The Landscape of the Spiked Tensor Model

We consider the problem of estimating a large rank-one tensor u ^⊗k ∈ (ℝⁿ)^⊗k , k ≥ 3 , in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio λ  _Bayes = O(1) above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably, no polynomial-time algorithm is known that achieved this goal unless λ ≥ Cn^{(k − 2)/4} , and even powerful semidefinite programming relaxations appear to fail for 1 ≪ λ ≪ n^{(k − 2)/4} . In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-k homogeneous polynomial over the unit sphere in n dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions n , and give exact formulas for the exponential growth rate. We show that (for λ larger than a constant) critical points are either very close to the unknown vector u or are confined in a band of width Θ(λ^{−1/(k − 1)}) around the maximum circle that is orthogonal to u . For local maxima, this band shrinks to be of size Θ(λ^{−1/(k − 2)}) . These “uninformative” local maxima are likely to cause the failure of optimization algorithms. © 2019 Wiley Periodicals, Inc.     

Certification of nitrate in spinach powder reference material SPIN-1 by high-precision isotope dilution GC–MS

A high-precision exact-matching quadruple isotope dilution method (ID⁴MS) was employed for the quantitation of nitrate in an air-dried spinach powder Certified Reference Material (CRM). The analyte was extracted in hot water following addition of ¹⁵NO\({}_{3}^{-}\) internal standard. The blend was then treated with sulfamic acid to remove nitrite and with triethyloxonium tetrafluoroborate to promote aqueous conversion of nitrate into volatile EtONO₂. The derivative was analyzed by headspace GC–MS with 3-min elution time. The method performance was validated with a series of tests which demonstrated adequate selectivity and ruggedness. This method supported the development of novel SPIN-1 CRM giving a modest contribution to its uncertainty (u_char = 0.85%). With respect to previous attempts, the SPIN-1 was proven stable, homogeneous (u_hom = 0.44%), and suitable for spinach monitoring under EU regulations. On dried basis, the nitrate content of SPIN-1 was found to be 22.53 ± 0.43 mg/g (U_c = 1.9%, k = 2). The material was also used in an inter-laboratory study where four laboratories employed a total of ten measurement methods.

SPIN-1 Certified Reference Material for nitrate in spinach powder

     

Correction to: convergence rates for Kaczmarz-type algorithms

Numerical Algorithms - We will refer to the paper “Convergence rates for Kaczmarz-type algorithms”, published in Numerical Algorithms, 79(1)(2018), 1-17. It was observed by Dr. Mokhtar...     

The Effect of Calcium-Silicate Cements on Reparative Dentinogenesis Following Direct Pulp Capping on Animal Models

Dental pulp vitality is a desideratum for preserving the health and functionality of the tooth. In certain clinical situations that lead to pulp exposure, bioactive agents are used in direct pulp-capping procedures to stimulate the dentin-pulp complex and activate reparative dentinogenesis. Hydraulic calcium-silicate cements, derived from Portland cement, can induce the formation of a new dentin bridge at the interface between the biomaterial and the dental pulp. Odontoblasts are molecularly activated, and, if necessary, undifferentiated stem cells in the dental pulp can differentiate into odontoblasts. An extensive review of literature was conducted on MedLine/PubMed database to evaluate the histological outcomes of direct pulp capping with hydraulic calcium-silicate cements performed on animal models. Overall, irrespective of their physico-chemical properties and the molecular mechanisms involved in pulp healing, the effects of cements on tertiary dentin formation and pulp vitality preservation were positive. Histological examinations showed different degrees of dental pulp inflammatory response and complete/incomplete dentin bridge formation during the pulp healing process at different follow-up periods. Calcium silicate materials have the ability to induce reparative dentinogenesis when applied over exposed pulps, with different behaviors, as related to the animal model used, pulpal inflammatory responses, and quality of dentin bridges.     

A Generalization of the Univalence on the Boundary Theorem with Applications to Sobolev Mappings

We give a generalization of a known theorem from classical complex analysis, namely the univalence on the boundary theorem. We apply this result to obtain some univalence conditions for Sobolev mappings \(f\in C({\overline{D}},{\mathbb {R}}^n)\bigcap W_{loc}^{1,q}(D,{\mathbb {R}}^n)\) which are injective on \(\partial D\), in connection with a known result of Ball from (Proc R Soc Edinb Sect A 88(3–4):315–328, 1981) modeling nonlinear elasticity.     

