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Gang Ma

Publications and source records attributed to Gang Ma.

11 recordsLinked to original sources
arXiv2025

Physics-Driven Learning Framework for Tomographic Tactile Sensing

Electrical impedance tomography (EIT) provides an attractive solution for large-area tactile sensing due to its minimal wiring and shape flexibility, but its nonlinear inverse problem often leads to severe artifacts and inaccurate contact reconstruction. This work presents PhyDNN, a physics-driven deep reconstruction framework that embeds the EIT forward model directly into the learning objective. By jointly minimizing the discrepancy between predicted and ground-truth conductivity maps and enforcing consistency with the forward PDE, PhyDNN reduces the black-box nature of deep networks and improves both physical plausibility and generalization. To enable efficient backpropagation, we design a differentiable forward-operator network that accurately approximates the nonlinear EIT response, allowing fast physics-guided training. Extensive simulations and real tactile experiments on a 16-electrode soft sensor show that PhyDNN consistently outperforms NOSER, TV, and standard DNNs in reconstructing contact shape, location, and pressure distribution. PhyDNN yields fewer artifacts, sharper boundaries, and higher metric scores, demonstrating its effectiveness for high-quality tomographic tactile sensing.

cs.LG↗
arXiv2025

Mathematical Modeling of Carbon Dioxide Emissions with GDP Linkage: Sensitivity Analysis and Optimal Control Strategy

Climate change and global warming are among the most significant issues that humanity is currently facing, and also among the issues that pose the greatest threats to all mankind. These issues are primarily driven by abnormal increases in greenhouse gas concentrations. Mathematical modeling serves as a powerful approach to analyze the dynamic patterns of atmospheric carbon dioxide. In this paper, we established a mathmetical model with four state variables to investigate the dynamic behavior of the interaction between atmospheric carbon dioxide, GDP, forest area and human population. Relevant theories were employed to analyze the system's boundedness and the stability of equilibrium points. The parameter values were estimated with the help of the actual data in China and numerical fitting was carried out to verify the results of the theoretical analysis. The sensitivity analysis of the compartments with respect to the model parameters was analyzed by using the Partial Rank Correlation Coefficient (PRCC) and the Latin Hypercube Sampling test. Apply the optimal control theory to regulate the atmospheric carbon dioxide level and provide the corresponding numerical fitting. Finally, corresponding discussions and suggestions were put forward with the help of the results of the theoretical analysis and numerical fitting.

math.OC↗
arXiv2024

On $\ell$-distance-balancedness of cubic Cayley graphs of dihedral groups

A connected graph $\Gamma$ of diameter ${\rm diam}(\Gamma) \ge \ell$ is $\ell$-distance-balanced if $|W_{xy}(\Gamma)|=|W_{yx}(\Gamma)|$ for every $x,y\in V(\Gamma)$ with $d_{\Gamma}(x,y)=\ell$, where $W_{xy}(\Gamma)$ is the set of vertices of $\Gamma$ that are closer to $x$ than to $y$. $\Gamma$ is said to be highly distance-balanced if it is $\ell$-distance-balanced for every $\ell\in [{\rm diam}(\Gamma)]$. It is proved that every cubic Cayley graph whose generating set is one of $\{a,a^{n-1},ba^r\}$ and $\{a^k,a^{n-k},ba^t\}$ is highly distance-balanced. This partially solves a problem posed by Miklavi\v{c} and \v{S}parl.

