5,057 research outputs found
Note on SLE and logarithmic CFT
It is discussed how stochastic evolutions may be linked to logarithmic
conformal field theory. This introduces an extension of the stochastic Loewner
evolutions. Based on the existence of a logarithmic null vector in an
indecomposable highest-weight module of the Virasoro algebra, the
representation theory of the logarithmic conformal field theory is related to
entities conserved in mean under the stochastic process.Comment: 10 pages, LaTeX, v2: version to be publishe
Models for energy and charge transport and storage in biomolecules
Two models for energy and charge transport and storage in biomolecules are
considered. A model based on the discrete nonlinear Schrodinger equation with
long-range dispersive interactions (LRI's) between base pairs of DNA is offered
for the description of nonlinear dynamics of the DNA molecule. We show that
LRI's are responsible for the existence of an interval of bistability where two
stable stationary states, a narrow, pinned state and a broad, mobile state,
coexist at each value of the total energy. The possibility of controlled
switching between pinned and mobile states is demonstrated. The mechanism could
be important for controlling energy storage and transport in DNA molecules.
Another model is offered for the description of nonlinear excitations in
proteins and other anharmonic biomolecules. We show that in the highly
anharmonic systems a bound state of Davydov and Boussinesq solitons can exist.Comment: 12 pages (latex), 12 figures (ps
SLE-type growth processes and the Yang-Lee singularity
The recently introduced SLE growth processes are based on conformal maps from
an open and simply-connected subset of the upper half-plane to the half-plane
itself. We generalize this by considering a hierarchy of stochastic evolutions
mapping open and simply-connected subsets of smaller and smaller fractions of
the upper half-plane to these fractions themselves. The evolutions are all
driven by one-dimensional Brownian motion. Ordinary SLE appears at grade one in
the hierarchy. At grade two we find a direct correspondence to conformal field
theory through the explicit construction of a level-four null vector in a
highest-weight module of the Virasoro algebra. This conformal field theory has
central charge c=-22/5 and is associated to the Yang-Lee singularity. Our
construction may thus offer a novel description of this statistical model.Comment: 12 pages, LaTeX, v2: thorough revision with corrections, v3: version
to be publishe
Polar cap index (PC) as a proxy for ionospheric electric field in the near‐pole region
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95640/1/grl13514.pd
Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes
Functional data are defined as realizations of random functions (mostly
smooth functions) varying over a continuum, which are usually collected with
measurement errors on discretized grids. In order to accurately smooth noisy
functional observations and deal with the issue of high-dimensional observation
grids, we propose a novel Bayesian method based on the Bayesian hierarchical
model with a Gaussian-Wishart process prior and basis function representations.
We first derive an induced model for the basis-function coefficients of the
functional data, and then use this model to conduct posterior inference through
Markov chain Monte Carlo. Compared to the standard Bayesian inference that
suffers serious computational burden and unstableness for analyzing
high-dimensional functional data, our method greatly improves the computational
scalability and stability, while inheriting the advantage of simultaneously
smoothing raw observations and estimating the mean-covariance functions in a
nonparametric way. In addition, our method can naturally handle functional data
observed on random or uncommon grids. Simulation and real studies demonstrate
that our method produces similar results as the standard Bayesian inference
with low-dimensional common grids, while efficiently smoothing and estimating
functional data with random and high-dimensional observation grids where the
standard Bayesian inference fails. In conclusion, our method can efficiently
smooth and estimate high-dimensional functional data, providing one way to
resolve the curse of dimensionality for Bayesian functional data analysis with
Gaussian-Wishart processes.Comment: Under revie
SLE local martingales in logarithmic representations
A space of local martingales of SLE type growth processes forms a
representation of Virasoro algebra, but apart from a few simplest cases not
much is known about this representation. The purpose of this article is to
exhibit examples of representations where L_0 is not diagonalizable - a
phenomenon characteristic of logarithmic conformal field theory. Furthermore,
we observe that the local martingales bear a close relation with the fusion
product of the boundary changing fields.
Our examples reproduce first of all many familiar logarithmic representations
at certain rational values of the central charge. In particular we discuss the
case of SLE(kappa=6) describing the exploration path in critical percolation,
and its relation with the question of operator content of the appropriate
conformal field theory of zero central charge. In this case one encounters
logarithms in a probabilistically transparent way, through conditioning on a
crossing event. But we also observe that some quite natural SLE variants
exhibit logarithmic behavior at all values of kappa, thus at all central
charges and not only at specific rational values.Comment: 40 pages, 7 figures. v3: completely rewritten, new title, new result
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