arXiv subjects

Peng Luo

Publications and source records attributed to Peng Luo.

At least 73 records · Page 4Linked to original sources

arXiv2021

UrbanVCA: a vector-based cellular automata framework to simulate the urban land-use change at the land-parcel level

Vector-based cellular automata (CA) based on real land-parcel has become an important trend in current urban development simulation studies. Compared with raster-based and parcel-based CA models, vector CA models are difficult to be widely used because of their complex data structures and technical difficulties. The UrbanVCA, a brand-new vector CA-based urban development simulation framework was proposed in this study, which supports multiple machine-learning models. To measure the simulation accuracy better, this study also first proposes a vector-based landscape index (VecLI) model based on the real land-parcels. Using Shunde, Guangdong as the study area, the UrbanVCA simulates multiple types of urban land-use changes at the land-parcel level have achieved a high accuracy (FoM=0.243) and the landscape index similarity reaches 87.3%. The simulation results in 2030 show that the eco-protection scenario can promote urban agglomeration and reduce ecological aggression and loss of arable land by at least 60%. Besides, we have developed and released UrbanVCA software for urban planners and researchers.

cs.CY↗

arXiv2021

Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two

We are concerned with the Lane-Emden problem \begin{equation*} \begin{cases} -Δu=u^{p} &{\text{in}~Ω},\\[0.5mm] u>0 &{\text{in}~Ω},\\[0.5mm] u=0 &{\text{on}~\partial Ω}, \end{cases} \end{equation*} where $Ω\subset \mathbb R^2$ is a smooth bounded domain and $p>1$ is sufficiently large. Improving some known asymptotic estimates on the solutions, we prove the non-degeneracy and local uniqueness of the multi-spikes positive solutions for general domains. Our methods mainly use ODE's theory, various local Pohozaev identities, blow-up analysis and the properties of Green's function.

math.AP↗

arXiv2021

The spectral gap to torsion problem for some non-convex domains

In this paper we study the following torsion problem \begin{equation*} \begin{cases} -Δu=1~&\mbox{in}\ Ω,\\[1mm] u=0~&\mbox{on}\ \partialΩ. \end{cases} \end{equation*} Let $Ω\subset \mathbb{R}^2$ be a bounded, convex domain and $u_0(x)$ be the solution of above problem with its maximum $y_0\in Ω$. Steinerberger proved that there are universal constants $c_1, c_2>0$ satisfying \begin{equation*} λ_{\max}\left(D^2u_0(y_0)\right)\leq -c_1\mbox{exp}\left(-c_2\frac{\text{diam}(Ω)}{\mbox{inrad}(Ω)}\right). \end{equation*} And he proposed following open problem: "Does above result hold true on domains that are not convex but merely simply connected or perhaps only bounded? The proof uses convexity of the domain $Ω$ in a very essential way and it is not clear to us whether the statement remains valid in other settings." Here by some new idea involving the computations on Green's function, we compute the spectral gap $λ_{\max}D^2u(y_0)$ for some non-convex smooth bounded domains, which gives a negative answer to above open problem. Also some extensions are given.

math.AP↗

arXiv2020

Co-Located vs Distributed vs Semi-Distributed MIMO: Measurement-Based Evaluation

With the growing interest in cell-free massive multiple-input multiple-output (MIMO) systems, the benefits of single-antenna access points (APs) versus multi-antenna APs must be analyzed in order to optimize deployment. In this paper, we compare various antenna system topologies based on achievable downlink spectral efficiency, using both measured and synthetic channel data in an indoor environment. We assume multi-user scenarios, analyzing both conjugate beamforming (or maximum-ratio transmission (MRT)) and zero-forcing (ZF) precoding methods. The results show that the semi-distributed multi-antenna APs can reduce the number of APs, and still achieve the comparable achievable rates as the fully-distributed single-antenna APs with the same total number of antennas.

eess.SP↗

arXiv2020

Experimental Investigation of Frequency Domain Channel Extrapolation in Massive MIMO Systems for Zero-Feedback FDD

Estimating downlink (DL) channel state information (CSI) in frequency division duplex (FDD) massive multi-input multi-output (MIMO) systems generally requires downlink pilots and feedback overheads. Accordingly, this paper investigates the feasibility of zero-feedback FDD massive MIMO systems based on channel extrapolation. We use the high-resolution parameter estimation (HRPE), specifically the space-alternating generalized expectation-maximization (SAGE) algorithm, to extrapolate the DL CSI based on the extracted parameters of multipath components in the uplink channel. We apply the HRPE to two different channel models: the vector spatial signature (VSS) model and the direction of arrival (DOA) model. We verify these methods through real-world channel data acquired from channel measurement campaigns with two different types of channel sounders: a) a switched array-based, real-time, time-domain, outdoors setup at 3.5 GHz, and b) a virtual array-based, high-accuracy, frequency-domain, indoors setup at 2.4 and 5-7 GHz. The performance metrics of the extrapolated channels that we evaluate include the mean squared error, beamforming efficiency, and spectral efficiency in multiuser MIMO scenarios. The results show that the HRPE-based channel extrapolation performs best under the simple VSS model, which does not require array calibration, and if the BS is in an open outdoor environment having line-of-sight (LOS) paths to well-separated users.

