30,539 research outputs found
Eigenvectors of Z-tensors associated with least H-eigenvalue with application to hypergraphs
Unlike an irreducible -matrices, a weakly irreducible -tensor
can have more than one eigenvector associated with the least
H-eigenvalue. We show that there are finitely many eigenvectors of
associated with the least H-eigenvalue. If is
further combinatorial symmetric, the number of such eigenvectors can be
obtained explicitly by the Smith normal form of the incidence matrix of
. When applying to a connected uniform hypergraph , we prove
that the number of Laplacian eigenvectors of associated with the zero
eigenvalue is equal to the the number of adjacency eigenvectors of
associated with the spectral radius, which is also equal to the number of
signless Laplacian eigenvectors of associated with the zero eigenvalue if
zero is an signless Laplacian eigenvalue
Homotopy Smoothing for Non-Smooth Problems with Lower Complexity than
In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS)
algorithm for solving a family of non-smooth problems that is composed of a
non-smooth term with an explicit max-structure and a smooth term or a simple
non-smooth term whose proximal mapping is easy to compute. The best known
iteration complexity for solving such non-smooth optimization problems is
without any assumption on the strong convexity. In this work,
we will show that the proposed HOPS achieved a lower iteration complexity of
\footnote{ suppresses a
logarithmic factor.} with capturing the local sharpness of the
objective function around the optimal solutions. To the best of our knowledge,
this is the lowest iteration complexity achieved so far for the considered
non-smooth optimization problems without strong convexity assumption. The HOPS
algorithm employs Nesterov's smoothing technique and Nesterov's accelerated
gradient method and runs in stages, which gradually decreases the smoothing
parameter in a stage-wise manner until it yields a sufficiently good
approximation of the original function. We show that HOPS enjoys a linear
convergence for many well-known non-smooth problems (e.g., empirical risk
minimization with a piece-wise linear loss function and norm
regularizer, finding a point in a polyhedron, cone programming, etc).
Experimental results verify the effectiveness of HOPS in comparison with
Nesterov's smoothing algorithm and the primal-dual style of first-order
methods.Comment: This is a long version of the paper accepted by NIPS 201
Learning Discriminators as Energy Networks in Adversarial Learning
We propose a novel framework for structured prediction via adversarial
learning. Existing adversarial learning methods involve two separate networks,
i.e., the structured prediction models and the discriminative models, in the
training. The information captured by discriminative models complements that in
the structured prediction models, but few existing researches have studied on
utilizing such information to improve structured prediction models at the
inference stage. In this work, we propose to refine the predictions of
structured prediction models by effectively integrating discriminative models
into the prediction. Discriminative models are treated as energy-based models.
Similar to the adversarial learning, discriminative models are trained to
estimate scores which measure the quality of predicted outputs, while
structured prediction models are trained to predict contrastive outputs with
maximal energy scores. In this way, the gradient vanishing problem is
ameliorated, and thus we are able to perform inference by following the ascent
gradient directions of discriminative models to refine structured prediction
models. The proposed method is able to handle a range of tasks, e.g.,
multi-label classification and image segmentation. Empirical results on these
two tasks validate the effectiveness of our learning method
Half-arc-transitive graphs of prime-cube order of small valencies
A graph is called {\em half-arc-transitive} if its full automorphism group
acts transitively on vertices and edges, but not on arcs. It is well known that
for any prime there is no tetravalent half-arc-transitive graph of order
or . Xu~[Half-transitive graphs of prime-cube order, J. Algebraic
Combin. 1 (1992) 275-282] classified half-arc-transitive graphs of order
and valency . In this paper we classify half-arc-transitive graphs of order
and valency or . In particular, the first known infinite family of
half-arc-transitive Cayley graphs on non-metacyclic -groups is constructed.Comment: 13 page
Bipartite bi-Cayley graphs over metacyclic groups of odd prime-power order
A graph is a bi-Cayley graph over a group if is a
semiregular group of automorphisms of having two orbits. Let be a
non-abelian metacyclic -group for an odd prime , and let be a
