Research
Research
Research
Research
2,720+ 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, …
One of the most exciting applications of vision models involve pixel-level reasoning. Despite the abundance of vision foundation models, we still lack representations that effectively embed spatio-tem…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal valu…
Agent benchmarks remain largely English-centric, while their multilingual versions are often built with machine translation (MT) and limited post-editing. We argue that, for agentic tasks, this minima…
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…
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…
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 prove a rigidity result for certain critical Z/2 eigensections of the Laplacian on S^2 associated to a flat real line bundle determined by a branch-point configuration. More precisely, we show that…
In this paper, we study the Chevalley property of Cayley-Hamilton Hopf algebras in the sense of De Concini-Procesi-Reshetikhin-Rosso using discriminant ideals. For any affine Cayley-Hamilton Hopf alge…
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate …
We formalize the Wu-Ritt characteristic set method for the triangular decomposition of polynomial systems in the Lean 4 theorem prover. Our development includes the core algebraic notions of the metho…
A proper orientation $D$ of an undirected graph $G$ is an orientation of $G$ such that $d_D^+(u)\not=d_D^+(v)$ for any edge $uv\in E(G)$. Denote the proper orientation number $\vec{\chi}(G)$ of an und…
Let $k \in \mathbb{N}$ and let $G$ be a simple graph with maximum degree $\Delta$. A $k$-colouring $\varphi$ of $G$ is an assignment of colours from $\{1,2,\ldots,k\}$ to the vertices of $G$. We call …
Multimodal attributed graphs (MAGs) combine multimodal node attributes with structured relations. However, existing methods usually perform shared message passing on a single graph and implicitly assu…
In this work we present the results of our analysis of medium-resolution LAMOST spectra of candidate members of the cluster NGC 1647 with the aim of determining the stellar parameters, activity level,…
We prove a structural upper bound on the $p$-adic valuation of denominators of rationals belonging to a missing-digit set $K_{m,D}$, generalizing a key step in recent work of Lin, Wu, and Yang [arXiv:…
We study online covariance matrix estimation for Polyak--Ruppert averaged stochastic gradient descent (SGD). The online batch-means estimator of Zhu, Chen and Wu (2023) achieves an operator-norm conve…
Local topological markers are used to characterize Chern insulators in the presence of spatial inhomogeneities, such as boundaries and disorder. In this paper, we study the local Chern marker in syste…
This paper presents an improved Matlab routine, FO_LE, for the numerical computation of Lyapunov exponents of fractional-order systems modeled by Caputo's derivative. It is conceived as an enhanced ve…
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