The Catalan simplicial set

The Catalan numbers are well-known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan numbers. We show how such a family can be given the structure of a simplicial set. We show how the low-dimensional parts of this simplicial set classify, in a precise sense, the structures of monoid and of monoidal category. This involves aspects of combinatorics, algebraic topology, quantum groups, logic, and category theory.Comment: 15 pages. Replaces and expands upon parts of arXiv:1307.0265; remaining parts of arXiv:1307.0265 will be incorporated into a sequel. Version 2: minor revision; to appear in Math. Proc. Camb. Phil. So

Visualization And Analysis Of Multiple Sclerosis Lesions In Magnetic Resonance Images

Magnetic Resonance Imaging (MRI) provides very sensitive indication of the presence and extent of the lesions of Multiple Sclerosis (MS). As a result, quantifying changes in the number and extent of lesions in MR images has been used to indicate disease activity in clinical trials of new therapies. However, lesion quantification is long, arduous, and subject to variability between and within operators. These factors limit the application of quantitative techniques and increase the duration, and thus cost, of clinical trials which rely on their measurements to assess therapeutic effect.;A computerised system was developed for assisted 3-D quantification and analysis of MS lesions in standard spin-echo MR exams. Manual and assisted quantification were compared using repeated measurements of lesions in MR exams of a phantom and MS patient. Results indicate that assisted quantification reduced inter-operator variability by 1/3, and reduced intra-operator variability by 1/2. The minimum significant change between two successive measurements of lesion volume by the same operator, was 0.64 cm{dollar}\sp3{dollar} for manual quantification, and 0.42 cm{dollar}\sp3{dollar} for assisted quantification. For two different operators making successive measurements, the minimum significant change was 0.94 cm{dollar}\sp3{dollar} for manual quantification, but only 0.47 cm{dollar}\sp3{dollar} for assisted quantification.;Repeated measurements were also used to determine the impact on operator variability of: (a) lesion quantification in high-field (1.5T) versus mid-field (0.5T) exams; and, (b) an anisotropic diffusion filter algorithm which reduces image noise without blurring or moving object boundaries. Results suggest that inter- and intra-operator variability are reduced by anisotropic filtering, and by quantification in 0.5T exams. Reduced operator variabilities may result from higher detail signal-to-noise ratios (dSNR\u27s) in 0.5T and filtered exams.;Finally, pathological change may occur within a lesion without a corresponding change in volume. Therefore, a new technique was developed to provide lesion composition information from MR exam intensities. Analysis of serial exams of 3 MS patients revealed changes in the intensity spectra within lesions, even when their volume remained constant. Together, assisted lesion quantification and analysis may provide additional insight into disease activity, and improve the sensitivity of clinical trials of new therapies

Study of the mechanism of enantioseparation of macrocyclic glycopeptide-based chiral stationary phases

The purpose of this research has been to investigate the mechanisms of chiral separations in HPLC. The goal was to develop a method of interrogating chiral separations that is applicable to all CSPs. This dissertation focuses on the development and application of this approach. The macrocyclic glycopeptide CSPs were used to experimentally test our model/approach and to provide proof of principle;The linear solvation energy relationship (LSER), developed by Kamlet, Taft, and Abraham, was selected for its ability to de-convolute the interactions a solute experiences in a biphasic system. The LSER model has a term for each type of interaction that a solute can experience or participate in. These include interactions through polarizable n and pi electrons (eE), dipolar interactions (sS), hydrogen bond acceptance ( aA) and donation (bB), and dispersion forces ( vV). Each term has a component for the system\u27s ability to participate in the specified interaction, the lower case variables which are called system constants, and a component for the solutes ability to participate in the specified interaction, the upper case variables called solute descriptors;We obtained system constants for the macrocyclic glycopeptide CSPs in the reverse phase mode and the normal phase mode. With knowledge of the system constants, it is possible to determine the solute descriptors of each enantiomer. This is achieved using multiple linear regression analysis, with the system constants of a CSP as the independent variables, and the logarithm of the retention factor of one enantiomer as the dependent variable. The solute descriptors for each enantiomer are determined, and the differences in the solute descriptors reveal the relative importance of each intermolecular interaction in generating enantioselectivity;We applied this method of analysis to the reverse phase mode separations with the teicoplanin CSP. Several neutral compounds and amino acids were eluted and the solute descriptors for each enantiomer were determined. The statistical fits of the regression were excellent. It was found that steric repulsions and ion-dipole interactions had the strongest influence on enantioselectivity, with both types of hydrogen bonding having a weak influence on enantioselectivity. Dipolar interactions were found to be unimportant in generating enantioselectivity

Green politics or environmental blues? Analyzing ecological democracy

Unlike several previous efforts that have discussed ecological forms of democracy in vague or esoteric terms, this article elucidates key factors that may affect the realization of ecological democracy. In the first section, ecological democracy is defined as an alternative democratic model that 1) strives to incorporate interested citizens into environmental decision-making, and 2) lacks structural features that systematically concentrate environmental amenities into the hands of particular social groups, while imposing environmental and ecological degradation on others. This leads to a discussion of several hindering and facilitating factors that either thwart or encourage ecological democracy. Two examples in support of this discussion on ecological democracy are provided: border contamination due to heavy industrial use along the US-Mexican border, and community forestry in the southeastern state of Oaxaca. By analyzing relevant factors that either have prevented or encouraged democratic environmental decision-making, this research will serve to improve environmental policy formulation and governance