Related papers: Conjugate Function Method and Conformal Mappings i…
We present a new systematic method to construct the conformal mapping from outside the unit disc to outside of a simply connected domain using the generalized polarization tensors. We also present some numerical results to validate…
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
Conformal Prediction offers a powerful framework for quantifying uncertainty in machine learning models, enabling the construction of prediction sets with finite-sample validity guarantees. While easily adaptable to non-probabilistic…
Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…
Boundary conforming coordinates are commonly used in plasma physics to describe the geometry of toroidal domains, for example, in three-dimensional magnetohydrodynamic equilibrium solvers. The magnetohydrodynamic equilibrium configuration…
We show that, given a non-degenerate, finitely connected domain $D$, its boundary, and the number of its boundary components, it is possible to compute a conformal mapping of $D$ onto a circular domain \emph{without} prior knowledge of the…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We make use of the Bergman kernel function to study quadrature domains for square-integrable holomorphic functions of several variables. Emphasis is given to generalizing biholomorphic mapping properties of planar quadrature domains to the…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Amp\`ere equation. While DDMs have been extensively studied for linear problems, their application to fully nonlinear partial differential…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively…
Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy…
Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of…
The method of boundary curve reparametrization is applied to construction of the approximate analytical conformal mapping of the unit disk onto an arbitrary given finite domain with a boundary smooth at every point but fininte number of…