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Lili Wang

Publications and source records attributed to Lili Wang.

At least 19 recordsLinked to original sources
arXiv2026

On the sharp critical mass threshold for the 3D Patlak--Keller--Segel--Navier--Stokes system via Couette flow

As is well-known, the solution of the Patlak--Keller--Segel system in 3D may blow up in finite time regardless of any initial cell mass. In this paper, we are interested in the suppression of blow-up and the critical mass threshold for the 3D Patlak--Keller--Segel--Navier--Stokes system via the Couette flow $(Ay, 0, 0)$. It is proved that if the Couette flow is sufficiently strong ($A$ is large enough), the initial cell mass is less than $16π^{2}$, and the zero modes of the initial velocity are sufficiently small, then the solutions for the system are global in time. The threshold $16π^2$ seems to be optimal: for every finite \(A>0\) and every \(M>16π^2\), we show that there exist smooth positive initial densities of mass \(M\), with zero initial velocity perturbation, whose corresponding solutions blow up in finite time. A key ingredient is a time-integrable decay estimate for the nonconstant part of the zero-mode velocity, which allows the logarithmic Hardy--Littlewood--Sobolev inequality to be used throughout the range $\frac{M}{2π}<8π$. Moreover, the global existence is obtained by combining quasi-linear space-time estimates proposed by Wei--Zhang (Comm. Pure Appl. Math., 2021) and a free-energy argument as in Bedrossian--He (SIAM J. Math. Anal., 2017) for the zero mode. The blow-up result follows from an exact invariant zero-mode reduction to the two-dimensional Patlak--Keller--Segel system and a localized virial argument.

math.AP↗
arXiv2026

Compatible additions on a six-element commutative semigroup: equational bases and subvariety lattices

Let $M$ be the six-element commutative semigroup occurring as the common multiplicative reduct of the semirings $SR_6$ and $TR_6$. The closing paragraph of Shao, Ren, and Gao~\cite{ShaoRenGao2026} asks for the finite-basis and subvariety questions for the four remaining compatible additions on $M$. We answer these questions for the four isomorphism types $R_{01},R_{02},R_{11},R_{12}$. First, we classify all compatible additions on $M$: there are nine labelled additions and six isomorphism types, parametrized by $R_{ij}$ with $0\leq i\leq j\leq 2$. For each of the four new types we give a graph-theoretic criterion for every identity, an explicit infinite basis, and a proof of nonfinite basability. The generated varieties $\V(R_{01})$ and $\V(R_{02})$ have eleven subvarieties each, while $\V(R_{11})$ has sixty-six. The lattice $\Sub(\V(R_{12}))$ is countably infinite. Every identity in this variety reduces to a subset of twenty-five fixed identities together with two monotone path families $γ_n$ and $\gammaD_n$. This yields a canonical signature $(H,p,q)$, complete normal forms, explicit meet and join operations, and a formula for all covers. There are 153 fixed nodes, 43 one-parameter families, and 9 two-parameter families; exactly eighteen subvarieties are finitely based, and the unique limit subvariety is $\V(SR_6)$. The strong nonfinite-basis status of the four finite semirings remains open.

math.GR↗
arXiv2026

Should This Case Be Adapted? Prediction Fragmentation Controls Test-Time Adaptation

Episodic test-time adaptation resets a frozen segmenter to source weights $M_0$ on each case and adapts for a fixed step count. A fixed horizon conflates a cohort-level question, how far to adapt, with an irreducibly per-case one, whether this case should be adapted at all. Cohort means hide that decision: on cross-vendor cardiac MRI the mean $Δ$Dice from adaptation is statistically indistinguishable from zero while 58.7% of cases are individually made worse. We quantify this harm as harmful accepted area (HA), the harmful fraction of the edited area a controller deploys. Held-out tuning gives a stronger baseline than a fixed horizon, but the budget it selects transfers on neither of the two main medical benchmarks, and no global budget can condition on the case. We show that prediction fragmentation---the disagreement geometry between $M_0$ and the adapted mask $M_k$---predicts HA with no labels or extra backward passes at decision time, comparably on three benchmarks (Spearman $ρ$ 0.50--0.60), at a quarter of gradient-norm's latency. A case-level router built on it cuts HA from 0.228 to 0.139 on a benchmark that took no part in its design, with the design frozen and only cut-points recalibrated there. On the cardiac benchmark the design was selected on, the router cuts HA from 0.129 to 0.013 at matched Dice and 1.10 deployed updates, against the retrospective-best budget found post hoc on evaluation labels, and reduces that 58.7% to 20.0%, an upper bound we quantify. Where the retained cases are not net-helped (as on prostate), the router still cuts HA but concedes accuracy, a boundary we report. Thresholds are fit once on a labeled split disjoint from evaluation; decisions use no labels or gradients. The template ports across architecture and domain (nnU-Net$\to$SegFormer, Cityscapes$\to$ACDC) with coordinate, thresholds and per-bucket actions instantiated per domain.

