arXiv subjects

Wen Xu

Publications and source records attributed to Wen Xu.

At least 19 recordsLinked to original sources

arXiv2026

Extinction and extinguishment properties for a nonlinear predator-prey branching model

We study extinction and extinguishment in a two-type continuous-state nonlinear branching model driven by Brownian branching noise and spectrally positive stable jumps. The populations are subject to nonlinear self-regulation and a mixed-sign predator--prey interaction: the second promotes the first, whereas the first suppresses the second. Two complementary structures are developed. An exact power--logarithmic cancellation functional removes the interaction drifts and yields stochastic Lyapunov estimates, nonexplosion, and boundary criteria. In the multiplicative regimes, integrating-factor identities and geometric L\'evy factorizations express extinction through weighted exposure clocks and reduce the long-time analysis to effective decay rates. These methods yield almost-sure extinction criteria and identify a regime in which finite-time extinction and nonextinction coexist. On nonextinction, both populations remain positive at all finite times and converge jointly to zero, exhibiting joint extinguishment rather than positive persistence.

math.PR↗

arXiv2026

Visualizing in the Mind's Eye: Icon Design Shapes Mental Imagery of Fire Risks

We introduce mental imagery, or seeing images in the "mind's eye," as a cognitive process that can be shaped by data visualization design and in turn impact decisions. We found in a preregistered study (n = 400) that abstract geometric icons visualizing fire risk data evoked more mental images than concrete house-on-fire icons, and also produced more diverse and personalized mental images. Mediation analysis showed that increased mental imagery subsequently led to risk-averse decisions through evoking negative affect. These findings reveal a nuanced mechanism through which visualization concreteness influences decisions: concrete designs may actually suppress affect-driven behavior by restricting mental imagery.

cs.HC↗

arXiv2026

Pathwise uniqueness for degenerate stochastic differential equations with H\"older continuous coefficients

We study pathwise uniqueness for cyclic catalytic stochastic differential equations whose state-dependent square-root diffusion coefficients are non-Lipschitz and degenerate on the boundary. The approach is the direct construction of a strong solution using a Malliavin compactness criterion. The key is the development of a new family of boundary-sensitive weighted Malliavin estimates for the tangent processes of the smooth approximations. Pathwise uniqueness then follows from the dual Yamada-Watanabe argument together with the weak uniqueness available in the literature.

math.PR↗

arXiv2026

Strong uniqueness and large deviation principle for mutually catalytic super Markov chains

In this paper, we study the strong uniqueness problem for the mutually catalytic super-Markov chain, which is a two-dimensional degenerate stochastic differential equation with H\"older continuous coefficients. The key step is to find a process which is a function of two coupled processes and satisfies an autonomous one-dimensional stochastic differential equation; uniqueness for this equation follows from a Yamada-Watanabe argument. A large deviation principle is then established, in the irreducible two-state case, by applying the weak-convergence approach of Budhiraja, Dupuis and Maroulas to the controlled equations.

math.PR↗

arXiv2026

RICH-SLAM: Radar SLAM with Incremental and Continuous Hilbert Mapping

Simultaneous localization and mapping using radar sensors has gained increasing attention due to radar's inherent robustness to adverse weather and lighting conditions. However, radar measurements are characteristically sparse and noisy compared to LiDAR and visual data, posing significant challenges in achieving dense, continuous, and consistent map representations. In this paper, we present RICH-SLAM, a radar SLAM framework designed to address these challenges. Our approach features a Rao-Blackwellized particle filter-based back end that employs particle filtering for pose estimation and Kalman filtering for map updates. We propose an incremental Hilbert-space reduced-rank Gaussian process mapping strategy that enables continuous and uncertainty-aware map representations given sparse radar inputs. We further introduce a posterior-aware particle weighting scheme that leverages the full posterior distribution of map parameters for more robust likelihood evaluation. Experiments on self-collected and public ColoRadar datasets show that RICH-SLAM constructs continuous occupancy maps from sparse radar measurements and supports uncertainty-aware planning for mobile robots.

