4,575 research outputs found
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
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