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Wenjing Chen

Publications and source records attributed to Wenjing Chen.

At least 37 records · Page 2Linked to original sources
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↗
arXiv2024

Multi-Head Attention Driven Dynamic Visual-Semantic Embedding for Enhanced Image-Text Matching

With the rapid development of multimodal learning, the image-text matching task, as a bridge connecting vision and language, has become increasingly important. Based on existing research, this study proposes an innovative visual semantic embedding model, Multi-Headed Consensus-Aware Visual-Semantic Embedding (MH-CVSE). This model introduces a multi-head self-attention mechanism based on the consensus-aware visual semantic embedding model (CVSE) to capture information in multiple subspaces in parallel, significantly enhancing the model's ability to understand and represent the complex relationship between images and texts. In addition, we adopt a parameterized feature fusion strategy to flexibly integrate feature information at different levels, further improving the model's expressive power. In terms of loss function design, the MH-CVSE model adopts a dynamic weight adjustment strategy to dynamically adjust the weight according to the loss value itself, so that the model can better balance the contribution of different loss terms during training. At the same time, we introduce a cosine annealing learning rate strategy to help the model converge more stably in the later stages of training. Extensive experimental verification on the Flickr30k dataset shows that the MH-CVSE model achieves better performance than previous methods in both bidirectional image and text retrieval tasks, fully demonstrating its effectiveness and superiority.

cs.CV↗
arXiv2024

Construction of solutions for the critical polyharmonic equation with competing potentials

In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Δ)^m u+V(|y'|,y'')u=Q(|y'|,y'')u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \mathbb{R}^3\times \mathbb{R}^{N-3}, \end{align*} where $N>4m+1$, $m\in \mathbb{N}^+$, $m^*=\frac{2N}{N-2m}$, $V(|y'|,y'')$ and $Q(|y'|,y'')$ are bounded nonnegative functions in $\mathbb{R}^+\times \mathbb{R}^{N-3}$. By using the reduction argument and local Pohouzaev identities, we prove that if $Q(r,y'')$ has a stable critical point $(r_0,y_0'')$ with $r_0>0$, $Q(r_0,y_0'')>0$, $D^αQ(r_0,y_0'')=0$ for any $|α|\leq 2m-1$ and $B_1V(r_0,y_0'')-B_2\sum\limits_{|α|=2m}D^αQ(r_0,y_0'')\int_{\mathbb{R}^N}y^αU_{0,1}^{m^*}dy>0$, then the above problem has a family of solutions concentrated at points lying on the top and the bottom circles of a cylinder, where $B_1$ and $B_2$ are positive constants that will be given later.

math.AP↗
arXiv2024

Blowing-up solutions for the Choquard type Brezis-Nirenberg problem in dimension three

In this paper, we are interested in the existence of solutions for the following Choquard type Brezis-Nirenberg problem \begin{align*} \left\{ \begin{array}{ll} -Δu=\displaystyle\Big(\int\limits_Ω\frac{u^{6-α}(y)}{|x-y|^α}dy\Big)u^{5-α}+λu, \ \ &\mbox{in}\ Ω, u=0, \ \ &\mbox{on}\ \partial Ω, \end{array} \right. \end{align*} where $Ω$ is a smooth bounded domain in $\mathbb{R}^3$, $α\in (0,3)$, $6-α$ is the upper critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality, and $λ$ is a real positive parameter. By applying the reduction argument, we find and characterize a positive value $λ_0$ such that if $λ-λ_0>0$ is small enough, then the above problem admits a solution, which blows up and concentrates at the critical point of the Robin function as $λ\rightarrow λ_0$. Moreover, we consider the above problem under zero Neumann boundary condition.

