Research
Research
Research
Research
6,409+ open-access research outputs.
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…
We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) da…
We initiate the study of Reidemeister hardness of Legendrian unknot front projections. Using normal rulings, we obstruct several infinite families of hard unknot diagrams from being drawn with max-tb …
We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. T…
Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…
Robust uncertainty quantification is increasingly important in modern data analysis and is often formalized under Huber's model, which allows an $\varepsilon$-fraction of arbitrary corruptions. In man…
Boundary controllers have been recently proposed in the literature, via modal decomposition, to achieve $H^1$ stabilization of linear parabolic equations in two and three dimensions. In one dimension …
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…
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. For $\alpha\in[0,1)$, we use $A_{\alpha}(G)$ and $\rho_{\alpha}(G)$ to denote the $A_{\alpha}$-matrix and the $A_{\alpha}$-spectral radiu…
The theory of 2-monads entails that, for a strict monoidal category C, there is a strict monoidal category L(C) such that strict monoidal functors from L(C) are precisely the lax monoidal functors fro…
We study the semi-discrete approximation of Aubry and Mather sets for Tonelli Lagrangians on the flat torus. Starting from the discrete Lax--Oleinik equation, we introduce natural discrete analogues o…
Suppose that pebbles are distributed on the vertices of a graph G. A pebbling step along an edge uv removes two pebbles from u and places one pebble on v. We introduce two new graph parameters: st…
We describe the Bandicoot GPU linear algebra toolkit, a C++ based library that prioritises ease of use without compromising efficiency. Bandicoot's API is compatible with the popular Armadillo CPU lin…
The rapid rise of scientific machine learning (SciML) has expanded the role of differentiable modeling, surrogate modeling, and data-driven constitutive laws in large-scale simulation. The JAX framewo…
We introduce a class of robust control problems formulated in min-max form, in which the principal agent is viewed as a central planner facing Nature. The agent's cost is a nonlinear function of all i…
In computational science workflows, it is often the case that 1) objective functions for optimization involve multiple simulation outputs, and 2) those simulations can be performed (at least partially…
The relativistic hydrodynamics (RHD) equations can give rise to solutions which have shocks, contact discontinuities, and other sharp structures, which interact and evolve over time. Capturing these s…
We study the $l_p$ Hausdorff distance from convex hull of a compact set $A\subset\mathbb{R}^n$, which is the distance \begin{equation*} d^{(l_p)}(A):=\sup_{x\in conv(A)}\inf_{a\in A}\|x-a\|_p, \end{…
Data-driven decision-making under uncertainty typically presumes the collection of historical data from an unknown target probability distribution. However, one may have no access to any data from the…
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