arXiv subjects

Jun Zheng

Publications and source records attributed to Jun Zheng.

At least 55 records · Page 3Linked to original sources

arXiv2022

ABODE-Net: An Attention-based Deep Learning Model for Non-intrusive Building Occupancy Detection Using Smart Meter Data

Occupancy information is useful for efficient energy management in the building sector. The massive high-resolution electrical power consumption data collected by smart meters in the advanced metering infrastructure (AMI) network make it possible to infer buildings' occupancy status in a non-intrusive way. In this paper, we propose a deep leaning model called ABODE-Net which employs a novel Parallel Attention (PA) block for building occupancy detection using smart meter data. The PA block combines the temporal, variable, and channel attention modules in a parallel way to signify important features for occupancy detection. We adopt two smart meter datasets widely used for building occupancy detection in our performance evaluation. A set of state-of-the-art shallow machine learning and deep learning models are included for performance comparison. The results show that ABODE-Net significantly outperforms other models in all experimental cases, which proves its validity as a solution for non-intrusive building occupancy detection.

cs.LG↗

arXiv2022

Exponential stabilization and continuous dependence of solutions on initial data in different norms for space-time-varying linear parabolic PDEs

For an arbitrary parameter $p\in [1,+\infty]$, we consider the problem of exponential stabilization in the spatial $L^{p}$-norm, and $W^{1,p}$-norm, respectively, for a class of anti-stable linear parabolic PDEs with space-time-varying coefficients in the absence of a Gevrey-like condition, which is often imposed on time-varying coefficients of PDEs and used to guarantee the existence of smooth (w.r.t. the time variable) kernel functions in the literature. Then, based on the obtained exponential stabilities, we show that the solution of the considered system depends continuously on the $L^{p}$-norm, and $W^{1,p}$-norm, respectively, of the initial data. In order to obtain time-independent (and thus sufficiently smooth) kernel functions without a Gevrey-like condition and deal with singularities arising in the case of $p\in[1,2)$, we apply a combinatorial method, i.e., the combination of backstepping and approximation of Lyapunov functionals (ALFs), to stabilize the considered system and establish the continuous dependence of solutions on initial data in different norms.

math.OC↗

arXiv2022

Effective suppression of parametric instabilities with decoupled broadband lasers in plasma

A theoretical analysis for the stimulated Raman scattering (SRS) instability driven by two laser beams with certain frequency difference is presented. It is found that strong coupling and enhanced SRS take place only when the unstable regions corresponding respectively to the two beams are overlapped in the wavenumber space. Hence a threshold of the beam frequency difference for their decoupling is found as a function of their intensity and plasma density. Based upon this, a strategy to suppress the SRS instability with decoupled broadband lasers (DBLs) is proposed. A DBL can be composed of tens or even hundreds of beamlets, where the beamlets are distributed uniformly in a broad spectrum range such as over 10\% of the central frequency. Decoupling among the beamlets is found due to the limited beamlet energy and suitable frequency difference between neighboring beamlets. Particle-in-cell simulations demonstrate that SRS can be almost completely suppressed with DBLs at the laser intensity $\sim10^{15}$ W/cm$^2$. Moreover, stimulated Brillouin scattering (SBS) will be suppressed simultaneously with DBLs as long as SRS is suppressed. DBLs can be attractive for driving inertial confined fusion.

physics.plasm-ph↗

arXiv2022

Towards the Maximum Traffic Demand and Throughput Supported by Relay-Assisted mmWave Backhaul Networks

This paper investigates the throughput performance issue of the relay-assisted mmWave backhaul network. The maximum traffic demand of small-cell base stations (BSs) and the maximum throughput at the macro-cell BS have been found in a tree-style backhaul network through linear programming under different network settings, which concern both the number of radio chains available on BSs and the interference relationship between logical links in the backhaul network. A novel interference model for the relay-assisted mmWave backhaul network in the dense urban environment is proposed, which demonstrates the limited interference footprint of mmWave directional communications. Moreover, a scheduling algorithm is developed to find the optimal scheduling for tree-style mmWave backhaul networks. Extensive numerical analysis and simulations are conducted to show and validate the network throughput performance and the scheduling algorithm.

