arXiv subjects

Wenjing Chen

Publications and source records attributed to Wenjing Chen.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group

We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group $\mathbb{H}^{n}$, \begin{equation}\label{nS} S_{HL}(Q,μ)\left(\int_{\mathbb{H}^{n}}\int_{\mathbb{H}^{n}} \frac{|u(ξ)|^{Q^{\ast}_μ}|u(η)|^{Q^{\ast}_μ}} {|η^{-1}ξ|^μ}\,dξdη\right)^{\frac{1}{Q^{\ast}_μ}} \leq \int_{\mathbb{H}^{n}}|\nabla_{\mathbb{H}}u|^{2}dξ, \qquad u\in S^{1,2}(\mathbb{H}^{n}), \end{equation} where $Q=2n+2$, $n\geq1$, $0<μ H_{BE}$ with the optimal stability constant for the local Folland-Stein-Sobolev inequality. We further prove that the sharp universal upper constant for the deficit-to-distance comparison is $1$ and characterize equality. Finally, for the associated Euler-Lagrange equation, we formulate the corresponding residual quotient and derive a strict single-bubble upper bound; this critical-point statement requires a separate expansion and does not follow from attainment of $H_{NS}$.

math.AP↗

arXiv2026

Radial Nodal Dirichlet Solutions of Singular Elliptic Equations: Global Branches, Endpoint Asymptotics, and Morse Indices

We establish sharp finite-ball shooting classifications for radial nodal Dirichlet solutions of the logarithmic equation and, within the maximal simple-zero shooting class, of the sublinear scalar-field equation. Recent whole-space uniqueness and phase-transition theorems are used as external inputs, while the finite-ball zero-curve ranges, endpoint asymptotics, and spectral consequences are proved here. The two models require different singular analyses: in the logarithmic problem the nonlinearity is not locally Lipschitz at a nodal zero and the linearized potential diverges there, whereas in the sublinear problem the limiting whole-space profile reaches a double zero at a finite support radius, beyond which continuation is nonunique. For every $R>0$ and $k\ge0$, the logarithmic problem has, up to sign, a unique radial Dirichlet solution with exactly $k$ interior zeros. Its shooting height $β_k^{\log}(R)$ is a strictly decreasing $C^1$ bijection from $(0,\infty)$ onto $(α_k^{\log},\infty)$ and satisfies \[ β_k^{\log}(R)\longrightarrowα_k^{\log} \quad(R\to\infty),\qquad \log\bigl(β_k^{\log}(R)^2\bigr) =\frac{ρ_{k+1}^2}{R^2}+κ_{k+1,n}+o(1) \quad(R\downarrow0), \] where $κ_{k+1,n}>0$ is given by an explicit Bessel integral. For the sublinear problem, the maximal simple-zero branch exists precisely for $R\in(ρ_{k+1},S_k)$, where $ρ_{k+1}$ is the $(k+1)$-st positive zero of the regular Bessel profile $Φ_n$, and $S_k$ is the support radius of the unique compactly supported $k$-node whole-space bound state.

math.AP↗

arXiv2026

Vision-Based Tactile Sensing for the Perception of the Object's Compliance and Hardness

Object compliance perception enables the identification of soft materials, supporting tasks such as fruit detection and assisted medical palpation. Compliance perception requires sensing an object's deformation and contact forces. Existing vision-based tactile sensing for compliance perception usually depends only on force or deformation. However, deformation-based approaches cannot reliably quantify object compliance, while force-based methods are overly sensitive to geometric variations. To address these limitations, this paper presents a framework that fuses temporal force sequences and deformation field information. Specifically, time-varying contact forces are inferred from tactile image sequences via a neural network, while deformation characteristics are encoded using depth maps. Crucially, the temporal force sequence is used as a dynamic force-response feature for compliance recognition. In standard experiments, the force prediction error reaches 0.06 N within a measurement range of 12 N. The proposed method achieves a 98.0% Shore-hardness classification accuracy for samples ranging from 10 HA to 80 HA. In practical scenarios, including abnormal fruit detection and soft matter, the overall accuracy exceeds 98.5%. This method improves the compliance perception ability of artificial tactile systems and facilitates their deployment in embodied perception applications.

