40,362 research outputs found
Occupation times of general L\'evy processes
For an arbitrary L\'evy process which is not a compound Poisson process,
we are interested in its occupation times. We use a quite novel and useful
approach to derive formulas for the Laplace transform of the joint distribution
of and its occupation times. Our formulas are compact, and more
importantly, the forms of the formulas clearly demonstrate the essential
quantities for the calculation of occupation times of . It is believed that
our results are important not only for the study of stochastic processes, but
also for financial applications
On the Formation of Elliptical Rings in Disk Galaxies
N-body simulations of galactic collisions are employed to investigate the
formation of elliptical rings in disk galaxies. The relative inclination
between disk and dwarf galaxies is studied with a fine step of five degrees. It
is confirmed that the eccentricity of elliptical ring is linearly proportional
to the inclination angle. Deriving from the simulational results, an analytic
formula which expresses the eccentricity as a function of time and inclination
angle is obtained. This formula shall be useful for the interpretations of the
observations of ring systems, and therefore reveals the merging histories of
galaxies.Comment: 22 pages, 10 figures, accepted for publication in Ap
Quantum ergodicity and mixing and their classical limits with quantum kicked rotor
We study the ergodicity and mixing of quantum kicked rotor (QKR) with two
distinct approaches. In one approach, we use the definitions of quantum
ergodicity and mixing recently proposed in [Phys. Rev. E 94, 022150 (2016)],
which involve only eigen-energies (Floquet quasi-energies for QKR). In the
other approach, we study ergodicity and mixing with quantum Poincar\`e section,
which is plotted with a method that maps a wave function unitarily onto quantum
phase space composed of Planck cells. Classical Poincar\`e section can be
recovered with the effective Planck constant gradually diminishing. We
demonstrate that the two approaches can capture the quantum and classical
characteristics of ergodicity and mixing of QKR, and give consistent results
with classical model at semiclassical limit. Therefore, we establish a
correspondence between quantum ergodicity (mixing) and classical ergodicity
(mixing).Comment: 5 figures, 9 page
Revisiting EmbodiedQA: A Simple Baseline and Beyond
In Embodied Question Answering (EmbodiedQA), an agent interacts with an
environment to gather necessary information for answering user questions.
Existing works have laid a solid foundation towards solving this interesting
problem. But the current performance, especially in navigation, suggests that
EmbodiedQA might be too challenging for the contemporary approaches. In this
paper, we empirically study this problem and introduce 1) a simple yet
effective baseline that achieves promising performance; 2) an easier and
practical setting for EmbodiedQA where an agent has a chance to adapt the
trained model to a new environment before it actually answers users questions.
In this new setting, we randomly place a few objects in new environments, and
upgrade the agent policy by a distillation network to retain the generalization
ability from the trained model. On the EmbodiedQA v1 benchmark, under the
standard setting, our simple baseline achieves very competitive results to
the-state-of-the-art; in the new setting, we found the introduced small change
in settings yields a notable gain in navigation.Comment: Accepted to IEEE Transactions on Image Processing (TIP
The Axis-Symmetric Ring Galaxies: AM 0053-353, AM 0147-350, AM 1133-245, AM 1413-243, AM 2302-322, ARP 318, and Head-On Penetrations
Axis-symmetric ring systems can be identified from the new catalog of
collisional ring galaxies in Madore et al. (2009). These are O-type-like
collisional ring galaxies. Head-on collisions by dwarf galaxies moving along
the symmetric axis were performed through N-body simulations to address their
origins. It was found that the simulations with smaller initial relative
velocities between two galaxies, or the cases with heavier dwarf galaxies,
could produce rings with higher density contrasts. There are more than one
generation of rings in one collision and the lifetime of any generation of
rings is about one dynamical time. It was concluded that head-on penetrations
could explain these O-type-like ring galaxies identified from the new catalog
in Madore et al. (2009), and the simulated rings resembling the observational
O-type-like collisional rings are those at the early stage of one of the
ring-generations.Comment: 33 pages, 15 figures, published in ApJ 201
On semi-convergence of generalized skew-Hermitian triangular splitting iteration methods for singular saddle-point problems
Recently, Krukier et al. [Generalized skew-Hermitian triangular splitting
iteration methods for saddle-point linear systems, Numer. Linear Algebra Appl.