cs.CV↗
arXiv2026

The variety generated by all semirings of order three is nonfinitely based

We prove that the variety generated by all semirings of order three is nonfinitely based, where addition is not required to be commutative and the signature has no constants. The same conclusion holds for the variety generated by all additively idempotent semirings of order three. We establish these conclusions by excluding a uniform bound on the number of variables in an identity basis. Our proof uses identities associated with anchored odd cycles. Three small commutative test semirings isolate a polynomial equivalence class consisting of exactly two polynomials. For a cycle of length $n$, every first nontrivial deduction between them requires an identity with at least $n+1$ variables, even under polynomial substitutions. A retraction followed by a band quotient transfers absorption identities to arbitrary addition and identifies the ai-subvariety of the full joint variety with the joint variety of the ai-generators. Validity of the cycle identities follows from a structural analysis of chain and flat addition. An elementary sixth-power lemma for semigroups of order at most three supplies the retraction.

math.GR↗
arXiv2026

Weinstock Inequality on Regular Trees

Let $T_n$ be the infinite $n$-regular tree, $n\ge3$. We prove that every finite connected vertex set $Ω\subset T_n$ satisfies the sharp inequality \[ σ_1(Ω)\le \frac{n}{(n-1)|Ω|+1}. \] Equality holds if and only if $Ω$ is a ball. Since \[ |δΩ|=(n-2)|Ω|+2, \] the result is equivalently a sharp upper bound at fixed external boundary cardinality, and hence a discrete Weinstock inequality on $T_n$.

math.SP↗
arXiv2026

Counterexamples to Escobar's conjecture

Escobar (J Funct Anal 165(1):101-116, 1999) conjectured that for every $n\ge 3$, an $n$-dimensional compact Riemannian manifold with nonnegative Ricci curvature and all boundary principal curvatures bounded below by $κ>0$ must satisfy $σ_1\geq κ$. We disprove this conjecture for every $n\geq 3$ by constructing conformal deformations of the Euclidean unit ball. We first establish a perturbative criterion, then construct explicit polynomial conformal factors satisfying this criterion. For every sufficiently small $t>0$, the resulting metrics $g_t=e^{2tΦ}g_{\mathbb{R}^n}$ have positive Ricci curvature, every boundary principal curvature is strictly larger than $1$, and $σ_1(\mathbb{B}^n,g_t)<1$. The proof requires several computations, some of which were carried out in Mathematica. The Mathematica code is attached to this submission.

math.SP↗
arXiv2026

Reinforcement Learning-Based Output Feedback LQR for Continuous-Time MIMO Systems

This article studies model-free output feedback linear quadratic regulation (LQR) for continuous-time linear systems with an $n$-dimensional state, an $m$-dimensional input, and a $p$-dimensional output, using filtered input--output data. Since the system state is unavailable, existing methods rely on dynamic filters to parameterize the hidden state using measurable input--output signals. However, the intrinsic dimension of the resulting filter-based parametrization can be smaller than the dimension of the complete filtered vector, and this deterministic redundancy can make the Bellman regressions rank deficient. We characterize this intrinsic dimension and show that the conventional filtered vector contains only $2n$ independent components for single-input multi-output (SIMO) systems and $n(m+1)$ independent components for general multi-input multi-output (MIMO) systems. Based on this characterization, a reduced filtered vector is extracted directly from data and used to develop reduced model-free output feedback policy iteration and value iteration equations, eliminating the redundant directions and decreasing the number of unknown parameters while retaining a fully input--output data-based implementation. A numerical example illustrates the rank reduction and the effectiveness of the learned controller.

eess.SY↗
arXiv2026

The Weinstock inequality for convex domains in hyperbolic space

We prove the Weinstock inequality for the first Steklov eigenvalue of convex domains in hyperbolic space $\mathbb{H}^{n}$, resolving Open Question 4.27 of Colbois-Girouard-Gordon-Sher(2024) for the remaining case $n=3$. Our argument replaces the global monotonicity required in earlier work Gu-Li-Wan(2025) with a one-crossing property, which is established via an explicit slope comparison. The proof works uniformly for all $n\geq 3$.

