Reflective and photoacoustic infrared spectroscopic techniques in assessment of binding media in paintings

This study proposes a method to estimate the lipid content in binding media in paintings that can be used at any laboratory equipped with an infrared spectrometer. The lipid content estimator, termed greasiness index (GI), is defined as a ratio of lipid ν(C=O) and protein amide I bands at 1743 and 1635 cm⁻¹, respectively. Three Fourier transform infrared (FTIR) sampling techniques were evaluated for GI determination: reflective attenuated total reflection—ATR, specular reflection microscopy—μSR and photoacoustic—PAS. A set of model painting samples containing three tempera binding media (casein, egg, egg + oil), seven pigments and one varnish type were used in the study. Multivariate analysis was used to evaluate the resulting data. A good reproducibility of GI was obtained by ATR and PAS but not with μSR. The discriminative power of the technique is higher for unvarnished samples, but, generally, the GI estimator can be used for the categorisation of binding media in large populations of painting samples analysed with the same FTIR technique (sampling technique, detection, etc.).     

S‐inequality for certain product measures

In this paper we prove the S‐inequality for certain product probability measures and ideals in . As a result, for the Weibull and Gamma product distributions we derive concentration of measure type estimates as well as optimal comparison of moments.     

Calderón–Zygmund Operators in the Bessel Setting for All Possible Type Indices

We show that many harmonic analysis operators in the Bessel setting,including maximal operators,Littlewood–Paley–Stein type square functions,multipliers of Laplace or Laplace–Stieltjes transform type and Riesz transforms are,or can be viewed as,Calderón–Zygmund operators for all possible values of type parameter λ in this context.This extends results existing in the literature,but being justified only for a restricted range of λ.     

MCQ4Structures to compute similarity of molecule structures

Comparison of molecular structures in order to identify their similarity is an important step in solving various problems derived from computational biology, like structure alignment and modelling, motif search or clustering. Thus, there is a constant need for the development of good measures to determine distances between the structures and tools to display these distances in an easily interpretable form. In the paper we present MCQ4Structures, a new method and tool for structural similarity computation based on molecule tertiary structure representation in torsional angle space. We discuss its unique features as compared with the other measures, including RMSD and LGA, and we show its experimental use in comparison of a number of 3D structures as well as evaluation of models predicted within RNA-Puzzles contest. MCQ4Structures software is available as a free Java WebStart application at: http://www.cs.put.poznan.pl/tzok/mcq/. The source code licensed under BSD can be downloaded from the same website.     

Unified encoding for hyper-heuristics with application to bioinformatics

This paper introduces a new approach to applying hyper-heuristic algorithms to solve combinatorial problems with less effort, taking into account the modelling and algorithm construction process. We propose a unified encoding of a solution and a set of low level heuristics which are domain-independent and which change the solution itself. This approach enables us to address NP-hard problems and generate good approximate solutions in a reasonable time without a large amount of additional work required to tailor search methodologies for the problem in hand. In particular, we focused on solving DNA sequencing by hybrydization with errors, which is known to be strongly NP-hard. The approach was extensively tested by solving multiple instances of well-known combinatorial problems and compared with results generated by meta heuristics that have been tailored for specific problem domains.     

Roth’s theorem in many variables

We prove that if A ? {1, ..., N} has no nontrivial solution to the equation x ₁ + x ₂ + x ₃ + x ₄ + x ₅ = 5y, then \(|A| \ll Ne^{ - c(\log N)^{1/7} } \) , c > 0. In view of the well-known Behrend construction, this estimate is close to best possible.     

1H NMR assignment corrections and 1H, 13C, 15N NMR coordination shifts structural correlations in Fe(II), Ru(II) and Os(II) cationic complexes with 2,2′‐bipyridine and 1,10‐phenanthroline

¹H, ¹³C and ¹⁵N NMR studies of iron(II), ruthenium(II) and osmium(II) tris‐chelated cationic complexes with 2,2′‐bipyridine and 1,10‐phenanthroline of the general formula [M(LL)₃]²⁺ (M = Fe, Ru, Os; LL = bpy, phen) were performed. Inconsistent literature ¹H signal assignments were corrected. Significant shielding of nitrogen‐adjacent protons [H(6) in bpy, H(2) in phen] and metal‐bonded nitrogens was observed, being enhanced in the series Ru(II) → Os(II) → Fe(II) for ¹H, Fe(II) → Ru(II) → Os(II) for ¹⁵N and bpy → phen for both nuclei. The carbons are deshielded, the effect increasing in the order Ru(II) → Os(II) → Fe(II). Copyright © 2010 John Wiley & Sons, Ltd.     

The Number of Monochromatic Schur Triples

In this paper, we prove that in every 2-coloring of the set {1, , N } = R B, one can find at least N² / 22 + O(N) monochromatic solutions of the equation x + y = z. This solves a problem of Graham et al. .     

Stereostructure of mycoheptin A2

The absolute configurations of all the stereogenic centers of the antibiotic mycoheptin A₂ were established upon previously elaborated general procedure, consisting of DQF‐COSY, NOESY, ROESY, HSQC and HMBC experiments as major tools. The structure of mycoheptin A₂ without stereochemistry of its aglycone has been reported before. Copyright © 2012 John Wiley & Sons, Ltd.     

The Cubical Cohomology Ring: An Algorithmic Approach

A cohomology ring algorithm in a dimension-independent framework of combinatorial cubical complexes is developed with the aim of applying it to the topological analysis of high-dimensional data. This approach is convenient in the cup-product computation and motivated, among others, by interpreting pixels or voxels in digital images as cubes. The S-complex theory and so called co-reductions are adopted to build a cohomology ring algorithm speeding up the algebraic computations.