Symmetric Gauss-Seidel Technique Based Alternating Direction Methods of Multipliers for Transform Invariant Low-Rank Textures Problem

Transform Invariant Low-Rank Textures, referred to as TILT, can accurately and robustly extract textural or geometric information in a 3D from user-specified windows in 2D in spite of significant corruptions and warping. It was discovered that the task can be characterized, both theoretically and numerically, by solving a sequence of matrix nuclear-norm and $\ell_1$-norm involved convex minimization problems. For solving this problem, the direct extension of Alternating Direction Method of Multipliers (ADMM) in an usual Gauss-Seidel manner often performs numerically well in practice but there is no theoretical guarantee on its convergence. In this paper, we resolve this dilemma by using the novel symmetric Gauss-Seidel (sGS) based ADMM developed by Li, Sun \& Toh (Math. Prog. 2016). The sGS-ADMM is guaranteed to converge and we shall demonstrate in this paper that it is also practically efficient than the directly extended ADMM. When the sGS technique is applied to this particular problem, we show that only one variable needs to be re-updated, and this updating hardly imposes any excessive computational cost. The sGS decomposition theorem of Li, Sun \& Toh (arXiv: 1703.06629) establishes the equivalent between sGS-ADMM and the classical ADMM with an additional semi-proximal term, so the convergence result is followed directly. Extensive experiments illustrate that the sGS-ADMM and its generalized variant have superior numerical efficiency over the directly extended ADMM.Comment: 9pages, 2 figures, 1 tabl

A Simple Method to improve Initialization Robustness for Active Contours driven by Local Region Fitting Energy

Active contour models based on local region fitting energy can segment images with intensity inhomogeneity effectively, but their segmentation results are easy to error if the initial contour is inappropriate. In this paper, we present a simple and universal method of improving the robustness of initial contour for these local fitting-based models. The core idea of proposed method is exchanging the fitting values on the two sides of contour, so that the fitting values inside the contour are always larger (or smaller) than the values outside the contour in the process of curve evolution. In this way, the whole curve will evolve along the inner (or outer) boundaries of object, and less likely to be stuck in the object or background. Experimental results have proved that using the proposed method can enhance the robustness of initial contour and meanwhile keep the original advantages in the local fitting-based models

Integral bases of cluster algebras and representations of tame quivers

In \cite{CK2005} and \cite{SZ}, the authors constructed the bases of cluster algebras of finite types and of type $\widetilde{A}_{1,1}$, respectively. In this paper, we will deduce $\mathbb{Z}$-bases for cluster algebras of affine types.Comment: 28 pages, an improvement of arXiv:0811.367

A Z\mathbb{Z}-basis for the cluster algebra associated to an affine quiver

The canonical bases of cluster algebras of finite types and rank 2 are given explicitly in \cite{CK2005} and \cite{SZ} respectively. In this paper, we will deduce $\mathbb{Z}$-bases for cluster algebras for affine types $\widetilde{A}_{n,n},\widetilde{D}$ and $\widetilde{E}$. Moreover, we give an inductive formula for computing the multiplication between two generalized cluster variables associated to objects in a tube.Comment: 21 page

Active Link Obfuscation to Thwart Link-flooding Attacks for Internet of Things

The DDoS attack is a serious threat to the Internet of Things (IoT). As a new class of DDoS attacks, Link-flooding attack (LFA) disrupts connectivity between legitimate IoT devices and target servers by flooding only a small number of links. Several mechanisms have been proposed to mitigate the sophisticated attack. However, they can only reactively mitigate LFA after target links have been flooded by the adversaries. In this paper, we propose an active LFA mitigation mechanism, called Linkbait, that is a proactive and preventive defense to throttle LFA for IoT. The fact behind Linkbait is that adversaries rely on the set of key links impacting the network connectivity (i.e.,linkmap) to identify target links. Linkbait mitigates the attacks by interfering with linkmap discovery and providing a fake linkmap to adversaries. Inspired by moving target defense (MTD), we propose a link obfuscation algorithm in Linkbait that selectively reroutes probing flows to hide target links from adversaries and mislead them to identify bait links as target links. By providing the faked linkmap to adversaries, Linkbait can actively mitigate LFA for IoT even without identifying compromised IoT devices while not affecting flows from legitimate IoT devices. To block attack traffic and further reduce the impact in IoT, we propose a compromised IoT devices detection algorithm that extracts unique traffic patterns of LFA for IoT and leverages support vector machine (SVM) to identify attack traffic. We evaluate the performance of Linkbait by using both real-world experiments and large-scale simulations. The experimental results demonstrate the effectiveness of Linkbait

