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Kui Wang

Publications and source records attributed to Kui Wang.

At least 55 records · Page 3Linked to original sources
arXiv2020

First Robin Eigenvalue of the $p$-Laplacian on Riemannian Manifolds

We consider the first Robin eigenvalue $ł_p(M,\a)$ for the $p$-Laplacian on a compact Riemannian manifold $M$ with nonempty smooth boundary, with $\a \in \R$ being the Robin parameter. Firstly, we prove eigenvalue comparison theorems of Cheng type for $ł_p(M,\a)$. Secondly, when $\a>0$ we establish sharp lower bound of $ł_p(M,\a)$ in terms of dimension, inradius, Ricci curvature lower bound and boundary mean curvature lower bound, via comparison with an associated one-dimensional eigenvalue problem. The lower bound becomes an upper bound when $\a<0$. Our results cover corresponding comparison theorems for the first Dirichlet eigenvalue of the $p$-Laplacian when letting $\a \to +\infty$.

math.AP↗
arXiv2020

On a class of quasilinear operators on smooth metric measure spaces

We derive sharp estimates on the modulus of continuity for solutions of a large class of quasilinear isotropic parabolic equations on smooth metric measure spaces (with Dirichlet or Neumann boundary condition in case the boundary is non-empty). We also derive optimal lower bounds for the first Dirichlet eigenvalue of a class of homogeneous quasilinear operators, which include non-variational operators. The main feature is that this class of operators have corresponding one-dimensional operators, which allow sharp comparisons with solutions of one-dimensional equations.

math.DG↗
arXiv2020

Sharp lower bound for the first eigenvalue of the Weighted $p$-Laplacian II

Combined with our previous work \cite{LW19eigenvalue}, we prove sharp lower bound estimates for the first nonzero eigenvalue of the weighted $p$-Laplacian with $1< p< \infty$ on a compact Bakry-Émery manifold $(M^n,g,f)$, without boundary or with a convex boundary and Neumann boundary condition, satisfying $\text{Ric}+\nabla^2 f \geq κ\, g$ for some $κ\in \mathbb{R}$.

math.AP↗
arXiv2020

On the second Robin eigenvalue of the Laplacian

We study the Robin eigenvalue problem for the Laplace-Beltrami operator on Riemannian manifolds. Our first result is a comparison theorem for the second Robin eigenvalue on geodesic balls in manifolds whose sectional curvatures are bounded from above. Our second result asserts that geodesic balls in nonpositively curved space forms maximize the second Robin eigenvalue among bounded domains of the same volume.

math.DG↗
arXiv2020

An upper bound for the first nonzero Steklov eigenvalue

Let $(M^n,g)$ be a complete simply connected $n$-dimensional Riemannian manifold with curvature bounds $\operatorname{Sect}_g\leq κ$ for $κ\leq 0$ and $\operatorname{Ric}_g\geq(n-1)Kg$ for $K\leq 0$. We prove that for any bounded domain $Ω\subset M^n$ with diameter $d$ and Lipschitz boundary, if $Ω^*$ is a geodesic ball in the simply connected space form with constant sectional curvature $κ$ enclosing the same volume as $Ω$, then $σ_1(Ω) \leq C σ_1(Ω^*)$, where $σ_1(Ω)$ and $ σ_1(Ω^*)$ denote the first nonzero Steklov eigenvalues of $Ω$ and $Ω^*$ respectively, and $C=C(n,κ, K, d)$ is an explicit constant. When $κ=K$, we have $C=1$ and recover the Brock-Weinstock inequality, asserting that geodesic balls uniquely maximize the first nonzero Steklov eigenvalue among domains of the same volume, in Euclidean space and the hyperbolic space.

math.DG↗
arXiv2020

Effective End-to-End Learning Framework for Economic Dispatch

Conventional wisdom to improve the effectiveness of economic dispatch is to design the load forecasting method as accurately as possible. However, this approach can be problematic due to the temporal and spatial correlations between system cost and load prediction errors. This motivates us to adopt the notion of end-to-end machine learning and to propose a task-specific learning criteria to conduct economic dispatch. Specifically, to maximize the data utilization, we design an efficient optimization kernel for the learning process. We provide both theoretical analysis and empirical insights to highlight the effectiveness and efficiency of the proposed learning framework.

math.OC↗
arXiv2019

Optimal Electricity Storage Sharing Mechanism for Single Peaked Time-of-Use Pricing Scheme

Sharing economy has disrupted many industries. We foresee that electricity storage systems could be the enabler for sharing economy in electricity sector, though its implementation is a delicate task. Unlike in the 2-tier Time-of-Use (ToU) pricing, where greedy arbitrage policy can achieve the maximal electricity bill savings, most existing ToU schemes consist of multiple tiers, which renders the arbitrage challenging. The difficulty comes from the hedging against multiple tiers and the coupling between the decisions across the day. In this work, we focus on designing the energy sharing mechanism for single peaked ToU scheme. To solve the problem, we identify that it suffices to understand the arbitrage policies for two forms of 3-tier ToU schemes. We submit that under mild conditions, the sharing mechanism yields a unique equilibrium, which supports the maximal social welfare.

eess.SY↗
arXiv2019

A Data-driven Storage Control Framework for Dynamic Pricing

Dynamic pricing is both an opportunity and a challenge to the demand side. It is an opportunity as it better reflects the real time market conditions and hence enables an active demand side. However, demand's active participation does not necessarily lead to benefits. The challenge conventionally comes from the limited flexible resources and limited intelligent devices in demand side. The decreasing cost of storage system and the widely deployed smart meters inspire us to design a data-driven storage control framework for dynamic prices. We first establish a stylized model by assuming the knowledge and structure of dynamic price distributions, and design the optimal storage control policy. Based on Gaussian Mixture Model, we propose a practical data-driven control framework, which helps relax the assumptions in the stylized model. Numerical studies illustrate the remarkable performance of the proposed data-driven framework.

