arXiv subjects

Xiong Wang

Publications and source records attributed to Xiong Wang.

At least 73 records · Page 4Linked to original sources

arXiv2021

Mean square stability of stochastic theta method for stochastic differential equations driven by fractional Brownian motion

In this paper, we study the mean-square stability of the solution and its stochastic theta scheme for the following stochastic differential equations drive by fractional Brownian motion with Hurst parameter $H\in (\frac 12,1)$: $$ dX(t)=f(t,X(t))dt+g(t,X(t))dB^{H}(t). $$ Firstly, we consider the special case when $f(t,X)=-λκt^{κ-1}X$ and $g(t,X)=μX$. The solution is explicit and is mean-square stable when $κ\geq 2H$. It is proved that if the parameter $2H\leqκ\le 3/2$ and $\frac{\sqrt{3/2}\cdot e}{\sqrt{3/2}\cdot e+1} (\approx 0.77)\leq θ\leq 1$ or $κ>3/2$ and $1/2<θ\le 1$, the stochastic theta method reproduces the mean-square stability; and that if $0<θ<\frac 12$, the numerical method does not preserve this stability unconditionally. Secondly, we study the stability of the solution and its stochastic theta scheme for nonlinear equations. Due to the presence of long memory, even the problem of stability in the mean square sense of the solution has not been well studied since the conventional techniques powerful for stochastic differential equations driven by Brownian motion are no longer applicable. Let alone the stability of numerical schemes. We need to develop a completely new set of techniques to deal with this difficulty. Numerical examples are carried out to illustrate our theoretical results.

math.NA↗

arXiv2021

Intermittency properties for a large class of stochastic PDEs driven by fractional space-time noises

In this paper, we study intermittency properties for various stochastic PDEs with varieties of space time Gaussian noises via matching upper and lower moment bounds of the solution. Due to the absence of the powerful Feynman Kac formula, the lower moment bounds have been missing for many interesting equations except for the stochastic heat equation. This work introduces and explores the Feynman diagram formula for the moments of the solution and the small ball nondegeneracy for the Green's function to obtain the lower bounds for all moments which match the upper moment bounds. Our upper and lower moments are valid for various interesting equations, including stochastic heat equations, stochastic wave equations, stochastic heat equations with fractional Laplcians, and stochastic diffusions which are both fractional in time and in space.

math.PR↗

arXiv2021

Efficient Conformer with Prob-Sparse Attention Mechanism for End-to-EndSpeech Recognition

End-to-end models are favored in automatic speech recognition (ASR) because of their simplified system structure and superior performance. Among these models, Transformer and Conformer have achieved state-of-the-art recognition accuracy in which self-attention plays a vital role in capturing important global information. However, the time and memory complexity of self-attention increases squarely with the length of the sentence. In this paper, a prob-sparse self-attention mechanism is introduced into Conformer to sparse the computing process of self-attention in order to accelerate inference speed and reduce space consumption. Specifically, we adopt a Kullback-Leibler divergence based sparsity measurement for each query to decide whether we compute the attention function on this query. By using the prob-sparse attention mechanism, we achieve impressively 8% to 45% inference speed-up and 15% to 45% memory usage reduction of the self-attention module of Conformer Transducer while maintaining the same level of error rate.

cs.SD↗

arXiv2021

Mean Field Equilibrium in Multi-Armed Bandit Game with Continuous Reward

Mean field game facilitates analyzing multi-armed bandit (MAB) for a large number of agents by approximating their interactions with an average effect. Existing mean field models for multi-agent MAB mostly assume a binary reward function, which leads to tractable analysis but is usually not applicable in practical scenarios. In this paper, we study the mean field bandit game with a continuous reward function. Specifically, we focus on deriving the existence and uniqueness of mean field equilibrium (MFE), thereby guaranteeing the asymptotic stability of the multi-agent system. To accommodate the continuous reward function, we encode the learned reward into an agent state, which is in turn mapped to its stochastic arm playing policy and updated using realized observations. We show that the state evolution is upper semi-continuous, based on which the existence of MFE is obtained. As the Markov analysis is mainly for the case of discrete state, we transform the stochastic continuous state evolution into a deterministic ordinary differential equation (ODE). On this basis, we can characterize a contraction mapping for the ODE to ensure a unique MFE for the bandit game. Extensive evaluations validate our MFE characterization, and exhibit tight empirical regret of the MAB problem.

cs.MA↗

arXiv2021

Joint D2D Collaboration and Task Offloading for Edge Computing: A Mean Field Graph Approach