eess.SP↗

arXiv2020

The number of positive solutions to the Brezis-Nirenberg problem

In this paper we are concerned with the well-known Brezis-Nirenberg problem \begin{equation*} \begin{cases} -Δu= u^{\frac{N+2}{N-2}}+\varepsilon u, &{\text{in}~Ω},\\ u>0, &{\text{in}~Ω},\\ u=0, &{\text{on}~\partial Ω}. \end{cases} \end{equation*} The existence of multi-peak solutions to the above problem for small $\varepsilon>0$ was obtained by Musso and Pistoia. However, the uniqueness or the exact number of positive solutions to the above problem is still unknown. Here we focus on the local uniqueness of multi-peak solutions and the exact number of positive solutions to the above problem for small $\varepsilon>0$. By using various local Pohozaev identities and blow-up analysis, we first detect the relationship between the profile of the blow-up solutions and the Green's function of the domain $Ω$ and then obtain a type of local uniqueness results of blow-up solutions. At last we give a description of the number of positive solutions for small positive $\varepsilon$, which depends also on the Green's function.

math.AP↗

arXiv2020

Strong solutions of forward-backward stochastic differential equations with measurable coefficients

This paper investigates solvability of fully coupled systems of forward-backward stochastic differential equations (FBSDEs) with irregular coefficients. In particular, we assume that the coefficients of the FBSDEs are merely measurable and bounded in the forward process. We crucially use compactness results from the theory of Malliavin calculus to construct strong solutions. Despite the irregularity of the coefficients, the solutions turn out to be differentiable, at least in the Malliavin sense and, as functions of the initial variable, in the Sobolev sense.

math.PR↗

arXiv2020

On the number and location of critical points of solutions of nonlinear elliptic equations in domains with a small hole

In this paper we study the following problem \begin{equation} \begin{cases} -Δu=f(u)~&\mbox{in}\ Ω_\varepsilon,\\ u>0~&\mbox{in}\ Ω_\varepsilon,\\ u=0~&\mbox{on}\ \partialΩ_\varepsilon, \end{cases} \end{equation} where $Ω_\varepsilon=Ω\backslash B(P,\varepsilon)$, $Ω\subset R^N$ with $N\geq 2$ is a smooth bounded domain, $B(P,\varepsilon)$ is the ball centered at $P$ and radius $\varepsilon>0$ and $f$ is a smooth nonlinearity. By some computations involving the Green function and degree theory, we compute the number and location of critical points of solutions for small $\varepsilon>0$.

math.AP↗

arXiv2020

Performance Analysis of Channel Extrapolation in FDD Massive MIMO Systems

Channel estimation for the downlink of frequency division duplex (FDD) massive MIMO systems is well known to generate a large overhead as the amount of training generally scales with the number of transmit antennas in a MIMO system. In this paper, we consider the solution of extrapolating the channel frequency response from uplink pilot estimates to the downlink frequency band, which completely removes the training overhead. We first show that conventional estimators fail to achieve reasonable accuracy. We propose instead to use high-resolution channel estimation. We derive theoretical lower bounds (LB) for the mean squared error (MSE) of the extrapolated channel. Assuming that the paths are well separated, the LB is simplified in an expression that gives considerable physical insight. It is then shown that the MSE is inversely proportional to the number of receive antennas while the extrapolation performance penalty scales with the square of the ratio of the frequency offset and the training bandwidth. The channel extrapolation performance is validated through numeric simulations and experimental measurements taken in an anechoic chamber. Our main conclusion is that channel extrapolation is a viable solution for FDD massive MIMO systems if accurate system calibration is performed and favorable propagation conditions are present.

eess.SP↗

arXiv2019

An FBSDE approach to market impact games with stochastic parameters

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has indeed a unique solution, which in turn yields the unique Nash equilibrium. We furthermore obtain closed-form solutions in special situations and analyze them numerically

q-fin.TR↗

arXiv2019

Characterization of Fully Coupled FBSDE in Terms of Portfolio Optimization

We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with random endowment under probability and discounting uncertainty. We show with explicit examples how to quantify the costs of incompleteness when using utility indifference pricing, as well as a way to find optimal solutions for recursive utilities.

