Research
Research
Research
Research
10,177+ open-access research outputs.
We study geodesic motion of a test particle in Schwarzschild spacetime. Bound and scattering geodesics are commonly described using Darwin variables, which provide a convenient parametrization of the …
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 $\tau(G)\geq \tau$…
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…
The Fock-Darwin (FD) quantum system describes the motion on the plane of a charged particle under the action of an isotropic oscillator potential together with a perpendicular constant magnetic field.…
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,…
We prove that for $C^{1+\beta}$ flows whose generating vector fields may have singularities, every weakly mixing hyperbolic SRB measure is Bernoullian.…
The controlled ramp down of the toroidal plasma current in the ITER tokamak is simulated using a simple model that employs cylindrical geometry. The magnetohydrodynamical (MHD) stability of the plasma…
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…
Highly magnified stars at cosmological distances ($z \gtrsim 0.7$) become detectable thanks to microlensing by intracluster stars near the critical curves of galaxy clusters. Multi-epoch photometric c…
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…
In 2016, Dowden initiated the study of planar Tur\'an-type problems, which has since attracted considerable attention. Recently, Bekos et al. proved that every $K_3$-free $1$-planar graph on $n\ge 4$ …
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…
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