The Physical projector and topological quantum field theories: U(1) Chern-Simons theory in (2+1)-dimensions

The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The physical projector is explicitely demonstrated to be capable of effecting the required projection from the initially infinite number of degrees of freedom to the finite set of gauge invariant physical states whose properties are determined by the topology of the underlying manifold. Comment: 24 pages, no figures, plain LaTeX file; one more reference added. Final version to appear in Jour. Phys.

Food Packaging and Labeling.

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The Physical Projector and Topological Quantum Field Theories: U(1) Chern-Simons Theory in 2+1 Dimensions

The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The physical projector is explicitely demonstrated to be capable of effecting the required projection from the initially infinite number of degrees of freedom to the finite set of gauge invariant physical states whose properties are determined by the topology of the underlying manifold.Comment: 24 pages, no figures, plain LaTeX file; one more reference added. Final version to appear in Jour. Phys.

Encompassing in stationary linear dynamic models

Digitised version produced by the EUI Library and made available online in 2020

Comparison of Three Widely Employed Extraction Methods for Metabolomic Analysis of Trypanosoma brucei

peer reviewedTrypanosoma brucei (Tb) is the causative agent of human African trypanosomiasis (HAT), also known as sleeping sickness, which can be fatal if left untreated. An understanding of the parasite's cellular metabolism is vital for the discovery of new antitrypanosomal drugs and for disease eradication. Metabolomics can be used to analyze numerous metabolic pathways described as essential to Tb. brucei but has some limitations linked to the metabolites' physicochemical properties and the extraction process. To develop an optimized method for extracting and analyzing Tb. brucei metabolites, we tested the three most commonly used extraction methods, analyzed the extracts by hydrophilic interaction liquid chromatography high-resolution mass spectrometry (HILIC LC-HRMS), and further evaluated the results using quantitative criteria including the number, intensity, reproducibility, and variability of features, as well as qualitative criteria such as the specific coverage of relevant metabolites. Here, we present the resulting protocols for untargeted metabolomic analysis of Tb. brucei using (HILIC LC-HRMS)

An advanced clustering approach for assessing the repeatability and statistical relevance of 2D-COSY spectra

NMR techniques are widely used together with multivariate analysis approaches in order to characterize perturbations in metabolic pathways occurring during biological processes. A large amount of recent scientific and statistical works are available concerning 1D spectra (principally ¹H-NMR spectra). More recently, two-dimensional NMR spectroscopy techniques have been investigated: homonuclear (COSY,…) and heteronuclear ones (HSQC,…). It is commonly accepted by users (biologists, pharmacologists) that the recent introduction of 2D-NMR methods represents a huge qualitative gap for metabolomics investigations in terms of metabolites and biomarkers identifications. Indeed, it seems obvious that additional dimension means more predictive power. But, until now, no statistical study clearly proved this assumption. Therefore, a fundamental question is “Is supplementary information equivalent to relevant and crucial information ?”. In order to extend the statistical properties and tools developed for 1D spectroscopy to the new challenges raised by 2D spectra, a rigorous study of the repeatability of 2D-NMR spectra is needed as a prerequisite. In the context of first homonuclear COSY experiments, we will present a methodology based on accurate multivariate clustering tools. Numerical quality indexes and graphical clustering results will be shown, obtained via binary vectors of positions, via recoded intensity vectors and through different levels of spectral resolution. A second objective is to compare these 2D results with corresponding 1D results (¹H-NMR) obtained in the same conditions. This methodology was applied to two real datasets (peak lists), corresponding to two different experimental designs: first, a 4-mixture cell culture system containing various supervised metabolites, and second, a human serum based design with time repetitions and multiple permutations. Our preliminary results seem already promising: COSY appears to be a statistically robust tool and, furthermore, additional information appears to be relevant