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Peng Luo

Publications and source records attributed to Peng Luo.

At least 55 records · Page 3Linked to original sources
arXiv2023

Turnpike properties for stochastic backward linear-quadratic optimal problems

This paper deals with the long time behavior of the optimal solution of stochastic backward linear-quadratic optimal control problem over the finite time horizon. Both weak and strong turnpike properties are established under appropriate conditions, including stabilizability condition. The key ingredients are to formulate the corresponding static optimization problem and determine the correction processes. However, our techniques are quite different from stochastic (forward) linear-quadratic case.

math.OC↗
arXiv2023

Well-posedness for a class of mean field type FBSDEs and classical solutions of related master equations

In this paper, we study a class of mean field type FBSDEs. We propose a class of motonotinity conditions, under which we show the uniformly Lipschitz continuity of the decoupling field and obtain the existence and uniqueness of solution. We further provide a representation result for the solution and the decoupling field. Finally, we obtain the regularity of the decoupling field and establish global well-posedness of classical solutions to related master equations.

math.PR↗
arXiv2023

Stochastic linear-quadratic optimal control problems with multi-dimensional state and non-Markovian regime switching

This paper investigates the stochastic linear-quadratic (LQ, for short) optimal control problems with non-Markovian regime switching in a finite time horizon where the state equation is multi-dimensional. Similar to the classical stochastic LQ problems, we establish the relationship between the stochastic LQ optimal control problems with non-Markovian regime switching and the related extended stochastic Riccati equations. To solve the extended stochastic Riccati equations, we construct a monotone Piccard iterative sequence and present the link bewteen this sequence and solutions of a family of forward-backward stochastic differential equations. Relying on $L^p$ estimates for FBSDEs, we show that the extended stochastic Riccati equation has a solution. This partially addresses one question left in Hu et al. (Ann. Appl. Probab. 32(1): 426-460, 2022). Finally, the stochastic LQ optimal control problems with non-Markovian regime switching is solved.

math.OC↗
arXiv2023

A unified approach to global solvability for FBSDEs with diagonal generators

In this paper, we study the global solvability of multidimensional forward-backward stochastic differential equations (FBSDEs) with diagonally Lipschitz, quadratic or super-quadratic generators. Under a certain "monotonicity" condition, we provide a unified approach which shows that there exists a decoupling field that is uniformly Lipschitz in its spatial variable. This decoupling field is closely related to bounded solution to an associated characteristic BSDE. For Lipschitz case, we provide some extensions and investigate $L^p$-solution and $L^p$ estimates. Our results gives a positive answer to a question proposed in Yong (Banach Center Publ. 122: 255-286, 2020). Applications to stochastic optimal controls and stochastic differential games are investigated.

math.PR↗
arXiv2023

Real-World Deep Local Motion Deblurring

Most existing deblurring methods focus on removing global blur caused by camera shake, while they cannot well handle local blur caused by object movements. To fill the vacancy of local deblurring in real scenes, we establish the first real local motion blur dataset (ReLoBlur), which is captured by a synchronized beam-splitting photographing system and corrected by a post-progressing pipeline. Based on ReLoBlur, we propose a Local Blur-Aware Gated network (LBAG) and several local blur-aware techniques to bridge the gap between global and local deblurring: 1) a blur detection approach based on background subtraction to localize blurred regions; 2) a gate mechanism to guide our network to focus on blurred regions; and 3) a blur-aware patch cropping strategy to address data imbalance problem. Extensive experiments prove the reliability of ReLoBlur dataset, and demonstrate that LBAG achieves better performance than state-of-the-art global deblurring methods without our proposed local blur-aware techniques.

cs.CV↗
arXiv2023

Mean-field backward stochastic differential equations with mean reflection and nonlinear resistance

The present paper is devoted to the study of the well-posedness of mean field BSDEs with mean reflection and nonlinear resistance. By the contraction mapping argument, we first prove that the mean-field BSDE with mean reflection and nonlinear resistance admits a unique deterministic flat local solution on a small time interval. Moreover, we build the global solution by introducing a two-step approach, which is a combination of stitching method and fixed point method. We further provide an application to the super-hedging problem with risk constraint.

math.PR↗
arXiv2022

Qualitative analysis for Moser-Trudinger nonlinearities with a low energy

We are concerned with the Moser-Trudinger problem \begin{equation*} \begin{cases} -Δu=λue^{u^2}~~&\mbox{in}~Ω,\\[0.5mm] u>0 ~~ &{\text{in}~Ω},\\[0.5mm] u=0~~&\mbox{on}~\partial Ω, \end{cases} \end{equation*} where $Ω\subset \mathbb{R}^2$ is a smooth bounded domain and $λ>0$ is sufficiently small. Qualitative analysis for Moser-Trudinger nonlinearities has been studied in recent decades, however there is still a lot of clarity about this issue, even for a low energy. The reason is that this problem is a critical exponent for dimension two and will lose compactness. Here by using a variety of local Pohozaev identities, we qualitatively analyze the positive solutions of Moser-Trudinger problem with a low energy, which contains the Morse index, non-degeneracy, asymptotic behavior, uniqueness and symmetry of solutions. Since the fundamental solution of $-Δ$ in $Ω\subset \mathbb{R}^2$ is in logarithmic form and the corresponding bubble is exponential growth, more precise asymptotic behavior of the solutions is needed, which is of independent interest. Moreover, to obtain our results, some ODE's theory will be used to a prior estimate of the solutions and some elliptic theory in dimension two will play a crucial role.

