Fractal tiles associated with shift radix systems

Shift radix systems form a collection of dynamical systems depending on a parameter $\mathbf{r}$ which varies in the $d$-dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings. In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters $\mathbf{r}$ these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials. We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter $\mathbf{r}$ of the shift radix system, these tiles provide multiple tilings and even tilings of the $d$-dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine)

Prandtl number of lattice Bhatnagar-Gross-Krook fluid

The lattice Bhatnagar-Gross-Krook modeled fluid has an unchangeable unit Prandtl number. A simple method is introduced in this letter to formulate a flexible Prandtl number for the modeled fluid. The effectiveness was demonstrated by numerical simulations of the Couette flow.Comment: 4 pages, uuencoded postscript fil

Characterization of the numbers which satisfy the height reducing property

Let $\alpha$ be a complex number. We show that there is a finite subset $F$ of the ring of the rational integers $\mathbb{Z}$, such that $F\left[ \alpha\right] =\mathbb{Z}\left[ \alpha\right]$, if and only if $\alpha$ is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one, or all of modulus greater than one. This completes the answer to a question, on the numbers satisfying the height reducing property, posed in [3].Comment: Indagationes Mathematicae (2014

The telomerase essential N-terminal domain promotes DNA synthesis by stabilizing short RNA-DNA hybrids.

Telomerase is an enzyme that adds repetitive DNA sequences to the ends of chromosomes and consists of two main subunits: the telomerase reverse transcriptase (TERT) protein and an associated telomerase RNA (TER). The telomerase essential N-terminal (TEN) domain is a conserved region of TERT proposed to mediate DNA substrate interactions. Here, we have employed single molecule telomerase binding assays to investigate the function of the TEN domain. Our results reveal telomeric DNA substrates bound to telomerase exhibit a dynamic equilibrium between two states: a docked conformation and an alternative conformation. The relative stabilities of the docked and alternative states correlate with the number of basepairs that can be formed between the DNA substrate and the RNA template, with more basepairing favoring the docked state. The docked state is further buttressed by the TEN domain and mutations within the TEN domain substantially alter the DNA substrate structural equilibrium. We propose a model in which the TEN domain stabilizes short RNA-DNA duplexes in the active site of the enzyme, promoting the docked state to augment telomerase processivity

Breadth-first serialisation of trees and rational languages

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.Comment: 15 page

Source Regions of the Type II Radio Burst Observed During a CME-CME Interaction on 2013 May 22

We report on our study of radio source regions during the type II radio burst on 2013 May 22 based on direction finding (DF) analysis of the Wind/WAVES and STEREO/WAVES (SWAVES) radio observations at decameter-hectometric (DH) wavelengths. The type II emission showed an enhancement that coincided with interaction of two coronal mass ejections (CMEs) launched in sequence along closely spaced trajectories. The triangulation of the SWAVES source directions posited the ecliptic projections of the radio sources near the line connecting the Sun and the STEREO-A spacecraft. The WAVES and SWAVES source directions revealed shifts in the latitude of the radio source indicating that the spatial location of the dominant source of the type II emission varies during the CME-CME interaction. The WAVES source directions close to 1 MHz frequencies matched the location of the leading edge of the primary CME seen in the images of the LASCO/C3 coronagraph. This correspondence of spatial locations at both wavelengths confirms that the CME-CME interaction region is the source of the type II enhancement. Comparison of radio and white-light observations also showed that at lower frequencies scattering significantly affects radio wave propagation.Comment: Accepted for publication in Ap

Inapproximability of maximal strip recovery

In comparative genomic, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given $d$ genomic maps as sequences of gene markers, the objective of \msr{d} is to find $d$ subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. For any constant $d \ge 2$, a polynomial-time 2d-approximation for \msr{d} was previously known. In this paper, we show that for any $d \ge 2$, \msr{d} is APX-hard, even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map. Moreover, we provide the first explicit lower bounds on approximating \msr{d} for all $d \ge 2$. In particular, we show that \msr{d} is NP-hard to approximate within $\Omega(d/\log d)$. From the other direction, we show that the previous 2d-approximation for \msr{d} can be optimized into a polynomial-time algorithm even if $d$ is not a constant but is part of the input. We then extend our inapproximability results to several related problems including \cmsr{d}, \gapmsr{\delta}{d}, and \gapcmsr{\delta}{d}.Comment: A preliminary version of this paper appeared in two parts in the Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009) and the Proceedings of the 4th International Frontiers of Algorithmics Workshop (FAW 2010

An Extremely Red Nucleus in an Absorbed QSO at z=0.65

The results of K-band-imaging observations of a candidate of an absorbed QSO at z=0.653, AX J131831+3341, are presented. The B-K color of the object is 4.85 mag, which is much redder than optically-selected QSOs. The K-band image shows nuclear and extended components, the same as in the optical V-, R-, and I-band images. The nuclear component (I-K = 4.29 mag) is much redder than the power-law models with energy indices of 0 to -1.0, which well reproduce the V-R and R-I optical colors of the nuclear component. A heavily absorbed (A_V = 3 mag) nucleus may emerge in the K-band, while optical light may originate from scattered nuclear light. The I-K color of the extended component is 2.2 mag, which is consistent with the post-starburst nature of the host galaxy, which is also suggested from the V-R and R-I colors of the extended component