10,501 research outputs found
Fractal tiles associated with shift radix systems
Shift radix systems form a collection of dynamical systems depending on a
parameter which varies in the -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
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 of the shift radix system, these tiles provide
multiple tilings and even tilings of the -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
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
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 genomic maps as sequences of gene markers, the
objective of \msr{d} is to find subsequences, one subsequence of each
genomic map, such that the total length of syntenic blocks in these
subsequences is maximized. For any constant , a polynomial-time
2d-approximation for \msr{d} was previously known. In this paper, we show that
for any , \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 . In particular, we show that
\msr{d} is NP-hard to approximate within . From the other
direction, we show that the previous 2d-approximation for \msr{d} can be
optimized into a polynomial-time algorithm even if 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
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