math.SP↗
arXiv2026

Upper bound for the first $p$-Steklov eigenvalue in $\mathbb{R}^n$

For $p\in(1,n]$ and any bounded convex domain $Ω\subset\mathbb{R}^n$, we prove the sharp inequality \[ Λ_p(Ω):=\frac{W_p(Ω)}{P(Ω)V(Ω)^{p/n}}\geqω_n^{-p/n}, \qquad W_p(Ω)=\int_{\partialΩ}|x|^p\ dS, \] with equality holding exactly at centered balls. Combining this with the isoperimetric inequality yields the explicit upper bound \[ σ_{1,p}(Ω)\leq \frac{A(n,p)}{r(Ω^*)^{p-1}}, \] where $Ω^*$ is a ball having the same perimeter as $Ω$, and $A(n,p)=1$ for $1<p\leq 2$, $A(n,p)=n^{p/2-1}$ for $2<p\leq n$. When $p=2$, the result recovers the higher-dimensional Weinstock inequality of Bucur et al. [J. Differential Geom. 2021]. We also obtain an explicit upper bound for the first Wentzell eigenvalue of the $p$-Laplacian on convex domains.

math.AP↗
arXiv2026

RFHNet: Relational and Frequency-Aware Hashing Network for Large-Scale Fine-Grained Food Image Retrieval

Fine-grained food image retrieval is a key task in computational gastronomy, with applications in food traceability, dietary monitoring, and smart catering systems. Although hashing-based retrieval is attractive for large-scale search due to its storage efficiency and fast Hamming-distance computation, existing methods often perform poorly in fine-grained food scenarios, where subtle local semantics and frequency-sensitive visual cues are essential. To address this challenge, we propose RFHNet, a cascaded hierarchical hashing network that captures both global structure and fine-grained local details through multi-level representations. RFHNet includes three components: (1) Fine-grained Relation Modeling (FRM) to capture subtle visual differences among similar food components; (2) Multi-Frequency Modulated Fusion (MFMF) to extract informative multi-frequency features; and (3) Hierarchical Semantic Synergy (HSS) to adaptively integrate multi-level representations and generate discriminative hash codes. Experiments on six food-specific benchmarks show that RFHNet consistently outperforms state-of-the-art hashing methods, with mAP gains of 4.44\% to 17.20\% at 12 bits. These results validate the effectiveness of RFHNet for large-scale visual food retrieval and smart catering applications. The source code will be released upon publication.

cs.CV↗
arXiv2026

Leaderless Collective Motion in Affine Formation Control over the Complex Plane

We propose a method for the collective maneuvering of affine formations in the plane by modifying the original weights of the Laplacian matrix used to achieve static formations of robot swarms. Specifically, the resulting collective motion is characterized as a time-varying affine transformation of a reference configuration, or shape. Unlike the traditional leader-follower strategy, our leaderless scheme allows agents to maintain distinct and possibly time-varying velocities, enabling a broader range of collective motions, including all the linear combinations of translations, rotations, scaling and shearing of a reference shape. Our analysis provides the analytic solution governing the resulting collective motion, explicitly designing the eigenvectors and eigenvalues that define this motion as a function of the modified weights in the new Laplacian matrix. To facilitate a more tractable analysis and design of affine formations in 2D, we propose the use of complex numbers to represent all relevant information. Simulations with up to 20 agents validate the theoretical results.

cs.RO↗
arXiv2026

LatentStealth: Unnoticeable and Efficient Adversarial Attacks on Expressive Human Pose and Shape Estimation

Expressive human pose and shape estimation (EHPS) plays a central role in digital human generation, particularly in live-streaming applications. However, most existing EHPS models focus primarily on minimizing estimation errors, with limited attention on potential security vulnerabilities, such as generating inappropriate content, violent actions, or racially offensive gestures and expressions. Current adversarial attacks on EHPS models often generate visually conspicuous perturbations, limiting their practicality and ability to expose real-world security threats. To address this limitation, we propose an unnoticeable adversarial method, termed \textbf{LatentStealth}, specifically tailored for EHPS models. The key idea is to exploit the structured latent representations of natural images as the medium for crafting perturbations. Instead of injecting noise directly into the pixel space, our method projects inputs into the latent space, where adversarial patterns are generated and progressively refined along optimized directions. This latent-space manipulation enables the attack to maintain high imperceptibility while preserving its effectiveness. Furthermore, as the optimization process is guided by only a small number of model output queries, the framework achieves competitive attack performance with low computational overhead, making it both practical and efficient for real-world scenarios. Extensive experiments on the 3DPW and UBody datasets demonstrate the superiority of LatentStealth, revealing critical vulnerabilities in current systems. These findings highlight the urgent need to address and mitigate security risks in digital human generation technologies.