cs.NI↗

arXiv2022

An efficient distributed scheduling algorithm for relay-assisted mmWave backhaul networks

In this paper, a novel distributed scheduling algorithm is proposed, which aims to efficiently schedule both the uplink and downlink backhaul traffic in the relay-assisted mmWave backhaul network with a tree topology. The handshaking of control messages, calculation of local schedules, and the determination of final valid schedule are all discussed. Simulation results show that the performance of the distributed algorithm can reach very close to the maximum traffic demand of the backhaul network, and it can also adapt to the dynamic traffic with sharp traffic demand change of small-cell BSs quickly and accurately.

cs.NI↗

arXiv2022

Ultra-compact Si/In$_2$O$_3$ hybrid plasmonic waveguide modulator with a high bandwidth beyond 40 GHz

Optical modulators are required to have high modulation bandwidths and a compact footprint. In this paper we experimentally demonstrate a novel Si/In$_2$O$_3$ hybrid plasmonic waveguide modulator, which is realized by an asymmetric directional coupler (ADC) consisting of a silicon photonic waveguide and a Si/In$_2$O$_3$ hybrid plasmonic waveguide. The optical signal is modulated by radio-frequency (RF) signal applied on the Au electrodes at the top of MOS capacitor and contacting the In$_2$O$_3$ thin film. The record-high modulation bandwidth of >40 GHz is realized by a silicon-doping-free metal-oxide-In$_2$O$_3$ capacitor integrated in a 3.5-$μ$m-long asymmetric directional coupler (ADC) for the first time.

physics.app-ph↗

arXiv2021

Microscopic analysis of the energy, momentum and spin distributions in a surface plasmon-polariton wave

We analyze the electromagnetic field near a plane interface between a conductive and a dielectric media, under conditions supporting surface plasmon-polariton (SPP) propagation. The conductive medium is described by the hydrodynamic electron-gas model that enables a consistent analysis of the field-induced variations of the electron density and velocity at the interface and its nearest vicinity. The distributions of electromagnetic dynamical characteristics: energy, energy flow, spin and momentum are calculated analytically and illustrated numerically, employing silver-vacuum interface as an example. A set of the "field" and material contributions to the energy, spin and momentum are explicitly identified and classified with respect to their physical origins and properties, and the orbital (canonical) and spin (Belinfante) momentum constituents are separately examined. In this context, a procedure for the spin-orbital momentum decomposition in the presence of free charges is proposed and substantiated. The microscopic results agree with the known phenomenological data but additionally show specific nanoscale structures in the near-interface behavior of the SPP energy and momentum, which can be deliberately created, controlled and used in nanotechnology applications.

physics.optics↗

arXiv2021

Relative Stability in the Sup-norm and Input-to-state Stability in the Spatial Sup-norm for Parabolic PDEs

In this paper, we introduce the notion of relative $\mathcal{K}$-equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturbances for nonlinear parabolic PDE systems. Based on the RKES, we prove the input-to-state stability (ISS) in the spatial sup-norm for a class of nonlinear parabolic PDEs with either Dirichlet or Robin boundary disturbances. Two examples, concerned respectively with a super-linear parabolic PDE with Robin boundary condition and a $1$-D parabolic PDE with a destabilizing term, are provided to illustrate the obtained ISS results. Besides, as an application of the notion of RKES, we conduct stability analysis for a class of parabolic PDEs in cascade coupled over the domain or on the boundary of the domain, in the spatial and time sup-norm, and in the spatial sup-norm, respectively. The technique of De Giorgi iteration is extensively used in the proof of the results presented in this paper.

math.OC↗

arXiv2020

A PDE--based Power Tracking Control of Heterogeneous TCL Populations

This chapter presents the development and the analysis of a scheme for aggregate power tracking control of heterogeneous populations of thermostatically controlled loads (TCLs) based on partial differential equations (PDEs) control theory and techniques. By employing a thermostat--based deadband control with forced switching in the operation of individual TCLs, the aggregated dynamics of TCL populations are governed by a pair of Fokker--Planck equations coupled via the actions located both on the boundaries and in the domain. The technique of input-output feedback linearization is used for the design of aggregate power tracking control, which results in a nonlinear system in a closed loop. As the considered setting is a problem with time-varying boundaries, well-posedness assessment and stability analysis are carried out to confirm the validity of the developed control scheme. A simulation study is contacted to evaluate the effectiveness and the performance of the proposed approach.

