Research
Research
Research
Research
5,269+ open-access research outputs.
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 proposes an algorithm for clipping line segment against an axis-aligned rectangular window. The conventional algorithms for line segment clipping treat the clipping boundary and/or the line…
Let $ n \in \mathbb{N} $ with $ n \geq 3 $, and let $\mathcal{G} = \{G_i:i\in [n]\} $ be a family of $ n $-vertex graphs on a common vertex set $V$, where the graphs in the family do not need to be di…
Stellarator fusion devices confine plasma by means of complex, non-planar electromagnetic coils. Understanding how the shape of the plasma boundary determines the required complexity of the coil set i…
We prove that any continuous function f from [0,1]^n to R representable by a finite computation tree with N internal nodes and compositional sparsity s = O(1) admits a deep Kolmogorov-Arnold Network (…
Recent advances in quantum computing have enabled the development of quantum processors with hundreds of qubits. However, noise continues to limit the amount of useful information that can be extracte…
Advances in quantum information science (QIS) are providing transformative insights into the complexity of quantum many-body systems, potentially defining new frontiers in nuclear and high-energy phys…
Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations,…
In this article, we develop an efficient algorithm based on three special variants of the nonlinear conjugate gradient method, namely, the Polak--Ribiere--Polyak, Hestenes--Stiefel, and Liu--Story sch…
Quantum computing instructors face a compounding problem: the concepts are counterintuitive, the mathematical formalism is dense, and qualified faculty are scarce outside a small number of well-resour…
A classical result of Cioab\u{a} states that if $G$ is a connected graph with the unit Perron vector $\mathbf{x}$, then any independent set $S$ of $G$ satisfies $\sum_{v\in S} x_v^2 \le \frac{1}{2}$, …
We analyze the universal approximation property of Kolmogorov-Arnold Networks (KANs) in terms of their edge functions. If these functions are all affine, then universality clearly fails. How many non-…
In 1965 Kraichnan pointed out that a sufficiently strong background magnetic field, i.e. the case of small Alfv\'en number, will reduce the nonlinear interaction and inhibit the formation of strong gr…
Machine learning methods that predict initial guesses from molecular geometry can reduce this cost, but matrix-prediction models fail when extrapolating to larger molecules, degrading rather than acce…
This paper considers constrained stochastic nonsmooth minimax optimization problem of the form $\min_{\mathbf{x}\in\mathcal{X}}\max_{\mathbf{y}\in\mathcal{Y}}f\left(\mathbf{x},\mathbf{y}\right)=\mathb…
We investigate the robustness of unbound states in one-dimensional quasiperiodic models with near-infinitely deep potentials. By constructing a deeper extension of the Liu-Xia model and combining inve…
In continuously monitored quantum systems, the feedback protocol of Garc\'ia-Pintos, Liu, and Gorshkov reshapes the arrow of time: a Hamiltonian $H_{\mathrm{meas}} = r A / \tau$ applied with gain $X$ …
We present a Python/CuPy FX software correlator for small radio interferometer arrays and evaluate it on QUEST (Qilu University Explorer Survey Telescope). The system combines multi-threaded data inge…
In this paper, we conduct a systematic literature review of (semi-) automated approaches to Quantum Software Engineering (QSE) and Quantum Artificial Intelligence (QAI). Prior work in the literature i…
It is well known that Erd\H{o}s Matching Conjecture concerns the maximum number of hyperedges in an $r$-uniform hypergraph with bounded matching number. As a generalization, it is natural to ask for t…
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