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Yuxiang Li

Publications and source records attributed to Yuxiang Li.

At least 37 records · Page 2Linked to original sources
arXiv2025

Critical mass for finite-time chemotactic collapse in the critical dimension via comparison

We study the Neumann initial-boundary value problem for the parabolic-elliptic chemotaxis system, proposed by Jäger and Luckhaus (1992). We confirm that their comparison methods can be simplified and refined, applicable to seek the critical mass $8π$ concerning finite-time blowup in the unit disk. As an application, we deal with a parabolic-elliptic-parabolic chemotaxis model involving indirect signal production in the unit ball of $\mathbb R^4$, proposed by Tao and Winkler (2025). Within the framework of radially symmetric solutions, we prove that if initial mass is less than $64π^2$, then solution is globally bounded; for any $m$ exceeding $64π^2$, there exist nonnegative initial data with prescribed mass $m$ such that the corresponding classical solutions exhibit a formation of Dirac-delta type singularity in finite time, termed a chemotactic collapse.

math.AP↗
arXiv2025

Generative AI-Aided QoE Maximization for RIS-Assisted Digital Twin Interaction

In this paper, we investigate a quality of experience (QoE)-aware resource allocation problem for reconfigurable intelligent surface (RIS)-assisted digital twin (DT) interaction with uncertain evolution. In the considered system, mobile users are expected to interact with a DT model maintained on a DT server that is deployed on a base station, via effective uplink and downlink channels assisted by an RIS. Our goal is to maximize the sum of all mobile users' joint subjective and objective QoE in DT interactions across various DT scenes, by jointly optimizing phase shift matrix, receive/transmit beamforming matrix, rendering resolution configuration and computing resource allocation. While solving this problem is challenging mainly due to the uncertain evolution of the DT model, which leads to multiple scene-specific problems, and require us to constantly re-solve each of them whenever DT model evolves. To this end, leveraging the dynamic optimization capabilities of decision transformers and the generalization strengths of generative artificial intelligence (GAI), we propose a novel GAI-aided approach, called the prompt-guided decision transformer integrated with zero-forcing optimization (PG-ZFO). Simulations are conducted to evaluate the proposed PG-ZFO, demonstrating its effectiveness and superiority over counterparts.

cs.NI↗
arXiv2025

Distributionally Robust Optimization for Digital Twin Service Provisioning over Edge Computing

Digital Twin (DT) is a transformative technology poised to revolutionize a wide range of applications. This advancement has led to the emergence of digital twin as a service (DTaaS), enabling users to interact with DT models that accurately reflect the real-time status of their physical counterparts. Quality of DTaaS primarily depends on the freshness of DT data, which can be quantified by the age of information (AoI). The reliance on remote cloud servers solely for DTaaS provisioning presents significant challenges for latency-sensitive applications with strict AoI demands. Edge computing, as a promising paradigm, is expected to enable the AoI-aware provision of real-time DTaaS for users. In this paper, we study the joint optimization of DT model deployment and DT model selection for DTaaS provisioning over edge computing, with the objective of maximizing the quality of DTaaS. To address the uncertainties of DT interactions imposed on DTaaS provisioning, we propose a novel distributionally robust optimization (DRO)-based approach, called Wasserstein DRO (WDRO), where we first reformulate the original problem to a robust optimization problem, with the objective of maximizing the quality of DTaaS under the unforeseen extreme request conditions. Then, we leverage multi-level dual transformations based on Wasserstein distance to derive a robust solution. Simulations are conducted to evaluate the performance of the proposed WDRO, and the results demonstrate its superiority over counterparts.

cs.NI↗
arXiv2025

LeakGuard: Detecting Memory Leaks Accurately and Scalably

Memory leaks are prevalent in various real-world software projects, thereby leading to serious attacks like denial-of-service. Though prior methods for detecting memory leaks made significant advance, they often suffer from low accuracy and weak scalability for testing large and complex programs. In this paper we present LeakGuard, a memory leak detection tool which provides satisfactory balance of accuracy and scalability. For accuracy, LeakGuard analyzes the behaviors of library and developer-defined memory allocation and deallocation functions in a path-sensitive manner and generates function summaries for them in a bottom-up approach. Additionally, we develop a pointer escape analysis technique to model the transfer of pointer ownership. For scalability, LeakGuard examines each function of interest independently by using its function summary and under-constrained symbolic execution technique, which effectively mitigates path explosion problem. Our extensive evaluation on 18 real-world software projects and standard benchmark datasets demonstrates that LeakGuard achieves significant advancements in multiple aspects: it exhibits superior MAD function identification capability compared to Goshawk, outperforms five state-of-the-art methods in defect detection accuracy, and successfully identifies 129 previously undetected memory leak bugs, all of which have been independently verified and confirmed by the respective development teams.