Metal-Free Arylation of Benzothiophenes at C4 by Activation as their Benzothiophene S-Oxides

Benzothiophenes, activated by oxidation to the corresponding S-oxides, undergo C−H/C−H-type coupling with phenols to give C4 arylation products. While an electron-withdrawing group at C3 of the benzothiophene is important, the process operates without a directing group and a metal catalyst, thus rendering it compatible with sensitive functionalities—e.g. halides and formyl groups. Quantum chemical calculations suggest a formal stepwise mechanism involving heterolytic cleavage of an aryloxysulfur species to give a π-complex of the corresponding benzothiophene and a phenoxonium cation. Subsequent addition of the phenoxonium cation to the C4 position of the benzothiophene is favored over the addition to C3; Fukui functions predict that the major regioisomer is formed at the more electron-rich position between C3 and C4. Varied selective manipulation of the benzothiophene products showcase the synthetic utility of the metal-free arylation process.     

A Combined Experimental and Computational Study of Chrysanthemin as a Pigment for Dye-Sensitized Solar Cells

The theoretical study of chrysanthemin (cyanidin 3-glucoside) as a pigment for TiO₂-based dye-sensitized solar cells (DSSCs) was performed with the GAUSSSIAN 09 simulation. The electronic spectra of neutral and anionic chrysanthemin molecules were calculated by density functional theory with B3LYP functional and DGDZVP basis set. A better energy level alignment was found for partially deprotonated molecules of chrysanthemin, with the excited photoelectron having enough energy in order to be transferred to the conduction band of TiO₂ semiconductor in DSSCs. In addition, we used the raw aqueous extracts of roselle (Hibiscus sabdariffa) calyces as the source of chrysanthemin and the extracts with various pH values were tested in DSSCs. The extracts and photosensitized semiconductor layers were characterized by UV-Vis spectroscopy, and DSSCs based on raw extracts were characterized by current density-voltage measurements.     

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer–drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of “kink–antikink pairs” dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.     

Synthesis of 1-(2-Fluorophenyl)pyrazoles by 1,3-Dipolar Cycloaddition of the Corresponding Sydnones

3-Arylsydnones bearing fluorine and bromine atoms on the benzene ring were synthesized from N-nitroso-2-fluorophenylglycines and characterized by NMR spectroscopy. These were employed further in synthesis of the corresponding 1-(2-fluorophenyl)pyrazoles by 1,3-dipolar cycloaddition reaction with dimethyl acetylenedicarboxylate (DMAD) as activated dipolarophile. The sydnones as reaction intermediates were characterized by single crystal X-ray diffraction analysis showing interesting features such as halogen bonding as an important interaction in modeling the crystal structure.     

Isoflavonoid-Antibiotic Thin Films Fabricated by MAPLE with Improved Resistance to Microbial Colonization

Staphylococcus aureus (Gram-positive) and Pseudomonas aeruginosa (Gram-negative) bacteria represent major infectious threats in the hospital environment due to their wide distribution, opportunistic behavior, and increasing antibiotic resistance. This study reports on the deposition of polyvinylpyrrolidone/antibiotic/isoflavonoid thin films by the matrix-assisted pulsed laser evaporation (MAPLE) method as anti-adhesion barrier coatings, on biomedical surfaces for improved resistance to microbial colonization. The thin films were characterized by Fourier transform infrared spectroscopy, infrared microscopy, and scanning electron microscopy. In vitro biological assay tests were performed to evaluate the influence of the thin films on the development of biofilms formed by Gram-positive and Gram-negative bacterial strains. In vitro biocompatibility tests were assessed on human endothelial cells examined for up to five days of incubation, via qualitative and quantitative methods. The results of this study revealed that the laser-fabricated coatings are biocompatible and resistant to microbial colonization and biofilm formation, making them successful candidates for biomedical devices and contact surfaces that would otherwise be amenable to contact transmission.