Euclidean Distance Between Haar Orthogonal and Gaussian Matrices

In this work, we study a version of the general question of how well a Haar-distributed orthogonal matrix can be approximated by a random Gaussian matrix. Here, we consider a Gaussian random matrix (Formula presented.) of order n and apply to it the Gram–Schmidt orthonormalization procedure by columns to obtain a Haar-distributed orthogonal matrix (Formula presented.). If (Formula presented.) denotes the vector formed by the first m-coordinates of the ith row of (Formula presented.) and (Formula presented.), our main result shows that the Euclidean norm of (Formula presented.) converges exponentially fast to (Formula presented.), up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm (Formula presented.) and we find a coupling that improves by a factor (Formula presented.) the recently proved best known upper bound on (Formula presented.). Our main result also has applications in Quantum Information Theory.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Microwave-assisted solvent extraction and analysis of shikimic acid from plant tissues.

2008

Synthesis of thioenol ether functionalized cyclooctyne and its orthogonal cycloaddition sequence

In this work, the synthesis of a new bifunctionalized cyclooctyne for a possible layer by layer surface functionalization is presented. The main objective is to find a more stable molecule than the literature known methyl enol ether substituted cyclooctyne. Accordingly, the two target functionalities are an internal alkyne group and a vinyl methyl sulfide group. The synthesis was achieved in 9 steps and consists first of all in the preparation of an aldehyde starting from 1,5-cyclooctadiene with a cyclopropanation reaction followed by a reduction and the SWERN oxidation to an aldehyde. The new functionality was introduced by exploiting the WITTIG reaction. For the alkyne group a bromination followed by a double elimination gave good results. The reactivity of the new molecule was tested using a sequential application of SPAAC and iEDDA reactions, comparing it with the cyclooctyne functionalized with a methyl enol ether. Concerning the comparison of both compounds the sulfur ether is significantly slower and therefore more stable. It will be tested in the future for surface functionalization from the KOERT group.

Orthogonal chirp division multiplexing: performance evaluation in the presence of phase noise

In Beyond 5G technologies, Terahertz communications will be used: frequency bands between 100 GHz and 10 THz will be exploited in order to have higher throughput and lower latency. Those frequency bands suffer from several impairments, and it is thought that phase noise is one of the most significant. Orthogonal Chirp Division Multiplexing (OCDM) might be used in Beyond 5G communications, thanks to its robustness to multipath fading: it outperforms Orthogonal Frequency Division Multiplexing (OFDM) systems. The aim of this thesis is to find a suitable model for describing phase noise in Terahertz communications, and to study the performance of an OCDM system affected by this impairment. After this, a simple compensation scheme is introduced, and the improvement that it provides is analysed. The thesis is organized as follow: in the first chapter Terahertz communications and Beyond 5G are introduced, in the second chapter phase noise is studied, in the third chapter OCDM is analysed, and in the fourth chapter numerical results are presented.

Solvent regeneration of activated carbon mixed-matrix membranes for the removal of micropollutants from wastewater

The constantly increasing demand of clean water has become challenging to deal with over the past years, water being an ever more precious resource. In recent times, the existing wastewater treatments had to be integrated with new steps, due to the detection of so-called organic micropollutants (OMPs). These compounds have been shown to adversely affect the environment and possibly human health, even when found in very low concentrations. In order to remove OMPs from wastewater, one possible technique is a hybrid process combining filtration and adsorption. In this work, polyethersulfone multi-channel mixed-matrix membranes with embedded powdered activated carbon (PAC) were tested to investigate the membrane’s adsorption and desorption performance. Micropollutants retention was analyzed using the pharmaceutical compounds diclofenac (DCF), paracetamol (PARA) and carbamazepine (CBZ) in filtration mode, combining the PAC adsorption process with the membrane’s ultrafiltration. Desorption performance was studied through solvent regeneration, using seven different solvents: pure water, pure ethanol, mixture of ethanol and water in different concentration, sodium hydroxide and a mixture of ethanol and sodium hydroxide. Regeneration experiments were carried out in forward-flushing. At first regeneration efficiency was investigated using a single-solute solution (diclofenac in water). The mixture Ethanol/Water (50:50) was found to be the most efficient with long-term retention of 59% after one desorption cycle. It was, therefore, later tested on a membrane previously loaded with a multi-solute solution. Three desorption cycles were performed after which, retention (after 30 min) reached values of 87% for PARA and 72% for CBZ and 55% for DCF, which indicates decent regenerability. A morphological analysis on the membranes confirmed that, in any case, the regeneration cycles did not affect either the membranes’ structure, or the content and distribution of PAC in the matrix.

