arXiv subjects

Xu Wang

Publications and source records attributed to Xu Wang.

At least 433 records · Page 24Linked to original sources

arXiv2019

On parareal algorithms for semilinear parabolic Stochastic PDEs

Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes, and have been designed to achieve a `parallel in real time' implementation. In this work, the fine integrator is given by the exponential Euler scheme. Two choices for the coarse integrator are considered: the linear implicit Euler scheme, and the exponential Euler scheme. The influence on the performance of the parareal algorithm, of the choice of the coarse integrator, of the regularity of the noise, and of the number of parareal iterations, is investigated, with theoretical analysis results and with extensive numerical experiments.

math.NA↗

arXiv2019

An Improved Dipole Extraction Method From Magnitude-Only Electromagnetic-Field Data

Infinitesimal electric and magnetic dipoles are widely used as an equivalent radiating source model. In this paper, an improved method for dipole extraction from magnitude-only electromagnetic-field data based on genetic algorithm and back-and-forth iteration algorithm [1] is proposed. Compared with conventional back-and-forth iteration algorithm, this method offers an automatic flow to extract the equivalent dipoles without prior decision of the type, position, orientation and number of dipoles. It can be easily applied to electromagnetic-field data on arbitrarily shaped surfaces and minimize the number of required dipoles. The extracted dipoles can be close to original radiating structure, thus being physical. Compared with conventional genetic algorithm based method, this method reduces the optimization time and will not easily get trapped into local minima during optimization, thus being more robust. This method is validated by both simulation data and measurement data and its advantages are proved. The potential application of this method in phase retrieval is also discussed.

eess.SP↗

arXiv2018

Combating Uncertainty with Novel Losses for Automatic Left Atrium Segmentation

Segmenting left atrium in MR volume holds great potentials in promoting the treatment of atrial fibrillation. However, the varying anatomies, artifacts and low contrasts among tissues hinder the advance of both manual and automated solutions. In this paper, we propose a fully-automated framework to segment left atrium in gadolinium-enhanced MR volumes. The region of left atrium is firstly automatically localized by a detection module. Our framework then originates with a customized 3D deep neural network to fully explore the spatial dependency in the region for segmentation. To alleviate the risk of low training efficiency and potential overfitting, we enhance our deep network with the transfer learning and deep supervision strategy. Main contribution of our network design lies in the composite loss function to combat the boundary ambiguity and hard examples. We firstly adopt the Overlap loss to encourage network reduce the overlap between the foreground and background and thus sharpen the predictions on boundary. We then propose a novel Focal Positive loss to guide the learning of voxel-specific threshold and emphasize the foreground to improve classification sensitivity. Further improvement is obtained with an recursive training scheme. With ablation studies, all the introduced modules prove to be effective. The proposed framework achieves an average Dice of 92.24 in segmenting left atrium with pulmonary veins on 20 testing volumes.

cs.CV↗

arXiv2018

Test of Covariance and Correlation Matrices

Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for some common one-sample tests, such as the tests of sphericity, identity and compound symmetry, and the $K$-sample tests of multivariate equality of covariance or correlation matrices. The proposed method is very flexible in the sense that it does not assume any underlying distributions and data generation models. Moreover, it allows data to have different marginal distributions in both the one-sample identity and $K$-sample tests. Through real datasets and extensive simulations, we demonstrate that the proposed method performs well in terms of empirical type I error and power in a variety of hypothesis testing situations in which data of different sizes and dimensions are generated using different distributions and generation models.

stat.ME↗

arXiv2018

A class of non-matchable distributive lattices

The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$-transformation directed graph of the graph. A finite distributive lattice is matchable if its Hasse diagram is isomorphic to a $Z$-transformation directed graph of a plane weakly elementary bipartite graph, otherwise non-matchable. We introduce the meet-irreducible cell with respect to a perfect matching of a plane (weakly) elementary bipartite graph and give its equivalent characterizations. Using these, we extend a result on non-matchable distributive lattices, and obtain a class of new non-matchable distributive lattices.

math.CO↗

arXiv2018

Alpha decay in intense laser fields: Calculations using realistic nuclear potentials

We calculate the effect of intense laser fields on nuclear alpha decay processes, using realistic and quantitative nuclear potentials. We show that alpha decay rates can indeed be modified by strong laser fields to some finite extent. We also predict that alpha decays with lower decay energies are relatively easier to be modified than those with higher decay energies, due to longer tunneling paths for the laser field to act on. Furthermore, we predict that modifications to angle-resolved penetrability are easier to achieve than modifications to angle-integrated penetrability.