Mobile edge computing (MEC) facilitates computation offloading to edge server, as well as task processing via device-to-device (D2D) collaboration. Existing works mainly focus on centralized network-assisted offloading solutions, which are unscalable to scenarios involving collaboration among massive users. In this paper, we propose a joint framework of decentralized D2D collaboration and efficient task offloading for a large-population MEC system. Specifically, we utilize the power of two choices for D2D collaboration, which enables users to beneficially assist each other in a decentralized manner. Due to short-range D2D communication and user movements, we formulate a mean field model on a finite-degree and dynamic graph to analyze the state evolution of D2D collaboration. We derive the existence, uniqueness and convergence of the state stationary point so as to provide a tractable collaboration performance. Complementing this D2D collaboration, we further build a Stackelberg game to model users' task offloading, where edge server is the leader to determine a service price, while users are followers to make offloading decisions. By embedding the Stackelberg game into Lyapunov optimization, we develop an online offloading and pricing scheme, which could optimize server's service utility and users' system cost simultaneously. Extensive evaluations show that our D2D collaboration can mitigate users' workloads by $73.8\%$ and task offloading can achieve high energy efficiency.

cs.DC↗

arXiv2021

An Online Scheduling Algorithm for Energy Minimization in Wireless Powered Mobile Edge Computing Networks

The integration of Mobile Edge Computing (MEC) and Wireless Power Transfer (WPT), which is usually referred to as Wireless Powered Mobile Edge Computing (WP-MEC), has been recognized as a promising technique to enhance the lifetime and computation capacity of wireless devices (WDs). Compared to the conventional battery-powered MEC networks, WP-MEC brings new challenges to the computation scheduling problem because we have to jointly optimize the resource allocation in WPT and computation offloading. In this paper, we consider the energy minimization problem for WP-MEC networks with multiple WDs and multiple access points. We design an online algorithm by transforming the original problem into a series of deterministic optimization problems based on the Lyapunov optimization theory. To reduce the time complexity of our algorithm, the optimization problem is relaxed and decomposed into several independent subproblems. After solving each subproblem, we adjust the computed values of variables to obtain a feasible solution. Extensive simulations are conducted to validate the performance of the proposed algorithm.

cs.NI↗

arXiv2021

Ferromagnetism in 2D Vanadium Diselenide

Two-dimensional (2D) Van der Waals ferromagnets carry the promise of ultimately miniature spintronics and information storage devices. Among the newly discovered 2D ferromagnets all inherit the magnetic ordering from their bulk ancestors. Here we report a new 2D ferromagnetic semiconductor at room temperature, 2H phase vanadium diselenide (VSe2) which show ferromagnetic at 2D form only. This unique 2D ferromagnetic semiconductor manifests an enhanced magnetic ordering owing to structural anisotropy at 2D limit.

cond-mat.mtrl-sci↗

arXiv2021

Stochastic Heat Equation with general noise

In this paper, we study a nonlinear one spatial dimensional stochastic heat equations driven by Gaussian noise: $\frac{\partial u }{\partial t}=\frac{\partial^2 u }{\partial x^2}+σ(u )\dot{W} $, where $\dot{W} $ is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in(\frac 14,\frac 12)$. We remove a critical and unnatural condition $σ(0)=0$ previously imposed in a recent paper by Hu, Huang, Lê, Nualart and Tindel. The idea is to work on a weighted space $\mathcal{Z}_{λ,T}^p$ for some power decay weight $λ(x)=c_H(1+|x|^2)^{H-1}$. We obtain the weak existence of solution. With additional decay conditions on $σ$ we obtain the existence of strong solution and the pathwise uniqueness of the strong solution. The reason to introduce the weight function is that the solution $u(t,x)$ may explode as $|x|\rightarrow \infty$ when the "diffusion coefficient" $σ(u)$ does not satisfy $σ(0)=0$ regardless of the initial condition. This motivates us to study the exact asympotics of the solution $u_{\rm add}(t,x)$ as $t$ and $x$ go to infinity when $σ(u)=1$ and when the initial condition $u_0(x)\equiv 0$. In particular, we find the exact growth of $\sup_{|x|\leq L}{|u_{\rm add}(t,x)|}$. Furthermore, we find the sharp growth rate for the Hölder coefficients, namely, $\sup_{|x|\leq L} \frac{| u_{\rm add}(t,x+h)-u_{\rm add}(t,x)|}{|h|^β}$ and $\sup_{|x|\leq L} \frac{| u_{\rm add}(t+τ,x)-u_{\rm add}(t,x)|}{τ^α}$. These results are interesting and fundamental themselves.