cs.CV↗
arXiv2026

HVG-3D: Bridging Real and Simulation Domains for 3D-Conditional Hand-Object Interaction Video Synthesis

Recent methods have made notable progress in the visual quality of hand-object interaction video synthesis. However, most approaches rely on 2D control signals that lack spatial expressiveness and limit the utilization of synthetic 3D conditional data. To address these limitations, we propose HVG-3D, a unified framework for 3D-aware hand-object interaction (HOI) video synthesis conditioned on explicit 3D representations. Specifically, we develop a diffusion-based architecture augmented with a 3D ControlNet, which encodes geometric and motion cues from 3D inputs to enable explicit 3D reasoning during video synthesis. To achieve high-quality synthesis, HVG-3D is designed with two core components: (i) a 3D-aware HOI video generation diffusion architecture that encodes geometric and motion cues from 3D inputs for explicit 3D reasoning; and (ii) a hybrid pipeline for constructing input and condition signals, enabling flexible and precise control during both training and inference. During inference, given a single real image and a 3D control signal from either simulation or real data, HVG-3D generates high-fidelity, temporally consistent videos with precise spatial and temporal control. Experiments on the TASTE-Rob dataset demonstrate that HVG-3D achieves state-of-the-art spatial fidelity, temporal coherence, and controllability, while enabling effective utilization of both real and simulated data.

cs.CV↗
arXiv2025

Isocapacitary constants for the $p$-Laplacian on compact manifolds

In this paper, we introduce Steklov and Neumann isocapacitary constants for the $p$-Laplacian on compact manifolds. These constants yield two-sided bounds for the $(p,α)$-Sobolev constants, which degenerate to upper and lower bounds for the first nontrivial Steklov and Neumann eigenvalues of the $p$-Laplacian when $α= 1$.

math.DG↗
arXiv2025

Blow-up suppression of the Patlak-Keller-Segel-Navier-Stokes system via Taylor-Couette flow

Motivated by the use of Taylor-Couette flow in extracorporeal circulation devices [K$\ddot{\rm o}$rfer et al., 2003, 26(4): 331-338], where it leads to an accumulation of platelets and plasma proteins in the vortex center and therefore to a decreased probability of contact between platelets and material surfaces and its protein adsorption per square unit is significantly lower than laminar flow. Increased platelet adhesion or protein adsorption on the device surface can induce platelet aggregation or thrombosis, which is analogous to the ``blow-up phenomenon" in mathematical modeling. Here we mathematically analyze this stability mechanism and demonstrate that sufficiently strong flow can prevent blow-up from occurring. In details, we investigate the two-dimensional Patlak-Keller-Segel-Navier-Stokes system in an annular domain around a Taylor-Couette flow $U(r,θ)=A\big(r+\frac{1}{r} \big)(-\sinθ, \cosθ)^{T}$ with $(r,θ)\in[1,R]\times\mathbb{S}^{1}$, and prove that the solutions are globally bounded without any smallness restriction on the initial cell mass or velocity when $A$ is large.

math.AP↗
arXiv2025

Sublattice Dichotomy in Monolayer FeSe Superconductor

The pairing mechanism behind the monolayer FeSe is one essential question for iron-based superconductors. In this work, we show the sublattice degree of freedoms of monolayer FeSe plays a special role in its pairing properties, namely the sublattice dichotomy. The high-quality monolayer FeSe samples with atomic flat $1\times1$ topography on the SrTiO$_3$(001) substrates are grown by molecular beam epitaxy. By comparing the tunneling spectra at $α$ and $β$ Fe sublattices, we find the coherence peak of $α$-Fe at the inner gap $+V_i$ is higher than $β$-Fe while the coherence peak of $β$-Fe at $-V_i$ is higher than $α$-Fe with a similar amount. We also observed a reversed effect at the outer gap $\pm V_o$. We propose the $η$-pairing mechanism between $k$ and $-k+Q$ is the key mechanism for this unconventional sublattice dichotomy effect.

cond-mat.supr-con↗
arXiv2025

Distributed Koopman Learning with Incomplete Measurements

Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that collaboratively estimate the dynamics of an NTIS. A distributed deep Koopman learning algorithm is developed by integrating Koopman operator theory, deep neural networks, and consensus-based coordination. In the proposed framework, each agent approximates the system dynamics using its partial measurements and lifted states exchanged with its neighbors. This cooperative scheme enables accurate reconstruction of the global dynamics despite the absence of full-state information at individual agents. Simulation results on the Lunar Lander environment from OpenAI Gym demonstrate that the proposed method achieves performance comparable to the centralized deep Koopman learning with full-state access.

eess.SY↗