15,349 research outputs found
Effect of finite computational domain on turbulence scaling law in both physical and spectral spaces
The well-known translation between the power law of the energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems
Retractions and Gorenstein homological properties
We associate to a localizable module a left retraction of algebras; it is a
homological ring epimorphism that preserves singularity categories. We study
the behavior of left retractions with respect to Gorenstein homological
properties (for example, being Gorenstein algebras or CM-free).
We apply the results to Nakayama algebras. It turns out that for a connected
Nakayama algebra , there exists a connected self-injective Nakayama algebra
such that there is a sequence of left retractions linking to ; in
particular, the singularity category of is triangle equivalent to the
stable category of . We classify connected Nakayama algebras with at most
three simple modules according to Gorenstein homological properties
Video Question Answering via Attribute-Augmented Attention Network Learning
Video Question Answering is a challenging problem in visual information
retrieval, which provides the answer to the referenced video content according
to the question. However, the existing visual question answering approaches
mainly tackle the problem of static image question, which may be ineffectively
for video question answering due to the insufficiency of modeling the temporal
dynamics of video contents. In this paper, we study the problem of video
question answering by modeling its temporal dynamics with frame-level attention
mechanism. We propose the attribute-augmented attention network learning
framework that enables the joint frame-level attribute detection and unified
video representation learning for video question answering. We then incorporate
the multi-step reasoning process for our proposed attention network to further
improve the performance. We construct a large-scale video question answering
dataset. We conduct the experiments on both multiple-choice and open-ended
video question answering tasks to show the effectiveness of the proposed
method.Comment: Accepted for SIGIR 201
Demonstration of Einstein-Podolsky-Rosen Steering with Enhanced Subchannel Discrimination
Einstein-Podolsky-Rosen (EPR) steering describes a quantum nonlocal
phenomenon in which one party can nonlocally affect the other's state through
local measurements. It reveals an additional concept of quantum nonlocality,
which stands between quantum entanglement and Bell nonlocality. Recently, a
quantum information task named as subchannel discrimination (SD) provides a
necessary and sufficient characterization of EPR steering. The success
probability of SD using steerable states is higher than using any unsteerable
states, even when they are entangled. However, the detailed construction of
such subchannels and the experimental realization of the corresponding task are
still technologically challenging. In this work, we designed a feasible
collection of subchannels for a quantum channel and experimentally demonstrated
the corresponding SD task where the probabilities of correct discrimination are
clearly enhanced by exploiting steerable states. Our results provide a concrete
example to operationally demonstrate EPR steering and shine a new light on the
potential application of EPR steering.Comment: 16 pages, 8 figures, appendix include
Monomial Hopf Algebras
Let be a field of characteristic 0 containing all roots of unity. We
classify all the Hopf structures on monomial -coalgebras, or, in dual
version, on monomial -algebras.Comment: 24 page
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