math.CO↗
arXiv2024

A Physics-Embedded Dual-Learning Imaging Framework for Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a promising noninvasive imaging technique that reconstructs the spatial conductivity distribution from boundary voltage measurements. However, it poses a highly nonlinear and ill-posed inverse problem. Traditional regularization-based methods are sensitive to noise and often produce significant artifacts. Physics-Embedded learning frameworks, particularly Physics-Informed Neural Networks (PINNs), have shown success in solving such inverse problems under ideal conditions with abundant internal data. Yet in practical EIT applications, only sparse and noisy boundary measurements are available. Moreover, changing boundary excitations require the simultaneous training of multiple forward networks and one inverse network, which significantly increases computational complexity and hampers convergence. To overcome these limitations, we propose a Physics-Embedded Dual-Learning Imaging Framework for EIT. The dual-learning strategy is composed of a supervised CNN-based forward network, which learns to predict a discrete internal potential distribution under fixed Neumann-to-Dirichlet boundary conditions, and an unsupervised PINN-based inverse network, which reconstructs the conductivity by enforcing the governing PDE through discrete numerical differentiation of the predicted potentials. This decoupled architecture removes the need for smooth conductivity assumptions, reduces the number of forward networks required from $K$ to 1, and improves reconstruction robustness and efficiency under realistic measurement constraints.(https://github.com/XuanxuanYang/CNN-PINNframework.git)

eess.SP↗
arXiv2024

A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT)

Electrical Impedance Tomography (EIT) is a highly ill-posed inverse problem, with the challenge of reconstructing internal conductivities using only boundary voltage measurements. Although Physics-Informed Neural Networks (PINNs) have shown potential in solving inverse problems, existing approaches are limited in their applicability to EIT, as they often rely on impractical prior knowledge and assumptions that cannot be satisfied in real-world scenarios. To address these limitations, we propose a two-stage hybrid learning framework that combines Convolutional Neural Networks (CNNs) and PINNs. This framework integrates data-driven and model-driven paradigms, blending supervised and unsupervised learning to reconstruct conductivity distributions while ensuring adherence to the underlying physical laws, thereby overcoming the constraints of existing methods.

cs.LG↗
arXiv2024

On $\{1,2\}$-distance-balancedness of generalized Petersen graphs

A connected graph $G$ of diameter ${\rm diam}(G) \ge \ell$ is $\ell$-distance-balanced if $|W_{xy}|=|W_{yx}|$ for every $x,y\in V(G)$ with $d_{G}(x,y)=\ell$, where $W_{xy}$ is the set of vertices of $G$ that are closer to $x$ than to $y$. It is proved that if $k\ge 3$ and $n>k(k+2)$, then the generalized Petersen graph $GP(n,k)$ is not distance-balanced and that $GP(k(k+2),k)$ is distance-balanced. This significantly improves the main result of Yang et al.\ [Electron.\ J.\ Combin.\ 16 (2009) \#N33]. It is also proved that if $k\ge 6$, where $k$ is even, and $n>\frac{5}{4}k^2+2k$, or if $k\ge 5$, where $k$ is odd, and $n>\frac{7}{4}k^2+\frac{3}{4}k$, then $GP(n,k)$ is not $2$-distance-balanced. These results partially resolve a conjecture of Miklavi\v{c} and \v{S}parl [Discrete Appl.\ Math.\ 244 (2018) 143--154].

math.CO↗
arXiv2024

On Support Relations Inference and Scene Hierarchy Graph Construction from Point Cloud in Clustered Environments

Over the years, scene understanding has attracted a growing interest in computer vision, providing the semantic and physical scene information necessary for robots to complete some particular tasks autonomously. In 3D scenes, rich spatial geometric and topological information are often ignored by RGB-based approaches for scene understanding. In this study, we develop a bottom-up approach for scene understanding that infers support relations between objects from a point cloud. Our approach utilizes the spatial topology information of the plane pairs in the scene, consisting of three major steps. 1) Detection of pairwise spatial configuration: dividing primitive pairs into local support connection and local inner connection; 2) primitive classification: a combinatorial optimization method applied to classify primitives; and 3) support relations inference and hierarchy graph construction: bottom-up support relations inference and scene hierarchy graph construction containing primitive level and object level. Through experiments, we demonstrate that the algorithm achieves excellent performance in primitive classification and support relations inference. Additionally, we show that the scene hierarchy graph contains rich geometric and topological information of objects, and it possesses great scalability for scene understanding.

