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87,739+ open-access research outputs.
We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a sing…
Denote by $p(k)$ the limit, as $n \rightarrow \infty$, of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$. We give an asymptotic formula for $p(k)$, sho…
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
For a graph \(G\), let $avm(G)$ denote the average size of its maximal matchings. This parameter was introduced by Engbers and Erey in the study of extremal problems for maximal matchings, and they as…
This work investigates minimal parametric networks in hyperspaces of closed subsets of metric spaces endowed with the Hausdorff distance. It is shown that the problems of finding such networks are non…
We show that every minimally generically globally rigid graph in $\mathbb R^d$ which contains a subgraph isomorphic to $K_{d+2}$ is itself isomorphic to $K_{d+2}$, confirming a conjecture by Garamv{\"…
We derive a sharp upper bound on the residuals produced by the flexible GMRES (FGMRES) method. The bound shows that FGMRES exhibits two phases of convergence depending on the residual tolerance of the…
We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace tr…
This paper studies data-driven approaches to the continuous-time linear quadratic regulator (LQR) problem based on two existing parameterizations, namely a closed-loop (CL) parameterization from behav…
We study scale-invariant geometric quantities associated with embedded closed curves in Euclidean three-space, with an emphasis on their behavior under optimization within a fixed knot type. Given a E…
The toughness of a graph $G$, denoted by $\tau(G)$, is defined by $\tau(G)=$min $\{\frac{|S|}{c(G-S)}:S\subseteq V(G)$ and $c(G-S)\geq2\}$. A graph $G$ is said to be $\tau$-tough if $\tau(G)\geq \tau$…
This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze…
In modern parametric model training, full-batch gradient descent (and its variants) suffers due to progressively stronger biasing towards the exact realization of training data; this drives the system…
The Etzion-Silberstein conjecture asserts that, for any finite field $\mathbb F$, Ferrers diagram $\mathcal D$, and integer $d$, there exists a linear matrix code supported on $\mathcal D$ with minimu…
We show that the VC-density in certain theories of oriented abelian groups is at most the size of parameter variables, which yields dp-minimality. We further prove that the VC-density of formulas in p…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph t…
Let $X_1,\ldots,X_n$ be independent random points in the closed unit ball of $\mathbb{R}^d$. Assume that each $X_i$ has a beta distribution with parameter $\beta_i \ge -1$: if $\beta_i>-1$, then $X_i$…
The main theorem of the paper provides an existence criterion of holomorphic discs for higher $A_\infty$ operations. The key step is to show that if a minimal disc in a K\"ahler manifold with boundary…
This work studies numerical integration by the M\"obius-transformed trapezoidal rule, which combines the classical trapezoidal rule with a change of variables induced by a M\"obius transformation that…
We introduce G\r{a}rding polynomials, a class of real multivariate polynomials defined via positivity regions invariant under translation by positive directions and closed under strictly positive affi…
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