Fractals from genomes: exact solutions of a biology-inspired problem

This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be described. This scheme leads to a class of self-similar and self-overlapping fractals in the limit of infinitely long constotuent strings. The calculation of their exact dimensions and the counting of true and redundant avoided strings at different string lengths turn out to be one and the same problem. We give exact solution of the problem using two independent methods: the Goulden-Jackson cluster method in combinatorics and the method of formal language theory.Comment: 24 pages, LaTeX, 5 PostScript figures (two in color), psfi

Dimensions of fractals related to languages defined by tagged strings in complete genomes

A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain "tag"-string and they define some fractals when K tends to infinite. The Box and Hausdorff dimensions of the limit set are discussed. Although the method proposed by Mauldin and Williams to calculate Box and Hausdorff dimension is valid in our case, a different and simpler method is proposed in this paper.Comment: 9 pages with two figure

Condensation and Evaporation of Mutually Repelling Particles :Steady states and limit cycles

We study condensation and evaporation of particles which repel each other, using a simple set of rules on a square lattice. Different results are obtained for a mobile and an immobile surface layer.A two point limit cycle is observed for high temperature and low pressure in both cases. Here the coverage oscillates between a high and a low value without ever reaching a steady state. The results for the immobile case depend in addition on the initial coverage.Comment: 8 pages, 3 figure

Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well?

The universal bifurcation property of the H\'enon map in parameter space is studied with symbolic dynamics. The universal-$L$ region is defined to characterize the bifurcation universality. It is found that the universal-$L$ region for relative small $L$ is not restricted to very small $b$ values. These results show that it is also a universal phenomenon that universal sequences with short period can be found in many nonlinear dissipative systems.Comment: 10 pages, figures can be obtained from the author, will appeared in J. Phys.

Searching for Black Hole Candidates by LAMOST and ASAS-SN

Most dynamically confirmed stellar-mass black holes (BHs) and their candidates were originally selected from X-ray outbursts. In the present work, we search for BH candidates in the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey using the spectra along with photometry from the All Sky Automated Survey for SuperNovae (ASAS-SN), where the orbital period of the binary may be revealed by the periodic light curve, such as the ellipsoidal modulation type. Our sample consists of nine binaries, where each source contains a giant star with large radial velocity variation (ΔV_R ≳ 70 km s^(-1)) and periods known from light curves. We focus on the nine sources with long periods (T_(ph) > 5 days) and evaluate the mass M_2 of the optically invisible companion. Since the observed ΔV_R from only a few repeating spectroscopic observations is a lower limit of the real amplitude, the real mass M_2 can be significantly higher than the current evaluation. It is likely an efficient method to place constraints on M 2 by combining ΔV_R from LAMOST and T_(ph) from ASAS-SN, particularly by the ongoing LAMOST Medium Resolution Survey

Paleomagnetic Study of Mesozoic Continental Sediments Along the Northern Tien Shan (China) and Heterogeneous Strain in Central Asia

A paleomagnetic study of rocks from the northern foot of the Tien Shan and the southern border of the Dzungar Basin, east of Urumqi (44.2°N, 86.0°E), spanning ages from middle Jurassic to early Tertiary was carried out to constrain the tectonic evolution in central Asia since Mesozoic time. Five middle Jurassic sites reveal a remagnetized direction close to the present Earth field in geographic coordinates: D = 6.6°, I = 72.6° (α_(95) = 7.4°). Thirteen out of 17 upper Jurassic and lower Cretaceous sites yield a characteristic direction (stratigraphic coordinates) of D = 12.7°, I = 48.6° (α_(95) = 5.5°). Nine of 16 upper Cretaceous and lower Tertiary sites provide a characteristic direction of D = 12.5°, I = 51.3° (α_(95) = 6.9°). The latter two directions pass fold and reversal tests. The pole positions are close to each other and to the Besse and Courtillot [1989, 1990] Eurasian apparent polar wander path, for ages ranging from 130 to 70 Ma. However, the difference in paleolatitudes amounts to about 5.9° ± 3.7°, which could indicate significant continental shortening in the Altai Mountains and perhaps further north, subsequent to India-Asia collision. The pole positions from the Dzungar Basin are close to those found for the Tarim [Li et al., 1988a], leading to an insignificant paleolatitude difference (3.0° ± 6.9°), but showing a larger difference in declination (8.6° ± 8.7°). These paleomagnetic results are compatible with a model of heterogeneous deformation in the western part of the collision zone between India and Siberia. A significant shortening in the Altai, a slight counterclockwise rotation of the Dzungar block, the westward-increasing shortening in the Tien Shan with attendant clockwise rotation of the Tarim block are all consistent with this model, in which Tibet, the Tien Shan and the Altai undergo differential strain along strike in a relay fashion, with the total India-Siberia convergence remaining approximately constant