physics.atom-ph↗

arXiv2018

On the longitudinal momentum of the electron at the tunneling exit

The longitudinal momentum of the electron at the tunneling exit is a useful quantity to make sense of the tunneling ionization process. It was usually assumed to be zero from a classical argument, but recent experiments show that it must be nonzero in order to explain the measured electron momentum distributions. In this article we show that the flow momentum of the probability fluid is a sensible quantum mechanical definition for tunneling-exit momentum, and it can be (and in general is) nonzero at the tunneling exit point where the kinetic energy is zero by definition. We show that this longitudinal momentum is nonzero even in the static or adiabatic limit, and this nonzero momentum is a purely quantum mechanical effect determined by the shape of the wave function in the vicinity of the tunneling exit point. Nonadiabaticity or finite wavelength may increase this momentum substantially, and the detailed value depends on both the atomic and the laser parameters.

physics.atom-ph↗

arXiv2018

A fixed-point model for semi-persistent scheduling of vehicular safety messages

In this paper, we focus on the performance analysis of a semi-persistent scheduling scheme for vehicular safety communications, motivated by the Mode 4 medium access control protocol in 3GPP Release 14 for Cellular-V2X. An analytical model is built and a fixed point method is used to calculate the collision probability and average delay in both fully connected and partially connected cases under the assumption of perfect PHY performance. We use Monte Carlo simulation to verify the results obtained in the analytical model. The simulation results show that our analytical model can give a good estimation of the collision probability and average delay. We verify that a trade-off between delay and collision probability can be achieved with a flexible resource block selection. Monte Carlo simulation results show that with the flexible resource selection scheme average delay can be shortened significantly with only a small compromise in collision probability.

cs.NI↗

arXiv2018

On-chip multipurpose microwave frequency identification

We demonstrate a multipurpose microwave frequency identification solution that is implemented based on a photonic integrated chip and is able to identify different types of microwave signals, including single-frequency, multiple-frequency, chirped and frequency-hopping microwave signals. The key component is a thermally-tunable high-Q-factor silicon microring resonator which is used to implement the frequency-to-time mapping. The frequency measurement range is ultra-wide, from 1 to 30 GHz, with a high resolution of 375 MHz and a low measurement error of 237.3 MHz. This demonstration opens the door for future fully integrated solution for high speed, wideband and multipurpose signal identification with high resolution.

physics.app-ph↗

arXiv2018

Time-domain theory of atomic photoionization

We present a combined numerical and theoretical study of atomic photoionization in the time domain. We show how a photoelectron wave packet rapidly changes its shape after being emitted, from a complex multi-peak structure to eventually a relatively simple single-peak structure. This time-domain shape evolution provides information beyond the time-dependent average position of the wave packet, which has been used to retrieve the Wigner time delay. For few-cycle laser pulses, the asymptotic velocity of the photoelectron can be different from long-pulse-based expectations due to non-negligible changes of the dipole matrix element within the spectra of the laser pulses.

physics.atom-ph↗

arXiv2018

Parareal exponential $θ$-scheme for longtime simulation of stochastic Schrödinger equations with weak damping

A parareal algorithm based on an exponential $θ$-scheme is proposed for the stochastic Schrödinger equation with weak damping and additive noise. It proceeds as a two-level temporal parallelizable integrator with the exponential $θ$-scheme as the propagator on the coarse grid. The proposed algorithm in the linear case increases the convergence order from one to $k$ for $θ\in[0,1]\setminus\{\frac12\}$. In particular, the convergence order increases to $2k$ when $θ=\frac12$ due to the symmetry of the algorithm. Furthermore, the algorithm is proved to be suitable for longtime simulation based on the analysis of the invariant distributions for the exponential $θ$-scheme. The convergence condition for longtime simulation is also established for the proposed algorithm in the nonlinear case, which indicates the superiority of implicit schemes. Numerical experiments are dedicated to illustrate the best choice of the iteration number $k$, as well as the convergence order of the algorithm for different choices of $θ$.

math.NA↗

arXiv2018

Strong convergence rate of Runge--Kutta methods and simplified step-$N$ Euler schemes for SDEs driven by fractional Brownian motions

This paper focuses on the strong convergence rate of both Runge--Kutta methods and simplified step-$N$ Euler schemes for stochastic differential equations driven by multi-dimensional fractional Brownian motions with $H\in(\frac12,1)$. Based on the continuous dependence of both stage values and numerical schemes on driving noises, order conditions of Runge--Kutta methods are proposed for the optimal strong convergence rate $2H-\frac12$. This provides an alternative way to analyze the convergence rate of explicit schemes by adding `stage values' such that the schemes are comparable with Runge--Kutta methods. Taking advantage of this technique, the optimal strong convergence rate of simplified step-N Euler scheme is obtained, which gives an answer to a conjecture in $[3]$ when $H\in(\frac12,1)$. Numerical experiments verify the theoretial convergence rate.