cs.RO↗

arXiv2026

Construction of $n$-cotorsion pairs in some abelian categories

In this paper, we mainly investigate $n$-cotorsion pairs in two types of abelian categories. Firstly, we construct left (right) $n$-cotorsion pairs in comma categories by improving some isomorphisms between homology groups and combining some classes of objects in comma categories. Secondly, based on known homological formulas over trivial ring extensions, we study some classes of modules satisfying certain conditions over such rings, and we establish left (right) $n$-cotorsion pairs over trivial ring extensions through these classes. Then corresponding conclusions over Morita rings with zero bimodule homomorphisms are directly presented. The hereditary property of left (right) $n$-cotorsion pairs is investigated in both cases. Finally, we apply main results obtained in comma categories and over trivial ring extensions to formal triangular matrix rings. At the same time, via these applications, we found that relevant conditions in known results have been improved and the known results have been elevated.

math.RA↗

arXiv2026

TimePre: Bridging Accuracy, Efficiency, and Stability in Probabilistic Time-Series Forecasting

We propose TimePre, a simple framework that unifies the efficiency of Multilayer Perceptron (MLP)-based models with the distributional flexibility of Multiple Choice Learning (MCL) for Probabilistic Time-Series Forecasting (PTSF). Stabilized Instance Normalization (SIN), the core of TimePre, is a normalization layer that explicitly addresses the trade-off among accuracy, efficiency, and stability. SIN stabilizes the hybrid architecture by correcting channel-wise statistical shifts, thereby resolving the catastrophic hypothesis collapse. Extensive experiments on six benchmark datasets demonstrate that TimePre achieves state-of-the-art (SOTA) accuracy on key probabilistic metrics. Critically, TimePre achieves inference speeds that are orders of magnitude faster than sampling-based models, and is more stable than prior MCL approaches.

cs.LG↗

arXiv2026

Concentration, Local Uniqueness, and Morse Index of Multi-bubble Solutions for a Critical Exponential Biharmonic Choquard Equation

Let $Ω\subset\mathbb R^4$ be a bounded domain of class $C^6$, let $0<α<4$, and let $K\in C^4(\overlineΩ)$ be positive. We study the Navier problem \[ Δ^2u=\varepsilon^{8-α}K(x)e^{u(x)} \left(\int_Ω\frac{K(y)e^{u(y)}}{|x-y|^α}\,dy\right), \qquad u=Δu=0\quad\text{on }\partialΩ. \] Let $G$ be the Navier Green function, let $H$ be its regular part, and put $M_α=8π^2(8-α)$. The concentration points are governed by \[ \mathcal F_m(\boldsymbolξ) =\sum_{i=1}^m \left[\log K(ξ_i)+\frac{M_α}{2}H(ξ_i,ξ_i)\right] +M_α\sum_{i<j}G(ξ_i,ξ_j). \] Every $C^1$-stable critical point of $\mathcal F_m$ produces a positive $m$-bubble solution whose scales are of order $\varepsilon^{-1}$ and whose nonlinear source converges to $M_α\sum_iδ_{ξ_i^*}$. If the critical point is nondegenerate, the corresponding $m$-bubble solution is locally unique, modulo permutations, in a fixed scaled modulation neighborhood. The linearized operator is nondegenerate on $H^2(Ω)\cap H_0^1(Ω)$, and \[ \operatorname{ind}(u_\varepsilon) =m+\operatorname{ind}\!\left(-D^2\mathcal F_m(\boldsymbolξ^*)\right). \] A critical four-dimensional capacity controls the scale directions. The dilation block of the reduced Hessian is positive and equals $8π^2b_α^2|\log\varepsilon|^{-1}I_m+o(|\log\varepsilon|^{-1})$, where $b_α=(8-α)/2$.

math.AP↗

arXiv2026

Complete Spectrum and Sharp Local Stability for the Critical Exponential Biharmonic Choquard Equation in $\mathbb R^{4}$

We study the conformally invariant exponential biharmonic Choquard equation in $\mathbb R^{4}$. Our principal result is the complete spectral resolution of the linearized operator at its conformal bubbles. After stereographic projection, the operator becomes a bounded zeroth-order perturbation of the Paneitz operator, with a compact Riesz component on $L^{2}(\mathbb S^{4})$. We justify the weak conformal transfer, remove every pole-supported distributional defect, and compute all eigenvalues. The Morse index is one. The kernel is the five-dimensional conformal space. All higher modes satisfy a uniform coercivity estimate. The transverse Hessian of the Adams--Choquard deficit is the same linearized operator. Hence the complete spectrum gives sharp local stability with respect to the Paneitz distance from the conformal extremal manifold. The optimal asymptotic constant is \[ γ_α =\frac{160-12α-α^{2}}{40(10-α)}, \] and the limiting quotient is minimized precisely by the second spherical harmonics. As a nonlinear preparation, we also prove that every normal distributional finite-mass solution satisfies the hypotheses of Niu's classification theorem and is therefore an explicit translation--dilation bubble.