On Secrecy Rate Analysis of MIMO Wiretap Channels Driven by Finite-Alphabet Input

This work investigates the effect of finite-alphabet source input on the secrecy rate of a multi-antenna wiretap system. Existing works have characterized maximum achievable secrecy rate or secrecy capacity for single and multiple antenna systems based on Gaussian source signals and secrecy code. Despite the impracticality of Gaussian sources, the compact closed-form expression of mutual information between linear channel Gaussian input and corresponding output has led to broad application of Gaussian input assumption in physical secrecy analysis. For practical considerations, we study the effect of finite discrete-constellation on the achievable secrecy rate of multiple-antenna wire-tap channels. Our proposed precoding scheme converts the multi-antenna system into a bank of parallel channels. Based on this precoding strategy, we propose a decentralized power allocation algorithm based on dual decomposition for maximizing the achievable secrecy rate. In addition, we analyze the achievable secrecy rate for finite-alphabet inputs in low and high SNR cases. Our results demonstrate substantial difference in secrecy rate between systems given finite-alphabet inputs and systems with Gaussian inputs.Comment: 21 pages, 5 figures, Submitted to IEEE Transactions on Communications, April 4, 2011. Revision submitted on December 21, 201

Constructing Narrative Event Evolutionary Graph for Script Event Prediction

Script event prediction requires a model to predict the subsequent event given an existing event context. Previous models based on event pairs or event chains cannot make full use of dense event connections, which may limit their capability of event prediction. To remedy this, we propose constructing an event graph to better utilize the event network information for script event prediction. In particular, we first extract narrative event chains from large quantities of news corpus, and then construct a narrative event evolutionary graph (NEEG) based on the extracted chains. NEEG can be seen as a knowledge base that describes event evolutionary principles and patterns. To solve the inference problem on NEEG, we present a scaled graph neural network (SGNN) to model event interactions and learn better event representations. Instead of computing the representations on the whole graph, SGNN processes only the concerned nodes each time, which makes our model feasible to large-scale graphs. By comparing the similarity between input context event representations and candidate event representations, we can choose the most reasonable subsequent event. Experimental results on widely used New York Times corpus demonstrate that our model significantly outperforms state-of-the-art baseline methods, by using standard multiple choice narrative cloze evaluation.Comment: This paper has been accepted by IJCAI 201

Realizing Enveloping Algebras via Varieties of Modules

By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra $L(\Lambda)$ generated by indecomposable constructible sets in the varieties of modules for any finite dimensional $\mathbb{C}$-algebra $\Lambda.$ We obtain a geometric realization of the universal enveloping algebra $R(\Lambda)$ of $L(\Lambda).$ This generalizes the main result of Riedtmann in \cite{R}. We also obtain Green's theorem in \cite{G} in a geometric form for any finite dimensional $\mathbb{C}$-algebra $\Lambda$ and use it to give the comultiplication formula in $R(\Lambda).

Bistable pulsating fronts for reaction-diffusion equations in a periodic habitat

This paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus especially on the influence of the spatial period and, under various assumptions on the reaction terms and by using different types of arguments, we show several existence results when the spatial period is small or large. We also establish some properties of the set of periods for which there exist non-stationary fronts. Furthermore, we prove the existence of stationary fronts or non-stationary partial fronts at any period which is on the boundary of this set. Lastly, we characterize the sign of the front speeds and we show the global exponential stability of the non-stationary fronts for various classes of initial conditions

Dimensions of automorphism group schemes of finite level truncations of FF-cyclic FF-crystals

Let $\mathcal{M}_{\pi}$ be an $F$-cyclic $F$-crystal $\mathcal{M}_{\pi}$ over an algebraically closed field defined by a permutation $\pi$ and a set of prescribed Hodge slopes. We prove combinatorial formulas for the dimension $\gamma_{\mathcal{M}_{\pi}}(m)$ of the automorphism group scheme of $\mathcal{M}_{\pi}$ at finite level $m$ and the number of connected components of the endomorphism group scheme of $\mathcal{M}_{\pi}$ at finite level $m$. As an application, we show that if $\mathcal{M}_{\pi}$ is a nonordinary Dieudonn\'e module defined by a cycle $\pi$, then $\gamma_{\mathcal{M}_{\pi}}(m+1) - \gamma_{\mathcal{M}_{\pi}}(m) < \gamma_{\mathcal{M}_{\pi}}(m) - \gamma_{\mathcal{M}_{\pi}}(m-1)$ for all $1 \leq m \leq n_{\mathcal{M}_{\pi}}$, where $n_{\mathcal{M}_{\pi}}$ is the isomorphism number of $\mathcal{M}_{\pi}$