math.AP↗
arXiv2022

Smart Name Lookup for NDN Forwarding Plane via Neural Networks

Name lookup is a key technology for the forwarding plane of content router in Named Data Networking (NDN). To realize the efficient name lookup, what counts is deploying a highperformance index in content routers. So far, the proposed indexes have shown good performance, most of which are optimized for or evaluated with URLs collected from the current Internet, as the large-scale NDN names are not available yet. Unfortunately, the performance of these indexes is always impacted in terms of lookup speed, memory consumption and false positive probability, as the distributions of URLs retrieved in memory may differ from those of real NDN names independently generated by content-centric applications online. Focusing on this gap, a smart mapping model named Pyramid-NN via neural networks is proposed to build an index called LNI for NDN forwarding plane. Through learning the distributions of the names retrieved in the static memory, LNI can not only reduce the memory consumption and the probability of false positive, but also ensure the performance of real NDN name lookup. Experimental results show that LNI-based FIB can reduce the memory consumption to 58.258 MB for 2 million names. Moreover, as it can be deployed on SRAMs, the throughput is about 177 MSPS, which well meets the current network requirement for fast packet processing.

cs.NI↗
arXiv2022

An unsupervised approach for semantic place annotation of trajectories based on the prior probability

Semantic place annotation can provide individual semantics, which can be of great help in the field of trajectory data mining. Most existing methods rely on annotated or external data and require retraining following a change of region, thus preventing their large-scale applications. Herein, we propose an unsupervised method denoted as UPAPP for the semantic place annotation of trajectories using spatiotemporal information. The Bayesian Criterion is specifically employed to decompose the spatiotemporal probability of the candidate place into spatial probability, duration probability, and visiting time probability. Spatial information in ROI and POI data is subsequently adopted to calculate the spatial probability. In terms of the temporal probabilities, the Term Frequency Inverse Document Frequency weighting algorithm is used to count the potential visits to different place types in the trajectories, and generates the prior probabilities of the visiting time and duration. The spatiotemporal probability of the candidate place is then combined with the importance of the place category to annotate the visited places. Validation with a trajectory dataset collected by 709 volunteers in Beijing showed that our method achieved an overall and average accuracy of 0.712 and 0.720, respectively, indicating that the visited places can be annotated accurately without any external data.

cs.LG↗
arXiv2022

Qualitative analysis on the critical points of the Robin function

Let $Ω\subset\mathbb{R}^N$ be a smooth bounded domain with $N\ge2$ and $Ω_ε=Ω\backslash B(P,ε)$ where $B(P,ε)$ is the ball centered at $P\inΩ$ and radius $ε$. In this paper, we establish the number, location and non-degeneracy of critical points of the Robin function in $Ω_ε$ for $ε$ small enough. We will show that the location of $P$ plays a crucial role on the existence and multiplicity of the critical points. The proof of our result is a consequence of delicate estimates on the Green function near to $\partial B(P,ε)$. Some applications to compute the exact number of solutions of related well-studied nonlinear elliptic problems will be showed.

math.AP↗
arXiv2022

Laplace principle for large population games with control interaction

This work investigates continuous time stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. The control processes are assumed to be open-loop. We give regularity conditions guaranteeing that if the finite-player game admits a Nash equilibrium, then both the sequence of equilibria and the corresponding states processes satisfy a Sanov-type large deviation principle. The result requires existence of a Lipschitz continuous solution of the master equation of the corresponding mean field game, and is based on concentration inequalities for Lipschitz FBSDEs. The result carries over to cooperative (i.e. central planner) games. We study the linear-quadratic case of such games in details.

math.PR↗
arXiv2022

RunnerDNA: Interpretable indicators and model to characterize human activity pattern and individual difference

Human activity analysis based on sensor data plays a significant role in behavior sensing, human-machine interaction, health care, and so on. The current research focused on recognizing human activity and posture at the activity pattern level, neglecting the effective fusion of multi-sensor data and assessing different movement styles at the individual level, thus introducing the challenge to distinguish individuals in the same movement. In this study, the concept of RunnerDNA, consisting of five interpretable indicators, balance, stride, steering, stability, and amplitude, was proposed to describe human activity at the individual level. We collected smartphone multi-sensor data from 33 volunteers who engaged in physical activities such as walking, running, and bicycling and calculated the data into five indicators of RunnerDNA. The indicators were then used to build random forest models and recognize movement activities and the identity of users. The results show that the proposed model has high accuracy in identifying activities (accuracy of 0.679) and is also effective in predicting the identity of running users. Furthermore, the accuracy of the human activity recognition model has significant improved by combing RunnerDNA and two motion feature indicators, velocity, and acceleration. Results demonstrate that RunnerDNA is an effective way to describe an individual's physical activity and helps us understand individual differences in sports style, and the significant differences in balance and amplitude between men and women were found.