21 (2014) 152-170] proposed an efficient generalized skew-Hermitian triangular
splitting (GSTS) iteration method for nonsingular saddle-point linear systems
with strong skew-Hermitian parts. In this work, we further use the GSTS method
to solve singular saddle-point problems. The semi-convergence properties of
GSTS method are analyzed by using singular value decomposition and
Moore-Penrose inverse, under suitable restrictions on the involved iteration
parameters. Numerical results are presented to demonstrate the feasibility and
efficiency of the GSTS iteration methods, both used as solvers and
preconditioners for GMRES method.Comment: 14 page
Spin-Wave Fiber
Spin waves are collective excitations propagating in the magnetic medium with
ordered magnetizations. Magnonics, utilizing the spin wave (magnon) as
information carrier, is a promising candidate for low-dissipation computation
and communication technologies. We discover that, due to the
Dzyaloshinskii-Moriya interaction, the scattering behavior of spin wave at a
magnetic domain wall follows a generalized Snell's law, where two magnetic
domains work as two different mediums. Similar to optical total reflection that
occurs at the water-air interfaces, spin waves may experience total reflection
at magnetic domain walls when their incident angle larger than a critical
value. We design a spin wave fiber using a magnetic domain structure with two
domain walls, and demonstrate that such a spin wave fiber can transmit spin
waves over long distance by total internal reflections, in analogy to an
optical fiber. Our design of spin wave fiber opens up new possibilities in pure
magnetic information processing.Comment: 5 pages, 3 figure
Convergence of Contrastive Divergence with Annealed Learning Rate in Exponential Family
In our recent paper, we showed that in exponential family, contrastive
divergence (CD) with fixed learning rate will give asymptotically consistent
estimates \cite{wu2016convergence}. In this paper, we establish consistency and
convergence rate of CD with annealed learning rate . Specifically,
suppose CD- generates the sequence of parameters
using an i.i.d. data sample of size ,
then converges in
probability to 0 at a rate of . The number () of MCMC
transitions in CD only affects the coefficient factor of convergence rate. Our
proof is not a simple extension of the one in \cite{wu2016convergence}. which
depends critically on the fact that is a homogeneous
Markov chain conditional on the observed sample . Under
annealed learning rate, the homogeneous Markov property is not available and we
have to develop an alternative approach based on super-martingales. Experiment
results of CD on a fully-visible Boltzmann Machine are provided to
demonstrate our theoretical results
General constraint preconditioning iteration method for singular saddle-point problems
For the singular saddle-point problems with nonsymmetric positive definite
block, we present a general constraint preconditioning (GCP) iteration
method based on a singular constraint preconditioner. Using the properties of
the Moore-Penrose inverse, the convergence properties of the GCP iteration
method are studied. In particular, for each of the two different choices of the
block of the singular constraint preconditioner, a detailed convergence
condition is derived by analyzing the spectrum of the iteration matrix.
Numerical experiments are used to illustrate the theoretical results and
examine the effectiveness of the GCP iteration method. Moreover, the
preconditioning effects of the singular constraint preconditioner for restarted
generalized minimum residual (GMRES) and quasi-minimal residual (QMR) methods
are also tested
Convergence of Contrastive Divergence Algorithm in Exponential Family
The Contrastive Divergence (CD) algorithm has achieved notable success in
training energy-based models including Restricted Boltzmann Machines and played
a key role in the emergence of deep learning. The idea of this algorithm is to
approximate the intractable term in the exact gradient of the log-likelihood
function by using short Markov chain Monte Carlo (MCMC) runs. The approximate
gradient is computationally-cheap but biased. Whether and why the CD algorithm
provides an asymptotically consistent estimate are still open questions. This
paper studies the asymptotic properties of the CD algorithm in canonical
exponential families, which are special cases of the energy-based model.
Suppose the CD algorithm runs MCMC transition steps at each iteration
and iteratively generates a sequence of parameter estimates given an i.i.d. data sample .
Under conditions which are commonly obeyed by the CD algorithm in practice, we
prove the existence of some bounded such that any limit point of the time
average as is a
consistent estimate for the true parameter . Our proof is based
on the fact that is a homogenous Markov chain
conditional on the data sample . This chain meets the
Foster-Lyapunov drift criterion and converges to a random walk around the
Maximum Likelihood Estimate. The range of the random walk shrinks to zero at
rate as the sample size
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