math.PR↗

arXiv2020

Cascade RNN-Transducer: Syllable Based Streaming On-device Mandarin Speech Recognition with a Syllable-to-Character Converter

End-to-end models are favored in automatic speech recognition (ASR) because of its simplified system structure and superior performance. Among these models, recurrent neural network transducer (RNN-T) has achieved significant progress in streaming on-device speech recognition because of its high-accuracy and low-latency. RNN-T adopts a prediction network to enhance language information, but its language modeling ability is limited because it still needs paired speech-text data to train. Further strengthening the language modeling ability through extra text data, such as shallow fusion with an external language model, only brings a small performance gain. In view of the fact that Mandarin Chinese is a character-based language and each character is pronounced as a tonal syllable, this paper proposes a novel cascade RNN-T approach to improve the language modeling ability of RNN-T. Our approach firstly uses an RNN-T to transform acoustic feature into syllable sequence, and then converts the syllable sequence into character sequence through an RNN-T-based syllable-to-character converter. Thus a rich text repository can be easily used to strengthen the language model ability. By introducing several important tricks, the cascade RNN-T approach surpasses the character-based RNN-T by a large margin on several Mandarin test sets, with much higher recognition quality and similar latency.

cs.SD↗

arXiv2020

Accent and Speaker Disentanglement in Many-to-many Voice Conversion

This paper proposes an interesting voice and accent joint conversion approach, which can convert an arbitrary source speaker's voice to a target speaker with non-native accent. This problem is challenging as each target speaker only has training data in native accent and we need to disentangle accent and speaker information in the conversion model training and re-combine them in the conversion stage. In our recognition-synthesis conversion framework, we manage to solve this problem by two proposed tricks. First, we use accent-dependent speech recognizers to obtain bottleneck features for different accented speakers. This aims to wipe out other factors beyond the linguistic information in the BN features for conversion model training. Second, we propose to use adversarial training to better disentangle the speaker and accent information in our encoder-decoder based conversion model. Specifically, we plug an auxiliary speaker classifier to the encoder, trained with an adversarial loss to wipe out speaker information from the encoder output. Experiments show that our approach is superior to the baseline. The proposed tricks are quite effective in improving accentedness and audio quality and speaker similarity are well maintained.

cs.SD↗

arXiv2020

The SLT 2021 children speech recognition challenge: Open datasets, rules and baselines

Automatic speech recognition (ASR) has been significantly advanced with the use of deep learning and big data. However improving robustness, including achieving equally good performance on diverse speakers and accents, is still a challenging problem. In particular, the performance of children speech recognition (CSR) still lags behind due to 1) the speech and language characteristics of children's voice are substantially different from those of adults and 2) sizable open dataset for children speech is still not available in the research community. To address these problems, we launch the Children Speech Recognition Challenge (CSRC), as a flagship satellite event of IEEE SLT 2021 workshop. The challenge will release about 400 hours of Mandarin speech data for registered teams and set up two challenge tracks and provide a common testbed to benchmark the CSR performance. In this paper, we introduce the datasets, rules, evaluation method as well as baselines.

cs.SD↗

arXiv2020

IEEE SLT 2021 Alpha-mini Speech Challenge: Open Datasets, Tracks, Rules and Baselines

The IEEE Spoken Language Technology Workshop (SLT) 2021 Alpha-mini Speech Challenge (ASC) is intended to improve research on keyword spotting (KWS) and sound source location (SSL) on humanoid robots. Many publications report significant improvements in deep learning based KWS and SSL on open source datasets in recent years. For deep learning model training, it is necessary to expand the data coverage to improve the robustness of model. Thus, simulating multi-channel noisy and reverberant data from single-channel speech, noise, echo and room impulsive response (RIR) is widely adopted. However, this approach may generate mismatch between simulated data and recorded data in real application scenarios, especially echo data. In this challenge, we open source a sizable speech, keyword, echo and noise corpus for promoting data-driven methods, particularly deep-learning approaches on KWS and SSL. We also choose Alpha-mini, a humanoid robot produced by UBTECH equipped with a built-in four-microphone array on its head, to record development and evaluation sets under the actual Alpha-mini robot application scenario, including noise as well as echo and mechanical noise generated by the robot itself for model evaluation. Furthermore, we illustrate the rules, evaluation methods and baselines for researchers to quickly assess their achievements and optimize their models.