math.AP↗

arXiv2026

CV-Arena: An Open Benchmark for Instructional Computer Vision Problem Solving with Human-AI Collaborative Preferences

Instruction-guided image editing is becoming a general interface for visual work, yet existing benchmarks still focus largely on narrow appearance edits and do not fully capture the diversity of real-image tasks in professional workflows. Here, we define instructional computer vision problem solving as a broader formulation of image editing: given a real input image and a natural-language instruction, a system must produce an edited output that realizes the requested transformation while satisfying explicit preservation, geometric, physical, and usability constraints. We introduce CV-Arena, an open benchmark designed to evaluate this capability at professional scales. CV-Arena contains 12K high-resolution real-image instruction pairs spanning 16 instruction-based visual task types, constructed using CogRetriever, a dual-track retrieval-and-curation pipeline that combines targeted web search, agentic query refinement, verification, and traceability. To evaluate models at scale while preserving human fidelity, we propose Active Elo, a human-AI collaborative preference protocol that leverages CV-Judge, a logic-gated, multi-dimensional VLM evaluator, to reject clear failures and resolve high-confidence comparisons; and to route close, high-quality comparisons to expert raters. Mixed human and AI supervision is then aggregated through reliability-weighted Elo updates. Our comprehensive evaluation of 21 systems, including proprietary, open-source, and agentic models, on CV-Arena reveals persistent gaps in instruction adherence, physical reasoning, structural control, and fine-grained detail preservation. We further develop CV-Agent, a lightweight agentic model that combines planning, editing, and verification, and demonstrate that closed-loop reasoning is a promising direction for professional-grade instruction-following visual editing.

cs.CV↗

arXiv2026

Quantum Mpemba-like effect in Unruh thermalization

We revisit the thermal nature of the Unruh effect within a quantum thermodynamic framework. For a Unruh-deWitt (UDW) detector in $n$-dimensional Minkowski spacetime, we demonstrate that its irreversible thermalization to a Gibbs equilibrium state follows distinct trajectories on the Bloch sphere, which depend on the types of fields the detector interacts with, as well as the spacetime dimensionality. Using thermodynamic process functions, particularly quantum coherence and heat that form the quantum First Law, we characterize the Unruh thermalization through a complementary time evolution between the trajectory-dependent rates of process functions. Grounded in information geometry, we further explore the kinematics of the detector state as it "flows" along the trajectory. In particular, we propose two heating/cooling protocols for the UDW detector undergoing Unruh thermalization. We observe a quantum Mpemba-like effect, characterized by faster heating than cooling in terms of Uhlmann fidelity "distance" change. Most significantly, we establish the maximum fidelity difference as a novel diagnostic that essentially distinguishes between Unruh thermalization and its classical counterpart, i.e., classical thermal bath-driven thermalization of an inertial UDW detector. This compelling criterion may serve as a hallmark of the quantum origin of the Unruh effect in future experimental detection and quantum simulation. Finally, we conclude with a general analysis of Unruh thermalization, starting from equal-fidelity non-thermal states, and demonstrate that the detectors' fidelity and "speed" of quantum evolution still exhibit a Mpemba-like behavior.

hep-th↗

arXiv2026

KANMixer: a minimal KAN-centered mixer for long-term time series forecasting

Long-term time series forecasting (LTSF) underpins critical applications from energy management to weather prediction, yet achieving reliable multi-step-ahead accuracy remains challenging. Existing LTSF approaches, dominated by MLP- and Transformer-based architectures, either rely on simple linear mappings or introduce increasingly complex hand-crafted inductive biases, raising the question of whether a more expressive and principled nonlinear core could offer a better alternative. Therefore, we investigate whether Kolmogorov-Arnold Networks (KANs), a recently proposed model featuring adaptive basis functions capable of granular modulation of nonlinearities, can improve LTSF performance, and under which design choices they are most effective. Specifically, we propose KANMixer, a minimal KAN-centered architecture consisting of a multi-scale pooling frontend, a KAN-based temporal mixing backbone, and prediction heads. By avoiding heavy auxiliary modules, KANMixer enables a clear assessment of KAN components in LTSF. Across 28 benchmark-horizon settings against nine baselines, KANMixer achieves the best MSE in 16 settings and the best MAE in 11. Furthermore, extensive ablations on three representative datasets show that KAN effectiveness depends strongly on the choice of edge function; B-spline bases outperform Fourier and Wavelet alternatives; the prediction head contributes most to the gains; moderate depth is preferred over deeper unstable stacks; and decomposition priors help MLP but harm KAN. Beyond practical guidance for integrating KAN into LTSF, these results reveal an underexplored dependency between structural priors and backbone nonlinearity: design choices that benefit MLP can degrade KAN.

