Research
Research
Research
Research
417+ open-access research outputs.
This paper introduces a conceptual framework of technology-dependent ternary quantum gates that could be implemented and fabricated into future superconducting and photonic quantum systems for operati…
This paper proves that a wide class of local search algorithms extend as is to the fully dynamic setting with an adaptive adversary, achieving an amortized $\tilde{O}(1)$ number of local-search steps …
Let $R$ be a commutative noetherian ring, and let $C$ be a semidualizing $R$-module. In this paper, we study levels of bounded complexes of finitely generated $R$-modules with respect to the full subc…
Abrupt transitions between distinct dynamical regimes are a hallmark of complex systems. Grokking in deep neural networks provides a striking example -- an abrupt transition from memorization to gener…
We study problems on covering $[0,1)$ by shrinking intervals centered at the points $\{q_n x\}$, where $(q_n)_{n\in \mathbb{N}}$ is a given real-valued sequence and $x \in [0,1)$ is random. For real-v…
We study the two-dimensional (geometric) knapsack problem with rotations (2DKR), in which we are given a square knapsack and a set of rectangles with associated profits. The objective is to find a max…
This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-…
We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and str…
Within the framework of quantum theory, we review the Chrestenson operator, the Weyl operator basis, and the Kronecker-Pauli operator basis in $d$-dimensional Hilbert spaces using Dirac notation, wher…
In Calgary, November 2005, Chad Hedrick was the first to skate the 5,000 m below 6:10. His world record time 6:09.68 was then beaten a week later, in Salt Lake City, by Sven Kramer's 6:08.78. Further …
Quality diversity (QD) is a branch of evolutionary computation that seeks high-quality and behaviorally diverse solutions to a problem. While adversarial problems are common, classical QD cannot be ea…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite st…
In this paper we consider the Gabor wave front set of ultradistributions in the frame of ultradifferentiable functions. We prove that such a wave front set, defined through a Gabor frame on a regular …
The question of when the derived category of a ring satisfies Brown--Adams representability is revisited via studying the transfer of pure homological dimension along definable functors: it is shown t…
We study when the variable-indexed matrix of pairwise $f$-mutual informations $M^{(f)}_{ij} = I_f(X_i;X_j)$ is positive semidefinite (PSD). Let $f:(0,\infty)\to R$ be convex with $f(1)=0$, finite in a…
We prove that the Kadison-Kastler and Christensen distances are stable under the Banach space injective tensor product (resp., the Banach space projective tensor product) of a Banach space with any un…
In this paper, we study the momentum distribution of an electron gas in a $3$-dimensional torus. The goal is to compute the occupation number of Fourier modes for some trial state obtained through ran…
Greedy minimum weight spanning tree packings have proven to be useful in connectivity-related problems. We study the process of greedy minimum weight base packings in general matroids and explore its …
The Effros-Shen algebra corresponding to an irrational number $\theta$ can be described by an inductive sequence of direct sums of matrix algebras, where the continued fraction expansion of $\theta$ e…
We develop relativistic causality theory in the setting of point-free topology by introducing a notion of causal coverage in ordered locales, generalising their canonical coverage relation to incorpor…
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