124,246 research outputs found
Statistical Properties of Strings
We investigate numerically the configurational statistics of strings. The
algorithm models an ensemble of global cosmic strings, or equivalently
vortices in superfluid He. We use a new method which avoids the
specification of boundary conditions on the lattice. We therefore do not have
the artificial distinction between short and long string loops or a `second
phase' in the string network statistics associated with strings winding around
a toroidal lattice. Our lattice is also tetrahedral, which avoids ambiguities
associated with the cubic lattices of previous work. We find that the
percentage of infinite string is somewhat lower than on cubic lattices, 63\%
instead of 80\%. We also investigate the Hagedorn transition, at which infinite
strings percolate, controlling the string density by rendering one of the
equilibrium states more probable. We measure the percolation threshold, the
critical exponent associated with the divergence of a suitably defined
susceptibility of the string loops, and that associated with the divergence of
the correlation length.Comment: 20 pages, 8 figures (uuencoded) appended, DAMTP-94-56, SUSX-TP-94-7
Statistical Properties of Convex Clustering
In this manuscript, we study the statistical properties of convex clustering.
We establish that convex clustering is closely related to single linkage
hierarchical clustering and -means clustering. In addition, we derive the
range of tuning parameter for convex clustering that yields a non-trivial
solution. We also provide an unbiased estimate of the degrees of freedom, and
provide a finite sample bound for the prediction error for convex clustering.
We compare convex clustering to some traditional clustering methods in
simulation studies.Comment: 20 pages, 5 figure
Statistical properties of contact vectors
We study the statistical properties of contact vectors, a construct to
characterize a protein's structure. The contact vector of an N-residue protein
is a list of N integers n_i, representing the number of residues in contact
with residue i. We study analytically (at mean-field level) and numerically the
amount of structural information contained in a contact vector. Analytical
calculations reveal that a large variance in the contact numbers reduces the
degeneracy of the mapping between contact vectors and structures. Exact
enumeration for lengths up to N=16 on the three dimensional cubic lattice
indicates that the growth rate of number of contact vectors as a function of N
is only 3% less than that for contact maps. In particular, for compact
structures we present numerical evidence that, practically, each contact vector
corresponds to only a handful of structures. We discuss how this information
can be used for better structure prediction.Comment: 20 pages, 6 figure
Statistical properties of charged interfaces
We consider the equilibrium statistical properties of interfaces submitted to
competing interactions; a long-range repulsive Coulomb interaction inherent to
the charged interface and a short-range, anisotropic, attractive one due to
either elasticity or confinement. We focus on one-dimensional interfaces such
as strings. Model systems considered for applications are mainly aggregates of
solitons in polyacetylene and other charge density wave systems, domain lines
in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature,
we find a shape instability which lead, via phase transitions, to tilted
phases. Depending on the regime, elastic or confinement, the order of the
zero-temperature transition changes. Thermal fluctuations lead to a pure
Coulomb roughening of the string, in addition to the usual one, and to the
presence of angular kinks. We suggest that such instabilities might explain the
tilting of stripes in cuprate oxides. The 3D problem of the charged wall is
also analyzed. The latter experiences instabilities towards various tilted
phases separated by a tricritical point in the elastic regime. In the
confinement regime, the increase of dimensionality favors either the melting of
the wall into a Wigner crystal of its constituent charges or a strongly
inclined wall which might have been observed in nickelate oxides.Comment: 17 pages, 11 figure
Statistical properties of neutral evolution
Neutral evolution is the simplest model of molecular evolution and thus it is
most amenable to a comprehensive theoretical investigation. In this paper, we
characterize the statistical properties of neutral evolution of proteins under
the requirement that the native state remains thermodynamically stable, and
compare them to the ones of Kimura's model of neutral evolution. Our study is
based on the Structurally Constrained Neutral (SCN) model which we recently
proposed. We show that, in the SCN model, the substitution rate decreases as
longer time intervals are considered, and fluctuates strongly from one branch
of the evolutionary tree to another, leading to a non-Poissonian statistics for
the substitution process. Such strong fluctuations are also due to the fact
that neutral substitution rates for individual residues are strongly correlated
for most residue pairs. Interestingly, structurally conserved residues,
characterized by a much below average substitution rate, are also much less
correlated to other residues and evolve in a much more regular way. Our results
could improve methods aimed at distinguishing between neutral and adaptive
substitutions as well as methods for computing the expected number of
substitutions occurred since the divergence of two protein sequences.Comment: 17 pages, 11 figure
Statistical Properties of Contact Maps
A contact map is a simple representation of the structure of proteins and
other chain-like macromolecules. This representation is quite amenable to
numerical studies of folding. We show that the number of contact maps
corresponding to the possible configurations of a polypeptide chain of N amino
acids, represented by (N-1)-step self avoiding walks on a lattice, grows
exponentially with N for all dimensions D>1. We carry out exact enumerations in
D=2 on the square and triangular lattices for walks of up to 20 steps and
investigate various statistical properties of contact maps corresponding to
such walks. We also study the exact statistics of contact maps generated by
walks on a ladder.Comment: Latex file, 15 pages, 12 eps figures. To appear on Phys. Rev.
Statistical Properties of Microstructure Noise
We study the estimation of moments and joint moments of microstructure noise.
Estimators of arbitrary order of (joint) moments are provided, for which we
establish consistency as well as central limit theorems. In particular, we
provide estimators of auto-covariances and auto-correlations of the noise.
Simulation studies demonstrate excellent performance of our estimators even in
the presence of jumps and irregular observation times. Empirical studies reveal
(moderate) positive auto-correlation of the noise for the stocks tested
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