Asymmetry in the Converse of Schur's Lemma

We show that the converse of Schur's Lemma can hold in the category of right modules, but not the category of left modules, over an appropriate ring. We exhibit classes of rings over which this left-right asymmetry does not occur, and provide new constructions of rings over whose module categories the converse of Schur's Lemma holds. We propose various open problems and avenues for further research concomitant to our work.     

ILs and MMPs Levels in Inflamed Human Dental Pulp: A Systematic Review

A wide range of mediators are released from the pulp tissue because of bacterial invasion which causes inflammation. Interleukins (ILs) and matrix metalloproteinases (MMPs) have a leading role in initiating and spreading of inflammation because of their synergic action. Biomarkers such as ILs and MMPs can be identified via several methods, establishing the inflammatory response of the dental pulp. The aim of this systematic review is to evaluate the levels of ILs and/or MMPs in human dental pulp. PubMed, OVID, Cochrane, Scopus, Web of Science and Wiley online library databases were searched for original clinical studies. After applying inclusion and exclusion criteria, a quality assessment of studies was performed based on a modified Newcastle-Ottawa scale. In the review were included articles that evaluated the presence of ILs and/or MMPs in pulp tissue using enzyme-linked immunosorbent assay (ELISA) or western blot or multiplex assay. Six articles were included in the present synthesis. Although various diagnostic methods were used, statistically significant higher levels of ILs and/or MMPs were mostly found in the experimental groups compared to healthy pulp samples. The biomarkers studied can be a promising tool to evaluate pulp tissue health or even in pulpitis treatment.     

The nucleolus and the core-center of multi-sided Böhm-Bawerk assignment markets

We prove that both the nucleolus and the core-center, i.e., the mass center of the core, of an m-sided Böhm-Bawerk assignment market can be respectively computed from the nucleolus and the core-center of a convex game defined on the set of m sectors. What is more, in the calculus of the nucleolus of this latter game only singletons and coalitions containing all agents but one need to be taken into account. All these results simplify the computation of the nucleolus and the core-center of a multi-sided Böhm-Bawerk assignment market with a large number of agents. As a consequence we can show that, contrary to the bilateral case, for multi-sided Böhm-Bawerk assignment markets the nucleolus and the core-center do not coincide in general.     

On the sub-optimality cost of immediate annuitization in DC pension funds

We consider the position of a member of a defined contribution (DC) pension scheme having the possibility of taking programmed withdrawals at retirement. According to this option, she can defer annuitization of her fund to a propitious future time, that can be found to be optimal according to some criteria. This option, that adds remarkable flexibility in the choice of pension benefits, is not available in many countries, where immediate annuitization is compulsory at retirement. In this paper, we address and try to answer the questions: “Is immediate annuitization optimal? If it is not, what is the cost to be paid by the retiree obliged to annuitize at retirement?”. In order to do this, we consider the model by Gerrard et?al. in Quant Finance, (2011) and extend it in two different ways. In the first extension, we prove a theorem that provides necessary and sufficient conditions for immediate annuitization being always optimal. The not surprising result is that compulsory immediate annuitization turns out to be sub-optimal. We then quantify the extent of sub-optimality, by defining the sub-optimality cost as the loss of expected present value of consumption from retirement to death and measuring it in many typical situations. We find that it varies in relative terms between 6 and 40%, depending on the risk aversion of the member. In the second extension, we make extensive numerical investigations of the model and seek the optimal annuitization time. We find that the optimal annuitization time depends on personal factors such as the retiree’s risk aversion and her subjective perception of remaining lifetime. It also depends on the financial market, via the Sharpe ratio of the risky asset. Optimal annuitization should occur a few years after retirement with high risk aversion, low Sharpe ratio and/or short remaining lifetime, and many years after retirement with low risk aversion, high Sharpe ratio and/or long remaining lifetime. This paper supports the availability of programmed withdrawals as an option to retirees of DC pension schemes, by giving insight into the extent of loss in wealth suffered by a retiree who cannot choose programmed withdrawals, but is obliged to annuitize immediately on retirement.     

On the topological equivalence of some fuzzy flows near hyperbolic equilibria

The purpose of this work is to study fuzzy dynamical systems associated with deterministic systems. The Grobman-Hartman theorem states that, near hyperbolic equilibria, there exists a homeomorphism between the nonlinear system's trajectories and the linearized correspondent system's trajectories. That is, these systems are topologically equivalent. A theorem similar to Grobman-Hartman theorem to fuzzy flows is the main result in this article. For fuzzy flows obtained from each system it states that the nonlinear and the linearized are topologically equivalent.     

How charging corannulene with one and two electrons affects its geometry and aggregation with sodium and potassium cations

Bowl-shaped mono- and dianions are prepared by reduction of corannulene (C(20)H(10), 1) with sodium and potassium metals in the presence of [18]crown-6 ether. Single-crystal X-ray diffraction studies of two sodium salts, [Na(THF)(2)([18]crown-6)](+)[1(-)] (2a) and [Na([18]crown-6)](+)[1(-)] (2b), reveal the presence of naked corannulene monoanions 1(-) in both cases. In contrast, the potassium adduct, [K([18]crown-6)](+)[1(-)] (3), shows an η(2)-binding of the K(+) ion to the convex face of 1(-). For the first time, corannulene dianions have been isolated as salts with sodium, [Na(2)([18]crown-6)](2+)[1(2-)] (4a) and [Na(THF)(2)([18]crown-6)](+)[Na([18]crown-6)](+)[1(2-)] (4b), and potassium counterions, [K([18]crown-6)](2)(+)[1(2-)] (5). Their structural characterization reveals geometry perturbations upon addition of two electrons to a bowl-shaped polyarene. It also demonstrates η(5)- or η(6)-binding of metals to the curved carbon surface of 1(2-), depending on the crystallization conditions. Both mono- and doubly-charged corannulene bowls show the preferential exo binding of Na(+) and K(+) ions in all investigated compounds. Various types of C-H···π interactions are found in the crystals of 2-5. The UV/Vis, ESR, and (1)H NMR spectroscopic studies of 2-5 indicate different coordination environment of corannulene anions in solution, depending on the metal ion.     

Click mechanochemistry: quantitative synthesis of "ready to use" chiral organocatalysts by efficient two-fold thiourea coupling to vicinal diamines

Mechanochemical methods of neat grinding and liquid-assisted grinding have been applied to the synthesis of mono- and bis(thiourea)s by using the click coupling of aromatic and aliphatic diamines with aromatic isothiocyanates. The ability to modify the reaction conditions allowed the optimization of each reaction, leading to the quantitative formation of chiral bis(thiourea)s with known uses as organocatalysts or anion sensors. Quantitative reaction yields, combined with the fact that mechanochemical reaction conditions avoid the use of bulk solvents, enabled solution-based purification methods (such as chromatography or recrystallization) to be completely avoided. Importantly, by using selected model reactions, we also show that the described mechanochemical reaction procedures can be readily scaled up to at least the one-gram scale. In that way, mechanochemical synthesis provides a facile method to fully transform valuable enantiomerically pure reagents into useful products that can immediately be applied in their designed purpose. This was demonstrated by using some of the mechanochemically prepared reagents as organocatalysts in a model Morita-Baylis-Hillman reaction and as cyanide ion sensors in organic solvents. The use of electronically and sterically hindered ortho-phenylenediamine revealed that mechanochemical reaction conditions can be readily optimized to form either the 1:1 or the 1:2 click-coupling product, demonstrating that reaction stoichiometry can be more efficiently controlled under these conditions than in solution-based syntheses. In this way, it was shown that excellent stoichiometric control by mechanochemistry, previously established for mechanochemical syntheses of cocrystals and coordination polymers, can also be achieved in the context of covalent-bond formation.     

On the utility of predictive chromatography to complement mass spectrometry based intact protein identification

The amino acid sequence determines the individual protein three-dimensional structure and its functioning in an organism. Therefore, “reading” a protein sequence and determining its changes due to mutations or post-translational modifications is one of the objectives of proteomic experiments. The commonly utilized approach is gradient high-performance liquid chromatography (HPLC) in combination with tandem mass spectrometry. While serving as a way to simplify the protein mixture, the liquid chromatography may be an additional analytical tool providing complementary information about the protein structure. Previous attempts to develop “predictive” HPLC for large biomacromolecules were limited by empirically derived equations based purely on the adsorption mechanisms of the retention and applicable to relatively small polypeptide molecules. A mechanism of the large biomacromolecule retention in reversed-phase gradient HPLC was described recently in thermodynamics terms by the analytical model of liquid chromatography at critical conditions (BioLCCC). In this work, we applied the BioLCCC model to predict retention of the intact proteins as well as their large proteolytic peptides separated under different HPLC conditions. The specific aim of these proof-of-principle studies was to demonstrate the feasibility of using “predictive” HPLC as a complementary tool to support the analysis of identified intact proteins in top-down, middle-down, and/or targeted selected reaction monitoring (SRM)-based proteomic experiments.     

Infrared spectroscopic analysis of mononuclear leukocytes in peripheral blood from Alzheimer’s disease patients

Peripheral mononuclear leukocytes from Alzheimer’s disease (AD) patients were analyzed by infrared spectroscopy and their spectroscopic properties were compared with those from age-matched healthy controls. Two-dimensional correlation analysis of mean spectra measured at various disease stages shows that the protein secondary structure from AD patients involves β-sheet enrichment and carbonyl intensity increase relative to healthy controls. The area percentages of β-sheets, which were obtained by using a peak ratio second-derivative spectral treatment, were used for receiver operating characteristic (ROC) analysis to distinguish between patients with AD and age-matched healthy controls. The critical concentration and area under the curve (AUC) were determined by this curve analysis which showed a good performance for this quantitative assay. The results were 90% sensitivity and 90.5% specificity for determinations involving mild and moderate AD patients, and 82.1% sensitivity and 90.5% specificity for determinations involving patients at the three AD stages (mild, moderate, and severe). The AUC was greater than 0.85 in both scenarios. Taken together these results show that healthy controls are distinguished from mild and moderate AD patients better than from patients with severe disease and suggest that this infrared analysis is a promising strategy for AD diagnostics.     

A study of the sign problem for lattice QCD with chemical potential

We study the expectation value of the phase of the fermion determinant for Wilson lattice fermions with chemical potential. We use quenched SU(3)$\mathrm{SU}(3)$ ensembles and implement a recently proposed exact dimensional reduction of the fermion determinant. Ensembles at several temperatures below and above the phase transition are studied and we analyze the role of the quark mass, the temperature, the volume and the topological sectors. We compare our numerical results to predictions from chiral perturbation theory.