A novel approach to Non-Orthogonal Random Access with application to NB-IoT NTN systems

In the Massive IoT vision, millions of devices need to be connected to the Internet through a wireless access technology. However, current IoT-focused standards are not fully prepared for this future. In this thesis, a novel approach to Non-Orthogonal techniques for Random Access, which is the main bottleneck in high density systems, is proposed. First, the most popular wireless access standards are presented, with a focus on Narrowband-IoT. Then, the Random Access procedure as implemented in NB-IoT is analyzed. The Non-Orthogonal Random Access technique is presented next, along with two potential algorithms for the detection of non-orthogonal preambles. Finally, the performance of the proposed solutions are obtained through numerical simulations.

Neural Network based Non Orthogonal Random Access for 6G NTN-IoT

Pervasive and distributed Internet of Things (IoT) devices demand ubiquitous coverage beyond No-man’s land. To satisfy plethora of IoT devices with resilient connectivity, Non-Terrestrial Networks (NTN) will be pivotal to assist and complement terrestrial systems. In a massiveMTC scenario over NTN, characterized by sporadic uplink data reports, all the terminals within a satellite beam shall be served during the short visibility window of the flying platform, thus generating congestion due to simultaneous access attempts of IoT devices on the same radio resource. The more terminals collide, the more average-time it takes to complete an access which is due to the decreased number of successful attempts caused by Back-off commands of legacy methods. A possible countermeasure is represented by Non-Orthogonal Multiple Access scheme, which requires the knowledge of the number of superimposed NPRACH preambles. This work addresses this problem by proposing a Neural Network (NN) algorithm to cope with the uncoordinated random access performed by a prodigious number of Narrowband-IoT devices. Our proposed method classifies the number of colliding users, and for each estimates the Time of Arrival (ToA). The performance assessment, under Line of Sight (LoS) and Non-LoS conditions in sub-urban environments with two different satellite configurations, shows significant benefits of the proposed NN algorithm with respect to traditional methods for the ToA estimation.

Study Of The Homogeneity Of Drug Loaded In Polymeric Films Using Near-infrared Chemical Imaging And Split-plot Design.

Split-plot design (SPD) and near-infrared chemical imaging were used to study the homogeneity of the drug paracetamol loaded in films and prepared from mixtures of the biocompatible polymers hydroxypropyl methylcellulose, polyvinylpyrrolidone, and polyethyleneglycol. The study was split into two parts: a partial least-squares (PLS) model was developed for a pixel-to-pixel quantification of the drug loaded into films. Afterwards, a SPD was developed to study the influence of the polymeric composition of films and the two process conditions related to their preparation (percentage of the drug in the formulations and curing temperature) on the homogeneity of the drug dispersed in the polymeric matrix. Chemical images of each formulation of the SPD were obtained by pixel-to-pixel predictions of the drug using the PLS model of the first part, and macropixel analyses were performed for each image to obtain the y-responses (homogeneity parameter). The design was modeled using PLS regression, allowing only the most relevant factors to remain in the final model. The interpretation of the SPD was enhanced by utilizing the orthogonal PLS algorithm, where the y-orthogonal variations in the design were separated from the y-correlated variation.

Polyphenol Extraction Optimisation From Ceylon Gooseberry (dovyalis Hebecarpa) Pulp.

