Applications of a graph related to conjugacy classes in finite groups

This article was written by the authors with a during the forth author's visit to Milano and, independently.     

On the Stability of DNA Origami Nanostructures in Low‐Magnesium Buffers

DNA origami structures have great potential as functional platforms in various biomedical applications. Many applications, however, are incompatible with the high Mg²⁺ concentrations commonly believed to be a prerequisite for maintaining DNA origami integrity. Herein, we investigate DNA origami stability in low‐Mg²⁺ buffers. DNA origami stability is found to crucially depend on the availability of residual Mg²⁺ ions for screening electrostatic repulsion. The presence of EDTA and phosphate ions may thus facilitate DNA origami denaturation by displacing Mg²⁺ ions from the DNA backbone and reducing the strength of the Mg²⁺–DNA interaction, respectively. Most remarkably, these buffer dependencies are affected by DNA origami superstructure. However, by rationally selecting buffer components and considering superstructure‐dependent effects, the structural integrity of a given DNA origami nanostructure can be maintained in conventional buffers even at Mg²⁺ concentrations in the low‐micromolar range.     

Determination of cyanide ion by homogeneous catalysis and gas chromatography

A simple procedure for the determination of trace levels of cyanide ions is described and evaluated. The procedure is based on the cyanide-catalyzed cleavage of benzil in the presence of methanol to produce benzaldehyde and methyl benzoate. The concentrations of these products are determined by gas chromatography. Linearity between gas chromatographic response and cyanide concentration is observed from 0.05 to 3 ppm cyanide; a detection limit of 1 ppb is calculated. A series of anions is shown not to interfere.     

Synthetic studies in the alkaloid field—VII: Stereochemistry of 1,2,3,4,6,7,12,12b-octahydroindolo [2,3-a]quinolizine derivatives prepared by alkaline decarboalkoxylative cyclization or acid-induced cyclization of appropriate tetrahydropyridines

The C(12b)-C(1)-C(2) stereochemical relationship in several racemic 1,2,3,4,6,7,12,12b-octahydroindolo [2,3-a]quinolizine derivatives has been determined by ¹³C NMR spectral analysis. The proper shift assignment was confirmed by recording the spectra of selectively deuterated derivatives. The C(12b)-C(1)-C(2) stereochemical relationship in indolo[2,3-a]quinolizines obtained either by alkaline decarboalkoxylative cyclization or by acid-induced cyclization of partially hydrogenated 1-[2-(3-indolyl)ethyl]-3-methoxycarbonylpyridine derivatives is discussed. The ambiguity existing in the preparation of dl-18,19-dihydroantirhine 2 by analogous decarboalkoxylative cyclization is considered.     

Hydrodynamic Green functions: paradoxes in unsteady Stokes conditions and infinite propagation velocity in incompressible viscous models

Meccanica - We present a simple representation of the hydrodynamic Green functions grounded on the free propagation of a vector field without any constraints (such as incompressibility) coupled...     

Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 3. Variable selection in classification

In multivariate regression and classification issues variable selection is an important procedure used to select an optimal subset of variables with the aim of producing more parsimonious and eventually more predictive models. Variable selection is often necessary when dealing with methodologies that produce thousands of variables, such as Quantitative Structure-Activity Relationships (QSARs) and highly dimensional analytical procedures.In this paper a novel method for variable selection for classification purposes is introduced. This method exploits the recently proposed Canonical Measure of Correlation between two sets of variables (CMC index). The CMC index is in this case calculated for two specific sets of variables, the former being comprised of the independent variables and the latter of the unfolded class matrix. The CMC values, calculated by considering one variable at a time, can be sorted and a ranking of the variables on the basis of their class discrimination capabilities results. Alternatively, CMC index can be calculated for all the possible combinations of variables and the variable subset with the maximal CMC can be selected, but this procedure is computationally more demanding and classification performance of the selected subset is not always the best one.The effectiveness of the CMC index in selecting variables with discriminative ability was compared with that of other well-known strategies for variable selection, such as the Wilks’ Lambda, the VIP index based on the Partial Least Squares-Discriminant Analysis, and the selection provided by classification trees.A variable Forward Selection based on the CMC index was finally used in conjunction of Linear Discriminant Analysis. This approach was tested on several chemical data sets. Obtained results were encouraging.     

Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data: Part 2. Variable reduction

This paper proposes a new method for determining the subset of variables that reproduce as well as possible the main structural features of the complete data set. This method can be useful for pre-treatment of large data sets since it allows discarding variables that contain redundant information. Reducing the number of variables often allows one to better investigate data structure and obtain more stable results from multivariate modelling methods.The novel method is based on the recently proposed canonical measure of correlation (CMC index) between two sets of variables [R. Todeschini, V. Consonni, A. Manganaro, D. Ballabio, A. Mauri, Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 1. Theory and simple chemometric applications, Anal. Chim. Acta submitted for publication (2009)]. Following a stepwise procedure (backward elimination), each variable in turn is compared to all the other variables and the most correlated is definitively discarded. Finally, a key subset of variables being as orthogonal as possible are selected. The performance was evaluated on both simulated and real data sets. The effectiveness of the novel method is discussed by comparison with results of other well known methods for variable reduction, such as Jolliffe techniques, McCabe criteria, Krzanowski approach and its modification based on genetic algorithms, loadings of the first principal component, Key Set Factor Analysis (KSFA), Variable Inflation Factor (VIF), pairwise correlation approach, and K correlation analysis (KIF). The obtained results are consistent with those of the other considered methods; moreover, the advantage of the proposed CMC method is that calculation is very quick and can be easily implemented in any software application.     

Nanoporosity of an organo-clay shown by hyperpolarized xenon and 2D NMR spectroscopy

Interlayer nanoporosity of hectorite pillared by tetraethylammonium ions is explored by hyperpolarized xenon NMR and relevant gases such as carbon dioxide revealing the adsorption capacity of the open galleries.     

Geographical classification of wine and olive oil by means of classification and influence matrix analysis (CAIMAN)

Classification and influence matrix analysis (CAIMAN) is a new classification method, recently proposed and based on the influence matrix (also called leverage matrix). Depending on the purposes of the classification analysis, CAIMAN can be used in three outlines: (1) D-CAIMAN is a discriminant classification method, (2) M-CAIMAN is a class modelling method allowing a sample to be classified, not classified at all, or assigned to more than one class (confused) and (3) A-CAIMAN deals with the asymmetric case, where only a reference class needs to be modelled.

In this work, the geographic classification of samples of wine and olive oil has been carried out by means of CAIMAN and its results compared with discriminant analysis, by focusing great attention on the model predictive capabilities. The geographic characterization has been carried out on three different datasets: extra virgin olive oils produced in a small area, with a “protected denomination of origin” label, wines with different denominations of origin, but produced in enclosed geographical areas, and olive oils belonging to different production areas.

Final results seem to indicate that the application of CAIMAN to the geographical origin identification offers several advantages: first, it shows – on an average basis – good performances; second, it is able to deal in a simple way classification problems related to tipicity, authenticity, and uniqueness characterization, which are of increasing interest in food quality issues.