5 papers · 1 filter
Fractional and Integer Order Sobolev Spaces for Compact Metric Graphs
Elsiddig Awadelkarim, David Bolin, Alexandre B. Simas
Given a compact metric graph and the Laplacian coupled with standard (Kirchhoff) vertex conditions, solutions to fractional elliptic partial differential equations of the…
Elliptic Bayesian Inverse Problems on Metric Graphs
David Bolin, Wenwen Li, Daniel Sanz-Alonso
This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connect…
rSPDE: tools for statistical modeling using fractional SPDEs
David Bolin, Alexandre B. Simas
The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example…
Log-Gaussian Cox Processes on General Metric Graphs
David Bolin, Damilya Saduakhas, Alexandre B. Simas
The modeling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We pro…
A new class of non-stationary Gaussian fields with general smoothness on metric graphs
David Bolin, Lenin Riera-Segura, Alexandre B. Simas
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivot…