arXiv subjects

Guopeng Li

Publications and source records attributed to Guopeng Li.

48 records · Page 3Linked to original sources

arXiv2024

Compact bilinear operators and paraproducts revisited

We present a new proof of the compactness of bilinear paraproducts with CMO symbols. By drawing an analogy to compact linear operators, we first explore further properties of compact bilinear operators on Banach spaces and present examples. We then prove compactness of bilinear paraproducts with CMO symbols by combining one of the properties of compact bilinear operators thus obtained with vanishing Carleson measure estimates and interpolation of bilinear compactness.

math.FA↗

arXiv2024

Intermediate long wave equation in negative Sobolev spaces

We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity $s = -\frac 12$ as the critical regularity for ILW with any depth parameter, by establishing the following two results. (i) By viewing ILW as a perturbation of the Benjamin-Ono equation (BO) and exploiting the complete integrability of BO, we establish a global-in-time a priori bound on the $H^s$-norm of a solution to ILW for $ - \frac 12 < s < 0$. (ii) By making use of explicit solutions, we prove that ILW is ill-posed in $H^s$ for $s < - \frac 12$. Our results apply to both the real line case and the periodic case.

math.AP↗

arXiv2024

Unleashing Unlabeled Data: A Paradigm for Cross-View Geo-Localization

This paper investigates the effective utilization of unlabeled data for large-area cross-view geo-localization (CVGL), encompassing both unsupervised and semi-supervised settings. Common approaches to CVGL rely on ground-satellite image pairs and employ label-driven supervised training. However, the cost of collecting precise cross-view image pairs hinders the deployment of CVGL in real-life scenarios. Without the pairs, CVGL will be more challenging to handle the significant imaging and spatial gaps between ground and satellite images. To this end, we propose an unsupervised framework including a cross-view projection to guide the model for retrieving initial pseudo-labels and a fast re-ranking mechanism to refine the pseudo-labels by leveraging the fact that ``the perfectly paired ground-satellite image is located in a unique and identical scene". The framework exhibits competitive performance compared with supervised works on three open-source benchmarks. Our code and models will be released on https://github.com/liguopeng0923/UCVGL.

cs.CV↗

arXiv2023

Global dynamics for the stochastic nonlinear beam equations on the four-dimensional torus

We study global-in-time dynamics of the stochastic nonlinear beam equations (SNLB) with an additive space-time white noise, posed on the four-dimensional torus. The roughness of the noise leads us to introducing a time-dependent renormalization, after which we show that SNLB is pathwise locally well-posed in all subcritical and most of the critical regimes. For the (renormalized) defocusing cubic SNLB, we establish pathwise global well-posedness below the energy space, by adapting a hybrid argument of Gubinelli- Koch-Oh-Tolomeo (2022) that combines the $I$-method with a Gronwall-type argument. Lastly, we show almost sure global well-posedness and invariance of the Gibbs measure for the stochastic damped nonlinear beam equations in the defocusing case.

math.AP↗

arXiv2023

A Conflict Resolution Dataset Derived from Argoverse-2: Analysis of the Safety and Efficiency Impacts of Autonomous Vehicles at Intersections

As the deployment of autonomous vehicles (AVs) in mixed traffic flow becomes increasingly prevalent, ensuring safe and smooth interactions between AVs and human agents is of critical importance. How road users resolve conflicts at intersections has significant impacts on driving safety and traffic efficiency. These impacts depend on both the behaviours of AVs and humans' reactions to the presence of AVs. Therefore, using real-world data to assess and compare the safety and efficiency measures of AV-involved and AV-free scenarios is crucial. To this end, this paper presents a high-quality conflict resolution dataset derived from the open Argoverse-2 motion forecasting data to analyse the safety and efficiency impacts of AVs. The contribution is twofold: First, we propose and apply a specific data processing pipeline to select scenarios of interest, rectify data errors, and enhance the raw data in Argoverse-2. As a result, 5000+ cases where an AV resolves conflict with a human road user and 16000+ conflict resolution cases without AVs are obtained. Motion data is smooth and consistent in these cases. This open dataset comprises diverse and balanced conflict resolution regimes. Second, this paper employs surrogate safety measures and a novel efficiency measure to assess the impact of AVs at intersections. The results suggest that human drivers exhibit similar safety and efficiency performances when interacting with AVs and with other human drivers. In contrast, pedestrians demonstrate more diverse reactions. Furthermore, due to the safety-prior strategy of AVs, the average efficiency of AV-involved conflict resolution decreases by 8.6% compared to AV-free cases. This informative dataset provides a valuable resource for researchers and the findings give insights into the possible impacts of AVs. The dataset is openly available via https://github.com/RomainLITUD/conflict_resolution_dataset.

cs.RO↗

arXiv2023

Pattern retrieval of traffic congestion using graph-based associations of traffic domain-specific features

The fast-growing amount of traffic data brings many opportunities for revealing more insightful information about traffic dynamics. However, it also demands an effective database management system in which information retrieval is arguably an important feature. The ability to locate similar patterns in big datasets potentially paves the way for further valuable analyses in traffic management. This paper proposes a content-based retrieval system for spatiotemporal patterns of highway traffic congestion. There are two main components in our framework, namely pattern representation and similarity measurement. To effectively interpret retrieval outcomes, the paper proposes a graph-based approach (relation-graph) for the former component, in which fundamental traffic phenomena are encoded as nodes and their spatiotemporal relationships as edges. In the latter component, the similarities between congestion patterns are customizable with various aspects according to user expectations. We evaluated the proposed framework by applying it to a dataset of hundreds of patterns with various complexities (temporally and spatially). The example queries indicate the effectiveness of the proposed method, i.e. the obtained patterns present similar traffic phenomena as in the given examples. In addition, the success of the proposed approach directly derives a new opportunity for semantic retrieval, in which expected patterns are described by adopting the relation-graph notion to associate fundamental traffic phenomena.

