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We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
We consider conformal nets on $S^1$ of von Neumann algebras, acting on the full Fock space, arising in free probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular…
We use Weyl transformations between the Minkowski spacetime and dS/AdS spacetime to show that one cannot well define the electrodynamics globally on the ordinary conformal compactification of the Minkowski spacetime (or dS/AdS spacetime),…
We study the problem of empirical coordination subject to a fidelity criterion for a general set-up. We prove a result which indicates a strong connection between our framework and the framework of empirical coordination developed in [1].…
This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode…
The influence of electromagnetic vacuum fluctuations in the presence of the perfectly conducting plate on electrons is studied with an interference experiment. The evolution of the reduced density matrix of the electron is derived by the…
Conformal prediction is emerging as a popular paradigm for providing rigorous uncertainty quantification in machine learning since it can be easily applied as a post-processing step to already trained models. In this paper, we extend…
The conformal heat flow of harmonic maps is a system of evolution equations combined with harmonic map flow with metric evolution in conformal direction. It is known that global weak solution of the flow exists and smooth except at mostly…
The experimental investigation of the Casimir force between a large metallized sphere and semiconductor plate is performed using an atomic force microscope. Improved calibration and measurement procedures permitted reduction in the role of…
Conformal prediction is a distribution-free technique for establishing valid prediction intervals. Although conventionally people conduct conformal prediction in the output space, this is not the only possibility. In this paper, we propose…
A broadband electromagnetic source is important for scientific and technological applications. Quantum vacuum fluctuations, which manifest most prominently in the Casimir effect, provide a fundamentally broadband electromagnetic source.…
We propose a new omnibus goodness-of-fit test based on trigonometric moments of probability-integral-transformed data. The test builds on the framework of the LK test introduced by Langholz and Kronmal [J. Amer. Statist. Assoc. 86 (1991),…
Training interatomic potentials for spin-polarized systems continues to be a difficult task for the molecular modeling community. In this note, a proof-of-concept, random initial spin committee approach is proposed for obtaining the ground…
Interference-fit joints are typically adopted to produce permanent assemblies among mechanical parts. The resulting contact pressure is generally used for element fixing or to allow load transmission. Nevertheless, some special designs take…
Conformal prediction, a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, the resulting uncertainty regions…
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
We present a constructive approach for approximating the conformal map (uniformization) of a polyhedral surface to a canonical domain in the plane. The main tool is a characterization of convex spaces of quasiconformal simplicial maps and…
An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…
First-principles based modeling on phonon dynamics and transport using density functional theory and Boltzmann transport equation has proven powerful in predicting thermal conductivity of crystalline materials, but it remains unfeasible for…
In this paper we present a geometric proof of the following fact. Let $D$ be a Jordan domain in $\mathbb{C}$, and let $f$ be analytic on $cl(D)$. Then there is an injective analytic map $\phi:D\to\mathbb{C}$, and a polynomial $p$, such that…