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Qiaoling Wang

Publications and source records attributed to Qiaoling Wang.

17 recordsLinked to original sources
arXiv2023

Gleam: An RDMA-accelerated Multicast Protocol for Datacenter Networks

RDMA has been widely adopted for high-speed datacenter networks. However, native RDMA merely supports one-to-one reliable connection, which mismatches various applications with group communication patterns (e.g., one-to-many). While there are some multicast enhancements to address it, they all fail to simultaneously achieve optimal multicast forwarding and fully unleash the distinguished RDMA capabilities. In this paper, we present Gleam, an RDMA-accelerated multicast protocol that simultaneously supports optimal multicast forwarding, efficient utilization of the prominent RDMA capabilities, and compatibility with the commodity RNICs. At its core, Gleam re-purposes the existing RDMA RC logic with careful switch coordination as an efficient multicast transport. Gleam performs the one-to-many connection maintenance and many-to-one feedback aggregation, based on an extended multicast forwarding table structure, to achieve integration between standard RC logic and in-fabric multicast. We implement a fully functional Gleam prototype. With extensive testbed experiments and simulations, we demonstrate Gleam's significant improvement in accelerating multicast communication of realistic applications. For instance, Gleam achieves 2.9X lower communication time of an HPC benchmark application and 2.7X higher data replication throughput.

cs.NI↗
arXiv2021

Estimates for eigenvalues of the Neumann and Steklov problems

We prove Li-Yau-Kröger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a biharmonic Steklov problem and of the Laplacian, which directly implies two sharp Reilly-type inequalities for the corresponding first nonzero eigenvalue.

math.DG↗
arXiv2020

NetReduce: RDMA-Compatible In-Network Reduction for Distributed DNN Training Acceleration

We present NetReduce, a novel RDMA-compatible in-network reduction architecture to accelerate distributed DNN training. Compared to existing designs, NetReduce maintains a reliable connection between end-hosts in the Ethernet and does not terminate the connection in the network. The advantage of doing so is that we can fully reuse the designs of congestion control and reliability in RoCE. In the meanwhile, we do not need to implement a high-cost network protocol processing stack in the switch, as IB does. The prototype implemented by using FPGA is an out-of-box solution without modifying commodity devices such as NICs or switches. For the coordination between the end-host and the switch, NetReduce customizes the transport protocol only on the first packet in a data message to comply with RoCE v2. The special status monitoring module is designed to reuse the reliability mechanism of RoCE v2 for dealing with packet loss. A message-level credit-based flow control algorithm is also proposed to fully utilize bandwidth and avoid buffer overflow. We study the effects of intra bandwidth on the training performance in multi-machines multi-GPUs scenario and give sufficient conditions for hierarchical NetReduce to outperform other algorithms. We also extend the design from rack-level aggregation to more general spine-leaf topology in the data center. NetReduce accelerates the training up to 1.7x and 1.5x for CNN-based CV and transformer-based NLP tasks, respectively. Simulations on large-scale systems indicate the superior scalability of NetReduce to the state-of-the-art ring all-reduce.

cs.NI↗
arXiv2020

Sharp Lower Bounds for the First Eigenvalues of the Bi-Laplace Operator

We obtain sharp lower bounds for the first eigenvalue of four types of eigenvalue problem defined by the bi-Laplace operator on compact manifolds with boundary and determine all the eigenvalues and the corresponding eigenfunctions of a Wentzell-type bi-Laplace problem on Euclidean balls.

math.AP↗
arXiv2020

On Ashbaugh-Benguria's Conjecture about Lower Order Dirichlet Eigenvalues of the Laplacian

In this paper, we prove an isoperimetric inequality for lower order eigenvalues of the Dirichlet Laplacian on bounded domains of a Euclidean space which strengthens the well-known Ashbaugh-Beguria inequality conjectured by Payne-Pólya-Weinberger on the ratio of the first two Dirichlet eigenvalues and makes an important step toward the proof of a conjecture by Ashbaugh-Benguria.

math.AP↗
arXiv2018

Pohozaev identity for the anisotropic $p$-Laplacian and estimates of torsion function

In this paper we prove the Pohozaev identity for the weighted anisotropic $p$-Laplace operator. As an application of our identity, we deduce the nonexistence of nontrivial solutions of the Dirichlet problem for the weighted anisotropic $p$-Laplacian in star-shaped domains of $\mathbb{R}^n$. We also provide an upper bound estimate for the first Dirichet eigenvalue of the anisotropic $p$-Laplacian on bounded domains of $\mathbb{R}^n$, some sharp estimates for the torsion function of compact manifolds with boundary and a nonexistence result for the solutions of the Laplace equation on closed Riemannian manifolds.

math.AP↗
arXiv2015

The Gagliardo-Nirenberg inequality on metric measure spaces

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Gagliardo-Nirenberg inequality with the same exponent $n$ $(n\geq 2)$, then it has exactly the $n$-dimensional volume growth. Besides, two interesting applications have also been given. The one is that we show that if a complete $n$-dimensional Finsler manifold of nonnegative $n$-Ricci curvature satisfies the Gagliardo-Nirenberg inequality with the sharp constant, then its flag curvature is identically zero. The other one is that we give an alternative proof to Mao's main result in [23] for smooth metric measure spaces with nonnegative weighted Ricci curvature.

math.DG↗
arXiv2015

Eigenvalues of the Wentzell-Laplace Operator and of the Fourth Order Steklov Problems

We prove a sharp upper bound and a lower bound for the first nonzero eigenvalue of the Wentzell-Laplace operator on compact manifolds with boundary and an isoperimetric inequality for the same eigenvalue in the case where the manifold is a bounded domain in a Euclidean space. We study some fourth order Stekolv problems and obtain isoperimetric upper bound for the first eigenvalue of them. We also find all the eigenvalues and eigenfunctions for two kind of fourth order Stekolv problems on a Euclidean ball.

