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Yimin Zhang

Publications and source records attributed to Yimin Zhang.

At least 19 recordsLinked to original sources
arXiv2025

Converting IEC 61131-3 LD into SFC Using Large Language Model: Dataset and Testing

In the domain of Programmable Logic Controller (PLC) programming, converting a Ladder Diagram (LD) into a Sequential Function Chart (SFC) is an inherently challenging problem, primarily due to the lack of domain-specific knowledge and the issue of state explosion in existing algorithms. However, the rapid development of Artificial Intelligence (AI) - especially Large Language Model (LLM) - offers a promising new approach. Despite this potential, data-driven approaches in this field have been hindered by a lack of suitable datasets. To address this gap, we constructed several datasets consisting of paired textual representations of SFC and LD programs that conform to the IEC 61131-3 standard. Based on these datasets, we explored the feasibility of automating the LD-SFC conversion using LLM. Our preliminary experiments show that a fine-tuned LLM model achieves up to 91% accuracy on certain dataset, with the lowest observed accuracy being 79%, suggesting that with proper training and representation, LLMs can effectively support LD-SFC conversion. These early results highlight the viability and future potential of this approach.

cs.PL↗
arXiv2025

Gagliardo-Nirenberg-Sobolev inequalities and ground states of Fermions in relativistic Hartree-Fock model

This paper presents a rigorous mathematical analysis of the relativistic Hartree-Fock model for finite Fermi systems. We first establish an optimal Gagliardo-Nirenberg-Sobolev (GNS) inequality with Hartree-type nonlinearities for orthonormal systems and characterize the qualitative properties of its optimizers. Furthermore, we derive a finite-rank Lieb-Thirring inequality involving convolution terms and show that it is the duality of the GNS-inequality-a result that, to our knowledge, has not previously appeared in the literature. For the relativistic Hartree-Fock model, we prove that ground states exist if and only if the coupling parameter $K<\mathcal{K}_\infty^{(N)}$, where $\mathcal{K}_\infty^{(N)}$ is the optimal constant in the GNS-inequality. Finally, under suitable assumptions on the external potentials, we calculate the precisely asymptotic behavior of ground states as $K\nearrow\mathcal{K}_\infty^{(N)}$.

math-ph↗
arXiv2024

Exploring LLM Support for Generating IEC 61131-3 Graphic Language Programs

The capabilities demonstrated by Large Language Models (LLMs) inspire researchers to integrate them into industrial production and automation. In the field of Programmable Logic Controller (PLC) programming, previous researchers have focused on using LLMs to generate Structured Text (ST) language, and created automatic programming workflows based on it. The IEC 61131 graphic programming languages, which still has the most users, have however been overlooked. In this paper we explore using LLMs to generate graphic languages in ASCII art to provide assistance to engineers. Our series of experiments indicate that, contrary to what researchers usually think, it is possible to generate a correct Sequential Function Chart (SFC) for simple requirements when LLM is provided with several examples. On the other hand, generating a Ladder Diagram (LD) automatically remains a challenge even for very simple use cases. The automatic conversion between LD and SFC without extra information also fails when using prompt engineering alone.

cs.PL↗
arXiv2023

On the Kirchhoff equation with prescribed mass and general nonlinearities

In the present paper, we apply a global branch approach to study the existence, non-existence and multiplicity of positive normalized solutions $(λ_c, u_c)\in \mathbb{R}\times H^1(\mathbb{R}^N)$ to the following Kirchhoff problem $$ -\left(a+b\int_{\mathbb{R}^N}|\nabla u|^2dx\right)Δu+λu=g(u)~\hbox{in}~\mathbb{R}^N,\;N\geq 1 $$ satisfying the normalization constraint $ \displaystyle\int_{\mathbb{R}^N}u^2=c, $ which appears in free vibrations of elastic strings. The parameters $a,b>0$ are prescribed as well as the mass $c>0$. Due to the presence of the non-local term $b\int_{\mathbb{R}^N}|\nabla u|^2dx Δu$, such problems lack the mountain pass geometry in the higher dimension case $N\geq 5$. Our result seems to be the first attempt in this aspect.

math.AP↗
arXiv2023

Understanding Community Bias Amplification in Graph Representation Learning

In this work, we discover a phenomenon of community bias amplification in graph representation learning, which refers to the exacerbation of performance bias between different classes by graph representation learning. We conduct an in-depth theoretical study of this phenomenon from a novel spectral perspective. Our analysis suggests that structural bias between communities results in varying local convergence speeds for node embeddings. This phenomenon leads to bias amplification in the classification results of downstream tasks. Based on the theoretical insights, we propose random graph coarsening, which is proved to be effective in dealing with the above issue. Finally, we propose a novel graph contrastive learning model called Random Graph Coarsening Contrastive Learning (RGCCL), which utilizes random coarsening as data augmentation and mitigates community bias by contrasting the coarsened graph with the original graph. Extensive experiments on various datasets demonstrate the advantage of our method when dealing with community bias amplification.

cs.LG↗
arXiv2023

Maximum Consensus Localization using an Objective Function based on Helmert's Point Error

Ego-localization is a crucial task for autonomous vehicles. On the one hand, it needs to be very accurate, and on the other hand, very robust to provide reliable pose (position and orientation) information, even in challenging environments. Finding the best ego-position is usually tied to optimizing an objective function based on the sensor measurements. The most common approach is to maximize the likelihood, which leads under the assumption of normally distributed random variables to the well-known least squares minimization, often used in conjunction with recursive estimation, e. g. using a Kalman filter. However, least squares minimization is inherently sensitive to outliers, and consequently, more robust loss functions, such as L1 norm or Huber loss have been proposed. Arguably the most robust loss function is the outlier count, also known as maximum consensus optimization, where the outcome is independent of the outlier magnitude. In this paper, we investigate in detail the performance of maximum consensus localization based on LiDAR data. We elaborate on its shortcomings and propose a novel objective function based on Helmert's point error. In an experiment using 3001 measurement epochs, we show that the maximum consensus localization based on the introduced objective function provides superior results with respect to robustness.

cs.RO↗
arXiv2021

Positive normalized solution to the Kirchhoff equation with general nonlinearities of mass super-critical

In present paper, we study the normalized solutions $(λ_c, u_c)\in \R\times H^1(\R^N)$ to the following Kirchhoff problem $$ -\left(a+b\int_{\R^N}|\nabla u|^2dx\right)Δu+λu=g(u)~\hbox{in}~\R^N,\;1\leq N\leq 3 $$ satisfying the normalization constraint $ \displaystyle\int_{\R^N}u^2=c, $ which appears in free vibrations of elastic strings. The parameters $a,b>0$ are prescribed as is the mass $c>0$. The nonlinearities $g(s)$ considered here are very general and of mass super-critical. Under some suitable assumptions, we can prove the existence of ground state normalized solutions for any given $c>0$. After a detailed analysis via the blow up method, we also make clear the asymptotic behavior of these solutions as $c\rightarrow 0^+$ as well as $c\rightarrow+\infty$.

math.AP↗
arXiv2020

Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces

We consider the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili (RMKP) equation \begin{align*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\partial_{x}(u^{2})\right)+\partial_{y}^{2}u-γu=0 \end{align*} in the anisotropic Sobolev spaces $H^{s_{1},\>s_{2}}(\mathbb{R}^{2})$. When $β<0$ and $γ>0,$ we prove that the Cauchy problem is locally well-posed in $H^{s_{1},\>s_{2}}(\mathbb{R}^{2})$ with $s_{1}>-\frac{1}{2}$ and $s_{2}\geq 0$. Our result considerably improves the Theorem 1.4 of R. M. Chen, Y. Liu, P. Z. Zhang( Transactions of the American Mathematical Society, 364(2012), 3395--3425.). The key idea is that we divide the frequency space into regular region and singular region. We further prove that the Cauchy problem for RMKP equation is ill-posed in $H^{s_{1},\>0}(\mathbb{R}^{2})$ with $s_{1}<-\frac{1}{2}$ in the sense that the flow map associated to the rotation-modified Kadomtsev-Petviashvili is not $C^{3}$. When $β<0,γ>0,$ by using the $U^{p}$ and $V^{p}$ spaces, we prove that the Cauchy problem is locally well-posed in $H^{-\frac{1}{2},\>0}(\mathbb{R}^{2})$.

math.AP↗
arXiv2020

Self-cleaning effect in an all-fiber spatiotemporal mode-locked laser based on graded-index multimode fiber

We demonstrate an all-fiber spatiotemporal mode-locked laser based on graded-index multimode fiber. Due to the high damage threshold of graded-index multimode fiber devices, the output single-pulse energy reach up to 11.67 nJ. The beam quality at mode-locked state is significantly improved compared with continuous wave state as a result of the self-cleaning effect. By amplifying the pulse in the multimode fiber amplifier, high power pulses with high beam quality can be obtained in the all-fiber system based on graded-index MMFs.

physics.optics↗
arXiv2020

Are We Ready for Service Robots? The OpenLORIS-Scene Datasets for Lifelong SLAM

Service robots should be able to operate autonomously in dynamic and daily changing environments over an extended period of time. While Simultaneous Localization And Mapping (SLAM) is one of the most fundamental problems for robotic autonomy, most existing SLAM works are evaluated with data sequences that are recorded in a short period of time. In real-world deployment, there can be out-of-sight scene changes caused by both natural factors and human activities. For example, in home scenarios, most objects may be movable, replaceable or deformable, and the visual features of the same place may be significantly different in some successive days. Such out-of-sight dynamics pose great challenges to the robustness of pose estimation, and hence a robot's long-term deployment and operation. To differentiate the forementioned problem from the conventional works which are usually evaluated in a static setting in a single run, the term \textit{lifelong SLAM} is used here to address SLAM problems in an ever-changing environment over a long period of time. To accelerate lifelong SLAM research, we release the OpenLORIS-Scene datasets. The data are collected in real-world indoor scenes, for multiple times in each place to include scene changes in real life. We also design benchmarking metrics for lifelong SLAM, with which the robustness and accuracy of pose estimation are evaluated separately. The datasets and benchmark are available online at https://lifelong-robotic-vision.github.io/dataset/scene.

cs.RO↗
arXiv2020

OpenLORIS-Object: A Robotic Vision Dataset and Benchmark for Lifelong Deep Learning

The recent breakthroughs in computer vision have benefited from the availability of large representative datasets (e.g. ImageNet and COCO) for training. Yet, robotic vision poses unique challenges for applying visual algorithms developed from these standard computer vision datasets due to their implicit assumption over non-varying distributions for a fixed set of tasks. Fully retraining models each time a new task becomes available is infeasible due to computational, storage and sometimes privacy issues, while naïve incremental strategies have been shown to suffer from catastrophic forgetting. It is crucial for the robots to operate continuously under open-set and detrimental conditions with adaptive visual perceptual systems, where lifelong learning is a fundamental capability. However, very few datasets and benchmarks are available to evaluate and compare emerging techniques. To fill this gap, we provide a new lifelong robotic vision dataset ("OpenLORIS-Object") collected via RGB-D cameras. The dataset embeds the challenges faced by a robot in the real-life application and provides new benchmarks for validating lifelong object recognition algorithms. Moreover, we have provided a testbed of $9$ state-of-the-art lifelong learning algorithms. Each of them involves $48$ tasks with $4$ evaluation metrics over the OpenLORIS-Object dataset. The results demonstrate that the object recognition task in the ever-changing difficulty environments is far from being solved and the bottlenecks are at the forward/backward transfer designs. Our dataset and benchmark are publicly available at at \href{https://lifelong-robotic-vision.github.io/dataset/object}{\underline{https://lifelong-robotic-vision.github.io/dataset/object}}.

cs.CV↗
arXiv2018

An all-fiber laser oscillating directly at single TE01 mode through ring-core fibers

Cylindrical vector beams (CVBs) have a wide range of applications owing to their particular polarization characteristics and optical field distributions. For the first time, an azimuthally polarized fiber laser without any polarization controller is proposed and demonstrated experimentally. The scheme is based on a self-designed ring-core fiber and transverse mode filter (TMF). The ring-core fiber can break the degeneracy of LP11 modes and make the TE01 mode propagate stably in the fiber laser. The TMF, which made from the ring-core fiber by depositing a layer of Aluminum on the cladding surface, can effectively suppress the modes other than TE01 mode. The fiber laser can stably operate at TE01 mode with a narrow 30dB linewidth of 0.18nm, which indicates the laser is polarization-maintained. This study opens a new avenue toward the true application of CVBs fiber lasers.

