18,342 research outputs found

### Penalized Maximum Tangent Likelihood Estimation and Robust Variable Selection

We introduce a new class of mean regression estimators -- penalized maximum
tangent likelihood estimation -- for high-dimensional regression estimation and
variable selection. We first explain the motivations for the key ingredient,
maximum tangent likelihood estimation (MTE), and establish its asymptotic
properties. We further propose a penalized MTE for variable selection and show
that it is $\sqrt{n}$-consistent, enjoys the oracle property. The proposed
class of estimators consists penalized $\ell_2$ distance, penalized exponential
squared loss, penalized least trimmed square and penalized least square as
special cases and can be regarded as a mixture of minimum Kullback-Leibler
distance estimation and minimum $\ell_2$ distance estimation. Furthermore, we
consider the proposed class of estimators under the high-dimensional setting
when the number of variables $d$ can grow exponentially with the sample size
$n$, and show that the entire class of estimators (including the aforementioned
special cases) can achieve the optimal rate of convergence in the order of
$\sqrt{\ln(d)/n}$. Finally, simulation studies and real data analysis
demonstrate the advantages of the penalized MTE.Comment: 30 pages, 3 figure

### Stability of circulant graphs

The canonical double cover $\mathrm{D}(\Gamma)$ of a graph $\Gamma$ is the
direct product of $\Gamma$ and $K_2$. If
$\mathrm{Aut}(\mathrm{D}(\Gamma))=\mathrm{Aut}(\Gamma)\times\mathbb{Z}_2$ then
$\Gamma$ is called stable; otherwise $\Gamma$ is called unstable. An unstable
graph is nontrivially unstable if it is connected, non-bipartite and distinct
vertices have different neighborhoods. In this paper we prove that every
circulant graph of odd prime order is stable and there is no arc-transitive
nontrivially unstable circulant graph. The latter answers a question of Wilson
in 2008. We also give infinitely many counterexamples to a conjecture of
Maru\v{s}i\v{c}, Scapellato and Zagaglia Salvi in 1989 by constructing a family
of stable circulant graphs with compatible adjacency matrices

### Dynamics of quantum correlations for central two-qubit coupled to an isotropic Lipkin-Meshkov-Glick bath

We investigate the dynamics of quantum discord and entanglement for two
central spin qubits coupled to an isotropic Lipkin-Meshkov-Glick bath. It is
found that both quantum discord and entanglement have quite distinct behaviors
with respect to the two different phases of the bath. In the case of the
symmetry broken phase bath, quantum discord and entanglement can remain as
constant. In the case of the symmetric phase bath, quantum discord and
entanglement always periodically oscillate with time. The critical point of
quantum phase transition of the bath can be revealed clearly by the distinct
behaviors of quantum correlations. Furthermore, it is observed that quantum
discord is significantly enhanced during the evolution while entanglement
periodically vanishes

### Dynamics of quantum correlations for two-qubit coupled to a spin chain with Dzyaloshinskii-Moriya interaction

We study the dynamics of quantum discord and entanglement for two spin qubits
coupled to a spin chain with Dzyaloshinsky-Moriya (DM) interaction. We
numerically and analytically investigate the time evolution of quantum discord
and entanglement for two-qubit initially prepared in a class of $X-$structure
state. In the case of evolution from a pure state, quantum correlations decay
to zero in a very short time at the critical point of the environment. In the
case of evolution from a mixed state, It is found that quantum discord may get
maximized due to the quantum critical behavior of the environment while
entanglement vanishes under the same condition. Moreover, we observed sudden
transition between classical and quantum decoherence when single qubit
interacts with the environment. The effects of DM interaction on quantum
correlations are also considered and revealed in the two cases. It can enhance
the decay of quantum correlations and its effect on quantum correlations can be
strengthened by anisotropy parameter

### Stability of generalized Petersen graphs

The canonical double cover $D(\Gamma)$ of a graph $\Gamma$ is the direct
product of $\Gamma$ and $K_2$. If $Aut(D(\Gamma))\cong Aut(\Gamma)\times Z_2$
then $\Gamma$ is called stable; otherwise $\Gamma$ is called unstable. An
unstable graph is said to be nontrivially unstable if it is connected,
non-bipartite and no two vertices have the same neighborhood. In 2008 Wilson
conjectured that, if the generalized Petersen graph $GP(n,k)$ is nontrivially
unstable, then both $n$ and $k$ are even, and either $n/2$ is odd and
$k^2\equiv\pm 1 \pmod{n/2}$, or $n=4k$. In this paper we prove that this
conjecture is true. At the same time we completely determine the full
automorphism group of the canonical double cover of $GP(n,k)$ for any pair of
integers $n, k$ with $1 \leqslant k < n/2$. As a by-product we determine all
possible isomorphisms among the generalized Petersen graphs, the canonical
double covers of the generalized Petersen graphs, and the double generalized
Petersen graphs.Comment: 12 page