math.OC↗

arXiv2020

Approximations of Lyapunov functions for ISS analysis of a class of nonlinear parabolic PDEs

This paper addresses the input-to-state stability (ISS) and integral input-to-state stability (iISS) for a class of nonlinear higher dimensional parabolic partial differential equations (PDEs) with different types of boundary disturbances (Robin or Neumann or Dirichlet) from different spaces by means of approximations of Lyapunov functions. Specifically, by constructing approximations of (coercive and non-coercive) ISS Lyapunov functions we establish: (i) the ISS and iISS in $L^1$-norm (and weighted $L^1$-norm) for PDEs with boundary disturbances from $L^q_{loc}(\mathbb{R}_+;L^1(\partialΩ))$-space for any $q\in [1,+\infty]$; (ii) the iISS in $L^1$-norm (and weighted $L^1$-norm) for PDEs with boundary disturbances from $L^Φ_{loc}(\mathbb{R}_+;L^1(\partialΩ))$-space for certain Young function $Φ$; and (iii) the ISS and iISS in $L^Φ$-norm (and weighted $K_Φ$-class) for PDEs with boundary disturbances from $L^q_{loc}(\mathbb{R}_+;K_Φ(\partialΩ))$-class for any $q\in [1,+\infty]$ and certain Young function $Φ$. The ISS properties stated in (ii) and (iii) are assessed in the framework of Orlicz space or Orlicz class.

math.AP↗

arXiv2020

A Note on the Maximum Principle-based Approach for ISS Analysis of Higher Dimensional Parabolic PDEs with Variable Coefficients

This paper presents a maximum principle-based approach in the establishment of input-to-state stability (ISS) for a class of nonlinear parabolic partial differential equations (PDEs) over higher dimensional domains with variable coefficients and different types of nonlinear boundary conditions. Technical development on ISS analysis of the considered systems is detailed, and an example of establishing ISS estimates for a nonlinear parabolic equation with, respectively, a nonlinear Robin boundary condition and a nonlinear Dirichlet boundary condition is provided to illustrate the application of the developed method.

math.AP↗

arXiv2020

A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances

In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with boundary disturbances. Based on the weak maximum principle, a classical result on the maximum estimate of solutions to linear parabolic PDEs has been extended, which enables the ISS analysis for certain {}{nonlinear} parabolic PDEs with boundary disturbances. To illustrate the application of this method, we establish ISS estimates for a linear reaction-diffusion PDE and a generalized Ginzburg-Landau equation with {}{mixed} boundary disturbances. Compared to some existing methods, the scheme proposed in this paper involves less intensive computations and can be applied to the ISS analysis for a {wide} class of nonlinear PDEs with boundary disturbances.

math.AP↗

arXiv2019

Aggregate Power Control of Heterogeneous TCL Populations Governed by Fokker-Planck Equations

This paper addresses the modeling and control of heterogeneous populations of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) schemes at level of each TCL. It is shown that the dynamics of such TCLs populations can be described by a pair of Fokker-Planck equations coupled via the actions in the domain. The technique of input-output feedback linearization is used in the design of aggregate power control, which leads to a nonlinear system in closed loop. Well-posedness analysis is carried out to validate the developed control scheme. The closed-loop stability of the system is assessed by a rigorous analysis. A simulation study is contacted, and the obtained results confirm the validity and the effectiveness of the proposed approach.

math.OC↗

arXiv2019

Unsupervised Euclidean Distance Attack on Network Embedding

Considering the wide application of network embedding methods in graph data mining, inspired by the adversarial attack in deep learning, this paper proposes a Genetic Algorithm (GA) based Euclidean Distance Attack strategy (EDA) to attack the network embedding, so as to prevent certain structural information from being discovered. EDA focuses on disturbing the Euclidean distance between a pair of nodes in the embedding space as much as possible through minimal modifications of the network structure. Since a large number of downstream network algorithms, such as community detection and node classification, rely on the Euclidean distance between nodes to evaluate the similarity between them in the embedding space, EDA can be considered as a universal attack on a variety of network algorithms. Different from traditional supervised attack strategies, EDA does not need labeling information, and, in other words, is an unsupervised network embedding attack method.

