Unique determination of a transversely isotropic perturbation in a linearized inverse boundary value problem for elasticity

We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor can be uniquely determined. From the linearized Dirichlet-to-Neumann map at two distinct positive frequencies, we show that a transversely isotropic perturbation of a homogeneous isotropic density can be identified at the same time

Non-Hermitian Weyl Semimetals: Non-Hermitian Skin Effect and non-Bloch Bulk-Boundary Correspondence

We investigate novel features of three dimensional non-Hermitian Weyl semimetals, paying special attention to its unconventional bulk-boundary correspondence. We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram, which is also confirmed by the energy spectra from our numerical results. It is shown that, in sharp contrast to Hermitian systems, the conventional (Bloch) bulk-boundary correspondence breaks down in non-Hermitian topological semimetals, which is caused by the non-Hermitian skin effect. We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals: the Fermi-arc edge modes are determined by the non-Bloch Chern number of the bulk bands. Moreover, these Fermi-arc edge modes can manifest as the unidirectional edge motion, and their signatures are consistent with the non-Bloch bulk-boundary correspondence. Our work establish the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.Comment: 6 pages, 4 figure

Asymptotics of stochastic 2D Hydrodynamical type systems in unbounded domains

In this paper, we prove a central limit theorem and establish a moderate deviation principle for 2D stochastic hydrodynamical type systems with multiplicative noise in unbounded domains, which covers 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic B?enard problem and also shell models of turbulence. The weak convergence method plays an important role in obtaining the moderate deviation principle

SPDEs with two reflecting walls and two singular drifts

We study SPDEs with two reflecting walls $\Lambda^1$, $\Lambda^2$ and two singular drifts $\frac{c_1}{(X-\Lambda^1)^{\vartheta}}$, $\frac{c_2}{(\Lambda^2-X)^{\vartheta}}$, driven by space-time white noise. First, we establish the existence and uniqueness of the solutions $X$ for $\vartheta\geq 0$. Second, we obtain the following pathwise properties of the solutions $X$. If $\vartheta>3$, then a.s. $\Lambda^1<X<\Lambda^2$ for all $t\geq0$; If $0<\vartheta<3$, then $X$ hits $\Lambda^1$ or $\Lambda^2$ with positive probability in finite time. Thus $\vartheta=3$ is the critical parameter for $X$ to hit reflecting walls

A Control Chart Approach to Power System Line Outage Detection Under Transient Dynamics

Online transmission line outage detection over the entire network enables timely corrective action to be taken, which prevents a local event from cascading into a large scale blackout. Line outage detection aims to detect an outage as soon as possible after it happened. Traditional methods either do not consider the transient dynamics following an outage or require a full Phasor Measurement Unit (PMU) deployment. Using voltage phase angle data collected from a limited number of PMUs, we propose a real-time dynamic outage detection scheme based on alternating current (AC) power flow model and statistical change detection theory. The proposed method can capture system dynamics since it retains the time-variant and nonlinear nature of the power system. The method is computationally efficient and scales to large and realistic networks. Extensive simulation studies on IEEE 39-bus and 2383-bus systems demonstrated the effectiveness of the proposed method.Comment: 9 pages, 8 figures, under review for IEEE Transactions on Power System

Large Deviations for SPDEs of Jump Type

In this paper, we establish a large deviation principle for a fully non-linear stochastic evolution equation driven by both Brownian motions and Poisson random measures on a given Hilbert space $H$. The weak convergence method plays an important role.Comment: arXiv admin note: substantial text overlap with arXiv:1203.4020 by other author

Optimal Placement of Limited PMUs for Transmission Line Outage Detection and Identification

Phasor Measurement Unit (PMU) technology is increasingly used for real-time monitoring applications, especially line outage detection and identification (D&I) in the power system. Current outage D&I schemes either assume a full PMU deployment or a partial deployment with fixed PMU placement. However, the placement of the PMUs has a fundamental impact on the effectiveness of the D&I scheme. Building on a dynamic relationship between the substation voltage phase angle and active power, we formulated the optimal PMU placement problem for outage D&I as an optimization problem readily solvable by any heuristic algorithm. We tested the formulation using a genetic algorithm and simulated outages of IEEE 39 bus system. The optimal placement found produces a better D&I result of single-line outages than a randomly scattered, tree-like, and degree-based placements.Comment: 6 pages, accepted in PMAPS 202

Permutation Matters: Anisotropic Convolutional Layer for Learning on Point Clouds

It has witnessed a growing demand for efficient representation learning on point clouds in many 3D computer vision applications. Behind the success story of convolutional neural networks (CNNs) is that the data (e.g., images) are Euclidean structured. However, point clouds are irregular and unordered. Various point neural networks have been developed with isotropic filters or using weighting matrices to overcome the structure inconsistency on point clouds. However, isotropic filters or weighting matrices limit the representation power. In this paper, we propose a permutable anisotropic convolutional operation (PAI-Conv) that calculates soft-permutation matrices for each point using dot-product attention according to a set of evenly distributed kernel points on a sphere's surface and performs shared anisotropic filters. In fact, dot product with kernel points is by analogy with the dot-product with keys in Transformer as widely used in natural language processing (NLP). From this perspective, PAI-Conv can be regarded as the transformer for point clouds, which is physically meaningful and is robust to cooperate with the efficient random point sampling method. Comprehensive experiments on point clouds demonstrate that PAI-Conv produces competitive results in classification and semantic segmentation tasks compared to state-of-the-art methods

Uncertainty-Aware Blind Image Quality Assessment in the Laboratory and Wild

Performance of blind image quality assessment (BIQA) models has been significantly boosted by end-to-end optimization of feature engineering and quality regression. Nevertheless, due to the distributional shift between images simulated in the laboratory and captured in the wild, models trained on databases with synthetic distortions remain particularly weak at handling realistic distortions (and vice versa). To confront the cross-distortion-scenario challenge, we develop a \textit{unified} BIQA model and an approach of training it for both synthetic and realistic distortions. We first sample pairs of images from individual IQA databases, and compute a probability that the first image of each pair is of higher quality. We then employ the fidelity loss to optimize a deep neural network for BIQA over a large number of such image pairs. We also explicitly enforce a hinge constraint to regularize uncertainty estimation during optimization. Extensive experiments on six IQA databases show the promise of the learned method in blindly assessing image quality in the laboratory and wild. In addition, we demonstrate the universality of the proposed training strategy by using it to improve existing BIQA models.Comment: Accepted to IEEE TIP. The implementations are available at https://github.com/zwx8981/UNIQU

Bilayer Graphene Growth via a Penetration Mechanism

From both fundamental and technical points of view, a precise control of the layer number of graphene samples is very important. To reach this goal, atomic scale mechanisms of multilayer graphene growth on metal surfaces should be understood. Although it is a geometrically favorable pathway to transport carbon species to interface and then form a new graphene layer there, penetration of a graphene overlayer is not a chemically straightforward process. In this study, the possibility of different active species to penetrate a graphene overlayer on Cu(111) surface is investigated based on first principles calculations. It is found that carbon atom penetration can be realized via an atom exchange process, which leads to a new graphene growth mechanism. Based on this result, a bilayer graphene growth protocol is proposed to obtain high quality samples. Such a penetration possibility also provides a great flexibility for designed growth of graphene nanostructures.Comment: J. Phys. Chem. C accepte