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Jing Zeng

Publications and source records attributed to Jing Zeng.

At least 19 recordsLinked to original sources
arXiv2026

A Forward-Inverse Dynamic Game Framework for Enhanced Multi-Agent Trajectory Planning

This paper studies feedback Nash equilibrium (FBNE) seeking for multi-agent trajectory planning in nonlinear dynamical systems with unknown agents' objectives and state-dependent inter-agent coupling. While dynamic game theory provides a principled framework for such problems, existing approaches typically assume fully rational agents with known objectives or rely on fixed regularization, limiting their ability to capture bounded rationality and spatially varying interaction intensity in safety-critical settings. To this end, we propose a KL-regularized dynamic game with a state-dependent weight that adaptively balances optimality and behavioral priors. To infer unknown cost parameters from demonstrated behaviors, we develop a context-aware inverse game module based on maximum-entropy inverse reinforcement learning with physics-informed regularization, ensuring structural consistency with the forward game. We establish per-iteration well-posedness of the regularized local game and show that the adaptive weighting function remains Lipschitz continuous under bounded nominal-trajectory updates. Numerical simulations and multi-robot experiments on cooperative navigation and merging scenarios validate the effectiveness of the proposed framework.

cs.RO↗
arXiv2026

Two problems on booksize and triangular edges in Nosal graphs

A graph $G$ with $m$ edges is said to be a Nosal graph if $\rho(G)>\sqrt{m}$. For a graph $G$, we write $bk(G)$ for its maximum book size and $\tau(G)$ for the number of edges contained in triangles. Li, Liu and Zhang [J. Combin. Theory Ser. B 179 (2026) 219--249] proved that every $m$-edge Nosal graph satisfies $bk(G)> \frac{1}{24}\sqrt{m}$ and $\tau(G) > \frac{1}{12}\sqrt{m}$. Recently, two results on the booksize constant are proved: $\frac{1}{9}$ by Zhai, Li and Lou [arXiv:2601.10163v2], and $\frac{1}{4}$ by Chen, Li and Tang [arXiv:2607.16746v1]. In this paper, we establish the following result: Every $m$-edge graph $G$ with no isolated vertices and $\rho(G)\geq \sqrt{m}$ that is not isomorphic to any complete bipartite graph satisfies $bk(G)\geq\frac{\rho(G)}{3}$ and $\tau(G)\geq \rho(G)$. As direct consequences, we answer a question of Li, Liu and Zhang [J. Combin. Theory Ser. B 179 (2026) 219--249] and confirm a conjecture of Li, Feng and Peng [J. Graph Theory 110 (4) (2025) 408--425].

math.CO↗
arXiv2026

The signless Laplacian spectral radius of graphs without disjoint cliques

A graph $G$ is $(t+1)K_{r+1}$-free if it contains no $t+1$ pairwise vertex-disjoint copies of $K_{r+1}$. Moon [Canad. J. Math. 20 (1968) 95-102] and Simonovits [Theory of Graphs (Proc. Colloq., Tihany, 1966)] independently determined that, for sufficiently large $n$, $K_{t}\vee T_{r}(n-t)$ is the unique $n$-vertex $(t+1)K_{r+1}$-free graph with the maximum number of edges. In 2023, Ni, Wang and Kang [Electron. J. Combin. 30 (2023) \#P1.20] showed that the graph $K_{t}\vee T_{r}(n-t)$ is also the unique adjacency spectral extremal graph over all $n$-vertex $(t+1)K_{r+1}$-free graphs for sufficiently large $n$. In this paper, for $r\geq 3$ and $t\geq 0$, we prove that $K_{t}\vee T_r(n-t)$ is the unique graph attaining the maximum signless Laplacian spectral radius among all $(t+1)K_{r+1}$-free graphs of sufficiently large order $n$.

math.CO↗
arXiv2026

The Signless Laplacian Spectral Radius of $tK_3$-Free Graphs

The signless Laplacian matrix of a graph $G$ is $Q(G)=D(G)+A(G)$, where $D(G)$ and $A(G)$ are the diagonal degree matrix and the adjacency matrix of $G$, respectively. The signless Laplacian spectral radius of $G$ is the largest eigenvalue of $Q(G)$. For a positive integer $t$, a graph is called $tK_3$-free if it contains no $t$ vertex-disjoint triangles. In this paper, for every fixed $t\geq 2$ and all $n\geq 28t-17$, we determine the unique graph achieving the maximum signless Laplacian spectral radius among all $tK_3$-free graphs of order $n$.

math.CO↗
arXiv2026

Passive all-optical synchronization for polarization-maintaining ultrafast fiber lasers