Originally from Asia, Dovyalis hebecarpa is a dark purple/red exotic berry now also produced in Brazil. However, no reports were found in the literature about phenolic extraction or characterisation of this berry. In this study we evaluate the extraction optimisation of anthocyanins and total phenolics in D. hebecarpa berries aiming at the development of a simple and mild analytical technique. Multivariate analysis was used to optimise the extraction variables (ethanol:water:acetone solvent proportions, times, and acid concentrations) at different levels. Acetone/water (20/80 v/v) gave the highest anthocyanin extraction yield, but pure water and different proportions of acetone/water or acetone/ethanol/water (with >50% of water) were also effective. Neither acid concentration nor time had a significant effect on extraction efficiency allowing to fix the recommended parameters at the lowest values tested (0.35% formic acid v/v, and 17.6 min). Under optimised conditions, extraction efficiencies were increased by 31.5% and 11% for anthocyanin and total phenolics, respectively as compared to traditional methods that use more solvent and time. Thus, the optimised methodology increased yields being less hazardous and time consuming than traditional methods. Finally, freeze-dried D. hebecarpa showed high content of target phytochemicals (319 mg/100g and 1,421 mg/100g of total anthocyanin and total phenolic content, respectively).

Communication: Transient Anion States Of Phenol…(h₂o)n (n = 1, 2) Complexes: Search For Microsolvation Signatures.

We report on the shape resonance spectra of phenol-water clusters, as obtained from elastic electron scattering calculations. Our results, along with virtual orbital analysis, indicate that the well-known indirect mechanism for hydrogen elimination in the gas phase is significantly impacted on by microsolvation, due to the competition between vibronic couplings on the solute and solvent molecules. This fact suggests how relevant the solvation effects could be for the electron-driven damage of biomolecules and the biomass delignification [E. M. de Oliveira et al., Phys. Rev. A 86, 020701(R) (2012)]. We also discuss microsolvation signatures in the differential cross sections that could help to identify the solvated complexes and access the composition of gaseous admixtures of these species.

Intensification Of Bioactive Compounds Extraction From Medicinal Plants Using Ultrasonic Irradiation.

Extraction processes are largely used in many chemical, biotechnological and pharmaceutical industries for recovery of bioactive compounds from medicinal plants. To replace the conventional extraction techniques, new techniques as high-pressure extraction processes that use environment friendly solvents have been developed. However, these techniques, sometimes, are associated with low extraction rate. The ultrasound can be effectively used to improve the extraction rate by the increasing the mass transfer and possible rupture of cell wall due the formation of microcavities leading to higher product yields with reduced processing time and solvent consumption. This review presents a brief survey about the mechanism and aspects that affecting the ultrasound assisted extraction focusing on the use of ultrasound irradiation for high-pressure extraction processes intensification.

Propylthiouracil Quantification In Human Plasma By High-performance Liquid Chromatography Coupled With Electrospray Tandem Mass Spectrometry: Application In A Bioequivalence Study.

A rapid, sensitive and specific method for quantifying propylthiouracil in human plasma using methylthiouracil as the internal standard (IS) is described. The analyte and the IS were extracted from plasma by liquid-liquid extraction using an organic solvent (ethyl acetate). The extracts were analyzed by high performance liquid chromatography coupled with electrospray tandem mass spectrometry (HPLC-MS/MS) in negative mode (ES-). Chromatography was performed using a Phenomenex Gemini C18 5μm analytical column (4.6mm×150mm i.d.) and a mobile phase consisting of methanol/water/acetonitrile (40/40/20, v/v/v)+0.1% of formic acid. For propylthiouracil and I.S., the optimized parameters of the declustering potential, collision energy and collision exit potential were -60 (V), -26 (eV) and -5 (V), respectively. The method had a chromatographic run time of 2.5min and a linear calibration curve over the range 20-5000ng/mL. The limit of quantification was 20ng/mL. The stability tests indicated no significant degradation. This HPLC-MS/MS procedure was used to assess the bioequivalence of two propylthiouracil 100mg tablet formulations in healthy volunteers of both sexes in fasted and fed state. The geometric mean and 90% confidence interval CI of Test/Reference percent ratios were, without and with food, respectively: 109.28% (103.63-115.25%) and 115.60% (109.03-122.58%) for Cmax, 103.31% (100.74-105.96%) and 103.40% (101.03-105.84) for AUClast. This method offers advantages over those previously reported, in terms of both a simple liquid-liquid extraction without clean-up procedures, as well as a faster run time (2.5min). The LOQ of 20ng/mL is well suited for pharmacokinetic studies. The assay performance results indicate that the method is precise and accurate enough for the routine determination of the propylthiouracil in human plasma. The test formulation with and without food was bioequivalent to reference formulation. Food administration increased the Tmax and decreased the bioavailability (Cmax and AUC).

