With Braxton Osting, we have considered spectral optimization of point set configurations for adjacency matrices and graphs on two dimensional surfaces. We study both tori and spheres. I will discuss our results, show several numerical simulations and review open problems and interesting directions to take this line of research.
Creator:
Marzuola, Jeremy L (University of North Carolina, Chapel Hill)
Created:
2016-12-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The interplay of experimental observations with mathematical models often requires conditioning models on data---for example, inferring the coefficients or boundary conditions of partial differential equations from noisy functionals of the solution field. The Bayesian approach to these problems in principle requires posterior sampling in high or...
Creator:
Marzouk, Youssef (Massachusetts Institute of Technology)
Created:
2013-01-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Bayesian inference provides a natural framework for quantifyinguncertainty in PDE-constrained inverse problems, for fusingheterogeneous sources of information, and for conditioning successivepredictions on data. In this setting, simulating from the posteriorvia Markov chain Monte Carlo (MCMC) constitutes a fundamentalcomputational bottleneck. We...
Creator:
Marzouk, Youssef (Massachusetts Institute of Technology)
Created:
2011-06-08
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Many inverse problems may involve a large number of observations. Yet these observations are seldom equally informative; moreover, practical constraints on storage, communication, and computational costs may limit the number of observations that one wishes to employ. We introduce strategies for selecting subsets of the data that yield accurate a...
Creator:
Marzouk, Youssef (Massachusetts Institute of Technology)
Created:
2017-09-06
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Shows the topography and election districts of Allegany County, Maryland. Waterways and man-made features such as roads, railroads, bridges, and buildings are indicated.
Creator:
Maryland Geological Survey
Contributor:
Geological Survey (U.S.)
Created:
1924
Contributed By:
University of Minnesota Libraries, John R. Borchert Map Library.