cs.CR↗
arXiv2025

Finite-time blowup in a fully parabolic chemotaxis model involving indirect signal production

This paper is concerned with a parabolic-parabolic-parabolic chemotaxis system with indirect signal production, modelling the impact of phenotypic heterogeneity on population aggregation \begin{equation*} \begin{cases} u_t = Δu - \nabla\cdot(u\nabla v),\\ v_t = Δv - v + w,\\ w_t = Δw - w + u, \end{cases} \end{equation*} posed on a ball in $\mathbb R^n$ with $n\geq5$, subject to homogeneous Neumann boundary conditions. The system has a four-dimensional critical mass phenomenon concerning blowup in finite or infinite time according to the seminal works of Fujie and Senba [J. Differential Equations, 263 (2017), 88--148; 266 (2019), 942--976]. We prove that for any prescribed mass $m > 0$, there exist radially symmetric and nonnegative initial data $(u_0,v_0,w_0)\in C^0(\overlineΩ)\times C^2(\overlineΩ)\times C^2(\overlineΩ)$ with $\int_Ωu_0 = m$ such that the corresponding classical solutions blow up in finite time. The key ingredient is a novel integral inequality for the cross-term integral $\int_Ωuv$ constructed via a Lyapunov functional.

math.AP↗
arXiv2024

3-circle Theorem for Willmore surfaces II--degeneration of the complex structure

We study the compactness of Willmore surfaces without assuming the convergence of the induced complex structures. In particular, we compute the energy loss in the neck in terms of the residue and we prove that the limit of the image of the Gauss map is a geodesic in the Grassmannian $G(2,n)$ whose length can also be computed in terms of the residue. Moreover, we provide a family of explicit Willmore surfaces in $\R^3$ that illustrate the denegeration phenomenon involved in the above results.

math.DG↗
arXiv2024

Global boundedness for a two-dimensional doubly degenerate nutrient taxis system

This paper is concerned with the doubly degenerate nutrient taxis system $u_t=\nabla \cdot(u^{l-1} v \nabla u)- \nabla \cdot\left(u^{l} v \nabla v\right)+ uv$ and $v_t=Δv-u v$ for some $l \geqslant 1$, subjected to homogeneous Neumann boundary conditions in a smooth bounded convex domain $Ω\subset \mathbb{R}^n$ $(n \leqslant 2)$. Through distinct approaches, we establish that for sufficiently regular initial data, in two-dimensional contexts, if $l \in[1,3]$, then the system possesses global weak solutions, and in one-dimensional settings, the same conclusion holds for $l \in[1,\infty)$. Notably, the solution remains uniformly bounded when $l \in[1,\infty)$ in one dimension or $l \in(1,3]$ in two dimensions.

math.AP↗
arXiv2024

Global weak solutions to a two-dimensional doubly degenerate nutrient taxis system with logistic source

In this work, we study the doubly degenerate nutrient taxis system with logistic source \begin{align} \begin{cases}\tag{$\star$}\label{eq 0.1} u_t=\nabla \cdot(u^{l-1} v \nabla u)- \nabla \cdot\left(u^{l} v \nabla v\right)+ u - u^2, \\ v_t=Δv-u v \end{cases} \end{align} in a smooth bounded domain $Ω\subset \mathbb{R}^2$, where $l \geqslant 1$. It is proved that for all reasonably regular initial data, the corresponding homogeneous Neumann initial-boundary value problem \eqref{eq 0.1} possesses a global weak solution which is continuous in its first and essentially smooth in its second component. We point out that when $l = 2$, our result is consistent with that of [G. Li and M. Winkler, Analysis and Applications, (2024)].

math.AP↗
arXiv2024

Global solvability and unboundedness in a fully parabolic quasilinear chemotaxis model with indirect signal production

This paper is concerned with a quasilinear chemotaxis model with indirect signal production, $u_t = \nabla\cdot(D(u)\nabla u - S(u)\nabla v)$, $v_t = Δv - v + w$ and $w_t = Δw - w + u$, posed on a bounded smooth domain $Ω\subset\mathbb R^n$, subjected to homogenerous Neumann boundary conditions, where nonlinear diffusion $D$ and sensitivity $S$ generalize the prototype $D(s) = (s+1)^{-α}$ and $S(s) = (s+1)^{β-1}s$. Ding and Wang [M.Ding and W.Wang, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 4665-4684.] showed that the system possesses a globally bounded classical solution if $α+ β<\min\{1+2/n,4/n\}$. While for the Jäger-Luckhaus variant of this model, namely the second equation replaced by $0=Δv - \int_Ωw/|Ω| + w$, Tao and Winkler [2023, preprint] announced that if $α+ β> 4/n$ and $β>2/n$ for $n\geq3$, with radial assumptions, the variant admits occurrence of finite-time blowup. We focus on the case $β<2/n$, and prove that $β< 2/n$ for $n\geq2$ is sufficient for global solvability of classical solutions; if $α+ β> 4/n$ for $n\geq4$, then radially symmetric initial data with large negative energy enforce blowup happening in finite or infinite time, both of which imply that the system allows infinite-time blowup if $α+ β> 4/n$ and $β< 2/n$ for $n\geq 4$.

math.AP↗
arXiv2024

Boundedness and finite-time blow-up in a repulsion-consumption system with flux limitation

We investigate the following repulsion-consumption system with flux limitation \begin{align}\tag{$\star$} \left\{ \begin{array}{ll} u_t=Δu+\nabla \cdot(uf(|\nabla v|^2) \nabla v), & x \in Ω, t>0, τv_t=Δv-u v, & x \in Ω, t>0, \end{array} \right. \end{align} under no-flux/Dirichlet boundary conditions, where $Ω\subset \mathbb{R}^n$ is a bounded domain and $f(ξ)$ generalizes the prototype given by $f(ξ)=(1+ξ)^{-α}$ ($ξ\geqslant 0$). We are mainly concerned with the global existence and finite time blow-up of system ($\star$). The main results assert that, for $α> \frac{n-2}{2n}$, then when $τ=1$ and under radial settings, or when $τ=0$ without radial assumptions, for arbitrary initial data, the problem ($\star$) possesses global bounded classical solutions; for $α<0$, $τ=0$, $n=2$ and under radial settings, for any initial data, whenever the boundary signal level large enough, the solutions of the corresponding problem blow up in finite time. Our results can be compared respectively with the blow-up phenomenon obtained by Ahn \& Winkler (2023) for the system with nonlinear diffusion and linear chemotactic sensitivity, and by Wang \& Winkler (2023) for the system with nonlinear diffusion and singular sensitivity .

math.AP↗
arXiv2024

Boundedness and finite-time blow-up in a repulsion-consumption system with nonlinear chemotactic sensitivity

This paper investigates the repulsion-consumption system \begin{align}\tag{$\star$} \left\{ \begin{array}{ll} u_t=Δu+\nabla \cdot(S(u) \nabla v), τv_t=Δv-u v, \end{array} \right. \end{align} under no-flux/Dirichlet conditions for $u$ and $v$ in a ball $B_R(0) \subset \mathbb R^n $. When $τ=\{0,1\}$ and $0 0$, we show that for any given radially symmetric initial data, the problem ($\star$) possesses a global bounded classical solution. Conversely, when $τ=0$, $n=2$ and $S(u) \geqslant k u^β$ for $u \geqslant 0$ with some $β>1$ and $k>0$, for any given initial data $u_0$, there exists a constant $M^{\star}=M^{\star}\left(u_0\right)>0$ with the property that whenever the boundary signal level $M\geqslant M^{\star}$, the corresponding radially symmetric solution blows up in finite time. Our results can be compared with that of the papers [J.~Ahn and M.~Winkler, {\it Calc. Var.} {\bf 64} (2023).] and [Y. Wang and M. Winkler, {\it Proc. Roy. Soc. Edinburgh Sect. A}, \textbf{153} (2023).], in which the authors studied the system ($\star$) with the first equation replaced respectively by $u_t=\nabla \cdot ((1+u)^{-α} \nabla u)+\nabla \cdot(u \nabla v)$ and $u_t=\nabla \cdot ((1+u)^{-α} \nabla u)+\nabla \cdot(\frac{u}{v} \nabla v)$. Among other things, they obtained that, under some conditions on $u_0(x)$ and the boundary signal level, there exists a classical solution blowing up in finite time whenever $α>0$.

