Related papers: Computing conformal maps onto circular domains
An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…
Sufficient conditions are given for the computation of accessing arcs and arcs that links boundary components of multiply connected domains. The existence of a not-computably-accessible but computable point on a computably compact arc is…
The presence of a boundary (or defect) in a conformal field theory allows one to generalize the notion of an exactly marginal deformation. Without a boundary, one must find an operator of protected scaling dimension $\Delta$ equal to the…
We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…
In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training…
Recently, versions of neural networks with infinite-dimensional affine operators inside the computational units (``neural operator'' networks) have been applied to learn solutions to differential equations. To enable practical computations,…
Feynman diagrams are calculated by means of their Taylor series expansion in terms of external momenta squared. It is demonstrated in various examples that by the application of conformal mapping and Pad\'{e} approximants, it is possible to…
Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Biharmonic and conformal-biharmonic maps are two fourth-order generalizations of the well-studied notion of harmonic maps in Riemannian geometry. In this article we consider maps into the Euclidean sphere and investigate a geometric…
Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a \emph{non-conformity score function} that…
Conformal prediction (CP) produces prediction regions with finite-sample, distribution free coverage guarantees, but its interpretation as a quantitative uncertainty tool is often left implicit. We develop a category-theoretic approach that…
We propose the extension of Fr\'{e}chet-Hoeffding copula bounds for circular data. The copula is a powerful tool for describing the dependency of random variables. In two dimensions, the Fr\'{e}chet-Hoeffding upper (lower) bound indicates…
We study the conformal capacity by using novel computational algorithms based on implementations of the fast multipole method, and analytic techniques. Especially, we apply domain functionals to study the capacities of condensers $(G,E)$…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
Category computation theory deals with a web-based systemic processing that underlies the morphic webs, which constitute the basis of categorial logical calculus. It is proven that, for these structures, algorithmically incompressible…
Creating accurate spatial representations that take into account uncertainty is critical for autonomous robots to safely navigate in unstructured environments. Although recent LIDAR based mapping techniques can produce robust occupancy…
This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
The use of Shap scores has become widespread in Explainable AI. However, their computation is in general intractable, in particular when done with a black-box classifier, such as neural network. Recent research has unveiled classes of…