We have proposed and implemented for the first time to our best knowledge a passive and all-optical pulse synchronization for polarization-maintaining ultrafast fiber lasers. Specifically, the synchronization system was comprised of two independent Yb-doped and Er-doped mode-locked fiber lasers in a master-slave configuration. Master pulses were injected into the slave laser cavity consisting of a nonlinear amplifying loop mirror, which provided an effective fast intensity modulator due to the periodic introduction of nonreciprocal phase difference. As a result, robust and tight timing synchronization was achieved with a cavity mismatch tolerance of 800 $\mu$m and a relative timing jitter of 26 fs within 1-MHz bandwidth. In combination with all-polarization-maintaining structure of fiber lasers, long-term stable operation was demonstrated over 12 hours without the need of temperature stabilization and vibration isolation. The implemented synchronous laser system could find immediate applications such as pump-probe microscopy, two-color spectroscopy and nonlinear frequency mixing.

physics.optics↗
arXiv2026

Observation of spectral mode splitting in a pump-enhanced ring cavity for mid-infrared generation

We report on experimental and theoretical investigation of mode-splitting dynamics in a ring cavity under the perturbation of fractional Bragg reflection from a periodically-poled nonlinear crystal. Counterintuitively, pronounced mode splitting in the spectral domain could been observed even with a tiny intensity reflection of 0.0003. The breaking of running-wave operation in the ring-cavity configuration resulted in comparable circulating fields in forward- and counter-propagation directions, which thus dramatically reduced the enhancing factor for the resonating field. In contrast, a linear cavity with intrinsically bidirectional operation was immune to the small intra-cavity reflection. Therefore, the linear-cavity layout could provide an expedient solution for a given internal reflection to obtain more stable and higher enhancement, which was confirmed by comparative studies of mid-infrared generation based on pump-enhanced difference frequency conversion. The underlying mechanism was further modeled by numerical simulations, which agreed well with experimental results. These findings could not only shed light on the understanding of the exotic feature of concatenated optical cavities, but also provide a useful guide to practical design of enhancement cavities for cavity-based frequency conversion with periodically-poled nonlinear crystals.

physics.optics↗
arXiv2026

Controlled generation of ultrafast vector vortex beams from a mode-locked fiber laser

We report on a new class of mode-locked fiber laser that allows direct creation of ultrafast vector vortex beams at arbitrary positions on the higher-order Poincar\'{e} sphere. The on-demand generation of space-variant polarization patterns was realized by controlling geometric phases inside the laser resonator to map polarization to orbital angular momentum. Thanks to the ingenious cavity design, the required intracavity manipulation of the geometric phase imposed no disturbance on the passively mode-locked operation, thus demonstrating robust and flexible switching of vectorial modes with a 8.5-ps pulse duration. Analytical expressions were deduced to model the generated cylindrically-symmetric polarization profiles, and agreed exceedingly well with experimental observations. The presented fiber laser would constitute a compact light source for producing ultrafast pulses in high-purity structured modes, which may find broad applications in classical and quantum optics.

physics.optics↗
arXiv2026

Passively synchronized dual-color mode-locked fiber lasers based on nonlinear amplifying loop mirrors

We have proposed and implemented a novel scheme for passive all-optical synchronization between erbium and ytterbium mode-locked fiber lasers. The passive locking of repetition rates for the dual-color pulses was realized by cross-phase modulation within phase-biased nonlinear amplifying loop mirrors. In contrast to previous demonstrations, the synchronization system was configured in an all-polarization-maintaining structure, thus gaining substantially improved stability and robustness. Consequently, the maximum tolerance of cavity-length mismatch of 16.2 mm was achieved unprecedentedly, which was at least one order of magnitude longer than previously reported results for comparable temporal durations of involved pulses. The corresponding relative timing jitter was measured to be 31 fs within 1-MHz bandwidth. Such tight and robust synchronization fiber laser system offers a great potential for various applications, such as pump-probe microscopy, Raman scattering spectroscopy and nonlinear frequency generation.

physics.optics↗
arXiv2026

A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs

Let $G$ be a unicyclic graph of order $n$, and let $k$ be the length of the unique cycle of $G$. For the adjacency eigenvalues of $G$, let $s^{+}(G)$ and $s^{-}(G)$ denote the sums of the squares of the positive and negative eigenvalues, respectively. Akbari, Kumar, Mohar, Pragada, and Zhang conjectured that, when $k$ is odd, the value of $k$ modulo $4$ determines which of $s^+(G)$ and $s^-(G)$ is greater than $n$. More precisely, if $k\equiv 3\pmod 4$, then $s^+(G)>n>s^-(G)$; if $k\equiv 1\pmod 4$, then $s^+(G)<n<s^-(G)$. We confirm this conjecture.

math.CO↗
arXiv2025

On the characterizations of $\mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$