cs.RO↗

arXiv2026

Convexity and non-Markovianity of Weyl Maps

We investigate the emergence of non-Markovian dynamics in finite-dimensional open quantum systems governed by Weyl dynamical maps and their convex combinations. Using the Hermite normal form, we provide a complete classification of the subgroups of the discrete phase space $\mathbb{Z}_d \times \mathbb{Z}_d$, establishing the algebraic framework underlying the Weyl maps. We characterize isotropic Weyl dynamical maps that generate Markovian semigroups and show that anisotropic Weyl maps with nonuniform weight distributions cannot possess the semigroup property. Furthermore, we analyze the role of convexity in the generation and suppression of memory effects. Remarkably, we prove that convex combinations of eternally non-Markovian Weyl dephasing maps can generate Markovian semigroups, demonstrating that non-Markovianity is not additive under mixing. Conversely, we establish a general condition under which convex mixtures of $N$ distinct Weyl semigroups exhibit eternal non-Markovianity. In contrast to the qubit Pauli setting, we further identify the existence of irreducible eternally non-Markovian Weyl dephasing maps, namely, individual dynamical maps that display eternal memory effects without requiring any mixing mechanism. Finally, explicit qutrit examples illustrate the transition among Markovian, non-Markovian and eternally non-Markovian regimes. Our results uncover a fundamental connection among finite phase-space algebra, convex structures, and quantum memory effects, thereby extending the theory of non-Markovian dynamics beyond the Pauli framework.

quant-ph↗

arXiv2026

Polar Coded Quantization for Distributed Source Coding

Scalar quantization and probabilistic shaping are applied to the distributed source coding of Gaussian sources, with mean-square error distortion. A coding scheme with a modulo interval, dithering, and truncated Gaussian shaping is shown to achieve the corner points of the Berger-Tung region. The theory is illustrated by designing short-block-length multilevel 5G polar codes for Wyner-Ziv (WZ) polar coded quantization (PCQ). WZ-PCQ substantially reduces the total distortion compared to separate PCQ of the source blocks.

cs.IT↗

arXiv2026

HoGS: Homophily-Oriented Graph Synthesis for Local Differentially Private GNN Training

Graph neural networks (GNNs) have demonstrated remarkable performance in various graph-based machine learning tasks by effectively modeling high-order interactions between nodes. However, training GNNs without protection may leak sensitive personal information in graph data, including links and node features. Local differential privacy (LDP) is an advanced technique for protecting data privacy in decentralized networks. Unfortunately, existing local differentially private GNNs either only preserve link privacy or suffer significant utility loss in the process of preserving link and node feature privacy. In this paper, we propose an effective LDP framework, called HoGS, which trains GNNs with link and feature protection by generating a synthetic graph. Concretely, HoGS first collects the link and feature information of the graph under LDP, and then utilizes the phenomenon of homophily in graph data to reconstruct the graph structure and node features separately, thereby effectively mitigating the negative impact of LDP on the downstream GNN training. We theoretically analyze the privacy guarantee of HoGS and conduct experiments using the generated synthetic graph as input to various state-of-the-art GNN architectures. Experimental results on three real-world datasets show that HoGS significantly outperforms baseline methods in the accuracy of training GNNs.

cs.LG↗

arXiv2025

Toward General Semantic Chunking: A Discriminative Framework for Ultra-Long Documents

Long-document topic segmentation plays an important role in information retrieval and document understanding, yet existing methods still show clear shortcomings in ultra-long text settings. Traditional discriminative models are constrained by fixed windows and cannot model document-level semantics; generative large language models can output paragraph boundaries, but inference is expensive and long inputs are difficult to support. To address these issues, we propose a discriminative segmentation model based on Qwen3-0.6B. On top of the backbone network, we add a cross-window context fusion layer and a boundary classification head, and combine them with an overlapping sliding-window strategy. Our model supports single-pass inputs of up to 13k tokens and can be extended to ultra-long documents for paragraph boundary detection. To further enhance downstream retrieval efficiency, we derive a vector fusion method with scalar correction, which compresses the representation of ultra-long segments into a single vector without semantic loss. Experiments on the Wikipedia long-document topic segmentation dataset WIKI-727K show that, compared with three generative models based on Qwen2-0.5B released by Jina, our method achieves a better macro-averaged F1 and delivers two orders of magnitude faster inference, substantially improving the practicality and scalability of long-document processing.