cs.SI↗

arXiv2018

A minimum problem with free boundary and subcritical growth in Orlicz spaces

The aim of this paper is to study the heterogeneous optimization problem \begin{align*} \mathcal {J}(u)=\int_Ω(G(|\nabla u|)+qF(u^+)+hu+λ_{+}χ_{\{u>0\}} )\text{d}x\rightarrow\text{min}, \end{align*} in the class of functions $ W^{1,G}(Ω)$ with $ u-φ\in W^{1,G}_{0}(Ω)$, for a given function $φ$, where $W^{1,G}(Ω)$ is the class of weakly differentiable functions with $\int_ΩG(|\nabla u|)\text{d}x<\infty$. The functions $G$ and $F$ satisfy structural conditions of Lieberman's type that allow for a different behavior at $0$ and at $\infty$. {}{Moreover, $F$ allows for a subcritical growth.} Given functions $q,h$ and constant $λ_+\geq 0$, we address several regularity results for minimizers of $\mathcal {J}(u)$, including local $C^{1,α}-$, and local Log-Lipschitz continuities for minimizers of $\mathcal {J}(u)$ with $λ_+=0$, and {}{$λ_+\geq 0$} respectively. We also establish growth rate near the free boundary for each non-negative minimizer of $\mathcal {J}(u)$ with $λ_+=0$, and $λ_+>0$ respectively. Furthermore, under additional assumption that $F\in C^1([0,+\infty); [0,+\infty))$, local Lipschitz regularity is carried out for non-negative minimizers of $\mathcal {J}(u)$ with $λ_{+}>0$.

math.AP↗

arXiv2018

ISS with Respect to Boundary and In-domain Disturbances for a Coupled Beam-String System

This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of input-to-state stability (ISS) theory. Well-posedness assessment is first carried out to determine the regularity of the disturbances required for guaranteeing the unique existence of the solution to the considered problem. Then, the method of Lyapunov functionals is applied in stability analysis, which results in the establishment of some ISS properties {}{with respect to} disturbances. As the analysis is based on the \emph{a priori} estimates of the solution to the PDEs, it allows avoiding the invocation of unbounded operators while obtaining the ISS gains in their original expression without involving the derivatives of boundary disturbances.

math.AP↗

arXiv2018

A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances

This note addresses input-to-state stability (ISS) properties with respect to (w.r.t.) boundary and in-domain disturbances for Burgers' equation. The developed approach is a combination of the method of De~Giorgi iteration and the technique of Lyapunov functionals by adequately splitting the original problem into two subsystems. The ISS properties in $L^2$-norm for Burgers' equation have been established using this method. Moreover, as an application of De~Giorgi iteration, ISS in $L^\infty$-norm w.r.t. in-domain disturbances and actuation errors in boundary feedback control for a 1-$D$ {linear} {unstable reaction-diffusion equation} have also been established. It is the first time that the method of De~Giorgi iteration is introduced in the ISS theory for infinite dimensional systems, and the developed method can be generalized for tackling some problems on multidimensional spatial domains and to a wider class of nonlinear {partial differential equations (PDEs)

math.AP↗

arXiv2018

Regularity in the two-phase free boundary problems under non-standard growth conditions

In this paper, we prove several regularity results for the heterogeneous, two-phase free boundary problems $\mathcal {J}_γ(u)=\int_Ω\big(f(x,\nabla u)+λ_{+} (u^{+})^γ+λ_{-}(u^{-})^γ+gu\big)\text{d}x\rightarrow \text{min}$ under non-standard growth conditions. Included in such problems are heterogeneous jets and cavities of Prandtl-Batchelor type with $γ=0$, chemical reaction problems with $0<γ<1$, and obstacle type problems with $γ=1$. Our results hold not only in the degenerate case of $p> 2$ for $p-$Laplace equations, but also in the singular case of $1<p<2$, which are extensions of \cite{LdT}.

math.AP↗