cs.CV↗
arXiv2023

Non-$\ell$-distance-balanced generalized Petersen graphs $GP(n,3)$ and $GP(n,4)$

A connected graph $G$ of diameter ${\rm diam}(G) \ge \ell$ is $\ell$-distance-balanced if $|W_{xy}|=|W_{yx}|$ for every $x,y\in V(G)$ with $d_{G}(x,y)=\ell$, where $W_{xy}$ is the set of vertices of $G$ that are closer to $x$ than to $y$. We prove that the generalized Petersen graph $GP(n,3)$ where $n>16$ is not $\ell$-distance-balanced for any $1\le \ell < {\rm diam}(GP(n,3))$, and $GP(n,4)$ where $n>24$ is not $\ell$-distance-balanced for any $1\le \ell < {\rm diam}(GP(n,4))$. This partially solves a conjecture posed by \v{S}. Miklavi\v{c} and P. \v{S}parl (Discrete Appl. Math. 244:143-154, 2018).

math.CO↗
arXiv2022

RaLiBEV: Radar and LiDAR BEV Fusion Learning for Anchor Box Free Object Detection Systems

In autonomous driving, LiDAR and radar are crucial for environmental perception. LiDAR offers precise 3D spatial sensing information but struggles in adverse weather like fog. Conversely, radar signals can penetrate rain or mist due to their specific wavelength but are prone to noise disturbances. Recent state-of-the-art works reveal that the fusion of radar and LiDAR can lead to robust detection in adverse weather. The existing works adopt convolutional neural network architecture to extract features from each sensor data, then align and aggregate the two branch features to predict object detection results. However, these methods have low accuracy of predicted bounding boxes due to a simple design of label assignment and fusion strategies. In this paper, we propose a bird's-eye view fusion learning-based anchor box-free object detection system, which fuses the feature derived from the radar range-azimuth heatmap and the LiDAR point cloud to estimate possible objects. Different label assignment strategies have been designed to facilitate the consistency between the classification of foreground or background anchor points and the corresponding bounding box regressions. Furthermore, the performance of the proposed object detector is further enhanced by employing a novel interactive transformer module. The superior performance of the methods proposed in this paper has been demonstrated using the recently published Oxford Radar RobotCar dataset. Our system's average precision significantly outperforms the state-of-the-art method by 13.1% and 19.0% at Intersection of Union (IoU) of 0.8 under 'Clear+Foggy' training conditions for 'Clear' and 'Foggy' testing, respectively.

cs.CV↗
arXiv2022

On distance-balanced generalized Petersen graphs

A connected graph $G$ of diameter ${\rm diam}(G) \ge \ell$ is $\ell$-distance-balanced if $|W_{xy}|=|W_{yx}|$ for every $x,y\in V(G)$ with $d_{G}(x,y)=\ell$, where $W_{xy}$ is the set of vertices of $G$ that are closer to $x$ than to $y$. We prove that the generalized Petersen graph $GP(n,k)$ is ${\rm diam}(GP(n,k))$-distance-balanced provided that $n$ is large enough relative to $k$. This partially solves a conjecture posed by Miklavi\v{c} and \v{S}parl \cite{Miklavic:2018}. We also determine ${\rm diam}(GP(n,k))$ when $n$ is large enough relative to $k$.

math.CO↗
arXiv2008

Canonical RNA pseudoknot structures

In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $\ge 4$. Let ${\sf T}_{k,σ}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the generating function ${\bf T}_{k,σ}^{[4]}(z)= \sum_n{\sf T}_{k,σ}^{[4]}(n)z^n$ and derive the asymptotic formulas ${\sf T}_{k,3}^{[4]}(n)^{}\sim c_k n^{-(k-1)^2-\frac{k-1}{2}} (γ_{k,3}^{[4]})^{-n}$ for $k=3,...,9$. In particular we have for $k=3$, ${\sf T}_{3,3}^{[4]}(n)^{}\sim c_3 n^{-5} 2.0348^n$. Our results prove that the set of biophysically relevant RNA pseudoknot structures is surprisingly small and suggest a new structure class as target for prediction algorithms.

math.CO↗