2,589 research outputs found
Spiral-wave Dynamics Depends Sensitively on nhomogeneities in Mathematical Models of Ventricular Tissue
Every sixth death in industrialised countries occurs because of cardiac
arrhythmias like ventricular tachycardia (VT) and ventricular fibrillation
(VF). There is growing consensus that VT is associated with an unbroken spiral
wave of electrical activation on cardiac tissue but VF with broken waves,
spiral turbulence, spatiotemporal chaos and rapid, irregular activation. Thus
spiral-wave activity in cardiac tissue has been studied extensively.
Nevertheless many aspects of such spiral dynamics remain elusive because of the
intrinsically high-dimensional nature of the cardiac-dynamical system. In
particular, the role of tissue heterogeneities in the stability of cardiac
spiral waves is still being investigated. Experiments with conduction blocks in
cardiac tissue yield a variety of results: some suggest that blocks can
eliminate VF partially or completely, leading to VT or quiescence, but others
show that VF is unaffected by obstacles. We propose theoretically that this
variety of results is a natural manifestation of a fractal boundary that must
separate the basins of the attractors associated, respectively, with VF and VT.
We substantiate this with extensive numerical studies of Panfilov and Luo-Rudy
I models, where we show that the suppression of VF depends sensitively on the
position, size, and nature of the inhomogeneity.Comment: 9 pages, 5 figures
The Exotic Barium Bismuthates
We review the remarkable properties, including superconductivity,
charge-density-wave ordering, and metal-insulator transitions, of lead- and
potassium-doped barium bismuthate. We discuss some of the early theoretical
studies of these systems. Our recent theoretical work, on the negative-U\/,
extended-Hubbard model for these systems, is also described. Both the large-
and intermediate-U\/ regimes of this model are examined, using mean-field and
random-phase approximations, particularly with a view to fitting various
experimental properties of these bismuthates. On the basis of our studies, we
point out possibilities for exotic physics in these systems. We also emphasize
the different consequences of electronic and phonon-mediated mechanisms for the
negative U.\/ We show that, for an electronic mechanism, the \secin
\,\,phases of these bismuthates must be unique, with their transport properties
{\it dominated by charge Cooperon bound states}. This can explain the
observed difference between the optical and transport gaps. We propose other
experimental tests for this novel mechanism of charge transport and comment on
the effects of disorder.Comment: UUencoded LaTex file, 122 pages, figures available on request To
appear in Int. J. Mod. Phys. B as a review articl
Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
We introduce a new quantity, that we term recoverable information, defined
for stabilizer Hamiltonians. For such models, the recoverable information
provides a measure of the topological information, as well as a physical
interpretation, which is complementary to topological entanglement entropy. We
discuss three different ways to calculate the recoverable information, and
prove their equivalence. To demonstrate its utility, we compute recoverable
information for fracton models using all three methods where appropriate. From
the recoverable information, we deduce the existence of emergent
Gauss-law type constraints, which in turn imply emergent conservation
laws for point-like quasiparticle excitations of an underlying topologically
ordered phase.Comment: Added additional cluster model calculation (SPT example) and a new
section discussing the general benefits of recoverable informatio
Aperture Supervision for Monocular Depth Estimation
We present a novel method to train machine learning algorithms to estimate
scene depths from a single image, by using the information provided by a
camera's aperture as supervision. Prior works use a depth sensor's outputs or
images of the same scene from alternate viewpoints as supervision, while our
method instead uses images from the same viewpoint taken with a varying camera
aperture. To enable learning algorithms to use aperture effects as supervision,
we introduce two differentiable aperture rendering functions that use the input
image and predicted depths to simulate the depth-of-field effects caused by
real camera apertures. We train a monocular depth estimation network end-to-end
to predict the scene depths that best explain these finite aperture images as
defocus-blurred renderings of the input all-in-focus image.Comment: To appear at CVPR 2018 (updated to camera ready version
Topological Entanglement Entropy of Fracton Stabilizer Codes
Entanglement entropy provides a powerful characterization of two-dimensional
gapped topological phases of quantum matter, intimately tied to their
description by topological quantum field theories (TQFTs). Fracton topological
orders are three-dimensional gapped topologically ordered states of matter, but
the existence of a TQFT description for these phases remains an open question.
We show that three-dimensional fracton phases are nevertheless characterized,
at least partially, by universal structure in the entanglement entropy of their
ground state wave functions. We explicitly compute the entanglement entropy for
two archetypal fracton models --- the `X-cube model' and `Haah's code' --- and
demonstrate the existence of a topological contribution that scales linearly in
subsystem size. We show via Schrieffer-Wolff transformations that the
topological entanglement of fracton models is robust against arbitrary local
perturbations of the Hamiltonian. Finally, we argue that these results may be
extended to characterize localization-protected fracton topological order in
excited states of disordered fracton models.Comment: published versio
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