5,886 research outputs found
GRMHD prediction of coronal variability in accreting black holes
On the basis of data from an energy-conserving 3D general relativistic MHD
simulation, we predict the statistical character of variability in the coronal
luminosity from accreting black holes. When the inner boundary of the corona is
defined to be the electron scattering photosphere, its location depends only on
the mass accretion rate in Eddington units (\dot{M}). Nearly independent of
viewing angle and \dot{M}, the power spectrum over the range of frequencies
from approximately the orbital frequency at the innermost stable circular orbit
(ISCO) to ~100 times lower is well approximated by a power-law with index -2,
crudely consistent with the observed power spectra of hard X-ray fluctuations
in AGN and the hard states of Galactic binary black holes. The underlying
physical driver for variability in the light curve is variations in the
accretion rate caused by the chaotic character of MHD turbulence, but the power
spectrum of the coronal light output is significantly steeper. Part of this
contrast is due to the fact that the mass accretion rate can be significantly
modulated by radial epicyclic motions that do not result in dissipation, and
therefore do not drive luminosity fluctuations. The other part of this contrast
is due to the inward decrease of the characteristic inflow time, which leads to
decreasing radial coherence length with increasing fluctuation frequency.Comment: Accepted for publication in ApJ, 35 pages, 11 figures (8 color and 3
greyscale), AASTEX. High-resolution versions can be found at the following
links: [PS] http://www.pha.jhu.edu/~scn/papers/grmhd_var.ps [PDF]
http://www.pha.jhu.edu/~scn/papers/grmhd_var.pd
Phase-space characterization of complexity in quantum many-body dynamics
We propose a phase-space Wigner harmonics entropy measure for many-body
quantum dynamical complexity. This measure, which reduces to the well known
measure of complexity in classical systems and which is valid for both pure and
mixed states in single-particle and many-body systems, takes into account the
combined role of chaos and entanglement in the realm of quantum mechanics. The
effectiveness of the measure is illustrated in the example of the Ising chain
in a homogeneous tilted magnetic field. We provide numerical evidence that the
multipartite entanglement generation leads to a linear increase of entropy
until saturation in both integrable and chaotic regimes, so that in both cases
the number of harmonics of the Wigner function grows exponentially with time.
The entropy growth rate can be used to detect quantum phase transitions. The
proposed entropy measure can also distinguish between integrable and chaotic
many-body dynamics by means of the size of long term fluctuations which become
smaller when quantum chaos sets in.Comment: 10 pages, 9 figure
An Internal Learning Approach to Video Inpainting
We propose a novel video inpainting algorithm that simultaneously
hallucinates missing appearance and motion (optical flow) information, building
upon the recent 'Deep Image Prior' (DIP) that exploits convolutional network
architectures to enforce plausible texture in static images. In extending DIP
to video we make two important contributions. First, we show that coherent
video inpainting is possible without a priori training. We take a generative
approach to inpainting based on internal (within-video) learning without
reliance upon an external corpus of visual data to train a one-size-fits-all
model for the large space of general videos. Second, we show that such a
framework can jointly generate both appearance and flow, whilst exploiting
these complementary modalities to ensure mutual consistency. We show that
leveraging appearance statistics specific to each video achieves visually
plausible results whilst handling the challenging problem of long-term
consistency.Comment: Accepted by ICCV 2019. Website:
https://cs.stanford.edu/~haotianz/publications/video_inpainting
Simultaneous Coherent Structure Coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity
The clustering of data into physically meaningful subsets often requires
assumptions regarding the number, size, or shape of the subgroups. Here, we
present a new method, simultaneous coherent structure coloring (sCSC), which
accomplishes the task of unsupervised clustering without a priori guidance
regarding the underlying structure of the data. sCSC performs a sequence of
binary splittings on the dataset such that the most dissimilar data points are
required to be in separate clusters. To achieve this, we obtain a set of
orthogonal coordinates along which dissimilarity in the dataset is maximized
from a generalized eigenvalue problem based on the pairwise dissimilarity
between the data points to be clustered. This sequence of bifurcations produces
a binary tree representation of the system, from which the number of clusters
in the data and their interrelationships naturally emerge. To illustrate the
effectiveness of the method in the absence of a priori assumptions, we apply it
to three exemplary problems in fluid dynamics. Then, we illustrate its capacity
for interpretability using a high-dimensional protein folding simulation
dataset. While we restrict our examples to dynamical physical systems in this
work, we anticipate straightforward translation to other fields where existing
analysis tools require ad hoc assumptions on the data structure, lack the
interpretability of the present method, or in which the underlying processes
are less accessible, such as genomics and neuroscience
Geometry of the ergodic quotient reveals coherent structures in flows
Dynamical systems that exhibit diverse behaviors can rarely be completely
understood using a single approach. However, by identifying coherent structures
in their state spaces, i.e., regions of uniform and simpler behavior, we could
hope to study each of the structures separately and then form the understanding
of the system as a whole. The method we present in this paper uses trajectory
averages of scalar functions on the state space to: (a) identify invariant sets
in the state space, (b) form coherent structures by aggregating invariant sets
that are similar across multiple spatial scales. First, we construct the
ergodic quotient, the object obtained by mapping trajectories to the space of
trajectory averages of a function basis on the state space. Second, we endow
the ergodic quotient with a metric structure that successfully captures how
similar the invariant sets are in the state space. Finally, we parametrize the
ergodic quotient using intrinsic diffusion modes on it. By segmenting the
ergodic quotient based on the diffusion modes, we extract coherent features in
the state space of the dynamical system. The algorithm is validated by
analyzing the Arnold-Beltrami-Childress flow, which was the test-bed for
alternative approaches: the Ulam's approximation of the transfer operator and
the computation of Lagrangian Coherent Structures. Furthermore, we explain how
the method extends the Poincar\'e map analysis for periodic flows. As a
demonstration, we apply the method to a periodically-driven three-dimensional
Hill's vortex flow, discovering unknown coherent structures in its state space.
In the end, we discuss differences between the ergodic quotient and
alternatives, propose a generalization to analysis of (quasi-)periodic
structures, and lay out future research directions.Comment: Submitted to Elsevier Physica D: Nonlinear Phenomen
A permutation Information Theory tour through different interest rate maturities: the Libor case
This paper analyzes Libor interest rates for seven different maturities and
referred to operations in British Pounds, Euro, Swiss Francs and Japanese Yen,
during the period years 2001 to 2015. The analysis is performed by means of two
quantifiers derived from Information Theory: the permutation Shannon entropy
and the permutation Fisher information measure. An anomalous behavior in the
Libor is detected in all currencies except Euro during the years 2006--2012.
The stochastic switch is more severe in 1, 2 and 3 months maturities. Given the
special mechanism of Libor setting, we conjecture that the behavior could have
been produced by the manipulation that was uncovered by financial authorities.
We argue that our methodology is pertinent as a market overseeing instrument.Comment: arXiv admin note: text overlap with arXiv:1304.039
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