cs.CY↗
arXiv2021

Existence and local uniqueness of normalized peak solutions for a Schrodinger-Newton system

In this paper, we investigate the existence and local uniqueness of normalized peak solutions for a Schrödinger-Newton system under the assumption that the trapping potential is degenerate and has non-isolated critical points. First we investigate the existence and local uniqueness of normalized single-peak solutions for the Schrödinger-Newton system. Precisely, we give the precise description of the chemical potential $μ$ and the attractive interaction $a$. Then we apply the finite dimensional reduction method to obtain the existence of single-peak solutions. Furthermore, using various local Pohozaev identities, blow-up analysis and the maximum principle, we prove the local uniqueness of single-peak solutions by precise analysis of the concentrated points and the Lagrange multiplier. Finally, we also prove the nonexistence of multi-peak solutions for the Schrödinger-Newton system, which is markedly different from the corresponding Schrödinger equation. The nonlocal term results in this difference. The main difficulties come from the estimates on Lagrange multiplier, the different degenerate rates along different directions at the critical point of $P(x)$ and some complicated estimates involved by the nonlocal term. To our best knowledge, it may be the first time to study the existence and local uniqueness of solutions with prescribed $L^{2}$-norm for the Schrödinger-Newton system.

math.AP↗
arXiv2021

Diagonally quadratic BSDE with oblique reflection and optimal switching

The present paper is devoted to the study of diagonally quadratic backward stochastic differential equation with oblique reflection. Using a penalization approach, we show the existence fo a solution by providing some delicated a priori estimates. We further obtain the uniqueness by verifying the first component of the solution is indeed the value of a switching probelm for quadratic BSDEs. Moreover, we provide an extension for the solvability and apply our results to study a risk-sensitive switching problem for functional stochastic differential equations.

math.PR↗
arXiv2021

Q-dependent Collective Relaxation Dynamics of Glass-Forming Liquid Ca0.4K0.6(NO3)1.4 Investigated by Wide-Angle Neutron Spin-Echo

Employing wide-angle neutron spin echo spectroscopy, we measured the Q-dependent coherent intermediate scattering function of the prototypical ionic glass former Ca0.4K0.6(NO3)1.4, in the equilibrium and supercooled liquid states beyond the hydrodynamic regime. The data reveal a clear two-step relaxation: an exponential fast process, and a stretched exponential slow alpha process. de Gennes narrowing is observed in all characteristic variables of the alpha process: the relaxation time, amplitude, and stretching exponent. At all length scales probed, the relative amplitude of the alpha-relaxation decreases with increasing temperature and levels off in the normal liquid state. The temperature dependence of the stretching exponent and the relaxation time at different Q's indicate that modifications of the relaxation mechanisms at the local length scales, manifested as temperature independent dynamic heterogeneity and smaller deviations from Arrhenius behavior, have occurred even above the alpha-beta (Johari-Goldstein) bifurcation temperature.

cond-mat.soft↗
arXiv2021

Concentrated solutions to fractional Schrödinger equations with prescribed $L^2$-norm

We investigate the existence and local uniqueness of normalized $k$-peak solutions for the fractional Schrödinger equations with attractive interactions with a class of degenerated trapping potential with non-isolated critical points. Precisely, applying the finite dimensional reduction method, we first obtain the existence of $k$-peak concentrated solutions and especially describe the relationship between the chemical potential $μ$ and the attractive interaction $a$. Second, after precise analysis of the concentrated points and the Lagrange multiplier, we prove the local uniqueness of the $k$-peak solutions with prescribed $L^2$-norm, by use of the local Pohozaev identities, the blow-up analysis and the maximum principle associated to the nonlocal operator $(-Δ)^s$. To our best knowledge, there is few results on the excited normalized solutions of the fractional Schrödinger equations before this present work. The main difficulty lies in the non-local property of the operator $(-Δ)^s$. First, it makes the standard comparison argument in the ODE theory invalid to use in our analysis. Second, because of the algebraic decay involving the approximate solutions, the estimates, on the Lagrange multiplier for example, would become more subtle. Moreover,when studying the corresponding harmonic extension problem, several local Pohozaev identities are constructed and we have to estimate several kinds of integrals that never appear in the classic local Schrödinger problems. In addition, throughout our discussion, we need to distinct the different cases of $p$, which are called respectively that the mass-subcritical, the mass-critical, and the mass-supercritical case, due to the mass-constraint condition. Another difficulty comes from the influence of the different degenerate rates along different directions at the critical points of the potential.

math.AP↗