The determinant of a tournament $T$, denoted by $\det(T)$, is defined as the determinant of the skew-adjacency matrix of $T$. It is well-known that $\det(T)$ is equal to $0$ if $n$ is odd, and $\det(T)$ is the square of an odd integer if $n$ is even. For a positive odd integer $k$, let $\mathcal{D}_k$ be the set of tournaments whose all subtournaments have determinant at most $k^2$. Former studies showed that for $k \in \{1,3,5\}$, a tournament $T \in \mathcal{D}_k \backslash \mathcal{D}_{k-2}$ ($T \in \mathcal{D}_1$ when $k=1$) if and only if $T$ is switching equivalent to a transitive blowup of $L_{k+1}$, where $L_{k+1}$ is a tournament of order $k+1$ with a specific structure. For $k \geq 7$, no characterization results are known. A natural problem is to characterize tournaments in $\mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$ that can be switching equivalent to a transitive blowup of $L_{k+1}$ for $k \geq 7$. To address this problem and to further explore the structural properties of tournaments in $\mathcal{D}_{k}$, we introduce CR tournaments, strong CR tournaments, basic tournaments and $Z$-matrices, and investigate their properties. We use these properties to characterize those tournaments $T \in \mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$ where $T$ contains a subtournament switching isomorphic to a basic strong CR tournament in $\mathcal{D}_{k} \backslash \mathcal{D}_{k-2}$. This result implies former characterizations of $\mathcal{D}_3\backslash \mathcal{D}_1$ and $\mathcal{D}_5 \backslash \mathcal{D}_3$. Using $Z$-matrices, we also show that for even $n$, $L_{n}$ is a basic strong CR tournament, and thus solve the open problem posed in [Discrete Math. 349 (2) (2026) 114766].

math.CO↗
arXiv2024

Multi-robot autonomous 3D reconstruction using Gaussian splatting with Semantic guidance

Implicit neural representations and 3D Gaussian splatting (3DGS) have shown great potential for scene reconstruction. Recent studies have expanded their applications in autonomous reconstruction through task assignment methods. However, these methods are mainly limited to single robot, and rapid reconstruction of large-scale scenes remains challenging. Additionally, task-driven planning based on surface uncertainty is prone to being trapped in local optima. To this end, we propose the first 3DGS-based centralized multi-robot autonomous 3D reconstruction framework. To further reduce time cost of task generation and improve reconstruction quality, we integrate online open-vocabulary semantic segmentation with surface uncertainty of 3DGS, focusing view sampling on regions with high instance uncertainty. Finally, we develop a multi-robot collaboration strategy with mode and task assignments improving reconstruction quality while ensuring planning efficiency. Our method demonstrates the highest reconstruction quality among all planning methods and superior planning efficiency compared to existing multi-robot methods. We deploy our method on multiple robots, and results show that it can effectively plan view paths and reconstruct scenes with high quality.

cs.RO↗
arXiv2024

On determinants of tournaments and $\mathcal{D}_k$

Let $T$ be a tournament with $n$ vertices $v_1,\ldots,v_n$. The skew-adjacency matrix of $T$ is the $n\times n$ zero-diagonal matrix $S_T = [s_{ij}]$ in which $s_{ij}=-s_{ji}=1$ if $ v_i $ dominates $ v_j $. We define the determinant $\det(T)$ of $ T $ as the determinant of $ S_T $. It is well-known that $\det(T)=0$ if $n$ is odd and $\det(T)$ is the square of an odd integer if $n$ is even. Let $\mathcal{D}_k$ be the set of tournaments whose all subtournaments have determinant at most $ k^{2} $, where $k$ is a positive odd integer. The necessary and sufficient condition for $T\in \mathcal{D}_1$ or $T\in \mathcal{D}_3$ has been characterized in $2023$. In this paper, we characterize the set $\mathcal{D}_5$, obtain some properties of $\mathcal{D}_k$. Moreover, for any positive odd integer $k$, we give a construction of a tournament $T$ satisfying that $\det(T)=k^2$, and $T\in \mathcal{D}_k\backslash\mathcal{D}_{k-2}$ if $k\geq 3$, which implies $\mathcal{D}_k\backslash\mathcal{D}_{k-2}$ is not an empty set for $k\geq 3$.

math.CO↗
arXiv2024

Autonomous Implicit Indoor Scene Reconstruction with Frontier Exploration

Implicit neural representations have demonstrated significant promise for 3D scene reconstruction. Recent works have extended their applications to autonomous implicit reconstruction through the Next Best View (NBV) based method. However, the NBV method cannot guarantee complete scene coverage and often necessitates extensive viewpoint sampling, particularly in complex scenes. In the paper, we propose to 1) incorporate frontier-based exploration tasks for global coverage with implicit surface uncertainty-based reconstruction tasks to achieve high-quality reconstruction. and 2) introduce a method to achieve implicit surface uncertainty using color uncertainty, which reduces the time needed for view selection. Further with these two tasks, we propose an adaptive strategy for switching modes in view path planning, to reduce time and maintain superior reconstruction quality. Our method exhibits the highest reconstruction quality among all planning methods and superior planning efficiency in methods involving reconstruction tasks. We deploy our method on a UAV and the results show that our method can plan multi-task views and reconstruct a scene with high quality.