Effects Of Sterilization Methods On The Physical, Chemical, And Biological Properties Of Silk Fibroin Membranes.

Silk fibroin has been widely explored for many biomedical applications, due to its biocompatibility and biodegradability. Sterilization is a fundamental step in biomaterials processing and it must not jeopardize the functionality of medical devices. The aim of this study was to analyze the influence of different sterilization methods in the physical, chemical, and biological characteristics of dense and porous silk fibroin membranes. Silk fibroin membranes were treated by several procedures: immersion in 70% ethanol solution, ultraviolet radiation, autoclave, ethylene oxide, and gamma radiation, and were analyzed by scanning electron microscopy, Fourier-transformed infrared spectroscopy (FTIR), X-ray diffraction, tensile strength and in vitro cytotoxicity to Chinese hamster ovary cells. The results indicated that the sterilization methods did not cause perceivable morphological changes in the membranes and the membranes were not toxic to cells. The sterilization methods that used organic solvent or an increased humidity and/or temperature (70% ethanol, autoclave, and ethylene oxide) increased the silk II content in the membranes: the dense membranes became more brittle, while the porous membranes showed increased strength at break. Membranes that underwent sterilization by UV and gamma radiation presented properties similar to the nonsterilized membranes, mainly for tensile strength and FTIR results.

Improved Selective Cholesterol Adsorption By Molecularly Imprinted Poly(methacrylic Acid)/silica (pmaa-sio₂) Hybrid Material Synthesized With Different Molar Ratios.

The present paper describes the synthesis of molecularly imprinted polymer - poly(methacrylic acid)/silica and reports its performance feasibility with desired adsorption capacity and selectivity for cholesterol extraction. Two imprinted hybrid materials were synthesized at different methacrylic acid (MAA)/tetraethoxysilane (TEOS) molar ratios (6:1 and 1:5) and characterized by FT-IR, TGA, SEM and textural data. Cholesterol adsorption on hybrid materials took place preferably in apolar solvent medium, especially in chloroform. From the kinetic data, the equilibrium time was reached quickly, being 12 and 20 min for the polymers synthesized at MAA/TEOS molar ratio of 6:1 and 1:5, respectively. The pseudo-second-order model provided the best fit for cholesterol adsorption on polymers, confirming the chemical nature of the adsorption process, while the dual-site Langmuir-Freundlich equation presented the best fit to the experimental data, suggesting the existence of two kinds of adsorption sites on both polymers. The maximum adsorption capacities obtained for the polymers synthesized at MAA/TEOS molar ratios of 6:1 and 1:5 were found to be 214.8 and 166.4 mg g(-1), respectively. The results from isotherm data also indicated higher adsorption capacity for both imprinted polymers regarding to corresponding non-imprinted polymers. Nevertheless, taking into account the retention parameters and selectivity of cholesterol in the presence of structurally analogue compounds (5-α-cholestane and 7-dehydrocholesterol), it was observed that the polymer synthesized at the MAA/TEOS molar ratio of 6:1 was much more selective for cholesterol than the one prepared at the ratio of 1:5, thus suggesting that selective binding sites ascribed to the carboxyl group from MAA play a central role in the imprinting effect created on MIP.