Inverse problems of symbolic dynamics

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by substitutional system, and dynamical properties are considered as criteria of superword being generated by interval exchange transformation. As a consequence, one can get a morphic word appearing in interval exchange transformation such that frequencies of letters are algebraic numbers of an arbitrary degree. Concerning multydimensional systems, our main result is the following. Let P(n) be a polynomial, having an irrational coefficient of the highest degree. A word $w$ (w=(w_n), n\in \nit) consists of a sequence of first binary numbers of $\{P(n)\}$ i.e. $w_n=[2\{P(n)\}]$. Denote the number of different subwords of $w$ of length $k$ by $T(k)$ . \medskip {\bf Theorem.} {\it There exists a polynomial $Q(k)$, depending only on the power of the polynomial $P$, such that $T(k)=Q(k)$ for sufficiently great $k$.

On cogrowth function of algebras and its logarithmical gap

Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a subword-minimal $I$-reducible word. A {\em cogrowth} function is number of obstructions of length $\le n$. We show that the cogrowth function of a finitely presented algebra is either bounded or at least logarithmical. We also show that an uniformly recurrent word has at least logarithmical cogrowth.Comment: 5 page

Information and communication technologies as the factor of a professional musician training

© Medwell Journals, 2015. The study from the perspective of the current conditions of information considers the issues of a professional musician training improvement from the perspective of the current information system development conditions. According to the researchers, a quick update and the obsolescence of information and communication technologies and computer resources in society is accompanied by a slow adaptation of a musical education system to their use. In order to resolve this situation, the researchers suggest the ways to improve the training of a professional musician which are based on the integration of methodological approaches: a design and technological, a competence-based, a contextual and other ones taking into account the development of computer technologies. The study offers the principles of integration, reflection, subjectivity and productivity. The researchers teaching experience is offered concerning the creation of tutorials that focus on the effectiveness of a professional musician training in terms of information-communicative educational environment

Off-limb EUV observations of the solar corona and transients with the CORONAS-F/SPIRIT telescope-coronagraph

The SPIRIT telescope aboard the CORONAS-F satellite (in orbit from 26 July 2001 to 5 December 2005), observed the off-limb solar corona in the 175 Å (Fe IX, X and XI lines) and 304 Å (He II and Si XI lines) bands. In the coronagraphic mode the mirror was tilted to image the corona at the distance of 1.1...5 <I>R</I><sub>sun</sub> from the solar center, the outer occulter blocked the disk radiation and the detector sensitivity was enhanced. This intermediate region between the fields of view of ordinary extreme-ultraviolet (EUV) telescopes and most of the white-light (WL) coronagraphs is responsible for forming the streamer belt, acceleration of ejected matter and emergence of slow and fast solar wind. We present here the results of continuous coronagraphic EUV observations of the solar corona carried out during two weeks in June and December 2002. The images showed a "diffuse" (unresolved) component of the corona seen in both bands, and non-radial, ray-like structures seen only in the 175 Å band, which can be associated with a streamer base. The correlations between latitudinal distributions of the EUV brightness in the corona and at the limb were found to be high in 304 Å at all distances and in 175 Å only below 1.5 <I>R</I><sub>sun</sub>. The temporal correlation of the coronal brightness along the west radial line, with the brightness at the underlying limb region was significant in both bands, independent of the distance. On 2 February 2003 SPIRIT observed an expansion of a transient associated with a prominence eruption seen only in the 304 Å band. The SPIRIT data have been compared with the corresponding data of the SOHO LASCO, EIT and UVCS instruments

Near-field spectroscopy and tuning of subsurface modes in plasmonic terahertz resonators

Highly confined modes in THz plasmonic resonators comprising two metallic elements can enhance light-matter interaction for efficient THz optoelectronic devices. We demonstrate that sub-surface modes in such double-metal resonators can be revealed with an aperture-type near-field probe and THz time-domain spectroscopy despite strong mode confinement in the dielectric spacer. The sub-surface modes couple a fraction of their energy to the resonator surface via surface waves, which we detected with the near-field probe. We investigated two resonator geometries: a λ/2 double-metal patch antenna with a 2 μm thick dielectric spacer, and a three-dimensional meta-atom resonator. THz time-domain spectroscopy analysis of the fields at the resonator surface displays spectral signatures of sub-surface modes. Investigations of strong light-matter coupling in resonators with sub-surface modes therefore can be assisted by the aperture-type THz near-field probes. Furthermore, near-field interaction of the probe with the resonator enables tuning of the resonance frequency for the spacer mode in the antenna geometry from 1.6 to 1.9 THz (~15%)

Dipolar resonances in conductive carbon micro-fibers probed by near-field terahertz spectroscopy

We observe dipole resonances in thin conductive carbon micro-fibers by detecting an enhanced electric field in the near-field of a single fiber at terahertz (THz) frequencies. Time-domain analysis of the electric field shows that each fiber sustains resonant current oscillations at the frequency defined by the fiber's length. Strong dependence of the observed resonance frequency and degree of field enhancement on the fibers' conductive properties enable direct non-contact probing of the THz conductivity in single carbon micro-fibers. We find the conductivity of the fibers to be within the range of 1– 5×104 S/m. This approach is suitable for experimental characterization of individual doped semiconductor resonators for THz metamaterials and devices

New words in human mutagenesis

<p>Abstract</p> <p>Background</p> <p>The substitution rates within different nucleotide contexts are subject to varying levels of bias. The most well known example of such bias is the excess of C to T (C > T) mutations in CpG (CG) dinucleotides. The molecular mechanisms underlying this bias are important factors in human genome evolution and cancer development. The discovery of other nucleotide contexts that have profound effects on substitution rates can improve our understanding of how mutations are acquired, and why mutation hotspots exist.</p> <p>Results</p> <p>We compared rates of inherited mutations in 1-4 bp nucleotide contexts using reconstructed ancestral states of human single nucleotide polymorphisms (SNPs) from intergenic regions. Chimp and orangutan genomic sequences were used as outgroups. We uncovered 3.5 and 3.3-fold excesses of T > C mutations in the second position of ATTG and ATAG words, respectively, and a 3.4-fold excess of A > C mutations in the first position of the ACAA word.</p> <p>Conclusions</p> <p>Although all the observed biases are less pronounced than the 5.1-fold excess of C > T mutations in CG dinucleotides, the three 4 bp mutation contexts mentioned above (and their complementary contexts) are well distinguished from all other mutation contexts. This provides a challenge to discover the underlying mechanisms responsible for the observed excesses of mutations.</p