4,668 research outputs found
Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations
We investigate the self-similar singularity of a 1D model for the 3D
axisymmetric Euler equations, which is motivated by a particular singularity
formation scenario observed in numerical computation. We prove the existence of
a discrete family of self-similar profiles for this model and analyze their
far-field properties. The self-similar profiles we find agree with direct
simulation of the model and seem to have some stability
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient
This paper addresses a multi-scale finite element method for second order
linear elliptic equations with arbitrarily rough coefficient. We propose a
local oversampling method to construct basis functions that have optimal local
approximation property. Our methodology is based on the compactness of the
solution operator restricted on local regions of the spatial domain, and does
not depend on any scale-separation or periodicity assumption of the
coefficient. We focus on a special type of basis functions that are harmonic on
each element and have optimal approximation property. We first reduce our
problem to approximating the trace of the solution space on each edge of the
underlying mesh, and then achieve this goal through the singular value
decomposition of an oversampling operator. Rigorous error estimates can be
obtained through thresholding in constructing the basis functions. Numerical
results for several problems with multiple spatial scales and high contrast
inclusions are presented to demonstrate the compactness of the local solution
space and the capacity of our method in identifying and exploiting this compact
structure to achieve computational savings
TIGS: An Inference Algorithm for Text Infilling with Gradient Search
Text infilling is defined as a task for filling in the missing part of a
sentence or paragraph, which is suitable for many real-world natural language
generation scenarios. However, given a well-trained sequential generative
model, generating missing symbols conditioned on the context is challenging for
existing greedy approximate inference algorithms. In this paper, we propose an
iterative inference algorithm based on gradient search, which is the first
inference algorithm that can be broadly applied to any neural sequence
generative models for text infilling tasks. We compare the proposed method with
strong baselines on three text infilling tasks with various mask ratios and
different mask strategies. The results show that our proposed method is
effective and efficient for fill-in-the-blank tasks, consistently outperforming
all baselines.Comment: The 57th Annual Meeting of the Association for Computational
Linguistics (ACL 2019
Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
The Sachdev-Ye-Kitaev model is an N-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-N limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size M ≤ N/2. We also consider generalizations of the SYK model with quadratic random hopping term or U(1) charge conservation
Local-set-based Graph Signal Reconstruction
Signal processing on graph is attracting more and more attentions. For a
graph signal in the low-frequency subspace, the missing data associated with
unsampled vertices can be reconstructed through the sampled data by exploiting
the smoothness of the graph signal. In this paper, the concept of local set is
introduced and two local-set-based iterative methods are proposed to
reconstruct bandlimited graph signal from sampled data. In each iteration, one
of the proposed methods reweights the sampled residuals for different vertices,
while the other propagates the sampled residuals in their respective local
sets. These algorithms are built on frame theory and the concept of local sets,
based on which several frames and contraction operators are proposed. We then
prove that the reconstruction methods converge to the original signal under
certain conditions and demonstrate the new methods lead to a significantly
faster convergence compared with the baseline method. Furthermore, the
correspondence between graph signal sampling and time-domain irregular sampling
is analyzed comprehensively, which may be helpful to future works on graph
signals. Computer simulations are conducted. The experimental results
demonstrate the effectiveness of the reconstruction methods in various sampling
geometries, imprecise priori knowledge of cutoff frequency, and noisy
scenarios.Comment: 28 pages, 9 figures, 6 tables, journal manuscrip
Landau meets Newton: time translation symmetry breaking in classical mechanics
Every classical Newtonian mechanical system can be equipped with a
nonstandard Hamiltonian structure, in which the Hamiltonian is the square of
the canonical Hamiltonian up to a constant shift, and the Poisson bracket is
nonlinear. In such a formalism, time translation symmetry can be spontaneously
broken, provided the potential function becomes negative. A nice analogy
between time translation symmetry breaking and the Landau theory of second
order phase transitions is established, together with several example cases
illustrating time translation breaking ground states. In particular, the
CDM model of FRW cosmology is reformulated as the time translation
symmetry breaking ground states.Comment: 10 pages, 1 figure. V2: minor correction
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