Riordan group involutions

We study involutions in the Riordan group, especially those with combinatorial meaning. We give a new determinantal criterion for a matrix to be a Riordan involution and examine several classes of examples. A complete characterization of involutions in the Appell subgroup is developed. In another direction we find several examples that generalize the RNA matrix but are of independent interest.     

Simple proofs of open problems about the structure of involutions in the Riordan group

We prove that if D=(g(x),f(x)) is an element of order 2 in the Riordan group then g(x)=±exp[Φ(x,xf(x)] for some antisymmetric function Φ(x,z). Also we prove that every element of order 2 in the Riordan group can be written as BMB^-1 for some element B and M=(1,-1) in the Riordan group. These proofs provide solutions to two open problems presented by L. Shapiro [L.W. Shapiro, Some open questions about random walks, involutions, limiting distributions and generating functions, Adv. Appl. Math. 27 (2001) 585-596].     

A Bootstrap Framework for Aggregating within and between Feature Selection Methods

In the past decade, big data has become increasingly prevalent in a large number of applications. As a result, datasets suffering from noise and redundancy issues have necessitated the use of feature selection across multiple domains. However, a common concern in feature selection is that different approaches can give very different results when applied to similar datasets. Aggregating the results of different selection methods helps to resolve this concern and control the diversity of selected feature subsets. In this work, we implemented a general framework for the ensemble of multiple feature selection methods. Based on diversified datasets generated from the original set of observations, we aggregated the importance scores generated by multiple feature selection techniques using two methods: the Within Aggregation Method (WAM), which refers to aggregating importance scores within a single feature selection; and the Between Aggregation Method (BAM), which refers to aggregating importance scores between multiple feature selection methods. We applied the proposed framework on 13 real datasets with diverse performances and characteristics. The experimental evaluation showed that WAM provides an effective tool for determining the best feature selection method for a given dataset. WAM has also shown greater stability than BAM in terms of identifying important features. The computational demands of the two methods appeared to be comparable. The results of this work suggest that by applying both WAM and BAM, practitioners can gain a deeper understanding of the feature selection process.     

Reaction of 3-chloroquinoline-2,4-diones with ethanolamine and rearrangement of the reaction products

The reaction of tertiary α-chloroketones with ethanolamine has not been hitherto described in the literature. Herein, we describe the reaction of tertiary 3-chloroquinoline-2,4-diones with ethanolamine to give novel 3-(2-hydroxyethylamino)quinoline-2,4-diones. These compounds provide 3-(2-oxooxazolidin-3-yl)quinoline-2,4(1H,3H)-diones and new compounds with dimeric character after reaction with triphosgene. Molecular rearrangement proceeds during the reaction of 3-(2-hydroxyethylamino)quinoline-2,4-diones with isocyanic acid. Three types of reaction products arise: 2-(2-hydroxyethyl)imidazo[1,5-c]quinazoline-3,5-diones, 3-(2-hydroxyethyl)-3,3a-dihydro-2H-imidazo[4,5-]quinoline-4(5H)diones and primarily 5-hydroxy-1-(hydroxyethyl)-1′H-spiro[imidazolidine-5,3′-indole]-2,2′-diones. The reaction mechanism and product stereochemistry are discussed. The ¹H, ¹³C and ¹⁵N NMR spectra of the prepared compounds were measured, and all resonances were assigned from appropriate two-dimensional experiments.     

Influence of HPAM on W/O emulsion separation properties

The present study reports on the influence of partially hydrolyzed polyacrylamide (HPAM) on essential w/o emulsion properties. The characterization has been undertaken with low field NMR to follow droplet sizes and distributions, sedimentation and coalescence kinetic, bench-scale electrocoalescence (E_crit) experiments to follow emulsion stability changes, and electrorheology to detect changes in the viscosity upon applying an external electric field. The result is that HPAM does not basically influence the droplet size distribution (DSD) and the stability level of the emulsions as can be expected of bulk polymers. However, there seems to be an interaction between added demulsifiers either through direct molecular interaction or via an interfacial complexation.     

Self‐Assembly of Coiled Coils in Synthetic Biology: Inspiration and Progress

Biological self‐assembly is very complex and results in highly functional materials. In effect, it takes a bottom‐up approach using biomolecular building blocks of precisely defined shape, size, hydrophobicity, and spatial distribution of functionality. Inspired by, and drawing lessons from self‐assembly processes in nature, scientists are learning how to control the balance of many small forces to increase the complexity and functionality of self‐assembled nanomaterials. The coiled‐coil motif, a multipurpose building block commonly found in nature, has great potential in synthetic biology. In this review we examine the roles that the coiled‐coil peptide motif plays in self‐assembly in nature, and then summarize the advances that this has inspired in the creation of functional units, assemblies, and systems.     

Regioisomeric analysis of triacylglycerols using silver-ion liquid chromatography-atmospheric pressure chemical ionization mass spectrometry: comparison of five different mass analyzers

Silver-ion high-performance liquid chromatography (HPLC) coupled to atmospheric pressure chemical ionization mass spectrometry (APCI-MS) is used for the regioisomeric analysis of triacylglycerols (TGs). Standard mixtures of TG regioisomers are prepared by the randomization reaction from 8 mono-acid TG standards (tripalmitin, tristearin, triarachidin, triolein, trielaidin, trilinolein, trilinolenin and tri-gamma-linolenin). In total, 32 different regioisomeric doublets and 11 triplets are synthesized, separated by silver-ion HPLC using three serial coupled chromatographic columns giving a total length of 75cm. The retention of TGs increases strongly with the double bond (DB) number and slightly for regioisomers having more DBs in sn-1/3 positions. DB positional isomers (linolenic vs. γ-linolenic acids) are also separated and their reverse retention order in two different mobile phases is demonstrated. APCI mass spectra of all separated regioisomers are measured on five different mass spectrometers: single quadrupole LC/MSD (Agilent Technologies), triple quadrupole API 3000 (AB SCIEX), ion trap Esquire 3000 (Bruker Daltonics), quadrupole time-of-flight micrOTOF-Q (Bruker Daltonics) and LTQ Orbitrap XL (Thermo Fisher Scientific). The effect of different types of mass analyzer on the ratio of [M+H-R(i)COOH](+) fragment ions in APCI mass spectra is lower compared to the effect of the number of DBs, their position on the acyl chain and the regiospecific distribution of acyl chains on the glycerol skeleton. Presented data on [M+H-R(i)COOH](+) ratios measured on five different mass analyzers can be used for the direct regioisomeric determination in natural and biological samples.