eess.SY↗
arXiv2019

An Algorithmic View on Optimal Storage Sizing

Users can arbitrage against Time-of-Use (ToU) pricing with storage by charging in off-peak period and discharge in peak periods. In this paper we design the optimal control policy and the solve optimal investment for general ToU scheme. We formulate the problem as dynamic programming for efficient solution. Our result is feasible facing multi-peaked ToU scheme. Simulation studies examine how the user's cost varies with respect to the user's demand randomness; we also demonstrate the performance of our scheme when aggregating users for extra savings.

eess.SY↗
arXiv2019

Conductor Galloping Prediction on Imbalanced Datasets: SVM with Smart Sampling

Conductor galloping is the high-amplitude, low-frequency oscillation of overhead power lines due to wind. Such movements may lead to severe damages to transmission lines, and hence pose significant risks to the power system operation. In this paper, we target to design a prediction framework for conductor galloping. The difficulty comes from imbalanced dataset as galloping happens rarely. By examining the impacts of data balance and data volume on the prediction performance, we propose to employ proper sample adjustment methods to achieve better performance. Numerical study suggests that using only three features, together with over sampling, the SVM based prediction framework achieves an F_1-score of 98.9%.

eess.SP↗
arXiv2019

Sharp lower bound for the first eigenvalue of the Weighted $p$-Laplacian

We prove sharp lower bound estimates for the first nonzero eigenvalue of the weighted $p$-Lapacian operator with $1< p< \infty$ on a compact Bakry-Emery manifold $(M^n,g,f)$ satisfying $\Ric+\nabla^2 f \geq κ\, g$, provided that either $1<p \leq 2$ or $κ\leq 0$. Same conclusions hold when the manifold has nonempty boundary if we assume it is strictly convex and put Neumann boundary conditions on it. For $1<p \leq 2$, we provide a simple proof via the modulus of continuity estimates method. The proof for $κ\leq 0$ is based on a sharp gradient comparison theorem for the eigenfunction and a careful analysis of the underlying one-dimensional model equation. Our results generalize the work of Valtorta\cite{Valtorta12} and Naber-Valtorta\cite{NV14} for the $p$-Laplacian (namely $f=\text{const}$), and the work of Bakry-Qian\cite{BQ00} for the $f$-Laplacian (namely $p=2$).

math.AP↗
arXiv2019

PAC it up: Towards Pointer Integrity using ARM Pointer Authentication

Run-time attacks against programs written in memory-unsafe programming languages (e.g., C and C++) remain a prominent threat against computer systems. The prevalence of techniques like return-oriented programming (ROP) in attacking real-world systems has prompted major processor manufacturers to design hardware-based countermeasures against specific classes of run-time attacks. An example is the recently added support for pointer authentication (PA) in the ARMv8-A processor architecture, commonly used in devices like smartphones. PA is a low-cost technique to authenticate pointers so as to resist memory vulnerabilities. It has been shown to enable practical protection against memory vulnerabilities that corrupt return addresses or function pointers. However, so far, PA has received very little attention as a general purpose protection mechanism to harden software against various classes of memory attacks. In this paper, we use PA to build novel defenses against various classes of run-time attacks, including the first PA-based mechanism for data pointer integrity. We present PARTS, an instrumentation framework that integrates our PA-based defenses into the LLVM compiler and the GNU/Linux operating system and show, via systematic evaluation, that PARTS provides better protection than current solutions at a reasonable performance overhead

cs.CR↗
arXiv2019

First eigenvalue for p-Laplacian with mixed boundary conditions on manifolds

In this paper, we mainly study eigenvalue problems of p-Laplacian on domains with an interior hole. Firstly we prove Faber-Krahn-type inequalities, and Cheng-type eigenvalue comparison theorems on manifolds. Secondly, we prove a comparison theorem for eigenvalues with inner Dirichlet and outer Neumann boundary in minimal submanifolds in Euclidean space. Lastly we give a sharp estimate of the eigenvalue (with outer Dirichlet and inner Neumann boundaries) in terms of the Dircihlet eigenvalue, and also we give an upper bound of the eigenvalue with inner Dirichlet and outer Neumann problems by the diameter of the hole inside.

math.DG↗
arXiv2018

Parabolic frequency monotonicity on compact manifolds

This work is devoted to the study of parabolic frequency for solutions of the heat equation on Riemannian manifolds. We show that the parabolic frequency functional is almost increasing on compact manifolds with nonnegative sectional curvature, which generalizes a monotonicity result proved by C. Poon and by L. Ni. The proof is based on a generalization of R. Hamilton's matrix Harnack inequality for small time. As applications, we obtain a unique continuation result. Monotonicity of a new quantity under two-dimensional Ricci flow, closely related to the parabolic frequency functional, is derived as well.

math.DG↗
arXiv2016

An alternative proof of lower bounds for the first eigenvalue on manifolds

Recently, Andrews and Clutterbuck [AC13] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [AC13]. More precisely, following Ni's method ([Ni13, Section 6]) we give an elliptic proof of this theorem.

math.DG↗
arXiv2015

Moduli of Continuity for Viscosity Solutions on Manifolds

We establish the estimates of modulus of continuity for viscosity solutions of nonlinear evolution equations on manifolds, extending previous work of B. Andrews and J. Clutterbuck for regular solutions on manifolds \cite{AC3} and the first author's recent work for viscosity solutions in Euclidean spaces \cite{me1}.

math.AP↗