Strategies of loop recombination in ciliates

The concept of breakpoint graph, known from the theory of sorting by reversal, has been successfully applied in the theory of gene assembly in ciliates. We further investigate its usage for gene assembly, and show that the graph allows for an efficient characterization of the possible orders of loop recombination operations (one of the three types of molecular operations that accomplish gene assembly) for a given gene during gene assembly. The characterization is based on spanning trees within a graph built upon the connected components in the breakpoint graph. We work in the abstract and more general setting of so-called legal strings.     

An EOX method for the detection of halogenated hydrocarbons in soil samples

Analytical and Bioanalytical Chemistry -     

Photochirogenesis: photochemical models on the absolute asymmetric formation of amino acids in interstellar space

Proteins of all living organisms including plants, animals, and humans are made up of amino acid monomers that show identical stereochemical L-configuration. Hypotheses for the origin of this symmetry breaking in biomolecules include the absolute asymmetric photochemistry model by which interstellar ultraviolet (UV) circularly polarized light (CPL) induces an enantiomeric excess in chiral organic molecules in the interstellar/circumstellar media. This scenario is supported by a) the detection of amino acids in the organic residues of UV-photo-processed interstellar ice analogues, b) the occurrence of L-enantiomer-enriched amino acids in carbonaceous meteorites, and c) the observation of CPL of the same helicity over large distance scales in the massive star-forming region of Orion. These topics are of high importance in topical biophysical research and will be discussed in this review. Further evidence that amino acids and other molecules of prebiotic interest are asymmetrically formed in space comes from studies on the enantioselective photolysis of amino acids by UV-CPL. Also, experiments have been performed on the absolute asymmetric photochemical synthesis of enantiomer-enriched amino acids from mixtures of astrophysically relevant achiral precursor molecules using UV-circularly polarized photons. Both approaches are based on circular dichroic transitions of amino acids that will be highlighted here as well. These results have strong implications on our current understanding of how life's precursor molecules were possibly built and how life selected the left-handed form of proteinogenic amino acids.     

Spectral dynamics of modulation instability described using Akhmediev breather theory

The Akhmediev breather formalism of modulation instability is extended to describe the spectral dynamics of induced multiple sideband generation from a modulated continuous wave field. Exact theoretical results describing the frequency domain evolution are compared with experiments performed using single mode fiber around 1550 nm. The spectral theory is shown to reproduce the depletion dynamics of an injected modulated continuous wave pump and to describe the Fermi-Pasta-Ulam recurrence and recovery towards the initial state. Realistic simulations including higher-order dispersion, loss, and Raman scattering are used to identify that the primary physical factors that preclude perfect recurrence are related to imperfect initial conditions.     

Akhmediev breather evolution in optical fiber for realistic initial conditions

We study numerically Akhmediev breather dynamics in optical fibers under initial conditions that do not correspond to an ideal infinitesimal modulation on a plane wave. We examine two modifications that are commonly encountered in realistic experiments: (i) a finite-amplitude (not necessarily weak) initial modulation; (ii) the use of pulsed excitation. In the first case, we derive an expression for the propagation distance required to generate a train of compressed breather pulses. In the second case, we show that breather dynamics with pulsed excitation can be interpreted in terms of local breather states at different points on the pulse envelope.     

On the spectrum of stiffness matrices arising from isogeometric analysis

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of \(\mathbb C\) . All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems.     

The Gibbs' phenomenon

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of given improper integrals, but also intuitive questions and some paradoxical results too (for example, a figure with an infinite longitude which closes the same area as the unit circumference, or an infinite figure with a finite volume). In particular, the students were asked to interpret most of the results they had obtained. Answers given by the students to each of the questions were categorized, which allowed some initial conclusions to be reached regarding this research. From analyses carried out, one can conclude that there are students who have difficulties in articulating the different systems of representation, and have problems in connecting and relating this knowledge as a generalization of previous concepts, such as definite integrals, series and sequences.     

Two remarks on generalized hexagons

In this paper, the point-distance-2-regular hexagons are characterized as the only hexagons for which the intersection sets have size one and containing on ovoidal subspace all the points of which are 3-regular. We also give a characterization of the finite split Cayley hexagon of even order.