cs.CL↗

arXiv2025

VIMS: A Visual-Inertial-Magnetic-Sonar SLAM System in Underwater Environments

In this study, we present a novel simultaneous localization and mapping (SLAM) system, VIMS, designed for underwater navigation. Conventional visual-inertial state estimators encounter significant practical challenges in perceptually degraded underwater environments, particularly in scale estimation and loop closing. To address these issues, we first propose leveraging a low-cost single-beam sonar to improve scale estimation. Then, VIMS integrates a high-sampling-rate magnetometer for place recognition by utilizing magnetic signatures generated by an economical magnetic field coil. Building on this, a hierarchical scheme is developed for visual-magnetic place recognition, enabling robust loop closure. Furthermore, VIMS achieves a balance between local feature tracking and descriptor-based loop closing, avoiding additional computational burden on the front end. Experimental results highlight the efficacy of the proposed VIMS, demonstrating significant improvements in both the robustness and accuracy of state estimation within underwater environments.

cs.RO↗

arXiv2025

Scalar Lattices and Probabilistic Shaping for Dithered Wyner-Ziv Quantization

Scalar lattice quantization with a modulo operator, dithering, and probabilistic shaping is applied to the Wyner-Ziv (WZ) problem with a Gaussian source and mean square error distortion. The method achieves the WZ rate-distortion pairs. The analysis is similar to that for dirty paper coding but requires additional steps to bound the distortion because the modulo shift is correlated with the source noise. The results extend to vector sources by reverse waterfilling on the spectrum of the covariance matrix of the source noise. Simulations with short polar codes illustrate the performance and compare with scalar quantizers and polar coded quantization without dithering.

cs.IT↗

arXiv2025

Near optimal controls for partially observed stochastic linear quadratic problems

In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the diffusion term of the state equation, the circular dependence between the control process and the filtration generated by the observation, and the observation process contains an unbounded drift term. We address these difficulties by first restricting the control to a smaller domain, which enables us to apply the Girsanov theorem using a conditional argument and thereby break the circular dependence. Subsequently, we study the restricted problem using a non-standard variation method. The desired near optimal control is then obtained by taking the limit of an approximating sequence.

math.OC↗

arXiv2025

A Flexible Fairness Framework with Surrogate Loss Reweighting for Addressing Sociodemographic Disparities

This paper presents a new algorithmic fairness framework called $\boldsymbol{\alpha}$-$\boldsymbol{\beta}$ Fair Machine Learning ($\boldsymbol{\alpha}$-$\boldsymbol{\beta}$ FML), designed to optimize fairness levels across sociodemographic attributes. Our framework employs a new family of surrogate loss functions, paired with loss reweighting techniques, allowing precise control over fairness-accuracy trade-offs through tunable hyperparameters $\boldsymbol{\alpha}$ and $\boldsymbol{\beta}$. To efficiently solve the learning objective, we propose Parallel Stochastic Gradient Descent with Surrogate Loss (P-SGD-S) and establish convergence guarantees for both convex and nonconvex loss functions. Experimental results demonstrate that our framework improves overall accuracy while reducing fairness violations, offering a smooth trade-off between standard empirical risk minimization and strict minimax fairness. Results across multiple datasets confirm its adaptability, ensuring fairness improvements without excessive performance degradation.

cs.LG↗

arXiv2025

The quantum non-Markovianity for a special class of generalized Weyl channel

A quantum channel is usually represented as a sum of Kraus operators. The recent study [Phys. Rev. A 98, 032328 (2018)] has shown that applying a perturbation to the Kraus operators in qubit Pauli channels, the dynamical maps exhibit interesting properties, such as non-Markovianity, singularity. This has sparked our interest in studying the properties of other quantum channels. In this work, we study a special class of generalized Weyl channel where the Kraus operators are proportional to the Weyl diagonal matrices and the rest are vanishing. We use the Choi matrix of intermediate map to study quantum non-Markovianity. The crossover point of the eigenvalues of Choi matrix is a singularity of the decoherence rates in the canonical form of the master equation. Moreover, we identify the non-Markovianity based on the methods of CP divisibility and distinguishability. We also quantify the non-Markovianity in terms of the Hall-Cresser-Li-Andersson (HCLA) measure and the Breuer-Laine-Piilo (BLP) measure, respectively. In particular, we choose mutually unbiased bases as a pair of orthogonal initial states to quantify the non-Markovianity based on the BLP measure.

