5,128 research outputs found
Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model
We analyze the scaling and finite-size-scaling behavior of the
two-dimensional 4-state Potts model. We find new multiplicative logarithmic
corrections for the susceptibility, in addition to the already known ones for
the specific heat. We also find additive logarithmic corrections to scaling,
some of which are universal. We have checked the theoretical predictions at
criticality and off criticality by means of high-precision Monte Carlo data.Comment: 46 pages including 8 figures. Self-unpacking file containing the tex
file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 8 ps file
The Topological Theory of the Milnor Invariant
We study a topological Abelian gauge theory that generalizes the Abelian
Chern-Simons one, and that leads in a natural way to the Milnor's link
invariant when the classical action on-shell is calculated.Comment: 4 pages; corrected equatio
Combinatorics and Geometry of Transportation Polytopes: An Update
A transportation polytope consists of all multidimensional arrays or tables
of non-negative real numbers that satisfy certain sum conditions on subsets of
the entries. They arise naturally in optimization and statistics, and also have
interest for discrete mathematics because permutation matrices, latin squares,
and magic squares appear naturally as lattice points of these polytopes.
In this paper we survey advances on the understanding of the combinatorics
and geometry of these polyhedra and include some recent unpublished results on
the diameter of graphs of these polytopes. In particular, this is a thirty-year
update on the status of a list of open questions last visited in the 1984 book
by Yemelichev, Kovalev and Kravtsov and the 1986 survey paper of Vlach.Comment: 35 pages, 13 figure
Lie Markov models with purine/pyrimidine symmetry
Continuous-time Markov chains are a standard tool in phylogenetic inference.
If homogeneity is assumed, the chain is formulated by specifying
time-independent rates of substitutions between states in the chain. In
applications, there are usually extra constraints on the rates, depending on
the situation. If a model is formulated in this way, it is possible to
generalise it and allow for an inhomogeneous process, with time-dependent rates
satisfying the same constraints. It is then useful to require that there exists
a homogeneous average of this inhomogeneous process within the same model. This
leads to the definition of "Lie Markov models", which are precisely the class
of models where such an average exists. These models form Lie algebras and
hence concepts from Lie group theory are central to their derivation. In this
paper, we concentrate on applications to phylogenetics and nucleotide
evolution, and derive the complete hierarchy of Lie Markov models that respect
the grouping of nucleotides into purines and pyrimidines -- that is, models
with purine/pyrimidine symmetry. We also discuss how to handle the subtleties
of applying Lie group methods, most naturally defined over the complex field,
to the stochastic case of a Markov process, where parameter values are
restricted to be real and positive. In particular, we explore the geometric
embedding of the cone of stochastic rate matrices within the ambient space of
the associated complex Lie algebra.
The whole list of Lie Markov models with purine/pyrimidine symmetry is
available at http://www.pagines.ma1.upc.edu/~jfernandez/LMNR.pdf.Comment: 32 page
Graphs of Transportation Polytopes
This paper discusses properties of the graphs of 2-way and 3-way
transportation polytopes, in particular, their possible numbers of vertices and
their diameters. Our main results include a quadratic bound on the diameter of
axial 3-way transportation polytopes and a catalogue of non-degenerate
transportation polytopes of small sizes. The catalogue disproves five
conjectures about these polyhedra stated in the monograph by Yemelichev et al.
(1984). It also allowed us to discover some new results. For example, we prove
that the number of vertices of an transportation polytope is a
multiple of the greatest common divisor of and .Comment: 29 pages, 7 figures. Final version. Improvements to the exposition of
several lemmas and the upper bound in Theorem 1.1 is improved by a factor of
tw
On the Nature of the Strong Emission-Line Galaxies in Cluster Cl 0024+1654: Are Some the Progenitors of Low Mass Spheroidals?
We present new size, line ratio, and velocity width measurements for six
strong emission-line galaxies in the galaxy cluster, Cl 0024+1654, at redshift
z~0.4. The velocity widths from Keck spectra are all narrow (30<sigma<120
km/s), with three profiles showing double peaks. Four galaxies have low masses
(M<10^{10} Mo). Whereas three galaxies were previously reported to be possible
AGNs, none exhibit AGN-like emission line ratios or velocity widths. Two or
three appear as very blue spirals with the remainder more akin to luminous H-II
galaxies undergoing a strong burst of star formation. We propose that after the
burst subsides, these galaxies will transform into quiescent dwarfs, and are
thus progenitors of some cluster spheroidals (We adopt the nomenclature
suggested by Kormendy & Bender (1994), i.e., low-density, dwarf ellipsoidal
galaxies like NGC 205 are called `spheroidals' instead of `dwarf ellipticals')
seen today.Comment: 14 pages + 2 figures + 1 table, LaTeX, Acc. for publ. in ApJL also
available at http://www.ucolick.org/~deep/papers/papers.htm
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