27,640 research outputs found
Geometry of Numbers
We develop a global cohomology theory for number fields by offering
topological cohomology groups, an arithmetical duality, a Riemann-Roch type
theorem, and two types of vanishing theorem. As applications, we study moduli
spaces of semi-stable lattices, and introduce non-abelian zeta functions for
number fields.Comment: A paper by Tsukasa Hayashi is adde
A new model to predict weak-lensing peak counts II. Parameter constraint strategies
Peak counts have been shown to be an excellent tool to extract the
non-Gaussian part of the weak lensing signal. Recently, we developped a fast
stochastic forward model to predict weak-lensing peak counts. Our model is able
to reconstruct the underlying distribution of observables for analyses. In this
work, we explore and compare various strategies for constraining parameter
using our model, focusing on the matter density and the
density fluctuation amplitude . First, we examine the impact from the
cosmological dependency of covariances (CDC). Second, we perform the analysis
with the copula likelihood, a technique which makes a weaker assumption
compared to the Gaussian likelihood. Third, direct, non-analytic parameter
estimations are applied using the full information of the distribution. Fourth,
we obtain constraints with approximate Bayesian computation (ABC), an
efficient, robust, and likelihood-free algorithm based on accept-reject
sampling. We find that neglecting the CDC effect enlarges parameter contours by
22%, and that the covariance-varying copula likelihood is a very good
approximation to the true likelihood. The direct techniques work well in spite
of noisier contours. Concerning ABC, the iterative process converges quickly to
a posterior distribution that is in an excellent agreement with results from
our other analyses. The time cost for ABC is reduced by two orders of
magnitude. The stochastic nature of our weak-lensing peak count model allows us
to use various techniques that approach the true underlying probability
distribution of observables, without making simplifying assumptions. Our work
can be generalized to other observables where forward simulations provide
samples of the underlying distribution.Comment: 15 pages, 11 figures. Accepted versio
Submillimeter Array CO(2-1) Imaging of the NGC 6946 Giant Molecular Clouds
We present a CO(2-1) mosaic map of the spiral galaxy NGC 6946 by combining
data from the Submillimeter Array and the IRAM 30 m telescope. We identify 390
giant molecular clouds (GMCs) from the nucleus to 4.5 kpc in the disk. GMCs in
the inner 1 kpc are generally more luminous and turbulent, some of which have
luminosities >10^6 K km/s pc^2 and velocity dispersions >10 km/s. Large-scale
bar-driven dynamics likely regulate GMC properties in the nuclear region.
Similar to the Milky Way and other disk galaxies, GMC mass function of NGC 6946
has a shallower slope (index>-2) in the inner region, and a steeper slope
(index<-2) in the outer region. This difference in mass spectra may be
indicative of different cloud formation pathways: gravitational instabilities
might play a major role in the nuclear region, while cloud coalescence might be
dominant in the outer disk. Finally, the NGC 6946 clouds are similar to those
in M33 in terms of statistical properties, but they are generally less luminous
and turbulent than the M51 clouds.Comment: Published in Ap
A Proximity-Aware Hierarchical Clustering of Faces
In this paper, we propose an unsupervised face clustering algorithm called
"Proximity-Aware Hierarchical Clustering" (PAHC) that exploits the local
structure of deep representations. In the proposed method, a similarity measure
between deep features is computed by evaluating linear SVM margins. SVMs are
trained using nearest neighbors of sample data, and thus do not require any
external training data. Clusters are then formed by thresholding the similarity
scores. We evaluate the clustering performance using three challenging
unconstrained face datasets, including Celebrity in Frontal-Profile (CFP),
IARPA JANUS Benchmark A (IJB-A), and JANUS Challenge Set 3 (JANUS CS3)
datasets. Experimental results demonstrate that the proposed approach can
achieve significant improvements over state-of-the-art methods. Moreover, we
also show that the proposed clustering algorithm can be applied to curate a set
of large-scale and noisy training dataset while maintaining sufficient amount
of images and their variations due to nuisance factors. The face verification
performance on JANUS CS3 improves significantly by finetuning a DCNN model with
the curated MS-Celeb-1M dataset which contains over three million face images
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