Rank Minimization over Finite Fields: Fundamental Limits and Coding-Theoretic Interpretations

This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements required are provided. It is shown that these conditions are sharp and the minimum-rank decoder is asymptotically optimal. The reliability function of this decoder is also derived by appealing to de Caen's lower bound on the probability of a union. The sufficient condition also holds when the sensing matrices are sparse - a scenario that may be amenable to efficient decoding. More precisely, it is shown that if the n\times n-sensing matrices contain, on average, \Omega(nlog n) entries, the number of measurements required is the same as that when the sensing matrices are dense and contain entries drawn uniformly at random from the field. Analogies are drawn between the above results and rank-metric codes in the coding theory literature. In fact, we are also strongly motivated by understanding when minimum rank distance decoding of random rank-metric codes succeeds. To this end, we derive distance properties of equiprobable and sparse rank-metric codes. These distance properties provide a precise geometric interpretation of the fact that the sparse ensemble requires as few measurements as the dense one. Finally, we provide a non-exhaustive procedure to search for the unknown low-rank matrix.Comment: Accepted to the IEEE Transactions on Information Theory; Presented at IEEE International Symposium on Information Theory (ISIT) 201

Thiourea Derivative of 2-[(1 R)-1-Aminoethyl]phenol: A Flexible Pocket-like Chiral Solvating Agent (CSA) for the Enantiodifferentiation of Amino Acid Derivatives by NMR Spectroscopy

Thiourea derivatives of 2-[(1R)-1-aminoethyl]phenol, (1S,2R)-1-amino-2,3-dihydro-1H-inden-2-ol, (1R,2R)-(1S,2R)-1-amino-2,3-dihydro-1H-inden-2-ol, and (R)-1-phenylethanamine have been compared as chiral solvating agents (CSAs) for the enantiodiscrimination of derivatized amino acids using nuclear magnetic resonance (NMR) spectroscopy. Thiourea derivative, prepared by reacting 2-[(1R)-1-aminoethyl]phenol with benzoyl isothiocyanate, constitutes an effective CSA for the enantiodiscrimination of N-3,5-dinitrobenzoyl (DNB) derivatives of amino acids with free or derivatized carboxyl functions. A base additive 1,4-diazabicyclo[2.2.2]octane(DABCO)/N,N-dimethylpyridin-4-amine (DMAP)/NBu4OH) is required both to solubilize amino acid derivatives with free carboxyl groups in CDCl3 and to mediate their interaction with the chiral auxiliary to attain efficient differentiation of the NMR signals of enantiomeric substrates. For ternary systems CSA/substrate/DABCO, the chiral discrimination mechanism has been ascertained through the NMR determination of complexation stoichiometry, association constants, and stereochemical features of the diastereomeric solvates

Renewable Resources for Enantiodiscrimination: Chiral Solvating Agents for NMR Spectroscopy from Isomannide and Isosorbide

A new family of chiral selectors was synthesized in a single synthetic step with yields up to 84% starting from isomannide and isosorbide. Mono- or disubstituted carbamate derivatives were obtained by reacting the isohexides with electron-donating arylisocyanate (3,5-dimethylphenyl- or 3,5-dimethoxyphenyl-) and electron-withdrawing arylisocyanate (3,5-bis(trifluoromethyl)phenyl-) groups to test opposite electronic effects on enantiodifferentiation. Deeper chiral pockets and derivatives with more acidic protons were obtained by derivatization with 1-naphthylisocyanate and p-toluenesulfonylisocyanate, respectively. All compounds were tested as chiral solvating agents (CSAs) in H-1 NMR experiments with rac-N-3,5-dinitrobenzoylphenylglycine methyl ester in order to determine the influence of different structural features on the enantiodiscrimination capabilities. Some selected compounds were tested with other racemic analytes, still leading to enantiodiscrimination. The enantiodiscrimination conditions were then optimized for the best CSA/analyte couple. Finally, a 2D- and 1D-NMR study was performed employing the best performing CSA with the two enantiomers of the selected analyte, aiming to determine the enantiodiscrimination mechanism, the stoichiometry of interaction, and the complexation constant