math.AP↗
arXiv2024

Prescribing positive curvature with conical singularities on $\mathbb S^2$

For conformal metrics with conical singularities and positive curvature on $\mathbb S^2$, we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an open region of the prescribing data. The core of our study is a fine analysis of the bubble trees and an area identity in the convergence process.

math.DG↗
arXiv2024

3-circle Theorem for Willmore surface I

In this paper, we study the blow-up of Willmore surfaces. By using the 3-circle theorem, we prove a decay estimate of the second fundamental form along the neck region. This estimate provides a new perspective and streamlined proofs to a few key results in this field, such as the energy identity(quantization), removable singularities and gap theorem.

math.DG↗
arXiv2024

Manifolds for which Huber's Theorem holds

Extensions of Huber's Theorem to higher dimensions with $L^\frac{n}{2}$ bounded scalar curvature have been extensively studied over the years. In this paper, we delve into the properties of conformal metrics on a punctured ball with $\|R\|_{L^\frac{n}{2}}<+\infty$, aiming to identify necessary geometric constraints for Huber's theorem to be applicable. Unexpectedly, such metrics are more rigid than we initially anticipated. For instance, we found that the volume density at infinity is precisely one, and the blow-down of the metric is $\mathbb{R}^n$. Specifically, in four dimensions, we derive the $L^2$-integrability of the Ricci curvature, which directly leads to the conclusion that the Pfaffian 4-form is integrable and adheres to a Gauss-Bonnet-Chern formula. Additionally, we demonstrate that a Gauss-Bonnet-Chern formula, previously verified by Lu and Wang under the assumption that the second fundamental form belongs to $L^4$, remains valid for $R \in L^2$. Consequently, on an orientable 4-dimensional manifold conformal to a domain in a closed manifold, Huber's Theorem holds when $R \in L^2$, if and only if the negative part of the Pfaffian 4-form is integrable.

math.DG↗
arXiv2023

Global Inequality in Cooling from Urban Green Spaces and its Climate Change Adaptation Potential

Heat extremes are projected to severely impact humanity and with increasing geographic disparities. Global South countries are more exposed to heat extremes and have reduced adaptation capacity. One documented source of such adaptation inequality is a lack of resources to cool down indoor temperatures. Less is known about the capacity to ameliorate outdoor heat stress. Here, we assess global inequality in green infrastructure, on which urban residents critically rely to ameliorate lethal heat stress outdoors. We use satellite-derived indicators of land surface temperature and urban green space area to quantify the daytime cooling capacity of urban green spaces in the hottest months across ~500 cities with population size over 1 million per city globally. Our results show a striking contrast with an about two-fold lower cooling capacity in Global South cities compared to the Global North (2.1 degrees Celsius vs. 3.8 degrees Celsius). A similar gap occurs for the cooling adaptation benefits received by an average urban resident (Global South 1.9 degrees Celsius vs. North 3.6 degrees Celsius), i.e., accounting for relative spatial distributions of people and urban green spaces. This cooling adaptation inequality is attributed to the discrepancies in urban green space quantity and quality between Global North and South cities, jointly shaped by natural and socioeconomic factors. Our analyses suggest vast potential for enhancing outdoor cooling adaptation while reducing its global inequality through expanding and optimizing urban green infrastructure.

stat.AP↗
arXiv2022

Molecular-scale Integration of Multi-modal Sensing and Neuromorphic Computing with Organic Electrochemical Transistors

Abstract: Bionic learning with fused sensing, memory and processing functions outperforms artificial neural networks running on silicon chips in terms of efficiency and footprint. However, digital hardware implementation of bionic learning suffers from device heterogeneity in sensors and processing cores, which incurs large hardware, energy and time overheads. Here, we present a universal solution to simultaneously perform multi-modal sensing, memory and processing using organic electrochemical transistors with designed architecture and tailored channel morphology, selective ion injection into the crystalline/amorphous regions. The resultant device work as either a volatile receptor that shows multi-modal sensing, or a non-volatile synapse that features record-high 10-bit analog states, low switching stochasticity and good retention without the integration of any extra devices. Homogeneous integration of such devices enables bionic learning functions such as conditioned reflex and real-time cardiac disease diagnose via reservoir computing, illustrating the promise for future smart edge health informatics.

cs.ET↗