66,594 research outputs found
PCA and K-Means decipher genome
In this paper, we aim to give a tutorial for undergraduate students studying
statistical methods and/or bioinformatics. The students will learn how data
visualization can help in genomic sequence analysis. Students start with a
fragment of genetic text of a bacterial genome and analyze its structure. By
means of principal component analysis they ``discover'' that the information in
the genome is encoded by non-overlapping triplets. Next, they learn how to find
gene positions. This exercise on PCA and K-Means clustering enables active
study of the basic bioinformatics notions. Appendix 1 contains program listings
that go along with this exercise. Appendix 2 includes 2D PCA plots of triplet
usage in moving frame for a series of bacterial genomes from GC-poor to GC-rich
ones. Animated 3D PCA plots are attached as separate gif files. Topology
(cluster structure) and geometry (mutual positions of clusters) of these plots
depends clearly on GC-content.Comment: 18 pages, with program listings for MatLab, PCA analysis of genomes
and additional animated 3D PCA plot
Persistent Orbital Degeneracy in Carbon Nanotubes
The quantum-mechanical orbitals in carbon nanotubes are doubly degenerate
over a large number of states in the Coulomb blockade regime. We argue that
this experimental observation indicates that electrons are reflected without
mode mixing at the nanotube-metal contacts. Two electrons occupying a pair of
degenerate orbitals (a ``shell'') are found to form a triplet state starting
from zero magnetic field. Finally, we observe unexpected low-energy excitations
at complete filling of a four-electron shell.Comment: 6 pages, 4 figure
Differential expansion for link polynomials
The differential expansion is one of the key structures reflecting group
theory properties of colored knot polynomials, which also becomes an important
tool for evaluation of non-trivial Racah matrices. This makes highly desirable
its extension from knots to links, which, however, requires knowledge of the
-symbols, at least, for the simplest triples of non-coincident
representations. Based on the recent achievements in this direction, we
conjecture a shape of the differential expansion for symmetrically-colored
links and provide a set of examples. Within this study, we use a special
framing that is an unusual extension of the topological framing from knots to
links. In the particular cases of Whitehead and Borromean rings links, the
differential expansions are different from the previously discovered.Comment: 11 page
Enhanced relativistic harmonics by electron nanobunching
It is shown that when an few-cycle, relativistically intense, p-polarized
laser pulse is obliquely incident on overdense plasma, the surface electrons
may form ultra-thin, highly compressed layers, with a width of a few
nanometers. These electron "nanobunches" emit synchrotron radiation coherently.
We calculate the one-dimensional synchrotron spectrum analytically and obtain a
slowly decaying power-law with an exponent of 4/3 or 6/5. This is much flatter
than the 8/3 power of the BGP (Baeva-Gordienko-Pukhov) spectrum, produced by a
relativistically oscillating bulk skin layer. The synchrotron spectrum cut-off
frequency is defined either by the electron relativistic -factor, or by
the thickness of the emitting layer. In the numerically demonstrated, locally
optimal case, the radiation is emitted in the form of a single attosecond
pulse, which contains almost the entire energy of the full optical cycle.Comment: to appear in Physics of Plasma
Why is the nuclear symmetry energy so uncertain at supra-saturation densities?
Within the interacting Fermi gas model for isospin asymmetric nuclear matter,
effects of the in-medium three-body interaction and the two-body short-range
tensor force due to the meson exchange as well as the short-range
nucleon correlation on the high-density behavior of the nuclear symmetry energy
are demonstrated respectively in a transparent way. Possible physics origins of
the extremely uncertain nuclear symmetry energy at supra-saturation densities
are discussed.Comment: Added discussions and revised format. Version to appear in Phys. Rev.
C (2010
Chiral expansion of the decay width
A chiral field theory of mesons has been applied to study the contribution of
the current quark masses to the decay width at
the next leading order. enhancement has been predicted and there is no
new parameter.Comment: 9 page
- …