sensing and geospatial data as they relate to agriculture. Since a complete review of the remote sensing research was not provided in the rice literature alone, some generic agricultural issues have been learned from applications not specifically dealing with rice. Remote sensing specialists may wish to skip to section 2