cs.RO↗
arXiv2022

Efficient View Path Planning for Autonomous Implicit Reconstruction

Implicit neural representations have shown promising potential for the 3D scene reconstruction. Recent work applies it to autonomous 3D reconstruction by learning information gain for view path planning. Effective as it is, the computation of the information gain is expensive, and compared with that using volumetric representations, collision checking using the implicit representation for a 3D point is much slower. In the paper, we propose to 1) leverage a neural network as an implicit function approximator for the information gain field and 2) combine the implicit fine-grained representation with coarse volumetric representations to improve efficiency. Further with the improved efficiency, we propose a novel informative path planning based on a graph-based planner. Our method demonstrates significant improvements in the reconstruction quality and planning efficiency compared with autonomous reconstructions with implicit and explicit representations. We deploy the method on a real UAV and the results show that our method can plan informative views and reconstruct a scene with high quality.

cs.RO↗
arXiv2022

Domain Shift-oriented Machine Anomalous Sound Detection Model Based on Self-Supervised Learning

Thanks to the development of deep learning, research on machine anomalous sound detection based on self-supervised learning has made remarkable achievements. However, there are differences in the acoustic characteristics of the test set and the training set under different operating conditions of the same machine (domain shifts). It is challenging for the existing detection methods to learn the domain shifts features stably with low computation overhead. To address these problems, we propose a domain shift-oriented machine anomalous sound detection model based on self-supervised learning (TranSelf-DyGCN) in this paper. Firstly, we design a time-frequency domain feature modeling network to capture global and local spatial and time-domain features, thus improving the stability of machine anomalous sound detection stability under domain shifts. Then, we adopt a Dynamic Graph Convolutional Network (DyGCN) to model the inter-dependence relationship between domain shifts features, enabling the model to perceive domain shifts features efficiently. Finally, we use a Domain Adaptive Network (DAN) to compensate for the performance decrease caused by domain shifts, making the model adapt to anomalous sound better in the self-supervised environment. The performance of the suggested model is validated on DCASE 2020 task 2 and DCASE 2022 task 2.

cs.SD↗
arXiv2022

NeurAR: Neural Uncertainty for Autonomous 3D Reconstruction with Implicit Neural Representations

Implicit neural representations have shown compelling results in offline 3D reconstruction and also recently demonstrated the potential for online SLAM systems. However, applying them to autonomous 3D reconstruction, where a robot is required to explore a scene and plan a view path for the reconstruction, has not been studied. In this paper, we explore for the first time the possibility of using implicit neural representations for autonomous 3D scene reconstruction by addressing two key challenges: 1) seeking a criterion to measure the quality of the candidate viewpoints for the view planning based on the new representations, and 2) learning the criterion from data that can generalize to different scenes instead of a hand-crafting one. To solve the challenges, firstly, a proxy of Peak Signal-to-Noise Ratio (PSNR) is proposed to quantify a viewpoint quality; secondly, the proxy is optimized jointly with the parameters of an implicit neural network for the scene. With the proposed view quality criterion from neural networks (termed as Neural Uncertainty), we can then apply implicit representations to autonomous 3D reconstruction. Our method demonstrates significant improvements on various metrics for the rendered image quality and the geometry quality of the reconstructed 3D models when compared with variants using TSDF or reconstruction without view planning. Project webpage https://kingteeloki-ran.github.io/NeurAR/

cs.CV↗
arXiv2021

Generalized Liquid Association Analysis for Multimodal Data Integration

Multimodal data are now prevailing in scientific research. A central question in multimodal integrative analysis is to understand how two data modalities associate and interact with each other given another modality or demographic variables. The problem can be formulated as studying the associations among three sets of random variables, a question that has received relatively less attention in the literature. In this article, we propose a novel generalized liquid association analysis method, which offers a new and unique angle to this important class of problems of studying three-way associations. We extend the notion of liquid association of \citet{li2002LA} from the univariate setting to the sparse, multivariate, and high-dimensional setting. We establish a population dimension reduction model, transform the problem to sparse Tucker decomposition of a three-way tensor, and develop a higher-order orthogonal iteration algorithm for parameter estimation. We derive the non-asymptotic error bound and asymptotic consistency of the proposed estimator, while allowing the variable dimensions to be larger than and diverge with the sample size. We demonstrate the efficacy of the method through both simulations and a multimodal neuroimaging application for Alzheimer's disease research.

stat.ME↗