Research
Research
Research
Research
6,496+ open-access research outputs.
Let $F$ be a finite field of odd characteristic. We prove that any set $A\subset F$ with $|A|\geq C|F|^{5/6}$ contains a nontrivial quadratic progression $(x, x+y, x+y^2), y\neq 0.$ For prime fields, …
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
Operating and maintaining (O&M) large-scale online engine systems (search, recommendation, advertising) demands substantial human effort for release monitoring, alert response, and root cause analysis…
Traffic signal control (TSC) plays a central role in reducing congestion and maintaining urban mobility. This dissertation introduces DGLight, a critic-guided reinforcement-learning framework for adap…
We present a framework for non-Abelian p-loop, fracton, and planon condensation in 3+1 dimensions by constructing extended cage-net fracton models using decoupled layers of the Hu-Geer-Wu (HGW) string…
Gate elimination is the primary technique for proving explicit lower bounds against general Boolean circuits, including Li and Yang's state-of-the-art $3.1n - o(n)$ bound for affine dispersers (STOC 2…
The random transposition shuffle on repeated cards induces a Markov chain on the quotient space of arrangements with multiplicities, and is equivalent to the many-urn mean-field Bernoulli-Laplace mode…
In 1965 Kraichnan pointed out that a sufficiently strong background magnetic field, i.e. the case of small Alfv\'en number, will reduce the nonlinear interaction and inhibit the formation of strong gr…
We prove that if $X$ is a smooth Fano threefold and $L$ is an ample $\mathbb{Q}$-divisor such that $(X,L)$ is K-polystable, then the automorphism group $\operatorname{Aut}(X)$ is reductive. This verif…
For a graph $G$, let $f_o(G)$ denote the maximum order of an induced subgraph of $G$ all of whose vertices have odd degree, and let $\chi(G)$ denote the chromatic number of $G$. Scott (CPC, 1992) prov…
Juniper Green is a simple combinatorial game invented by Rob Porteous and popularized by Ian Stewart. It was originally designed to familiarize school children with the concepts of multiplication and …
We study charge transport through a trivial-topological-trivial junction described by the continuous Qi-Wu-Zhang model, which realizes a two-dimensional Chern-insulating phase. The central region is t…
Generative engines (GEs) are reshaping information access by replacing ranked links with citation-grounded answers, yet current Generative Engine Optimization (GEO) methods optimize each instance in i…
We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed prop…
Reasoning segmentation requires models to ground complex, implicit textual queries into precise pixel-level masks. Existing approaches rely on a single segmentation token $\texttt{<SEG>}$, whose hidde…
Existing AI agent safety benchmarks focus on generic criminal harm (cybercrime, harassment, weapon synthesis), leaving a systematic blind spot for a distinct and commercially consequential threat cate…
Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(\varphi,\Gamma)$-…
We prove a relative volume comparison theorem of Petersen-Wei for both $L^P$-bound of Bakry-\'{E}mery Ricci curvature and gradient of potential function. As an application, we give a modified proof fo…
The ensemble Kalman filter (EnKF) is widely used for nonlinear and high-dimensional state estimation because it replaces complex covariance propagation with simple ensemble statistics. However, conven…
Human Activity Recognition (HAR) involves the automatic identification of user activities and has gained significant research interest due to its broad applicability. Most HAR systems rely on supervis…
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