math.AP↗
arXiv2015

On the H-almost ricci soliton

We introduce the concept {\it $h$-almost Ricci soliton} which extends naturally the {\it almost Ricci soliton} by Pigola-Rigoli-Rimoldi-Setti and show that a compact nontrivial $h$-almost Ricci soliton of dimension no less than three with $h$ having defined signal and constant scalar curvature is isometric to a standard sphere with the potential function well determined. We also consider the {\it $h$-Ricci soliton} which is a particular case of the $h$-almost Ricci soliton and a generalization of the {\it Ricci soliton} and give characterizations for a special class of gradient $h$-Ricci solitons.

math.DG↗
arXiv2010

Inequalities for eigenvalues of the buckling problem of arbitrary order

This paper studies eigenvalues of the buckling problem of arbitrary order on bounded domains in Euclidean spaces and spheres. We prove universal bounds for the k-th eigenvalue in terms of the lower ones independent of the domains. Our results strengthen the recent work in [28] and generalize Cheng-Yang's recent estimates [16] on the buckling eigenvalues of order two to arbitrary order.

math.DG↗
arXiv2010

Estimates for eigenvalues of a system of of elliptic equations and of the biharmonic operator

Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &Δ{\mathbf u}+ α{\rm grad}(\text{div}{\mathbf u})=-σ{\mathbf u}, \ \text{in $Ω$}, &{\mathbf u}|_{\partial Ω}={\mathbf 0}. \aligned . $$ Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, we obtain an upper bound on the $(k+1)^{\text{th}}$ eigenvalue $σ_{k+1}$. We also obtain sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator on compact manifolds with boundary and positive Ricci curvature.

math.DG↗
arXiv2010

Inequalities for Eigenvalues of the Buckling Problem of Higher Orders

This paper studies eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We prove universal bounds for the $k$-th eigenvalue in terms of the lower ones independent of the domains. Our results strengthens the recent work by Jost, Li-Jost, Wang and Xia and generalizes Cheng-Yang's recent estimates on the buckling eigenvalues of order two to arbitrary order.

math.AP↗
arXiv2010

Inequalities for the Steklov Eigenvalues

This paper studies eigenvalues of some Steklov problems. Among other things, we show the following sharp estimtes. Let $Ω$ be a bounded smooth domain in an $n(\geq 2)$-dimensional Hadamard manifold an let $0=λ_0 < λ_1\leq λ_2\leq ... $ denote the eigenvalues of the Steklov problem: $Δu=0$ in $Ω$ and $(\partial u)/(\partial ν)=λu$ on $\partial Ω$. Then $\sum_{i=1}^{n} λ^{-1}_i \geq (n^2|Ω|)/(|\partialΩ|) $ with equality holding if and only if $Ω$ is isometric to an $n$-dimensional Euclidean ball. Let $M$ be an $n(\geq 2)$-dimensional compact connected Riemannian manifold with boundary and non-negative Ricci curvature. Assume that the mean curvature of $\pa M$ is bounded below by a positive constant $c$ and let $q_1$ be the first eigenvalue of the Steklov problem: $ Δ^2 u= 0$ in $ M$ and $u= (\partial^2 u)/(\partial ν^2) -q(\partial u)/(\partial ν) =0$ on $ \partial M$. Then $q_1\geq c$ with equality holding if and only if $M $ is isometric to a ball of radius $1/c$ in ${\bf R}^n$.

math.SP↗
arXiv2009

Universal Bounds for Eigenvalues of the Polyharmonic Operators

We study eigenvalues of polyharmonic operators on compact Riemannian manifolds with boundary (possibly empty). In particular, we prove a universal inequality for the eigenvalues of the polyharmonic operators on compact domains in a Euclidean space. This inequality controls the $k$th eigenvalue by the lower eigenvalues, independently of the particular geometry of the domain. Our inequality is sharper than the known Payne-Pólya-Weinberg type inequality and also covers the important Yang inequality on eigenvalues of the Dirichlet Laplacian. We also prove universal inequalities for the lower order eigenvalues of the polyharmonic operator on compact domains in a Euclidean space which in the case of the biharmonic operator and the buckling problem strengthen the estimates obtained by Ashbaugh. Finally, we prove universal inequalities for eigenvalues of polyharmonic operators of any order on compact domains in the sphere.

math.DG↗
arXiv2006

Photodetachment of H$^{-}$ by a Short Laser Pulse in Crossed Static Electric and Magnetic Fields

We present a detailed quantum mechanical treatment of the photodetachment of H$^{-}$ by a short laser pulse in the presence of crossed static electric and magnetic fields. An exact analytic formula is presented for the final state electron wave function (describing an electron in both static electric and magnetic fields and a short laser pulse of arbitrary intensity). In the limit of a weak laser pulse, final state electron wave packet motion is examined and related to the closed classical electron orbits in crossed static fields predicted by Peters and Delos [Phys. Rev. A \textbf{47}, 3020 (1993)]. Owing to these closed orbit trajectories, we show that the detachment probability can be modulated, depending on the time delay between two laser pulses and their relative phase, thereby providing a means to partially control the photodetachment process. In the limit of a long, weak pulse (i.e., a monochromatic radiation field) our results reduce to those of others; however, for this case we analyze the photodetachment cross section numerically over a much larger range of electron kinetic energy (i.e., up to 500 cm$^{-1}$) than in previous studies and relate the detailed structures both analytically and numerically to the above-mentioned, closed classical periodic orbits.

physics.atom-ph↗