cs.LG↗

arXiv2026

Multi-Agent Reinforcement Learning with Submodular Reward

In this paper, we study cooperative multi-agent reinforcement learning (MARL) where the joint reward exhibits submodularity, which is a natural property capturing diminishing marginal returns when adding agents to a team. Unlike standard MARL with additive rewards, submodular rewards model realistic scenarios where agent contributions overlap (e.g., multi-drone surveillance, collaborative exploration). We provide the first formal framework for this setting and develop algorithms with provable guarantees on sample efficiency and regret bound. For known dynamics, our greedy policy optimization achieves a $1/2$-approximation with polynomial complexity in the number of agents $K$, overcoming the exponential curse of dimensionality inherent in joint policy optimization. For unknown dynamics, we propose a UCB-based learning algorithm achieving a $1/2$-regret of $O(H^2KS\sqrt{AT})$ over $T$ episodes.

cs.LG↗

arXiv2026

Remainder terms and sharp quantitative stability for a nonlocal Sobolev inequality on the Heisenberg group

In this paper, we study the following nonlocal Sobolev inequality on the Heisenberg group \begin{equation}\label{eq:HLS} S_{HL}(Q,μ) \left(\int_{\mathbb{H}^{n}}\int_{\mathbb{H}^{n}}\frac{|u(ξ)|^{Q^{\ast}_μ}|u(η)|^{Q^{\ast}_μ}}{|η^{-1}ξ|^μ}{d}ξ{d}η\right)^{\frac{1}{Q^{\ast}_μ}}\leq \int_{\mathbb{H}^{n}}|\nabla_{\mathbb{H}}u|^{2}dξ,\quad \forall \, u\in S^{1,2}(\mathbb{H}^{n}), \end{equation} where $Q=2n+2$ is the homogeneous dimension of the Heisenberg group $\mathbb{H}^{n}$, $n\geq1$, $μ\in(0,Q)$, $Q^{\ast}_μ=\frac{2Q-μ}{Q-2}$ is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality and the Folland-Stein-Sobolev inequality on the Heisenberg group, $S_{HL}(Q,μ)$ is the sharp constant of \eqref{eq:HLS}, and $S^{1,2}(\mathbb{H}^{n})$ is the Folland-Stein-Sobolev space. %of the nonlocal-Sobolev inequality. It is well-known that, up to a translation and suitable scaling, \begin{equation}\label{eq:abs} -Δ_{\mathbb{H}} u=\left(\int_{\mathbb{H}^{n}}\frac{|u(η)| ^{Q^{\ast}_μ}}{|η^{-1}ξ|^μ}{d}η\right)|u|^{Q_μ^*-2}u,~~u\in S^{1,2}(\mathbb{H}^{n}) \end{equation} is the Euler-Lagrange equation corresponding to the associated minimization problem. On the one hand, we show the existence of a gradient-type remainder term for inequality \eqref{eq:HLS} when $Q\geq4$, $μ\in (0,4]$, and as a corollary, derive the existence of a remainder term in the weak $L^{\frac{Q}{Q-2}}$-norm on bounded domains. On the other hand, we establish the quantitative stability of critical points for equation \eqref{eq:abs} in the multi-bubble case when $Q=4$ and $μ\in (2,4)$.

math.AP↗

arXiv2026

Bicriteria Algorithms for Submodular Cover with Partition and Fairness Constraints

In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be in some sense balanced, fair, or resource-constrained across these partitions. While existing work on submodular cover largely overlooks this structure, we initiate a comprehensive study of the problem of Submodular Cover with Partition Constraints (SCP) and its key variants. Our main contributions are the development and analysis of scalable bicriteria approximation algorithms for these NP-hard optimization problems for both monotone and nonmonotone objectives. Notably, the algorithms proposed for the monotone case achieve optimal approximation guarantees while significantly reducing query complexity compared to existing methods. Finally, empirical evaluations on real-world and synthetic datasets further validate the efficiency and effectiveness of the proposed algorithms.

cs.DS↗

arXiv2025

LAVQA: A Latency-Aware Visual Question Answering Framework for Shared Autonomy in Self-Driving Vehicles

