627 research outputs found
Revisiting perfect fluid dark matter: Observational constraints from our galaxy
We revisit certain features of an assumed spherically symmetric perfect fluid
dark matter halo in the light of the observed data of our galax
On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness
In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type
classes of functions, given by integral representations of moduli of
smoothness, in terms of series over the moduli of smoothness. Also, necessary
and sufficient conditions in terms of monotone or lacunary Fourier coefficients
for a function to belong to a such a class are given. In order to prove our
results, we make use of certain recent reverse Copson- and Leindler-type
inequalities.Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1208.612
On the structure of non-full-rank perfect codes
The Krotov combining construction of perfect 1-error-correcting binary codes
from 2000 and a theorem of Heden saying that every non-full-rank perfect
1-error-correcting binary code can be constructed by this combining
construction is generalized to the -ary case. Simply, every non-full-rank
perfect code is the union of a well-defined family of -components
, where belongs to an "outer" perfect code , and these
components are at distance three from each other. Components from distinct
codes can thus freely be combined to obtain new perfect codes. The Phelps
general product construction of perfect binary code from 1984 is generalized to
obtain -components, and new lower bounds on the number of perfect
1-error-correcting -ary codes are presented.Comment: 8 page
Taylor approximations of operator functions
This survey on approximations of perturbed operator functions addresses
recent advances and some of the successful methods.Comment: 12 page
Improving Sequential Determinantal Point Processes for Supervised Video Summarization
It is now much easier than ever before to produce videos. While the
ubiquitous video data is a great source for information discovery and
extraction, the computational challenges are unparalleled. Automatically
summarizing the videos has become a substantial need for browsing, searching,
and indexing visual content. This paper is in the vein of supervised video
summarization using sequential determinantal point process (SeqDPP), which
models diversity by a probabilistic distribution. We improve this model in two
folds. In terms of learning, we propose a large-margin algorithm to address the
exposure bias problem in SeqDPP. In terms of modeling, we design a new
probabilistic distribution such that, when it is integrated into SeqDPP, the
resulting model accepts user input about the expected length of the summary.
Moreover, we also significantly extend a popular video summarization dataset by
1) more egocentric videos, 2) dense user annotations, and 3) a refined
evaluation scheme. We conduct extensive experiments on this dataset (about 60
hours of videos in total) and compare our approach to several competitive
baselines
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