64,566 research outputs found
Sparse Laplacian Shrinkage with the Graphical Lasso Estimator for Regression Problems
This paper considers a high-dimensional linear regression problem where there
are complex correlation structures among predictors. We propose a
graph-constrained regularization procedure, named Sparse Laplacian Shrinkage
with the Graphical Lasso Estimator (SLS-GLE). The procedure uses the estimated
precision matrix to describe the specific information on the conditional
dependence pattern among predictors, and encourages both sparsity on the
regression model and the graphical model. We introduce the Laplacian quadratic
penalty adopting the graph information, and give detailed discussions on the
advantages of using the precision matrix to construct the Laplacian matrix.
Theoretical properties and numerical comparisons are presented to show that the
proposed method improves both model interpretability and accuracy of
estimation. We also apply this method to a financial problem and prove that the
proposed procedure is successful in assets selection
Deciding Nonnegativity of Polynomials by MAPLE
There have been some effective tools for solving (constant/parametric)
semi-algebraic systems in Maple's library RegularChains since Maple 13. By
using the functions of the library, e.g., RealRootClassfication, one can prove
and discover polynomial inequalities. This paper is more or less a user guide
on using RealRootClassfication to prove the nonnegativity of polynomials. We
show by examples how to use this powerful tool to prove a polynomial is
nonnegative under some polynomial inequality and/or equation constraints. Some
tricks for using the tool are also provided.Comment: A user guide on using RealRootClassfication to prove the
nonnegativity of polynomials with 10 example
The thickness of the Kronecker product of graphs
The thickness of a graph is the minimum number of planar subgraphs whose
union is . In this paper, we present sharp lower and upper bounds for the
thickness of the Kronecker product of two graphs and . We
also give the exact thickness numbers for the Kronecker product graphs
, and .Comment: 19 page
A note on the 4-girth-thickness of K_{n,n,n}
The -girth-thickness of a graph is the minimum number of
planar subgraphs of girth at least four whose union is . In this paper, we
obtain that the 4-girth-thickness of complete tripartite graph is
except for . And we
also show that the -girth-thickness of the complete graph is three
which disprove the conjecture posed by Rubio-Montiel (Ars
Math Contemp 14(2) (2018) 319)
Deep Reference Generation with Multi-Domain Hierarchical Constraints for Inter Prediction
Inter prediction is an important module in video coding for temporal
redundancy removal, where similar reference blocks are searched from previously
coded frames and employed to predict the block to be coded. Although
traditional video codecs can estimate and compensate for block-level motions,
their inter prediction performance is still heavily affected by the remaining
inconsistent pixel-wise displacement caused by irregular rotation and
deformation. In this paper, we address the problem by proposing a deep frame
interpolation network to generate additional reference frames in coding
scenarios. First, we summarize the previous adaptive convolutions used for
frame interpolation and propose a factorized kernel convolutional network to
improve the modeling capacity and simultaneously keep its compact form. Second,
to better train this network, multi-domain hierarchical constraints are
introduced to regularize the training of our factorized kernel convolutional
network. For spatial domain, we use a gradually down-sampled and up-sampled
auto-encoder to generate the factorized kernels for frame interpolation at
different scales. For quality domain, considering the inconsistent quality of
the input frames, the factorized kernel convolution is modulated with
quality-related features to learn to exploit more information from high quality
frames. For frequency domain, a sum of absolute transformed difference loss
that performs frequency transformation is utilized to facilitate network
optimization from the view of coding performance. With the well-designed frame
interpolation network regularized by multi-domain hierarchical constraints, our
method surpasses HEVC on average 6.1% BD-rate saving and up to 11.0% BD-rate
saving for the luma component under the random access configuration
Noncommutative Theory in Light of Neutrino Oscillation
Solar neutrino problem and atmospheric neutrino anomaly which are both
long-standing issues studied intensively by physicists in the past several
decades, are reckoned to be able to be solved simultaneously in the framework
of the assumption of the neutrino oscillation. For the presence of the Lorentz
invariance in the Standard Model, the massless neutrino can't have flavor
mixing and oscillation. However, we exploit the q-deformed noncommutative
theory to derive a general modified dispersion relation, which implies some
