相关论文: The boundary layer problem in Bayesian adaptive qu…
In bounded, polygonal domains $\Omega\subset \mathbb{R}^2$ with Lipschitz boundary $\partial\Omega$ consisting of a finite number of Jordan curves admitting analytic parametrizations, we analyze $hp$-FEM discretizations of linear, second…
A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often…
This study presents a dynamic Bayesian network framework that facilitates intuitive gradual edge changes. We use two conditional dynamics to model the edge addition and deletion, and edge selection separately. Unlike previous research that…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…
This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of…
A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…
Regional aggregates of health outcomes over delineated administrative units (e.g., states, counties, zip codes), or areal units, are widely used by epidemiologists to map mortality or incidence rates and capture geographic variation. To…
We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains are…
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated…
We provide an algorithm, running in polynomial time in the number of vertices, computing the unique solution to the biased infinity Laplacian Boundary Problem on finite graphs. The algorithm is based on the general outline and approach…
We discuss BF theories defined on manifolds with spatial boundaries. Variational arguments show that one needs to augment the usual action with a boundary term for specific types of boundary conditions. We also show how to use this…
We introduce a new class of absorbing boundary conditions (ABCs) for the Helmholtz equation. The proposed ABCs are obtained by using $L$ discrete layers and the $Q_N$ Lagrange finite element in conjunction with the $N$-point Gauss-Legendre…
This paper studies the theoretical construction and analytic error estimation of complex Bessel function-based conformal mappings in regions with randomly perturbed boundaries. First, we construct a conformal mapping applicable to such…
Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
Adaptive Bayesian quadrature (ABQ) is a powerful approach to numerical integration that empirically compares favorably with Monte Carlo integration on problems of medium dimensionality (where non-adaptive quadrature is not competitive). Its…
We consider the problem of boundary detection for areal data, focusing on situations where for each areal unit multiple observations are available. We propose a Bayesian nonparametric mixture model for the area-specific population…
In this thesis, we present various contributions to the study of free boundary minimal surfaces. After introducing some basic tools and discussing some delicate aspects related to the definition of Morse index when allowing for a contact…
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These…
We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the boundary where these conditions are imposed. We devote…