2-Methyl-β-cyclodextrin grafted ammonium chitosan: synergistic effects of cyclodextrin host and polymer backbone in the interaction with amphiphilic prednisolone phosphate salt as revealed by NMR spectroscopy

Reduced molecular weight chitosan was quaternized with 2-chloro-N,N-diethylethylamine to obtain a water soluble derivative (N+-rCh). Methylated-β-cyclodextrin (MCD), with 0.5 molar substitution, was covalently linked to N+-rCh through 1,6-hexamethylene diisocyanate spacer to give the derivatized ammonium chitosan N+-rCh-MCD. To shed light on the role of the cyclodextrin pendant in guiding binding interactions with amphiphilic active ingredients, corticosteroid prednisolone phosphate salt (PN) was considered. The deep inclusion of PN into cyclodextrin in PN/MCD model system was pointed out by analysis of 1H NMR complexation shifts, 1D ROESY spectra, and diffusion measurements (DOSY). By using proton selective relaxation rates measurements as investigation tool, the superior affinity of N+-rCh-MCD towards PN was demonstrated in comparison with parent ammonium chitosan N+-rCh

Induced sputum cellularity. Reference values and distribution in normal volunteers.

Abstract Sputum induction has recently been proposed as the only direct noninvasive method for measuring airway inflammatory indices. The reference values and the distribution of cells in induced sputum in a control population have not yet been well defined. We therefore evaluated data from a large number of healthy volunteers. One hundred fourteen healthy, nonatopic, nonsmoking volunteers without airway hyperreactivity were enrolled (age: 38 +/- 13 yr [mean +/- SD]; FEV(1): 105 +/- 10% predicted; provocative dose of methacholine inducing a 20% decrease FEV(1) > 3,200 microgram). Ninety-six subjects (84%) produced adequate analysis samples. The subjects had a normal age distribution. Their induced sputum was rich in macrophages (69.2 +/- 13%) and neutrophils (27.3 +/- 13%), and poor in eosinophils (0.6 +/- 0.8%), lymphocytes (1.0 +/- 1.2%), and epithelial cells (1.5 +/- 1.8%). Only macrophages and neutrophils showed a normal distribution; total and differential counts of other cells did not. We propose that these data be used in comparison of the induced sputum cells of normal subjects and those of patients with airway inflammation

Methylammonium-formamidinium reactivity in aged organometal halide perovskite inks

Over the past 10 years, organometal halide perovskites have revolutionized the field of optoelectronics, particularly of emerging photovoltaic technologies. Today's best perovskite solar cells use triple-cation compositions containing a mixture of formamidinium, methylammonium, and cesium to enable more reproducible and stable device performance. The common procedure uses as-prepared precursor ink to avoid an undesirable decrease in device performance, attributed recently to a chemical reaction between methylammonium and formamidinium in solution. Here we employ nuclear magnetic resonance spectroscopy to explore different experimental conditions that can significantly modify these reaction kinetics; in particular, we find that the presence of cesium as the third cation can substantially slow down methylammonium-formamidinium reactivity. Our findings allow us to draw up a protocol for extended overtime perovskite ink stabilization

Carba-D,L-allal- and -D,L-galactal-derived vinyl N-nosyl aziridines as useful tools for the synthesis of 4-deoxy-4-(N-nosylamino)-2,3-unsaturated-5a-carbasugars

The novel carba-D,L-allal- and carba-D,L-galactal-derived vinyl N-nosyl aziridines were prepared and the regio- and stereoselective behavior in opening reactions with O- and N-nucleophiles examined. The carbaglycosylating ability of the novel aziridines, as deduced by the amount of 1,4-addition products (1,4-regioselectivity) obtained in the acid-catalyzed methanolysis taken as a model reaction, is similar or superior to that observed with the corresponding carba-D,L-allal- and -D,L-galactal-derived vinyl epoxides, respectively. In all 1,2- and 1,4-addition products obtained, a –(N-nosylamino) group is regio- and stereoselectively introduced at the C(4) carbon of a 1,2- or 2,3-unsaturated carbasugar, susceptible to further elaborations toward aminocyclitol derivatives. The stereoselective synthesis of the corresponding, enantiomerically pure carba-D,L-allal- and -D,L-galactal-derived vinyl N-acetyl aziridines is also described