cs.CV↗

arXiv2023

Global well-posedness of one-dimensional cubic fractional nonlinear Schrödinger equations in negative Sobolev spaces

We study the Cauchy problem for the cubic fractional nonlinear Schrödinger equation (fNLS) on the real line and on the circle. In particular, we prove global well-posedness of the cubic fNLS with all orders of dispersion higher than the usual Schrödinger equation in negative Sobolev spaces. On the real line, our well-posedness result is sharp in the sense that a contraction argument does not work below the threshold regularity. On the circle, due to ill-posedness of the cubic fNLS in negative Sobolev spaces, we study the renormalized cubic fNLS. In order to overcome the failure of local uniform continuity of the solution map in negative Sobolev spaces, by applying a gauge transform and partially iterating the Duhamel formulation, we study the resulting equation with a cubic-quintic nonlinearity. In proving uniqueness, we present full details justifying the use of the normal form reduction for rough solutions, which seem to be missing from the existing literature. Our well-posedness result on the circle extends those in Miyaji-Tsutsumi (2018) and Oh-Wang (2018) to the endpoint regularity.

math.AP↗

arXiv2023

Large Car-following Data Based on Lyft level-5 Open Dataset: Following Autonomous Vehicles vs. Human-driven Vehicles

Car-Following (CF), as a fundamental driving behaviour, has significant influences on the safety and efficiency of traffic flow. Investigating how human drivers react differently when following autonomous vs. human-driven vehicles (HV) is thus critical for mixed traffic flow. Research in this field can be expedited with trajectory datasets collected by Autonomous Vehicles (AVs). However, trajectories collected by AVs are noisy and not readily applicable for studying CF behaviour. This paper extracts and enhances two categories of CF data, HV-following-AV (H-A) and HV-following-HV (H-H), from the open Lyft level-5 dataset. First, CF pairs are selected based on specific rules. Next, the quality of raw data is assessed by anomaly analysis. Then, the raw CF data is corrected and enhanced via motion planning, Kalman filtering, and wavelet denoising. As a result, 29k+ H-A and 42k+ H-H car-following segments are obtained, with a total driving distance of 150k+ km. A diversity assessment shows that the processed data cover complete CF regimes for calibrating CF models. This open and ready-to-use dataset provides the opportunity to investigate the CF behaviours of following AVs vs. HVs from real-world data. It can further facilitate studies on exploring the impact of AVs on mixed urban traffic.

eess.SY↗

arXiv2023

Distil the informative essence of loop detector data set: Is network-level traffic forecasting hungry for more data?

Network-level traffic condition forecasting has been intensively studied for decades. Although prediction accuracy has been continuously improved with emerging deep learning models and ever-expanding traffic data, traffic forecasting still faces many challenges in practice. These challenges include the robustness of data-driven models, the inherent unpredictability of traffic dynamics, and whether further improvement of traffic forecasting requires more sensor data. In this paper, we focus on this latter question and particularly on data from loop detectors. To answer this, we propose an uncertainty-aware traffic forecasting framework to explore how many samples of loop data are truly effective for training forecasting models. Firstly, the model design combines traffic flow theory with graph neural networks, ensuring the robustness of prediction and uncertainty quantification. Secondly, evidential learning is employed to quantify different sources of uncertainty in a single pass. The estimated uncertainty is used to "distil" the essence of the dataset that sufficiently covers the information content. Results from a case study of a highway network around Amsterdam show that, from 2018 to 2021, more than 80\% of the data during daytime can be removed. The remaining 20\% samples have equal prediction power for training models. This result suggests that indeed large traffic datasets can be subdivided into significantly smaller but equally informative datasets. From these findings, we conclude that the proposed methodology proves valuable in evaluating large traffic datasets' true information content. Further extensions, such as extracting smaller, spatially non-redundant datasets, are possible with this method.

cs.LG↗

arXiv2023

Towards Generic and Controllable Attacks Against Object Detection

Existing adversarial attacks against Object Detectors (ODs) suffer from two inherent limitations. Firstly, ODs have complicated meta-structure designs, hence most advanced attacks for ODs concentrate on attacking specific detector-intrinsic structures, which makes it hard for them to work on other detectors and motivates us to design a generic attack against ODs. Secondly, most works against ODs make Adversarial Examples (AEs) by generalizing image-level attacks from classification to detection, which brings redundant computations and perturbations in semantically meaningless areas (e.g., backgrounds) and leads to an emergency for seeking controllable attacks for ODs. To this end, we propose a generic white-box attack, LGP (local perturbations with adaptively global attacks), to blind mainstream object detectors with controllable perturbations. For a detector-agnostic attack, LGP tracks high-quality proposals and optimizes three heterogeneous losses simultaneously. In this way, we can fool the crucial components of ODs with a part of their outputs without the limitations of specific structures. Regarding controllability, we establish an object-wise constraint that exploits foreground-background separation adaptively to induce the attachment of perturbations to foregrounds. Experimentally, the proposed LGP successfully attacked sixteen state-of-the-art object detectors on MS-COCO and DOTA datasets, with promising imperceptibility and transferability obtained. Codes are publicly released in https://github.com/liguopeng0923/LGP.git

cs.CV↗

arXiv2022

Global well-posedness of the 4-d energy-critical stochastic nonlinear Schrödinger equations with non-vanishing boundary condition

We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on $\mathbb R^4$ with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrödinger equation on $\mathbb R^4$, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.

math.AP↗

arXiv2020

Almost conservation laws for stochastic nonlinear Schrödinger equations

In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the $I$-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on $\mathbb R^3$ with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the $I$-method with Ito's lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.

math.AP↗