On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions

Let X = X ₁ ... X _n and Y = Y ₁ ... Y _n be two binary sequences with length n. A common subsequence of X and Y is any subsequence of X that at the same time is a subsequence of Y; The common subsequence with maximal length is called the longest common subsequence (LCS) of X and Y. LCS is a common tool for measuring the closeness of X and Y. In this note, we consider the case when X and Y are both i.i.d. Bernoulli sequences with the parameters ϵ and 1 − ϵ, respectively. Hence, typically the sequences consist of large and short blocks of different colors. This gives an idea to the so-called block-by-block alignment, where the short blocks in one sequence are matched to the long blocks of the same color in another sequence. Such and alignment is not necessarily a LCS, but it is computationally easy to obtain and, therefore, of practical interest. We investigate the asymptotical properties of several block-by-block type of alignments. The paper ends with the simulation study, where the of block-by-block type of alignments are compared with the LCS.     

On the structure of the Bochner–Martinelli residue currents

The paper presents a survey of the main results of I.M. Vinogradov.     

Organic‐acid mediated bulk polymerization of ε‐caprolactam and its copolymerization with ε‐caprolactone

Polyamides (PA) constitute one of the most important classes of polymeric materials and have gained strong position in different areas, such as textiles, fibers, and construction materials. Whereas most PA are synthesized by step‐growth polycondensation, PA 6 is synthesized by ring opening polymerization (ROP) of ε‐caprolactam (ε‐CLa). The most popular ROP methods involve the use of alkaline metal catalyst difficult to handle at large scale. In this article, we propose the use of organic acids for the ROP of ε‐CLa in bulk at 180 °C (below the polymer's melting point). Among evaluated organic acids, sulfonic acids were found to be the most effective for the polymerization of ε‐CLa , being the Brønsted acid ionic liquid: 1‐(4‐sulfobutyl)?3‐methylimidazolium hydrogen sulfate the most suitable due to its higher thermal stability. End‐group analysis by ¹H nuclear magnetic resonance and model reactions provided mechanistic insights and suggested that the catalytic activity of sulfonic acids was a function of not only the acid strength, but of the nucleophilic character of conjugate base as well. Finally, the ability of sulfonic acid to promote the copolymerization of ε‐CLa and ε‐caprolactone is demonstrated. As a result, poly(ε‐caprolactam‐co‐ε‐caprolactone) copolymers with considerably randomness are obtained. This benign route allows the synthesis of poly(ester amide)s with different thermal and mechanical properties. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 2394–2402