physics.optics↗
arXiv2018

Passively Q-switching cylindrical vector beam fiber laser operating in high-order mode

We experimentally demonstrate a linear-cavity all-fiber passively Q-switching cylindrical vector beam (CVB) laser operating in high-order mode. This CVB fiber laser operates without any mode converter which always leads to high insertion loss, and it can realize high efficiency. In this fiber laser, the stable Q-switching pulse is achieved with a slope efficiency of 39%. By properly adjusting the polarization controllers, radially polarized and azimuthally polarized beams can be obtained. Our work proves the feasibility of achieving the stable Q-switching CVB pulse with high-order mode directly oscillating, and it may have an enormous potential for enhancing the efficiency.

physics.optics↗
arXiv2018

Global well-posedness of the generalized KP-II equation in anisotropic Sobolev spaces

In this paper, we consider the Cauchy problem for the generalized KP-II equation \begin{eqnarray*} u_{t}-|D_{x}|^αu_{x}+\partial_{x}^{-1}\partial_{y}^{2}u+\frac{1}{2}\partial_{x}(u^{2})=0,α\geq4. \end{eqnarray*} The goal of this paper is two-fold. Firstly, we prove that the problem is locally well-posed in anisotropic Sobolev spaces H^{s_{1},\>s_{2}}(\R^{2}) with s_{1}>\frac{1}{4}-\frac{3}{8}α, s_{2}\geq 0 and α\geq4. Secondly, we prove that the problem is globally well-posed in anisotropic Sobolev spaces H^{s_{1},\>0}(\R^{2}) with -\frac{(3α-4)^{2}}{28α}<s_{1}\leq0. and α\geq4. Thus, our global well-posedness result improves the global well-posedness result of Hadac (Transaction of the American Mathematical Society, 360(2008), 6555-6572.) when 4\leq α\leq6.

math.AP↗
arXiv2017

Global well-posedness of the Cauchy problem for a fifth-order KP-I equation in anisotropic Sobolev spaces

In this paper, we consider the Cauchy problem for the fifth-order KP-I equation \begin{align*} u_t + \partial_x^5u+\partial_x^{-1}\partial_y^2u + \frac{1}{2}\partial_x(u^2)=0. \end{align*} Firstly, we establish the local well-posedness of the problem in the anisotropic Sobolev spaces $H^{s_1, s_2}(\mathbb{R}^2)$ with $s_1>-\frac{9}{8}$ and $s_2\geq 0$. Secondly, we establish the global well-posedness of the problem in $H^{s_1,0}(\mathbb{R}^2)$ with $s_1>-\frac{4}{7}$. Our result improves considerably the results of Saut and Tzvetkov (J. Math.\ Pures Appl.\ 79(2000), 307--338.) and Li and Xiao (J. Math.\ Pures Appl.\ 90(2008), 338--352.) and Guo, Huo and Fang (J. Diff.\ Eqns.\ 263 (2017), 5696--5726).

math.AP↗
arXiv2017

Existence and Uniqueness of Normalized Solutions for the Kirchhoff equation

For a class of Kirchhoff functional, we first give a complete classification with respect to the exponent $p$ for its $L^2$-normalized critical points, and show that the minimizer of the functional, if exists, is unique up to translations. Secondly, we search for the mountain pass type critical point for the functional on the $L^2$-normalized manifold, and also prove that this type critical point is unique up to translations. Our proof relies only on some simple energy estimates and avoids using the concentration-compactness principles. These conclusions extend some known results in previous papers.

math.AP↗
arXiv2017

Existence and asymptotic behavior for the ground state of quasilinear elliptic equation

In this paper, we are concerned with the existence and asymptotic behavior of minimizers for a minimization problem related to some quasilinear elliptic equations. Firstly, we proved that there exist minimizers when the exponent $q$ equals to the critical case $q^*=2+\frac{4}{N}$, which is different from that of \cite{cjs}. Then, we proved that all minimizers are compact as $q$ tends to the critical case $q^*$ when $a a^*$.

math.AP↗