When uncertainty is high, self-driving vehicles may halt for safety and benefit from the access to remote human operators who can provide high-level guidance. This paradigm, known as {shared autonomy}, enables autonomous vehicle and remote human operators to jointly formulate appropriate responses. To address critical decision timing with variable latency due to wireless network delays and human response time, we present LAVQA, a latency-aware shared autonomy framework that integrates Visual Question Answering (VQA) and spatiotemporal risk visualization. LAVQA augments visual queries with Latency-Induced COllision Map (LICOM), a dynamically evolving map that represents both temporal latency and spatial uncertainty. It enables remote operator to observe as the vehicle safety regions vary over time in the presence of dynamic obstacles and delayed responses. Closed-loop simulations in CARLA, the de-facto standard for autonomous vehicle simulator, suggest that that LAVQA can reduce collision rates by over 8x compared to latency-agnostic baselines.

cs.RO↗

arXiv2025

Reliable quantum master equation of the Unruh-DeWitt detector

In this paper, we present a method for estimating the validity range of the quantum Markovian master equation as applied to the Unruh-DeWitt (UDW) detector within a broader context, particularly without necessitating an exact solution for the detector's evolution. We propose a relaxed van Hove limit (i.e., late-time limit) and offer a perturbative estimate of the error order resulting from the standard derivation procedure of open quantum dynamics. Our primary findings include reliability criteria for the Markov approximation and conditions for the applicability of the rotating wave approximation. Nevertheless, the specific forms of these validity conditions rely on the details of the detector-field system, such as the spacetime background, the trajectory of the detector, and the type of quantum field being analyzed. Finally, we illustrate our results by reexamining the open dynamics of an accelerating UDW detector undergoing the Unruh effect, where the validity conditions narrow the parameter space to ensure the solution's reliability regarding the quantum Markovian master equation.

gr-qc↗

arXiv2025

Breaking Barriers: Combinatorial Algorithms for Non-monotone Submodular Maximization with Sublinear Adaptivity and $1/e$ Approximation

With the rapid growth of data in modern applications, parallel algorithms for maximizing non-monotone submodular functions have gained significant attention. In the parallel computation setting, the state-of-the-art approximation ratio of $1/e$ is achieved by a continuous algorithm (Ene & Nguyen, 2020) with adaptivity $ O\left(\log(n)\right)$. In this work, we focus on size constraints and present the first combinatorial algorithm matching this bound -- a randomized parallel approach achieving $1/e-\varepsilon$ approximation ratio. This result bridges the gap between continuous and combinatorial approaches for this problem. As a byproduct, we also develop a simpler $(1/4-\varepsilon)$-approximation algorithm with high probability ($\ge 1-1/n$). Both algorithms achieve $ O\left(\log(n)\log(k)\right)$ adaptivity and $O\left(n\log(n)\log(k)\right)$ query complexity. Empirical results show our algorithms achieve competitive objective values, with the $(1/4-\varepsilon)$-approximation algorithm particularly efficient in queries.

cs.DS↗

arXiv2025

Work extraction from long-lived quantum coherence of a three-level system

We analyze work extraction protocols using the long-lived quantum coherence of a three-level quantum system, which is coupled to a thermal bath through dipole-monopole interactions. We identify situations where persistent quantum coherence arises, i.e., for systems with degenerate excited states with aligned transition dipoles or nearly degenerate systems with small energy splittings. By designing two innovative thermodynamic protocols involving energy-preserving unitary operations, we show that quantum coherence can be transformed into population asymmetry, serving as a quantum resource for work extraction. As the system approaches final thermal equilibrium, the initial quantum coherence effectively acts as fuel, being progressively consumed. Specifically, we propose an optimized protocol capable of extracting the maximal extractable work (MEW), measured by the free energy difference (FED), from quantum coherence in a single-shot thermodynamic cycle. Our results highlight the thermodynamic advantages of long-lived coherence in a three-level quantum system and could influence future designs of coherence-driven quantum thermal machines.

quant-ph↗

arXiv2025

Quantum thermodynamics in a rotating BTZ black hole spacetime

We address the problem of the thermalization process for an Unruh-DeWitt (UDW) detector outside a BTZ black hole, from a perspective of quantum thermodynamics. In the context of an open quantum system, we derive the complete dynamics of the detector, which encodes a complicated response to scalar background fields. Using various information theory tools, such as quantum relative entropy, quantum heat, coherence, quantum Fisher information, and quantum speed of evolution, we examined three quantum thermodynamic laws for the UDW detector, where the influences from BTZ angular momentum and Hawking radiation are investigated. In particular, based on information geometry theory, we find an intrinsic asymmetry in the detector's thermolization process as it undergoes Hawking radiation from the BTZ black hole. In particular, we find that the detector consistently heats faster than it cools, analogous to the quantum Mpemba effect for nonequilibrium systems. Moreover, we demonstrate that the spin of a black hole significantly influences the magnitude of the asymmetry, while preserving the dominance of heating over cooling.

hep-th↗