Mechanical Stimulation of Fibroblasts by Extracorporeal Shock Waves: Modulation of Cell Activation and Proliferation Through a Transient Proinflammatory Milieu

Extracorporeal shock waves (ESWTs) are \u201cmechanical\u201d waves, widely used in regenerative medicine, including soft tissue wound repair. Although already being used in the clinical practice, the mechanism of action underlying their biological activities is still not fully understood. In the present paper we tried to elucidate whether a proinflammatory effect may contribute to the regenerative potential of shock waves treatment. For this purpose, we exposed human foreskin fibroblasts (HFF1 cells) to an ESWT treatment (100 pulses using energy flux densities of 0.19 mJ/mm2 at 3 Hz), followed by cell analyses after 5 min, up to 48 h. We then evaluated cell proliferation, reactive oxygen species generation, ATP release, and cytokine production. Cells cultured in the presence of lipopolysaccharide (LPS), to induce inflammation, were used as a positive control, indicating that LPS-mediated induction of a proinflammatory pattern in HFF1 increased their proliferation. Here, we provide evidence that ESWTs affected fibroblast proliferation through the overexpression of selected cytokines involved in the establishment of a proinflammatory program, superimposable to what was observed in LPS-treated cells. The possibility that inflammatory circuits can be modulated by ESWT mechanotransduction may disclose novel hypothesis on their biological underpinning and expand the fields of their biomedical application

Isolating stem cells from skin: designing a novel highly efficient non-enzymatic approach

Stem cells are undifferentiated elements capable to acquire a specific cellular phenotype under the influence of specific stimuli, thus being involved in tissue integrity and maintenance. In the skin tissue self-renewal and wound healing after injury is a complex process, especially in adulthood, due to the aging process and the continuous exposure to damaging agents. The importance of stem cells in regenerative medicine is well known and defining or improving their isolation methods is therefore a primary and crucial step. In the present paper we present a novel method to isolate stem cells from human skin, including the involvement of a novel medium for the maintenance and expansion of in vitro cultures. The biopsies were mechanically digested and put in culture. The migrating cells were positive selected with magnetic cell sorting, characterized by flow-cytometry analysis, and viability detected by MTT assay. Cells exhibited a mesenchymal phenotype, as demonstrated by the positive acquirement of an osteogenic or adipogenic phenotype when cultured in specific conditioned media. Taken together our results disclose a novel method for culturing and expanding stem cells from skin and pave the way for future clinical applications in tissue regeneration

Thiolated 2-Methyl-β-Cyclodextrin as a Mucoadhesive Excipient for Poorly Soluble Drugs: Synthesis and Characterization

Thiolated cyclodextrins are structurally simple mucoadhesive macromolecules, which are able to host drugs and increase their apparent water solubility, as well as interact with the mucus layer prolonging drug residence time on the site of absorption. The aim of this study was to synthesize through green microwave-assisted process a freely soluble thiolated 2-methyl-β-cyclodextrin (MβCD-SH). Its inclusion complex properties with dexamethasone (Dex), a poor water soluble drug, and mucoadhesive characteristics were also determined. The product was deeply characterized through NMR spectroscopy (2D COSY, 2D HSQC, 1D/2D TOCSY, and 1D ROESY), showing a thiolation degree of 67%, a selective thiolation on the C6 residues and a monomeric structure. The association constant of MβCD and MβCD-SH with Dex resulted in 2514.3 ± 32.3 M−1 and 2147.0 ± 69.3 M−1, respectively, indicating that both CDs were able to host the drug. Microrheological analysis of mucin in the presence of MBCD-SH showed an increase of complex viscosity, G′ and G′′, due to disulphide bond formation. The cytotoxicity screening on fibroblast BALB/3T3 clone A31 cells indicated an IC50 of 27.7 mg/mL and 30.0 mg/mL, for MβCD and MβCD-SH, respectively. Finally, MβCD-SH was able to self-assemble in water into nanometric structures, both in the presence and absence of the complexed drug