10,488 research outputs found
Current-Current Deformations of Conformal Field Theories, and WZW Models
Moduli spaces of conformal field theories corresponding to current-current
deformations are discussed. For WZW models, CFT and sigma model considerations
are compared. It is shown that current-current deformed WZW models have
WZW-like sigma model descriptions with non-bi-invariant metrics, additional
B-fields and a non-trivial dilaton.Comment: 30 pages, latex, v2: remarks and references adde
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Clustering Scatter Plots Using Data Depth Measures.
Clustering is rapidly becoming a powerful data mining technique, and has been broadly applied to many domains such as bioinformatics and text mining. However, the existing methods can only deal with a data matrix of scalars. In this paper, we introduce a hierarchical clustering procedure that can handle a data matrix of scatter plots. To more accurately reflect the nature of data, we introduce a dissimilarity statistic based on "data depth" to measure the discrepancy between two bivariate distributions without oversimplifying the nature of the underlying pattern. We then combine hypothesis testing with hierarchical clustering to simultaneously cluster the rows and columns of the data matrix of scatter plots. We also propose novel painting metrics and construct heat maps to allow visualization of the clusters. We demonstrate the utility and power of our new clustering method through simulation studies and application to a microbe-host-interaction study
Tracking Vector Magnetograms with the Magnetic Induction Equation
The differential affine velocity estimator (DAVE) developed in Schuck (2006)
for estimating velocities from line-of-sight magnetograms is modified to
directly incorporate horizontal magnetic fields to produce a differential
affine velocity estimator for vector magnetograms (DAVE4VM). The DAVE4VM's
performance is demonstrated on the synthetic data from the anelastic
pseudospectral ANMHD simulations that were used in the recent comparison of
velocity inversion techniques by Welsch (2007). The DAVE4VM predicts roughly
95% of the helicity rate and 75% of the power transmitted through the
simulation slice. Inter-comparison between DAVE4VM and DAVE and further
analysis of the DAVE method demonstrates that line-of-sight tracking methods
capture the shearing motion of magnetic footpoints but are insensitive to flux
emergence -- the velocities determined from line-of-sight methods are more
consistent with horizontal plasma velocities than with flux transport
velocities. These results suggest that previous studies that rely on velocities
determined from line-of-sight methods such as the DAVE or local correlation
tracking may substantially misrepresent the total helicity rates and power
through the photosphere.Comment: 30 pages, 13 figure
Correlations and Renormalization in Lattice Gases
A complete formulation is given of an exact kinetic theory for lattice gases.
This kinetic theory makes possible the calculation of corrections to the usual
Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of
correlations. It is shown that renormalized transport coefficients can be
calculated perturbatively by summing terms in an infinite series. A
diagrammatic notation for the terms in this series is given, in analogy with
the diagrammatic expansions of continuum kinetic theory and quantum field
theory. A closed-form expression for the coefficients associated with the
vertices of these diagrams is given. This method is applied to several standard
lattice gases, and the results are shown to correctly predict experimentally
observed deviations from the Boltzmann analysis.Comment: 94 pages, pure LaTeX including all figure
Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction
We reframe linear dimensionality reduction as a problem of Bayesian inference
on matrix manifolds. This natural paradigm extends the Bayesian framework to
dimensionality reduction tasks in higher dimensions with simpler models at
greater speeds. Here an orthogonal basis is treated as a single point on a
manifold and is associated with a linear subspace on which observations vary
maximally. Throughout this paper, we employ the Grassmann and Stiefel manifolds
for various dimensionality reduction problems, explore the connection between
the two manifolds, and use Hybrid Monte Carlo for posterior sampling on the
Grassmannian for the first time. We delineate in which situations either
manifold should be considered. Further, matrix manifold models are used to
yield scientific insight in the context of cognitive neuroscience, and we
conclude that our methods are suitable for basic inference as well as accurate
prediction.Comment: All datasets and computer programs are publicly available at
http://www.ics.uci.edu/~babaks/Site/Codes.htm
Canonical Transformation Path to Gauge Theories of Gravity
In this paper, the generic part of the gauge theory of gravity is derived,
based merely on the action principle and on the general principle of
relativity. We apply the canonical transformation framework to formulate
geometrodynamics as a gauge theory. The starting point of our paper is
constituted by the general De~Donder-Weyl Hamiltonian of a system of scalar and
vector fields, which is supposed to be form-invariant under (global) Lorentz
transformations. Following the reasoning of gauge theories, the corresponding
locally form-invariant system is worked out by means of canonical
transformations. The canonical transformation approach ensures by construction
that the form of the action functional is maintained. We thus encounter amended
Hamiltonian systems which are form-invariant under arbitrary spacetime
transformations. This amended system complies with the general principle of
relativity and describes both, the dynamics of the given physical system's
fields and their coupling to those quantities which describe the dynamics of
the spacetime geometry. In this way, it is unambiguously determined how spin-0
and spin-1 fields couple to the dynamics of spacetime.
A term that describes the dynamics of the free gauge fields must finally be
added to the amended Hamiltonian, as common to all gauge theories, to allow for
a dynamic spacetime geometry. The choice of this "dynamics Hamiltonian" is
outside of the scope of gauge theory as presented in this paper. It accounts
for the remaining indefiniteness of any gauge theory of gravity and must be
chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of
the gauge theory of gravity is shown to be at least quadratic in the conjugate
momenta of the gauge fields -- this is beyond the Einstein-Hilbert theory of
General Relativity.Comment: 16 page
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