Research
Research
Research
Research
1,954+ open-access research outputs.
We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system le…
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, …
We extend the entropy-stable oscillation-eliminating discontinuous Galerkin spectral element method (ES-OEDG) on curvilinear meshes to adaptive mesh refinement (AMR) grids with nonconforming interface…
Inference for time series of networks often relies on accurate vertex correspondence between network realizations at different times. In practice, however, such vertex alignments can be misspecified o…
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…
The extent to which the geometry of an object is determined by some associated spectral data is a longstanding problem. We investigate this problem in the context of the Steklov spectrum, focusing on …
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…
This paper examines a stochastic deconvolution problem on compact symmetric spaces which is referred to as decompounding. This involves estimating the step distributions of a random walk, where in add…
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…
We consider the interacting Bose gas in the thermodynamic limit in a large box in $\R^d$ at positive temperature $1/\beta\in(0,\infty)$ with particle density $\sim\rho\in(0,\infty)$. We follow a path-…
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 …
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:…
The almost Golomb equation of order $r$ is the implicit functional equation $$a\Bigl(\sum_{j=0}^{r-1} a(n{-}j)\Bigr) = n$$ for nondecreasing sequences of positive integers with $a(1)=1$. Its earliest …
Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparame…
The low-rank alternating direction implicit (ADI) method is an efficient and effective solver for large-scale standard continuous-time algebraic Riccati equations that admit low-rank solutions. Howeve…
Gradient normalization is central in deep-learning optimization because it stabilizes training and reduces sensitivity to scale. For deep architectures, parameters are naturally grouped into matrices …
Let $E_1,\dots,E_n \subset \mathbb{R}^d$ be compact sets of positive diameter with Feng--Wu thickness at least $c>0$. Feng and Wu proved that $E_1+\cdots+E_n$ has non-empty interior when $n>2^{11}c^{-…
Constructing $C^r$ conforming finite element spaces in any dimension is a long-standing problem. For general triangulations, this problem was recently addressed by Hu-Lin-Wu (2024), under certain cond…
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