Research
Research
Research
Research
583+ open-access research outputs.
Since the pioneering work of Korteweg (1901) and the subsequent refinement of capillary fluid models by Dunn and Serrin (1985), the global existence of strong solutions to the multi-dimensional compre…
In [arXiv:2409.08465], Quastel and Gu use Stein's equation and integration by parts to give a direct proof that drifted Brownian motions are stationary (modulo height shifts) for the full-line KPZ equ…
Let $G$ be an $n$-vertex graph with Laplacian eigenvalues $0=\lambda_1(G)\le \lambda_2(G)\le\cdots\le \lambda_n(G)$. Motivated by the Alon-Boppana bound and the Ramanujan phenomenon for regular graphs…
Effective code generation requires both model capability and a problem representation that carefully structures how models reason and plan. Existing approaches augment reasoning steps or inject specif…
We study narrative coherence in visually grounded stories by comparing human-written narratives with those generated by vision-language models (VLMs) on the Visual Writing Prompts corpus. Using a set …
Consider a parabolic SPDE \[ \partial_t u = \Delta u + \sigma(u)\eta, \] on $(0\,,\infty)\times\mathbb{R}^d$, where $\eta$ is a centered, generalized Gaussian noise with $\text{Cov}[\eta(t\,,x)\…
We study the fixed-time spatial covariance of the KPZ equation with flat initial profile. Using Malliavin calculus and a Clark-Ocone representation, we show that as $|x|\to\infty$, $\mathrm{Cov}[h(t,x…
We study market making in aggregator-routed RFQ markets where platform routing depends on slowly varying dealer performance scores. We propose a two-tier stochastic control model that separates RFQ-le…
Unmanned Aerial Vehicular Networks (UAVNs) are envisioned to provide flexible connectivity, wide-area coverage, and low-latency services in dynamic environments. From an agentic artificial intelligenc…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretica…
Representing the past in a compressed, efficient, and informative manner is a central problem for systems trained on sequential data. The HiPPO framework, originally proposed by Gu & Dao et al., provi…
The China Space Station Telescope (CSST) will conduct wide-field multiband photometric imaging and slitless spectroscopic surveys, advancing cosmology and galaxy evolution studies. Achieving CSST's co…
For a bounded open set $\Omega \subset \mathbb{R}^N$ with $N\geq 2$, and for positive continuous functions $w,g$ on $\overline{\Omega}$, we consider the weighted eigenvalue problem \begin{equation*}…
We give a new integral representation of the $\wedge^2 \otimes \mathrm{std}_2$ $L$-function of generic cusp forms on $\mathbf{GU}_{2,2}\times \mathbf{GL}_2$ and $\mathbf{GL}_4 \times \mathbf{GL}_2$ an…
Tensor networks offer a sign-problem-free approach to study lattice gauge theories, but extracting precise universal information associated with the deconfinement transition remains challenging. In th…
Graph unlearning (GU), which removes nodes, edges, or features from trained graph neural networks (GNNs), is crucial in Web applications where graph data may contain sensitive, mislabeled, or maliciou…
Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field with residue field of odd characteristic, $\mathfrak{p}$ be its maximal ideal and let $\mathfrak{o}_\ell = \mathfrak{o}/\mat…
Vulnerabilities severely threaten software systems, making the timely application of security patches crucial for mitigating attacks. However, software vendors often silently patch vulnerabilities wit…
Evaluating machine learning (ML) model bias is key to building trustworthy and robust ML systems. Counterfactual Fairness (CF) audits allow the measurement of bias of ML models with a causal framework…
Star formation is governed by multiple physical processes, making it inherently complicated. One excellent example is the Canis Major OB1/R1 Association, whose complex history of star formation is rel…
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