253 research outputs found
Operators on random hypergraphs and random simplicial complexes
Random hypergraphs and random simplicial complexes have potential
applications in computer science and engineering. Various models of random
hypergraphs and random simplicial complexes on n-points have been studied. Let
L be a simplicial complex. In this paper, we study random sub-hypergraphs and
random sub-complexes of L. By considering the minimal complex that a
sub-hypergraph can be embedded in and the maximal complex that can be embedded
in a sub-hypergraph, we define some operators on the space of probability
functions on sub-hypergraphs of L. We study the compositions of these operators
as well as their actions on the space of probability functions. As applications
in computer science, we give algorithms generating large sparse random
hypergraphs and large sparse random simplicial complexes.Comment: 22 page
Weighted (Co)homology and Weighted Laplacian
In this paper, we generalize the combinatorial Laplace operator of Horak and
Jost by introducing the -weighted coboundary operator induced by a weight
function . Our weight function is a generalization of Dawson's
weighted boundary map. We show that our above-mentioned generalizations include
new cases that are not covered by previous literature. Our definition of
weighted Laplacian for weighted simplicial complexes is also applicable to
weighted/unweighted graphs and digraphs.Comment: 22 page
Crossing Generative Adversarial Networks for Cross-View Person Re-identification
Person re-identification (\textit{re-id}) refers to matching pedestrians
across disjoint yet non-overlapping camera views. The most effective way to
match these pedestrians undertaking significant visual variations is to seek
reliably invariant features that can describe the person of interest
faithfully. Most of existing methods are presented in a supervised manner to
produce discriminative features by relying on labeled paired images in
correspondence. However, annotating pair-wise images is prohibitively expensive
in labors, and thus not practical in large-scale networked cameras. Moreover,
seeking comparable representations across camera views demands a flexible model
to address the complex distributions of images. In this work, we study the
co-occurrence statistic patterns between pairs of images, and propose to
crossing Generative Adversarial Network (Cross-GAN) for learning a joint
distribution for cross-image representations in a unsupervised manner. Given a
pair of person images, the proposed model consists of the variational
auto-encoder to encode the pair into respective latent variables, a proposed
cross-view alignment to reduce the view disparity, and an adversarial layer to
seek the joint distribution of latent representations. The learned latent
representations are well-aligned to reflect the co-occurrence patterns of
paired images. We empirically evaluate the proposed model against challenging
datasets, and our results show the importance of joint invariant features in
improving matching rates of person re-id with comparison to semi/unsupervised
state-of-the-arts.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1702.03431 by
other author
Merging of a CO WD and a He-rich white dwarf to produce a type Ia supernovae
Context: Although type Ia supernovae (SNe Ia) play a key role in
astrophysics, the companions of the exploding carbon-oxygen white dwarfs (CO
WDs) are still not completely identified. It has been suggested recently that a
He-rich WD (a He WD or a hybrid HeCO WD) merges with a CO WD may produce an SN
Ia. This theory was based on the double-detonation model, in which the shock
compression in the CO core caused by the surface explosion of the He-rich shell
might lead to the explosion of the whole CO WD. However, so far, very few
binary population synthesis (BPS) studies have been made on the merger scenario
of a CO WD and a He-rich WD in the context of SNe Ia. Aims: We aim to
systematically study the Galactic birthrates and delay-time distributions of
SNe Ia based on the merger scenario of a CO WD and a He-rich WD. Methods: We
performed a series of Monte Carlo BPS simulations to investigate the properties
of SNe Ia from the merging of a CO WD and a He-rich WD based on the Hurley
rapid binary evolution code. We also considered the influence of different
metallicities on the final results. Results: From our simulations, we found
that no more than 15% of all SNe Ia stem from the merger scenario of a CO WD
and a He-rich WD, and their delay times range from ~110 Myr to the Hubble time.
This scenario mainly contributes to SN Ia explosions with intermediate and long
delay times. The present work indicates that the merger scenario of a CO WD and
a He-rich WD can roughly reproduce the birthrates of SN 1991bg-like events, and
cover the range of their delay times. We also found that SN Ia birthrates from
this scenario would be higher for the cases with low metallicities.Comment: 8 pages, 8 figures, accepted for publication in A&
First Observational Signature of Rotational Deceleration in a Massive, Intermediate-age Star Cluster in the Magellanic Clouds
While the extended main-sequence turn-offs (eMSTOs) found in almost all 1--2
Gyr-old star clusters in the Magellanic Clouds are often explained by
postulating extended star-formation histories, the tight subgiant branches
(SGBs) seen in some clusters challenge this popular scenario. Puzzlingly, the
SGB of the eMSTO cluster NGC 419 is significantly broader at bluer than at
redder colors. We carefully assess and confirm the reality of this
observational trend. If we would assume that the widths of the features in
color--magnitude space were entirely owing to a range in stellar ages, the
star-formation histories of the eMSTO stars and the blue SGB region would be
significantly more prolonged than that of the red part of the SGB. This cannot
be explained by assuming an internal age spread. We show that rotational
deceleration of a population of rapidly rotating stars, a currently hotly
debated alternative scenario, naturally explains the observed trend along the
SGB. Our analysis shows that a `converging' SGB could be produced if the
cluster is mostly composed of rapidly rotating stars that slow down over time
owing to the conservation of angular momentum during their evolutionary
expansion from main-sequence turn-off stars to red giants.Comment: 11 pages, preprint format (uses aastex6.cls); ApJ Letters, in pres
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