2,247 research outputs found
On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues
For an indecomposable stochastic matrix (i.e., 1-step transition
probability matrix) with coinciding negative eigenvalues, a new necessary and
sufficient condition of the imbedding problem for time homogeneous Markov
chains is shown by means of an alternate parameterization of the transition
rate matrix (i.e., intensity matrix, infinitesimal generator), which avoids
calculating matrix logarithm or matrix square root. In addition, an implicit
description of the imbedding problem for the stochastic matrix in
Johansen [J. Lond. Math. Soc., 8, 345-351. (1974)] is pointed out.Comment: 17 page
Weighted projective lines of tubular type and equivariantization
We prove that the categories of coherent sheaves over weighted projective
lines of tubular type are explicitly related to each other via the
equivariantization with respect to certain cyclic group actions
Pr\"ufer sheaves and generic sheaves over the weighted projective lines and elliptic curves
In the present paper, we introduce the concepts of Pr\"{u}fer sheaves and
adic sheaves over a weighted projective line of genus one or an elliptic curve,
show that Pr\"{u}fer sheaves and adic sheaves can classify the category of
coherent sheaves. Moreover, we describe the relationship between Pr\"{u}fer
sheaves and generic sheaves, and provide two methods to construct generic
sheaves by using coherent sheaves and Pr\"{u}fer sheaves.Comment: 27 page
Monadicity theorem and weighted projective lines of tubular type
We formulate a version of Beck's monadicity theorem for abelian categories,
which is applied to the equivariantization of abelian categories with respect
to a finite group action. We prove that the equivariantization is compatible
with the construction of quotient abelian categories by Serre subcategories. We
prove that the equivariantization of the graded module category over a graded
ring is equivalent to the graded module category over the same ring but with a
different grading. We deduce from these results two equivalences between the
category of (equivariant) coherent sheaves on a weighted projective line of
tubular type and that on an elliptic curve, where the acting groups are cyclic
and the two equivalences are somehow adjoint to each other.Comment: 3 table
GeoCapsNet: Aerial to Ground view Image Geo-localization using Capsule Network
The task of cross-view image geo-localization aims to determine the
geo-location (GPS coordinates) of a query ground-view image by matching it with
the GPS-tagged aerial (satellite) images in a reference dataset. Due to the
dramatic changes of viewpoint, matching the cross-view images is challenging.
In this paper, we propose the GeoCapsNet based on the capsule network for
ground-to-aerial image geo-localization. The network first extracts features
from both ground-view and aerial images via standard convolution layers and the
capsule layers further encode the features to model the spatial feature
hierarchies and enhance the representation power. Moreover, we introduce a
simple and effective weighted soft-margin triplet loss with online batch hard
sample mining, which can greatly improve image retrieval accuracy. Experimental
results show that our GeoCapsNet significantly outperforms the state-of-the-art
approaches on two benchmark datasets
Tilting objects in the stable category of vector bundles on the weighted projective line of type (2,2,2,2;\lambda)
We construct a tilting object for the stable category of vector bundles on a
weighted projective line X of type (2,2,2,2;\lambda), consisting of five rank
two bundles and one rank three bundle, whose endomorphism algebra is a
canonical algebra associated with X of type (2,2,2,2)
Towards Open-Set Identity Preserving Face Synthesis
We propose a framework based on Generative Adversarial Networks to
disentangle the identity and attributes of faces, such that we can conveniently
recombine different identities and attributes for identity preserving face
synthesis in open domains. Previous identity preserving face synthesis
processes are largely confined to synthesizing faces with known identities that
are already in the training dataset. To synthesize a face with identity outside
the training dataset, our framework requires one input image of that subject to
produce an identity vector, and any other input face image to extract an
attribute vector capturing, e.g., pose, emotion, illumination, and even the
background. We then recombine the identity vector and the attribute vector to
synthesize a new face of the subject with the extracted attribute. Our proposed
framework does not need to annotate the attributes of faces in any way. It is
trained with an asymmetric loss function to better preserve the identity and
stabilize the training process. It can also effectively leverage large amounts
of unlabeled training face images to further improve the fidelity of the
synthesized faces for subjects that are not presented in the labeled training
face dataset. Our experiments demonstrate the efficacy of the proposed
framework. We also present its usage in a much broader set of applications
including face frontalization, face attribute morphing, and face adversarial
example detection
Ranking the Importance of Nodes of Complex Networks by the Equivalence Classes Approach
Identifying the importance of nodes of complex networks is of interest to the
research of Social Networks, Biological Networks etc.. Current researchers have
proposed several measures or algorithms, such as betweenness, PageRank and HITS
etc., to identify the node importance. However, these measures are based on
different aspects of properties of nodes, and often conflict with the others. A
reasonable, fair standard is needed for evaluating and comparing these
algorithms. This paper develops a framework as the standard for ranking the
importance of nodes. Four intuitive rules are suggested to measure the node
importance, and the equivalence classes approach is employed to resolve the
conflicts and aggregate the results of the rules. To quantitatively compare the
algorithms, the performance indicators are also proposed based on a similarity
measure. Three widely used real-world networks are used as the test-beds. The
experimental results illustrate the feasibility of this framework and show that
both algorithms, PageRank and HITS, perform well with bias when dealing with
the tested networks. Furthermore, this paper uses the proposed approach to
analyze the structure of the Internet, and draws out the kernel of the Internet
with dense links
CVAE-GAN: Fine-Grained Image Generation through Asymmetric Training
We present variational generative adversarial networks, a general learning
framework that combines a variational auto-encoder with a generative
adversarial network, for synthesizing images in fine-grained categories, such
as faces of a specific person or objects in a category. Our approach models an
image as a composition of label and latent attributes in a probabilistic model.
By varying the fine-grained category label fed into the resulting generative
model, we can generate images in a specific category with randomly drawn values
on a latent attribute vector. Our approach has two novel aspects. First, we
adopt a cross entropy loss for the discriminative and classifier network, but a
mean discrepancy objective for the generative network. This kind of asymmetric
loss function makes the GAN training more stable. Second, we adopt an encoder
network to learn the relationship between the latent space and the real image
space, and use pairwise feature matching to keep the structure of generated
images. We experiment with natural images of faces, flowers, and birds, and
demonstrate that the proposed models are capable of generating realistic and
diverse samples with fine-grained category labels. We further show that our
models can be applied to other tasks, such as image inpainting,
super-resolution, and data augmentation for training better face recognition
models.Comment: to appear in ICCV 201
Revisiting Distributed Synchronous SGD
Distributed training of deep learning models on large-scale training data is
typically conducted with asynchronous stochastic optimization to maximize the
rate of updates, at the cost of additional noise introduced from asynchrony. In
contrast, the synchronous approach is often thought to be impractical due to
idle time wasted on waiting for straggling workers. We revisit these
conventional beliefs in this paper, and examine the weaknesses of both
approaches. We demonstrate that a third approach, synchronous optimization with
backup workers, can avoid asynchronous noise while mitigating for the worst
stragglers. Our approach is empirically validated and shown to converge faster
and to better test accuracies.Comment: 10 page
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