math.NA↗

arXiv2018

A remark on the Alexandrov-Fenchel inequality

In this article, we give a complex-geometric proof of the Alexandrov-Fenchel inequality without using toric compactifications. The idea is to use the Legendre transform and develop the Brascamp-Lieb proof of the Prékopa theorem. New ingredients in our proof include an integration of Timorin's mixed Hodge-Riemann bilinear relation and a mixed norm version of Hörmander's $L^2$-estimate, which also implies a non-compact version of the Khovanskiĭ-Teissier inequality.

math.CV↗

arXiv2018

The impact of bundling licensed and unlicensed wireless service

Unlicensed spectrum has been viewed as a way to increase competition in wireless access and promote innovation in new technologies and business models. However, several recent papers have shown that the openness of such spectrum can also lead to it becoming over congested when used by competing wireless service providers (SPs). This in turn can result in the SPs making no profit and may deter them from entering the market. However, this prior work assumes that unlicensed access is a separate service from any service offered using licensed spectrum. Here, we instead consider the more common case were service providers bundle both licensed and unlicensed spectrum as a single service and offer this with a single price. We analyze a model for such a market and show that in this case SPs are able to gain higher profit than the case without bundling. It is also possible to get higher social welfare with bundling. Moreover, we explore the case where SPs are allowed to manage the customers' average percentage of time they receive service on unlicensed spectrum and characterize the social welfare gap between the profit maximizing and social welfare maximizing setting.

cs.GT↗

arXiv2017

Stochastic K-symplectic integrators for stochastic non-canonical Hamiltonian systems and applications to the Lotka--Volterra model

We give a theoretical framework of stochastic non-canonical Hamiltonian systems as well as their modified symplectic structure which is named stochastic K-symplectic structure. The framework can be applied to the study of the Lotka--Volterra model perturbed by external noises. In terms of internal properties of the stochastic Lotka--Volterra model, we propose different kinds of stochastic K-symplectic integrators which could inherit the positivity of the solution. The K-symplectic conditions are also obtained to ensure that the proposed schemes admit the same geometric structure as the original system. Besides, the first-order condition of the proposed schemes in $L^1(Ω)$ sense are given based on the uniform boundedness of both the exact solution and the numerical one. Several numerical examples are illustrated to verify above properties of proposed schemes compared with non-K-symplectic ones.

math.NA↗

arXiv2017

Virtual Detector Theory of Free-Particle Wave Packets

We apply a recently emerging "virtual detector" method to general free-particle wave packets. We discuss what is actually detected by a virtual detector and give analytical expressions in both the real space and the momentum space. We prove that in the asymptotic limit when the time difference between wave packet creation and detection is large, resembling real detection processes, the obtained differential momentum distribution is equivalent to Fourier transforming the free-particle wave packets. We further consider the situation with the presence of laser fields.

physics.atom-ph↗

arXiv2017

Notes on variation of Lefschetz star operator and $T$-Hodge theory

These notes were written to serve as an easy reference for \cite{Wang-AF}. All the results in this presentation are well-known (or quasi-well-known) theorems in Hodge theory. Our main purpose was to give a unified approach based on a variation formula of the Lefschetz star operator, following \cite{Wang-k}. It fits quite well with Timorin's $T$-Hodge theory, i.e. the Hodge theory on the space of differential forms divided by $T$ (i.e. forms like $T\wedge u$), where $T$ is a finite wedge product of Kähler forms.

math.CV↗

arXiv2017

Coordinating Collaborative Chat in Massive Open Online Courses

An earlier study of a collaborative chat intervention in a Massive Open Online Course (MOOC) identified negative effects on attrition stemming from a requirement for students to be matched with exactly one partner prior to beginning the activity. That study raised questions about how to orchestrate a collaborative chat intervention in a MOOC context in order to provide the benefit of synchronous social engagement without the coordination difficulties. In this paper we present a careful analysis of an intervention designed to overcome coordination difficulties by welcoming students into the chat on a rolling basis as they arrive rather than requiring them to be matched with a partner before beginning. The results suggest the most positive impact when experiencing a chat with exactly one partner rather than more or less. A qualitative analysis of the chat data reveals differential experiences between these configurations that suggests a potential explanation for the effect and raises questions for future research.

cs.CY↗