The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

Phytosterols from Spondias mombin Linn with Antimycobacterial Activities

The growing problems of tuberculosis have led to the search for new anti-Mtb agents from higher plants. The stem bark of Spondias mombin was evaluated for its in vitro activity against Mycobacterium tuberculosis (H37Rv strain). Bioassay-guided fractionation of the methanol extract was carried out by Vacuum Liquid Chromatography (VLC) on Silica gel (230-400 mesh) and purification was done using HPLC and TLC. In vitro antimycobacterial susceptibility was performed by a fluorometric microplate alamar blue assay (MABA) and percentage mycobacterial inhibition was calculated. The structures of the isolated compounds were established by spectroscopic analysis. The active VLC fraction exhibited 91% inhibition against M. tuberculosis H37Rv at a concentration of 40 µg/mL. The HPLC fraction SMi-15 containing compounds 1 and 2 showed 92.8% inhibition against M. tuberculosis. Two new antimycobacterial phytosterols were isolated from the stem bark of S. mombin and the structureswere identified as mombintane I (1) and mombintane II (2). The stem bark extractives of S. mombin contain antitubercular principles of the class phytosterol and support an important potential of triterpenoids

Deferring the learning for better generalization in radial basis neural networks

Proceeding of: International Conference Artificial Neural Networks — ICANN 2001. Vienna, Austria, August 21–25, 2001The level of generalization of neural networks is heavily dependent on the quality of the training data. That is, some of the training patterns can be redundant or irrelevant. It has been shown that with careful dynamic selection of training patterns, better generalization performance may be obtained. Nevertheless, generalization is carried out independently of the novel patterns to be approximated. In this paper, we present a learning method that automatically selects the most appropriate training patterns to the new sample to be predicted. The proposed method has been applied to Radial Basis Neural Networks, whose generalization capability is usually very poor. The learning strategy slows down the response of the network in the generalisation phase. However, this does not introduces a significance limitation in the application of the method because of the fast training of Radial Basis Neural Networks

Gaussian cubature arising from hybrid characters of simple Lie groups

Lie groups with two different root lengths allow two mixed sign homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas leading to the Gaussian cubature formulas for families of polynomials arising from the characters of irreducible representations of any simple Lie group, to new cubature formulas based on the corresponding hybrid characters. These formulas are new forms of Gaussian cubature in the short root length case and new forms of Radau cubature in the long root case. The nodes for the cubature arise quite naturally from the (computationally efficient) elements of finite order of the Lie group.Comment: 23 pages, 3 figure

Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure

Using Total Solids Concentration to Estimate Nutrient Content of Feedlot Runoff Effluent from Solid Settling Basins, Vegetative Infiltration Basins, and Vegetative Treatment Areas

Increased environmental awareness has promoted the need for improved feedlot runoff control. The use of vegetative treatment systems (VTSs) to control and treat feedlot runoff may enhance environmental security and protect water quality. Knowledge of effluent nutrient concentrations throughout the vegetative treatment system is required to evaluate impact on water quality and system performance. Previously collected VTS monitoring data has provided the opportunity to investigate relationships between effluent quality parameters. The objective of this study was to evaluate, through correlation and regression, the relationships between total solids, nutrients, and effluent quality indicator concentrations of feedlot runoff at various stages of treatment in a VTS, including solid settling basin, vegetative infiltration basin, and vegetative treatment area effluent. Results of a correlation and primary factor analysis showed that most of the parameters’ concentrations were strongly correlated to each other, with a single factor capable of describing more than 60% of the variability of monitored parameters. Regression equations were developed to relate nutrient content and effluent quality indicator concentrations to total solids concentrations. Results were satisfactory for most parameters, indicating that total solids concentrations provided significant insight into VTS performance relative to nutrient concentration and effluent quality indicators. A comparison between predicted, based on total solids content, and monitored mass release of the parameters was conducted. No statistical difference was found for most parameters; indicating that effluent volume release along with total solids concentrations can be used to provide an estimate of nutrient mass in solid settling basin, vegetative infiltration basin, and vegetative treatment area effluent

The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation

We introduce CASC: a new, modern, and header-only C++ library which provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension. This is accomplished by using the latest C++ language features including variadic template parameters introduced in C++11 and automatic function return type deduction from C++14. Effectively CASC decouples the representation of the topology from the interactions of user data. We present the innovations and design principles of the data structure and related algorithms. This includes a metadata aware decimation algorithm which is general for collapsing simplices of any dimension. We also present an example application of this library to represent an orientable surface mesh.Comment: 24 pages, 6 figure