quant-ph↗

arXiv2025

Linear-quadratic control for mean-field backward stochastic differential equations with random coefficients

In this paper, we study the linear-quadratic control problem for mean-field backward stochastic differential equations (MF-BSDE) with random coefficients. We first derive a preliminary stochastic maximum principle to analyze the unique solvability of the optimality system for this control problem through the variational method. Subsequently, we reformulate the mean-field linear-quadratic (MF-BSLQ) problem as a constrained BSDE control problem by imposing constraints on the expectation processes, which we solve using the Extended Lagrange multiplier method. Finally, we derive an explicit expression for the optimal control associated with Problem (MF-BSLQ).

math.OC↗

arXiv2024

Sum Rate Maximization in the Constant Envelope MIMO Downlink with the RZF Precoder

Feeding power amplifiers (PAs) with constant envelope (CE) signals is an effective way to reduce the power consumption in massive multiple-input-multiple-output (MIMO) systems. The nonlinear distortion caused by CE signaling must be mitigated by means of signal processing to improve the achievable sum rates. To this purpose, many linear and nonlinear precoding techniques have been developed for the CE MIMO downlink. The vast majority of these CE precoding techniques do not include a power allocation scheme, which is indispensable to achieve adequate performances in the downlink with channel gain imbalances between users. In this paper, we present two algorithms to produce a power allocation scheme for regularized zero-forcing (RZF) precoding in CE MIMO downlink. Both techniques are based on transforming the CE quantized MIMO downlink to an approximately equivalent system of parallel single-input-single-output (SISO) channels. The first technique is proven to solve the sum rate maximization problem in the approximate system optimally, whereas the second technique obtains the local maximum with lower complexity. We also extend another state-of-the-art quantization aware sum rate maximization algorithm with linear precoding to the CE downlink. Numerical results illustrate significant gains for the performance of the RZF precoder when the CE quantization is taken into account in a power allocation. Another key numerical result is that the proposed RZF techniques achieve almost the identical performance so that the one with lower computational complexity is chosen as the main method. Results also show that the proposed RZF precoding schemes perform at least as good as the state-of-the-art method with an advantage that the main RZF method has significantly lower computational complexity than the state-of-the-art.

eess.SP↗

arXiv2024

Formation mechanisms and fluorescence properties of carbon dots in coal burning dust from coal fired power plants

Carbon dots (CDs) shows great application potential with their unique and excellent performances. Coal and its derivatives are rich in aromatic ring structure, which is suitable for preparing CDs in microstructure. Coal burning dust from coal-fired power plants can be utilized as a rich resource to separate and extract CDs. It has been shown in our results that there have two main possible mechanisms for the formation of CDs in coal burning dust. One is the self-assembly of polycyclic aromatic hydrocarbons contained in coal or produced by incomplete combustion of coal. The other mechanism is that the bridge bonds linking different aromatic structures in coal are breaking which would form CDs with different functional groups when the coals are burning at high temperature. Under violet light excitation at 310-340 nm or red light at 610-640 nm, CDs extracted from coal burning dust can emit purple fluorescence around 410 nm. The mechanism of up-conversion fluorescence emission of CDs is due to a two-photon absorption process. The recycling of CDs from coal burning dust from coal-fired power plants are not only good to protect environment but also would be helpful for mass production of CDs.

cond-mat.mes-hall↗

arXiv2024

Mean-field stochastic linear quadratic control problem with random coefficients

In this paper, we first prove that the mean-field stochastic linear quadratic (MFSLQ for short) control problem with random coefficients has a unique optimal control and derive a preliminary stochastic maximum principle to characterize this optimal control by an optimality system. However, because of the term of the form $\mathbb{E}[A_1(\cdot)^\top Y(\cdot)] $ in the adjoint equation, which cannot be represented in the form $\mathbb{E}[A_1(\cdot)^\top]\mathbb{E} [Y(\cdot)] $, we cannot solve this optimality system explicitly. To this end, we decompose the MFSLQ control problem into two problems without the mean-field terms, and one of them is a constrained problem. The constrained SLQ control problem is solved explicitly by an extended LaGrange multiplier method developed in this article.

math.OC↗