Research
Research
Research
Research
4,228+ 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, …
Interest in studying the interaction of small molecules with DNA is caused by the need to develop new, highly effective, and low-toxic drugs for cancer treatment. The strong and highly specific bindin…
Accurate and real-time sensing of targets in three-dimensional (3D) environments is essential for modern machine vision, underpinning emerging technologies such as autonomous systems, robotic manipula…
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…
Let $k$ denote an algebraically closed field of characteristic zero and let $X$ denote a smooth elliptic curve over $k$. Given a three-periodic elliptic helix $\underline{\mathcal{E}}$ of vector bundl…
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…
The light-dependent magnetic compass of night-migratory songbirds is widely hypothesized to rely on the radical pair mechanism within retinal cryptochrome. However, bridging the mechanistic gap betwee…
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…
GPU-based concurrent data structures (CDSs) achieve high throughput for read-only queries, but efficient support for dynamic updates on fully GPU-resident data remains challenging. Ordered CDSs (e.g.,…
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…
Disentanglement techniques used in collaborative filtering uncover interaction intents between nodes, improving the interpretability of node representations and enhancing recommendation performance. H…
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…
DNA-based storage has emerged as a promising approach to the global data crisis, offering molecular-scale density and millennial-scale stability at low maintenance cost. Over the past decade, substant…
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 …
Non-commutative crepant resolutions (NCCRs) are non-commutative versions of classical crepant resolutions in algebraic geometry. For 3-dimensional terminal Gorenstein singularities Iyama and Wemyss pr…
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:…
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