q-fin.MF↗

arXiv2019

Excited states on Bose-Einstein condensates with attractive interactions

We study the Bose-Einstein condensates (BEC) in two or three dimensions with attractive interactions, described by $L^{2}$ constraint Gross-Pitaevskii energy functional. First, we give the precise description of the chemical potential of the condensate $μ$ and the attractive interaction $a$. Next, for a class of degenerated trapping potential with non-isolated critical points, we obtain the existence and the local uniqueness of excited states by precise analysis of the concentrated points and the Lagrange multiplier. To our best knowledge, this is the first result concerning on excited states of BEC in Mathematics. Also, our results show that $ka_*$ are critical values in two dimension when the concentration occurs for any positive integer $k$ with some positive constant $a_*$. And we point out that our results on degenerated trapping potential with non-isolated critical points are also new even for the classical Schrödinger equations. Here our main tools are finite-dimensional reduction and various Pohozave identities. The main difficulties come from the estimates on Lagrange multiplier and the different degenerate rate along different directions at the critical points of $V(x)$.

math.AP↗

arXiv2019

Positive multi-peak solutions for a logarithmic Schrodinger equation

In this manuscript, we consider the logarithmic Schrödinger equation \begin{eqnarray*} -\varepsilon^2Δu+V(x)u=u\log u^{2},\,\,\,u>0, & \text{in}\,\,\,\mathbb{R}^{N}, \end{eqnarray*} where $N\geq3$, $\varepsilon>0$ is a small parameter. Under some assumptions on $V(x)$, we show the existence of positive multi-peak solutions by Lyapunov-Schmidt reduction. It seems to be the first time to study singularly perturbed logarithmic Schrödinger problem by reduction. And here using a new norm is the crucial technique to overcome the difficulty caused by the logarithmic nonlinearity. At the same time, we consider the local uniqueness of the multi-peak solutions by using a type of local Pohozaev identities.

math.AP↗

arXiv2019

Channel Extrapolation for FDD Massive MIMO: Procedure and Experimental Results

Application of massive multiple-input multiple-output (MIMO) systems to frequency division duplex (FDD) is challenging mainly due to the considerable overhead required for downlink training and feedback. Channel extrapolation, i.e., estimating the channel response at the downlink frequency band based on measurements in the disjoint uplink band, is a promising solution to overcome this bottleneck. This paper presents measurement campaigns obtained by using a wideband (350 MHz) channel sounder at 3.5 GHz composed of a calibrated 64 element antenna array, in both an anechoic chamber and outdoor environment. The Space Alternating Generalized Expectation-Maximization (SAGE) algorithm was used to extract the parameters (amplitude, delay, and angular information) of the multipath components from the attained channel data within the training (uplink) band. The channel in the downlink band is then reconstructed based on these path parameters. The performance of the extrapolated channel is evaluated in terms of mean squared error (MSE) and reduction of beamforming gain (RBG) in comparison to the ground truth, i.e., the measured channel at the downlink frequency. We find strong sensitivity to calibration errors and model mismatch, and also find that performance depends on propagation conditions: LOS performs significantly better than NLOS.

eess.SP↗

arXiv2019

Recent Advances of Image Steganography with Generative Adversarial Networks

In the past few years, the Generative Adversarial Network (GAN) which proposed in 2014 has achieved great success. GAN has achieved many research results in the field of computer vision and natural language processing. Image steganography is dedicated to hiding secret messages in digital images, and has achieved the purpose of covert communication. Recently, research on image steganography has demonstrated great potential for using GAN and neural networks. In this paper we review different strategies for steganography such as cover modification, cover selection and cover synthesis by GANs, and discuss the characteristics of these methods as well as evaluation metrics and provide some possible future research directions in image steganography.

cs.CR↗

arXiv2019

A type of globally solvable BSDEs with triangularly quadratic generators

The present paper is devoted to the study of the well-posedness of a type of BSDEs with triangularly quadratic generators. This work is motivated by the recent results obtained by Hu and Tang [14] and Xing and Žitković [28]. By the contraction mapping argument, we first prove that this type of triangularly quadratic BSDEs admits a unique local solution on a small time interval whenever the terminal value is bounded. Under additional assumptions, we build the global solution on the whole time interval by stitching local solutions. Finally, we give solvability results when the generators have path dependence in value process.

math.PR↗

arXiv2019

How Many Antennas Do We Need for Massive MIMO Channel Sounding? - Validating Through Measurement

This paper investigates the impact of the number of antennas (8 to 64) and the array configuration on massive MIMO channel parameters estimation for multiple propagation scenarios at 3.5 GHz. Different measurement environments are artificially created by placing several reflectors and absorbers in an anechoic chamber. Ground truth channel parameters, e.g, path angles, are obtained by geometry and trigonometric rules. Then, these are compared to the channel parameters extracted by the applying Space-Alternating Generalized Expectation-Maximization (SAGE) algorithm on the measurements. Overall, the estimation errors for various array configurations and the multiple environments are compared. This paper will help to determine the appropriate configuration of the antenna array and the parameter extraction algorithm for outdoor massive MIMO channel sounding campaigns.

eess.SP↗

arXiv2017

Multidimensional quadratic BSDEs with separated generators

We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the terminal condition or the dependence in the system are small enough.

math.PR↗