math.AP↗
arXiv2024

Fair Submodular Cover

Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a diverse solution set that is fairly distributed with respect to these attributes. Motivated by this, we initiate the study of Fair Submodular Cover (FSC), where given a ground set $U$, a monotone submodular function $f:2^U\to\mathbb{R}_{\ge 0}$, a threshold $τ$, the goal is to find a balanced subset of $S$ with minimum cardinality such that $f(S)\geτ$. We first introduce discrete algorithms for FSC that achieve a bicriteria approximation ratio of $(\frac{1}ε, 1-O(ε))$. We then present a continuous algorithm that achieves a $(\ln\frac{1}ε, 1-O(ε))$-bicriteria approximation ratio, which matches the best approximation guarantee of submodular cover without a fairness constraint. Finally, we complement our theoretical results with a number of empirical evaluations that demonstrate the effectiveness of our algorithms on instances of maximum coverage.

cs.LG↗
arXiv2024

Linear Submodular Maximization with Bandit Feedback

Submodular optimization with bandit feedback has recently been studied in a variety of contexts. In a number of real-world applications such as diversified recommender systems and data summarization, the submodular function exhibits additional linear structure. We consider developing approximation algorithms for the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where $f=\sum_{i=1}^dw_iF_{i}$. It is assumed that we have value oracle access to the functions $F_i$, but the coefficients $w_i$ are unknown, and $f$ can only be accessed via noisy queries. We develop algorithms for this setting inspired by adaptive allocation algorithms in the best-arm identification for linear bandit, with approximation guarantees arbitrarily close to the setting where we have value oracle access to $f$. Finally, we empirically demonstrate that our algorithms make vast improvements in terms of sample efficiency compared to algorithms that do not exploit the linear structure of $f$ on instances of move recommendation.

cs.LG↗
arXiv2024

New type of solutions for the critical polyharmonic equation

In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Δ)^m u+V(|y'|,y'')u=u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \mathbb{R}^3\times \mathbb{R}^{N-3}, \end{align*} where $m^*=\frac{2N}{N-2m}$, $N>4m+1$, $m\in \mathbb{N}^+$, and $V(|y'|,y'')$ is a bounded nonnegative function in $\mathbb{R}^+\times \mathbb{R}^{N-3}$. By using the reduction argument and local Pohouzaev identities, we prove that if $r^{2m}V(r,y'')$ has a stable critical point $(r_0,y_0'')$ with $r_0>0$ and $V(r_0,y_0'')>0$, then the above problem has a new type of solutions, which concentrate at points lying on the top and the bottom circles of a cylinder.

math.AP↗
arXiv2024

A Threshold Greedy Algorithm for Noisy Submodular Maximization

We consider the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where the objective $f$ is not accessed as a value oracle but instead subject to noisy queries. We introduce a versatile adaptive sampling procedure called which determines whether the marginal gain of the function $f$ is approximately above or below an input threshold with high probability in as few noisy samples as possible. Using the sampling procedure as a subroutine, we propose sample efficient algorithms for monotone submodular maximization with cardinality and matroid constraints, as well as unconstrained non-monotone submodular maximization. The proposed algorithms achieve approximation guarantees arbitrarily close to those of the standard value oracle setting. We further provide an experimental evaluation on real instances of submodular maximization and demonstrate the sample efficiency of our proposed algorithm relative to alternative approaches.

cs.DS↗
arXiv2024

New type of solutions for the critical Lane-Emden system

In this paper, we consider the critical Lane-Emden system \begin{align*} \begin{cases} -Δu=K_1(y)v^p,\quad y\in \mathbb{R}^N,&\\ -Δv=K_2(y)u^q,\quad y\in \mathbb{R}^N,&\\ u,v>0, \end{cases} \end{align*} where $N\geq 5$, $p,q\in (1,\infty)$ with $\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}$, $K_1(y)$ and $K_2(y)$ are positive radial potentials. Under suitable conditions on $K_1(y)$ and $K_2(y)$, we construct a new family of solutions to this system, which are centred at points lying on the top and the bottom circles of a cylinder.

math.AP↗
arXiv2024

TR-DETR: Task-Reciprocal Transformer for Joint Moment Retrieval and Highlight Detection