connected bipartite bi-Cayley graph over the group . In this paper, we prove
that is normal in the full automorphism group of
when is a Sylow -subgroup of . As an
application, we classify half-arc-transitive bipartite bi-Cayley graphs over
the group of valency less than . Furthermore, it is shown that there
are no semisymmetric and no arc-transitive bipartite bi-Cayley graphs over the
group of valency less than .Comment: 20 pages, 1 figur
A Combinatorial Method for Computing Characteristic Polynomials of Starlike Hypergraphs
By using the Poisson formula for resultants and the variants of chip-firing
game on graphs, we provide a combinatorial method for computing a class of of
resultants, i.e. the characteristic polynomials of the adjacency tensors of
starlike hypergraphs including hyperpaths and hyperstars,which are given
recursively and explicitly
The layered compound CaClFeP is an Arsenic-free high iron-pnictide
We first analyze why the iron pnictides with high superconductivity so
far are As-based, by the Hund's rule correlation picture, then examine the
P-based and Sb-based cases, respectively. Consequently, we propose that CaClFeP
with ZrCuSiAs-type structure is an As-free high iron-pnictide. The
subsequent density functional theory calculations show that the ground state of
CaClFeP is of a collinearly antiferromagnetic order on Fe moments with
structural distortion, resulting from the interplay between the strong nearest
and next-nearest neighbor antiferromagnetic superexchange interactions bridged
by P atoms, similar as the As-based pnictides. The other P-based pnictides are
either nonmagnetic or magnetic but with weak exchange interactions. The
Sb-based pnictides unlikely show high superconductivity because of the
existence of robust ferromagnetic order.Comment: 4 pages, 5 figures, and 1 tabl
A Note On the Rank of the Optimal Matrix in Symmetric Toeplitz Matrix Completion Problem
We consider the symmetric Toeplitz matrix completion problem, whose matrix
under consideration possesses specific row and column structures. This problem,
which has wide application in diverse areas, is well-known to be
computationally NP-hard. This note provides an upper bound on the objective of
minimizing the rank of the symmetric Toeplitz matrix in the completion problem
based on the theorems from the trigonometric moment problem and semi-infinite
problem. We prove that this upper bound is less than twice the number of linear
constraints of the Toeplitz matrix completion problem. Compared with previous
work in the literature, ours is one of the first efforts to investigate the
bound of the objective value of the Toeplitz matrix completion problem
DSNet: Deep and Shallow Feature Learning for Efficient Visual Tracking
In recent years, Discriminative Correlation Filter (DCF) based tracking
methods have achieved great success in visual tracking. However, the
multi-resolution convolutional feature maps trained from other tasks like image
classification, cannot be naturally used in the conventional DCF formulation.
Furthermore, these high-dimensional feature maps significantly increase the
tracking complexity and thus limit the tracking speed. In this paper, we
present a deep and shallow feature learning network, namely DSNet, to learn the
multi-level same-resolution compressed (MSC) features for efficient online
tracking, in an end-to-end offline manner. Specifically, the proposed DSNet
compresses multi-level convolutional features to uniform spatial resolution
features. The learned MSC features effectively encode both appearance and
semantic information of objects in the same-resolution feature maps, thus
enabling an elegant combination of the MSC features with any DCF-based methods.
Additionally, a channel reliability measurement (CRM) method is presented to
further refine the learned MSC features. We demonstrate the effectiveness of
the MSC features learned from the proposed DSNet on two DCF tracking
frameworks: the basic DCF framework and the continuous convolution operator
framework. Extensive experiments show that the learned MSC features have the
appealing advantage of allowing the equipped DCF-based tracking methods to
perform favorably against the state-of-the-art methods while running at high
frame rates.Comment: To appear at ACCV 2018. 14 pages, 8 figure
Quantum speed limit time of a qubit system with non-Hermitian detuning
We investigated the quantum speed limit time of a qubit system with
non-Hermitian detuning. Our results show that, with respect to two
distinguishable states of the non-Hermitian system, the evolutionary time does
not have a nonzero lower bound. And the quantum evolution of the system can be
effectively accelerated by adjusting the non-Hermitian detuning parameter, as
well as the quantum speed limit time can be arbitrarily small even be zero
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