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 $G$ is the minimum number of planar subgraphs whose union is $G$. In this paper, we present sharp lower and upper bounds for the thickness of the Kronecker product $G\times H$ of two graphs $G$ and $H$. We also give the exact thickness numbers for the Kronecker product graphs $K_n\times K_2$, $K_{m,n}\times K_2$ and $K_{n,n,n}\times K_2$.Comment: 19 page

A note on the 4-girth-thickness of K_{n,n,n}

The $4$-girth-thickness $\theta(4,G)$ of a graph $G$ is the minimum number of planar subgraphs of girth at least four whose union is $G$. In this paper, we obtain that the 4-girth-thickness of complete tripartite graph $K_{n,n,n}$ is $\big\lceil\frac{n+1}{2}\big\rceil$ except for $\theta(4,K_{1,1,1})=2$. And we also show that the $4$-girth-thickness of the complete graph $K_{10}$ is three which disprove the conjecture $\theta(4,K_{10})=4$ 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