Video moment retrieval (MR) and highlight detection (HD) based on natural language queries are two highly related tasks, which aim to obtain relevant moments within videos and highlight scores of each video clip. Recently, several methods have been devoted to building DETR-based networks to solve both MR and HD jointly. These methods simply add two separate task heads after multi-modal feature extraction and feature interaction, achieving good performance. Nevertheless, these approaches underutilize the reciprocal relationship between two tasks. In this paper, we propose a task-reciprocal transformer based on DETR (TR-DETR) that focuses on exploring the inherent reciprocity between MR and HD. Specifically, a local-global multi-modal alignment module is first built to align features from diverse modalities into a shared latent space. Subsequently, a visual feature refinement is designed to eliminate query-irrelevant information from visual features for modal interaction. Finally, a task cooperation module is constructed to refine the retrieval pipeline and the highlight score prediction process by utilizing the reciprocity between MR and HD. Comprehensive experiments on QVHighlights, Charades-STA and TVSum datasets demonstrate that TR-DETR outperforms existing state-of-the-art methods. Codes are available at \url{https://github.com/mingyao1120/TR-DETR}.

cs.CV↗
arXiv2023

Blow-up solutions concentrated along minimal submanifolds for asymptotically critical Lane-Emden systems on Riemannian manifolds

Let $(\mathcal{M},g)$ and $(\mathcal{K},κ)$ be two Riemannian manifolds of dimensions $N$ and $m$, respectively. Let $ω\in C^2(\mathcal{M})$, $ω>0$. The warped product $\mathcal{M}\times_ω\mathcal{K}$ is the $(N+m)$-dimensional product manifold $\mathcal{M}\times \mathcal{K}$ furnished with metric $g+ω^2κ$. We are concerned with the following elliptic system $$\begin{align}\label{yuanshi} \left\{ \begin{array}{ll} -Δ_{g+ω^2κ} u+h(x)u=v^{p-α\varepsilon}, \ \ &\mbox{in $(\mathcal{M}\times_ω\mathcal{K},g+ω^2κ)$},\\ -Δ_{g+ω^2κ} v+h(x)v=u^{q-β\varepsilon}, \ \ &\mbox{in $(\mathcal{M}\times_ω\mathcal{K},g+ω^2κ)$},\\ u,v>0, \ \ &\mbox{in $(\mathcal{M}\times_ω\mathcal{K},g+ω^2κ)$}, \end{array} \right.\qquad(0.1)\end{align}$$ where $Δ_{g+ω^2κ} = div_{g+ω^2κ} \nabla$ is the Laplace-Beltrami operator on $\mathcal{M}\times_ω\mathcal{K}$, $h(x)$ is a $C^1$-function on $\mathcal{M}\times_ω\mathcal{K}$, $\varepsilon>0$ is a small parameter, $α,β>0$ are real numbers, $\varepsilon$ is a positive parameter, $(p,q)\in (1,+\infty)\times (1,+\infty)$ satisfies $\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}$. For any given integer $k\geq2$, using the Lyapunov-Schmidt reduction, we prove that problem (0.1) has a $k$-peaks solution concentrated along a $m$-dimensional minimal submanifold of $(\mathcal{M}\times_ω\mathcal{K})^k$.

math.AP↗
arXiv2023

Multiple blowing-up solutions for asymptotically critical Lane-Emden systems on Riemannian manifolds

