Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Non-invasive strategy in assessing asthma through biofluids metabolomics exploration: exhaled breath and urine potentialities

Asthma is a significant health issue in the pediatric population with a noteworthy growth over the years. The proposed challenge for this PhD thesis was the development of advanced methodologies to establish metabolomic patterns in urine and exhaled breath associated with asthma whose applicability was subsequently exploited to evaluate the disease state, the therapy adhesion and effect and for diagnostic purposes. The volatile composition of exhaled breath was studied combining headspace solid phase microextraction (HS-SPME) with gas chromatography coupled to mass spectrometry or with comprehensive two-dimensional gas chromatography coupled to mass spectrometry with a high resolution time of flight analyzer (GC×GC–ToFMS). These methodologies allowed the identification of several hundred compounds from different chemical families. Multivariate analysis (MVA) led to the conclusion that the metabolomic profile of asthma individuals is characterized by higher levels of compounds associated with lipid peroxidation, possibly linked to oxidative stress and inflammation (alkanes and aldehydes) known to play an important role in asthma. For future applications in clinical settings a set of nine compounds was defined and the clinical applicability was proven in monitoring the disease status and in the evaluation of the effect and / or adherence to therapy. The global volatile metabolome of urine was also explored using an HSSPME/GC×GC–ToFMS method and c.a. 200 compounds were identified. A targeted analysis was performed, with 78 compounds related with lipid peroxidation and consequently to oxidative stress levels and inflammation. The urinary non-volatile metabolomic pattern of asthma was established using proton nuclear magnetic resonance (1H NMR). This analysis allowed identifying central metabolic pathways such as oxidative stress, amino acid and lipid metabolism, gut microflora alterations, alterations in the tricarboxylic acid (TCA) cycle, histidine metabolism, lactic acidosis, and modification of free tyrosine residues after eosinophil stimulation. The obtained results allowed exploring and demonstrating the potential of analyzing the metabolomic profile of exhaled air and urine in asthma. Besides the successful development of analysis methodologies, it was possible to explore through exhaled air and urine biochemical pathways affected by asthma, observing complementarity between matrices, as well as, verify the clinical applicability.

Optimisation of stir bar sorptive extraction and liquid desorption combined with large volume injection-gas chromatography–quadrupole mass spectrometry for the determination of volatile compounds in wines

Stir bar sorptive extraction and liquid desorption followed by large volume injection coupled to gas chromatography–quadrupole mass spectrometry (SBSE–LD/LVI-GC–qMS) had been applied for the determination of volatiles in wines. The methodology was optimised in terms of extraction time and influence of ethanol in the matrix; LD conditions, and instrumental settings. The optimisation was carried out by using 10 standards representative of the main chemical families of wine, i.e. guaiazulene, E,E-farnesol, β-ionone, geranylacetone, ethyl decanoate, β-citronellol, 2-phenylethanol, linalool, hexyl acetate and hexanol. The methodology shows good linearity over the concentration range tested, with correlation coefficients higher than 0.9821, a good reproducibility was attained (8.9–17.8%), and low detection limits were achieved for nine volatile compounds (0.05–9.09 μg L−1), with the exception of 2-phenylethanol due to low recovery by SBSE. The analytical ability of the SBSE–LD/LVI-GC–qMS methodology was tested in real matrices, such as sparkling and table wines using analytical curves prepared by using the 10 standards where each one was applied to quantify the structurally related compounds. This methodology allowed, in a single run, the quantification of 67 wine volatiles at levels lower than their respective olfactory thresholds. The proposed methodology demonstrated to be easy to work-up, reliable, sensitive and with low sample requirement to monitor the volatile fraction of wine.

Simultaneous analysis of free amino acids and biogenic amines in honey and wine samples using in loop orthophthalaldeyde derivatization procedure

This work presents a RP-HPLC method for the simultaneous quantification of free amino acids and biogenic amines in liquid food matrices and the results of the application to honey and wine samples obtained from different production processes and geographic origins. The developed methodology is based on a pre-column derivatization with o-phthaldialdehyde carried out in the sample injection loop. The compounds were separated in a Nova-Pack RP-C18 column (150 mm × 3.9 mm, 4 μm) at 35 °C. The mobile phase used was a mixture of phase A: 10 mM sodium phosphate buffer (pH 7.3), methanol and tetrahydrofuran (91:8:1); and phase B: methanol and phosphate buffer (80:20), with a flow rate of 1.0 ml/min. Fluorescence detection was used at an excitation wavelength of 335 nm and an emission wavelength of 440 nm. The separation and quantification of 19 amino acids and 6 amines was carried out in a single run as their OPA/MCE derivatives elute within 80 min, ensuring a reproducible quantification. The method showed to be adequate for the purpose, with an average RSD of 2% for the different amino acids; detection limits varying between 0.71 mg/l (Asn) and 8.26 mg/l (Lys) and recovery rates between 63.0% (Cad) and 98.0% (Asp). The amino acids present at the highest concentration in honey and wine samples were phenylalanine and arginine, respectively. Only residual levels of biogenic amines were detected in the analysed samples.