### A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity

In this paper, we propose a variational multiphase image segmentation model
based on fuzzy membership functions and L1-norm fidelity. Then we apply the
alternating direction method of multipliers to solve an equivalent problem. All
the subproblems can be solved efficiently. Specifically, we propose a fast
method to calculate the fuzzy median. Experimental results and comparisons show
that the L1-norm based method is more robust to outliers such as impulse noise
and keeps better contrast than its L2-norm counterpart. Theoretically, we prove
the existence of the minimizer and analyze the convergence of the algorithm.Comment: 28 pages, 8 figures, 3 table

### Heptavalent symmetric graphs with solvable stabilizers admitting vertex-transitive non-abelian simple groups

A graph $\Gamma$ is said to be symmetric if its automorphism group $\rm
Aut(\Gamma)$ acts transitively on the arc set of $\Gamma$. In this paper, we
show that if $\Gamma$ is a finite connected heptavalent symmetric graph with
solvable stabilizer admitting a vertex-transitive non-abelian simple group $G$
of automorphisms, then either $G$ is normal in $\rm Aut(\Gamma)$, or $\rm
Aut(\Gamma)$ contains a non-abelian simple normal subgroup $T$ such that $G\leq
T$ and $(G,T)$ is explicitly given as one of $11$ possible exception pairs of
non-abelian simple groups. Furthermore, if $G$ is regular on the vertex set of
$\Gamma$ then the exception pair $(G,T)$ is one of $7$ possible pairs, and if
$G$ is arc-transitive then the exception pair $(G,T)=(A_{17},A_{18})$ or
$(A_{35},A_{36})$.Comment: 9. arXiv admin note: substantial text overlap with arXiv:1701.0118

### The equivalence between doubly nonnegative relaxation and semidefinite relaxation for binary quadratic programming problems

It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009)
that a large class of NP-hard nonconvex quadratic programming problems can be
modeled as so called completely positive programming problems, which are convex
but still NP-hard in general. A basic tractable relaxation is gotten by doubly
nonnegative relaxation, resulting in a doubly nonnegative programming. In this
paper, we prove that doubly nonnegative relaxation for binary quadratic
programming (BQP) problem is equivalent to a tighter semidifinite relaxation
for it. When problem (BQP) reduces to max-cut (MC) problem, doubly nonnegative
relaxation for it is equivalent to the standard semidifinite relaxation.
Furthermore, some compared numerical results are reported

### The applications of the general and reduced Yangian algebras

The applications of the general and reduced Yangian Y(sl(2)) and Y(su(3))
algebras are discussed. By taking a special constraint, the representation of
Y(sl(2)) and Y(su(3)) can be divided into two 2 \times 2 and three 3 \times 3
blocks diagonal respectively. The general and reduced Yangian Y(sl(2)) and
Y(su(3)) are applied to the bi-qubit system and the mixed light pseudoscalar
meson state, respectively. We can find that the general ones are not able to
make the initial states disentangled by acting on the initial states, however
the reduced ones are able to make the initial state disentangled. In addition,
we show the effects of Y(su(3)) generators on the the decay channel

### Collaborative Filtering with Stability

Collaborative filtering (CF) is a popular technique in today's recommender
systems, and matrix approximation-based CF methods have achieved great success
in both rating prediction and top-N recommendation tasks. However, real-world
user-item rating matrices are typically sparse, incomplete and noisy, which
introduce challenges to the algorithm stability of matrix approximation, i.e.,
small changes in the training data may significantly change the models. As a
result, existing matrix approximation solutions yield low generalization
performance, exhibiting high error variance on the training data, and
minimizing the training error may not guarantee error reduction on the test
data. This paper investigates the algorithm stability problem of matrix
approximation methods and how to achieve stable collaborative filtering via
stable matrix approximation. We present a new algorithm design framework, which
(1) introduces new optimization objectives to guide stable matrix approximation
algorithm design, and (2) solves the optimization problem to obtain stable
approximation solutions with good generalization performance. Experimental
results on real-world datasets demonstrate that the proposed method can achieve
better accuracy compared with state-of-the-art matrix approximation methods and
ensemble methods in both rating prediction and top-N recommendation tasks

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