Let $(\mathcal{M},g)$ be a smooth compact Riemannian manifold of dimension $N\geq 8$. We are concerned with the following elliptic system \begin{align*} \left\{ \begin{array}{ll} -Δ_g u+h(x)u=v^{p-α\varepsilon}, \ \ &\mbox{in}\ \mathcal{M}, -Δ_g v+h(x)v=u^{q-β\varepsilon}, \ \ &\mbox{in}\ \mathcal{M}, u,v>0, \ \ &\mbox{in}\ \mathcal{M}, \end{array} \right. \end{align*} where $Δ_g=div_g \nabla$ is the Laplace-Beltrami operator on $\mathcal{M}$, $h(x)$ is a $C^1$-function on $\mathcal{M}$, $\varepsilon>0$ is a small parameter, $α,β>0$ are real numbers, $(p,q)\in (1,+\infty)\times (1,+\infty)$ satisfies $\frac{1}{p+1}+\frac{1}{q+1}=\frac{N-2}{N}$. Using the Lyapunov-Schmidt reduction method, we obtain the existence of multiple blowing-up solutions for the above problem.

math.AP↗
arXiv2023

Normalized solutions for a fractional $N/s$-Laplacian Choquard equation with exponential critical nonlinearities

In this paper, we are concerned with the following fractional $N/s$-Laplacian Choquard equation \begin{align*} \begin{cases} (-Δ)^s_{N/s}u=λ|u|^{\frac{N}{s}-2}u +(I_μ*F(u))f(u),\ \ \mbox{in}\ \mathbb{R}^N, \displaystyle\int_{\mathbb{R}^N}|u|^{N/s} \mathrm{d}x=a^{N/s}, \end{cases} \end{align*} where $s\in(0,1)$, $1<\frac{N}{s}\in \mathbb{N}^+$, $a>0$ is a prescribed constant, $λ\in \mathbb{R}$, $I_μ(x)=\frac{1}{|x|^μ}$ with $μ\in(0,N)$, $F$ is the primitive function of $f$, and $f$ is a continuous function with exponential critical growth of Trudinger-Moser type. Under some suitable assumptions on $f$, we prove that the above problem admits a ground state solution for any given $a>0$, by using the constraint variational method and minimax technique.

math.AP↗
arXiv2023

Bicriteria Approximation Algorithms for the Submodular Cover Problem

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $τ$. In particular, we consider several variants of SCP including the general case, the case where $f$ is additionally assumed to be monotone, and finally the case where $f$ is a regularized monotone submodular function. Our most significant contributions are that: (i) We propose a scalable algorithm for monotone SCP that achieves nearly the same approximation guarantees as the standard greedy algorithm in significantly faster time; (ii) We are the first to develop an algorithm for general SCP that achieves a solution arbitrarily close to being feasible; and finally (iii) we are the first to develop algorithms for regularized SCP. Our algorithms are then demonstrated to be effective in an extensive experimental section on data summarization and graph cut, two applications of SCP.

cs.DS↗
arXiv2023

Normalized ground states for a fractional Choquard system in $\mathbb{R}$

In this paper, we study the following fractional Choquard system \begin{align*} \begin{split} \left\{ \begin{array}{ll} (-Δ)^{1/2}u=λ_1 u+(I_μ*F(u,v))F_u (u,v), \quad\mbox{in}\ \ \mathbb{R}, (-Δ)^{1/2}v=λ_2 v+(I_μ*F(u,v)) F_v(u,v), \quad\mbox{in}\ \ \mathbb{R}, \displaystyle\int_{\mathbb{R}}|u|^2\mathrm{d}x=a^2,\quad \displaystyle\int_{\mathbb{R}}|v|^2\mathrm{d}x=b^2,\quad u,v\in H^{1/2}(\mathbb{R}), \end{array} \right. \end{split} \end{align*} where $(-Δ)^{1/2}$ denotes the $1/2$-Laplacian operator, $a,b>0$ are prescribed, $λ_1,λ_2\in \mathbb{R}$, $I_μ(x)=\frac{1}{|x|^μ}$ with $μ\in(0,1)$, $F_u,F_v$ are partial derivatives of $F$ and $F_u,F_v$ have exponential critical growth in $\mathbb{R}$. By using a minimax principle and analyzing the monotonicity of the ground state energy with respect to the prescribed masses, we obtain at least one normalized ground state solution for the above system.

math.AP↗