Relative difference in diversity between populations

An entropy is conceived as a functional on the space of probability distributions. It is used as a measure of diversity (variability) of a population. Cross entropy leads to a measure of dissimilarity between populations. In this paper, we provide a new approach to the construction of a measure of dissimilarity between two populations, not depending on the choice of an entropy function, measuring diversity. The approach is based on the principle of majorization which provides an intrinsic method of comparing the diversities of two populations. We obtain a general class of measures of dissimilarity and show some interesting properties of the proposed index. In particular, it is shown that the measure provides a metric on a probability space. The proposed measure of dissimilarity is essentially a measure of relative difference in diversity between two populations. It satisfies an invariance property which is not shared by other measures of dissimilarity which are used in ecological studies. A statistical application of the new method is given.     

Protein-binding molecular switches via host-guest stabilized DNA hairpins

Molecular switches, with target protein-binding activity controlled by prior binding to specific input stimuli, are ubiquitously used in Nature. However, the emulation of such responsive systems, especially in a de novo fashion, remains a significant challenge. Herein, we disclose a strategy that harnesses an intramolecular β-CD/adamantane host-guest interaction to generate a stabilized DNA hairpin (ΔT(m) = 17 °C) that undergoes an input oligonucleotide (ODN)-selective structural transformation from a stem-loop conformation to a duplex. This ODN-induced conformational switch allows for the transition from an inactive state (wherein the adamantane protein-binding headgroup is encapsulated) to an activated protein-binding complex, with a freely accessible adamantane moiety. Given that hairpin domains can be readily modulated to be responsive to alternative ODN triggering sequences and that encapsulating macrocycles, such as β-CD, are good hosts for a number of protein-binding small molecules, this strategy may furnish a general method to develop ODN-responsive protein-binders.     

Even (s̄,t̄)-core partitions and self-associate characters of S̃n

We extend a method of Olsson and Bessenrodt to determine the number of even partitions that are simultaneously $\stackrel{?}{s}$-core and $\stackrel{?}{t}$-core. When $p$ and $q$ are distinct primes, this also determines the number of self-associate characters of ${\stackrel{?}{S}}_n$ that are simultaneously defect 0 for $p$ and $q$.     

Sample introduction in gas chromatography using a coiled wire filament

A simple device for field sampling and concentration of analytes for subsequent introduction into an injection port for gas chromatographic (GC) analysis has been developed. It consists of a tiny, coiled platinum wire filament (CWF) that is attached to a retractable plunger wire, which fits inside a syringe needle housing. Sampling is accomplished by dipping the end of the CWF in a liquid sample, which is drawn into the wire coil by capillary action, and introducing it into the injection port either before or after allowing the solvent to evaporate. The CWF can be used with or without a nonvolatile chemical coating. A major advantage of this sampling device is that nonvolatile sample matrix components remain on the wire coil, reducing the required injection port and liner cleaning frequency and contamination of the head of the chromatographic column. The coil itself can be easily cleaned between analyses by rinsing and/or burning off residual material in a small flame. The sampling coil facilitates specifically designed chemical reactions in the injection port, such as thermochemolysis and methylation. Applications demonstrated in this work include: (1) direct introduction of samples with little or no pre-treatment, (2) simultaneous thermochemolysis and methylation of lipid-containing samples such as bacteria and bacterial endospores for analysis of biomarkers, and (3) solid phase micro-extraction (SPME) using temporary wire coatings. The CWF allowed for significant reduction in sample preparation time, in most cases to less than a few minutes. The peak shapes examined for polycyclic aromatic hydrocarbon analytes (PAHs) were significantly better (asymmetry factors <1.3) when using the CWF sampling technique compared to splitless and on-column injection techniques (asymmetry factors >1.3). Extraction efficiencies for SPME (especially for high boiling point components such as PAHs) improved by an average of 2.5 times when using the CWF compared to the performance of commercially available SPME fibers. Coiled wire filaments and GC injection port liners were used for more than 100 Bacillus endospore thermochemolysis methylation analyses without the need for cleaning or replacement.     

Linear independence of the principal solutions at ∞ and −∞ for formally self-adjoint differential systems

Linear independence of the principal solutions at ∞ and ?∞ for identically normal, formally self-adjoint differential systems $\text{U′ = AU + BV, V′ = CU ? A}{}^1\text{V}$, with B ? 0, which are disconjugate on (?∞, ∞), is characterized by the condition W_?∞ < W_∞ on (?∞, ∞), where W_∞, [W_?∞], is the distinguished solution of the associated Riccati equation at ∞, [?∞]. A comparison type theorem between the above system and certain Sturmian majorants gives order relations for the corresponding distinguished solutions. The work is motivated by that of Anderson and Lazer for self-adjoint scalar equations of order 2n. For certain types of such equations, the results allow a direct sum decomposition into two n dimensional families, one whose solutions are in L₂(?∞, 0] and the other whose solutions are in L₂[0, ∞).