176 research outputs found
Lassoing and corraling rooted phylogenetic trees
The construction of a dendogram on a set of individuals is a key component of
a genomewide association study. However even with modern sequencing
technologies the distances on the individuals required for the construction of
such a structure may not always be reliable making it tempting to exclude them
from an analysis. This, in turn, results in an input set for dendogram
construction that consists of only partial distance information which raises
the following fundamental question. For what subset of its leaf set can we
reconstruct uniquely the dendogram from the distances that it induces on that
subset. By formalizing a dendogram in terms of an edge-weighted, rooted
phylogenetic tree on a pre-given finite set X with |X|>2 whose edge-weighting
is equidistant and a set of partial distances on X in terms of a set L of
2-subsets of X, we investigate this problem in terms of when such a tree is
lassoed, that is, uniquely determined by the elements in L. For this we
consider four different formalizations of the idea of "uniquely determining"
giving rise to four distinct types of lassos. We present characterizations for
all of them in terms of the child-edge graphs of the interior vertices of such
a tree. Our characterizations imply in particular that in case the tree in
question is binary then all four types of lasso must coincide
spectra in elementary cellular automata and fractal signals
We systematically compute the power spectra of the one-dimensional elementary
cellular automata introduced by Wolfram. On the one hand our analysis reveals
that one automaton displays spectra though considered as trivial, and on
the other hand that various automata classified as chaotic/complex display no
spectra. We model the results generalizing the recently investigated
Sierpinski signal to a class of fractal signals that are tailored to produce
spectra. From the widespread occurrence of (elementary) cellular
automata patterns in chemistry, physics and computer sciences, there are
various candidates to show spectra similar to our results.Comment: 4 pages (3 figs included
Sierpinski signal generates spectra
We investigate the row sum of the binary pattern generated by the Sierpinski
automaton: Interpreted as a time series we calculate the power spectrum of this
Sierpinski signal analytically and obtain a unique rugged fine structure with
underlying power law decay with an exponent of approximately 1.15. Despite the
simplicity of the model, it can serve as a model for spectra in a
certain class of experimental and natural systems like catalytic reactions and
mollusc patterns.Comment: 4 pages (4 figs included). Accepted for publication in Physical
Review
Multi-triangulations as complexes of star polygons
Maximal -crossing-free graphs on a planar point set in convex
position, that is, -triangulations, have received attention in recent
literature, with motivation coming from several interpretations of them.
We introduce a new way of looking at -triangulations, namely as complexes
of star polygons. With this tool we give new, direct, proofs of the fundamental
properties of -triangulations, as well as some new results. This
interpretation also opens-up new avenues of research, that we briefly explore
in the last section.Comment: 40 pages, 24 figures; added references, update Section
A Monte Carlo study of the three-dimensional Coulomb frustrated Ising ferromagnet
We have investigated by Monte-Carlo simulation the phase diagram of a
three-dimensional Ising model with nearest-neighbor ferromagnetic interactions
and small, but long-range (Coulombic) antiferromagnetic interactions. We have
developed an efficient cluster algorithm and used different lattice sizes and
geometries, which allows us to obtain the main characteristics of the
temperature-frustration phase diagram. Our finite-size scaling analysis
confirms that the melting of the lamellar phases into the paramgnetic phase is
driven first-order by the fluctuations. Transitions between ordered phases with
different modulation patterns is observed in some regions of the diagram, in
agreement with a recent mean-field analysis.Comment: 14 pages, 10 figures, submitted to Phys. Rev.
Graphical representations and cluster algorithms for critical points with fields
A two-replica graphical representation and associated cluster algorithm is
described that is applicable to ferromagnetic Ising systems with arbitrary
fields. Critical points are associated with the percolation threshold of the
graphical representation. Results from numerical simulations of the Ising model
in a staggered field are presented. The dynamic exponent for the algorithm is
measured to be less than 0.5.Comment: Revtex, 12 pages with 2 figure
New Precision Electroweak Tests of SU(5) x U(1) Supergravity
We explore the one-loop electroweak radiative corrections in supergravity via explicit calculation of vacuum-polarization and
vertex-correction contributions to the and
parameters. Experimentally, these parameters are obtained from a global fit to
the set of observables , and . We
include -dependent effects, which induce a large systematic negative shift
on for light chargino masses (m_{\chi^\pm_1}\lsim70\GeV). The
(non-oblique) supersymmetric vertex corrections to \Zbb, which define the
parameter, show a significant positive shift for light chargino
masses, which for can be nearly compensated by a negative
shift from the charged Higgs contribution. We conclude that at the 90\%CL, for
m_t\lsim160\GeV the present experimental values of and
do not constrain in any way supergravity in
both no-scale and dilaton scenarios. On the other hand, for m_t\gsim160\GeV
the constraints on the parameter space become increasingly stricter. We
demonstrate this trend with a study of the m_t=170\GeV case, where only a
small region of parameter space, with \tan\beta\gsim4, remains allowed and
corresponds to light chargino masses (m_{\chi^\pm_1}\lsim70\GeV). Thus
supergravity combined with high-precision LEP data would
suggest the presence of light charginos if the top quark is not detected at the
Tevatron.Comment: LaTeX, 11 Pages+4 Figures(not included), the figures available upon
request as an uuencoded file(0.4MB) or 4 PS files from [email protected],
CERN-TH.7078/93, CTP-TAMU-68/93, ACT-24/9
- …