violation of the Lorentz invariance. Then it is found that the application of
the q-deformed dispersion relation to the neutrino oscillation can provide a
sound explanation for the current data from the reactor and long baseline
experiments.Comment: 8 pages,1 figure,Latex Fil
A fast algorithm for globally solving Tikhonov regularized total least squares problem
The total least squares problem with the general Tikhonov regularization can
be reformulated as a one-dimensional parametric minimization problem (PM),
where each parameterized function evaluation corresponds to solving an
n-dimensional trust region subproblem. Under a mild assumption, the parametric
function is differentiable and then an efficient bisection method has been
proposed for solving (PM) in literature. In the first part of this paper, we
show that the bisection algorithm can be greatly improved by reducing the
initially estimated interval covering the optimal parameter. It is observed
that the bisection method cannot guarantee to find the globally optimal
solution since the nonconvex (PM) could have a local non-global minimizer. The
main contribution of this paper is to propose an efficient branch-and-bound
algorithm for globally solving (PM), based on a novel underestimation of the
parametric function over any given interval using only the information of the
parametric function evaluations at the two endpoints. We can show that the new
algorithm(BTD Algorithm) returns a global \epsilon-approximation solution in a
computational effort of at most O(n^3/\epsilon) under the same assumption as in
the bisection method. The numerical results demonstrate that our new global
optimization algorithm performs even much faster than the improved version of
the bisection heuristic algorithm.Comment: 26 pages, 1 figur
3D Prominence-hosting Magnetic Configurations: Creating a Helical Magnetic Flux Rope
The magnetic configuration hosting prominences and their surrounding coro-
nal structure is a key research topic in solar physics. Recent theoretical and
observational studies strongly suggest that a helical magnetic flux rope is an
es- sential ingredient to fulfill most of the theoretical and observational
requirements for hosting prominences. To understand flux rope formation details
and obtain magnetic configurations suitable for future prominence formation
studies, we here report on three-dimensional isothermal magnetohydrodynamic
simulations including finite gas pressure and gravity. Starting from a
magnetohydrostatic corona with a linear force-free bipolar magnetic field, we
follow its evolution when introducing vortex flows around the main polarities
and converging flows towards the polarity inversion line near the bottom of the
corona. The con- verging flows bring feet of different loops together at the
polarity inversion line and magnetic reconnection and flux cancellation
happens. Inflow and outflow signatures of the magnetic reconnection process are
identified, and the thereby newly formed helical loops wind around pre-existing
ones so that a complete flux rope grows and ascends. When a macroscopic flux
rope is formed, we switch off the driving flows and find that the system
relaxes to a stable state containing a helical magnetic flux rope embedded in
an overlying arcade structure. A major part of the formed flux rope is threaded
by dipped field lines which can stably support prominence matter, while the
total mass of the flux rope is in the order of 4-5.e14 g
NetFence: Preventing Internet Denial of Service from Inside Out
Denial of Service (DoS) attacks frequently happen on the Internet, paralyzing
Internet services and causing millions of dollars of financial loss. This work
presents NetFence, a scalable DoS-resistant network architecture. NetFence uses
a novel mechanism, secure congestion policing feedback, to enable robust
congestion policing inside the network. Bottleneck routers update the feedback
in packet headers to signal congestion, and access routers use it to police
senders' traffic. Targeted DoS victims can use the secure congestion policing
feedback as capability tokens to suppress unwanted traffic. When compromised
senders and receivers organize into pairs to congest a network link, NetFence
provably guarantees a legitimate sender its fair share of network resources
without keeping per-host state at the congested link. We use a Linux
implementation, ns-2 simulations, and theoretical analysis to show that
NetFence is an effective and scalable DoS solution: it reduces the amount of
state maintained by a congested router from per-host to at most per-(Autonomous
System).Comment: The original paper is published in SIGCOMM 201
Supersymmetric Two-Boson Equation: Bilinearization and Solutions
A bilinear formulation for the supersymmetric two-boson equation is derived.
As applications, some solutions are calculated for it. We also construct a
bilinear Backlund transformation.Comment: 8 page
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