cs.SD↗

arXiv2018

Dielectric Metasurface for Generating Broadband Millimeter Wave Orbital Angular Momentum Beams

Electromagnetic waves carrying orbital angular momentum (OAM) have found many applications. This work reports a broadband millimeter wave OAM generator applying a dielectric metasurface with high-refractive-index dielectric elements distributed on a low-refractive-index substrate. Proper adjustment of the dimensions of the dielectric elements can make a broadband OAM generator from 53 to 70 GHz. OAM generators with different mode numbers are designed and validated by simulation. Such structures can find potential applications in high-capacity communications and imaging.

physics.app-ph↗

arXiv2016

Sensitive dependence and transitivity of fuzzified dynamical systems

This paper proves that a set-valued dynamical system is sensitively dependent on initial conditions (resp., $\mathscr{F}$-sensitive, multi-sensitive) if and only if its $g$-fuzzification is sensitively dependent on initial conditions (resp., $\mathscr{F}$-sensitive, multi-sensitive), where $\mathscr{F}$ is a Furstenberg family. As an application, it is shown that there exists a sensitive dynamical system whose $g$-fuzzification does not have such sensitive dependence for any $g$ in a certain domain. Moreover, a sufficient condition ensuring that the $g$-fuzzification of every nontrivial dynamical system is not transitive is obtained. These give an answer to a question posed in \cite[J. Kupka, Information Sciences, {\bf 279} (2014): 642--653]{Kupka2014}.

math.DS↗

arXiv2016

On the large deviations theorem of weaker types

In this paper, we introduce the concepts of the large deviations theorem of weaker types, i.e., type I, type I', type II, type II', type III, and type III', and present a systematic study of the ergodic and chaotic properties of dynamical systems satisfying the large eviations theorem of various types. Some characteristics of the ergodic measure are obtained and then applied to prove that every dynamical system satisfying the large deviations theorem of type I' is ergodic, which is equivalent to the large deviations theorem of type II' in this regard, and that every uniquely ergodic dynamical system restricted on its support satisfies the large deviations theorem. Moreover, we prove that every dynamical system satisfying the large deviations theorem of type III is an $E$-system. Finally, we show that a dynamical system satisfying the central limit theorem, introduced in [Y. Niu, Y. Wang, Statist. Probab. Lett., {\bf 80} (2010), 1180--1184], does not exist.

math.DS↗

arXiv2016

Topological dynamics of Zadeh's extension on the space of upper semi-continuous fuzzy sets

In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of all upper semi-continuous fuzzy sets with the level-wise metric are obtained. In particular, it is proved that a dynamical system is weakly mixing (resp., mildly mixing, weakly mixing and $\mathbf{a}$-transitive, equicontinuous, uniformly rigid) if and only if the Zadeh's extension is transitive (resp., mildly mixing, $\mathbf{a}$-transitive, equicontinuous, uniformly rigid).

math.DS↗

arXiv2012

Constructing a chaotic system with any number of equilibria

In the chaotic Lorenz system, Chen system and Rössler system, their equilibria are unstable and the number of the equilibria are no more than three. This paper shows how to construct some simple chaotic systems that can have any preassigned number of equilibria. First, a chaotic system with no equilibrium is presented and discussed. Then, a methodology is presented by adding symmetry to a new chaotic system with only one stable equilibrium, to show that chaotic systems with any preassigned number of equilibria can be generated. By adjusting the only parameter in these systems, one can further control the stability of their equilibria. This result reveals an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of a chaotic system.

nlin.CD↗

arXiv2011

A chaotic system with only one stable equilibrium

If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is actually chaotic? Although chaos theory for three-dimensional autonomous systems has been intensively and extensively studied since the time of Lorenz in the 1960s, and the theory has become quite mature today, it seems that no one would anticipate a possibility of finding a three-dimensional autonomous quadratic chaotic system with only one stable equilibrium. The discovery of the new system, to be reported in this Letter, is indeed striking because for a three-dimensional autonomous quadratic system with a single stable node-focus equilibrium, one typically would anticipate non-chaotic and even asymptotically converging behaviors. Although the new system is not of saddle-focus type, therefore the familiar Ši'lnikov homoclinic criterion is not applicable, it is demonstrated to be chaotic in the sense of having a positive largest Lyapunov exponent, a fractional dimension, a continuous broad frequency spectrum, and a period-doubling route to chaos.

nlin.CD↗