Imaging of buried objects from experimental backscattering time dependent measurements using a globally convergent inverse algorithm

We consider the problem of imaging of objects buried under the ground using backscattering experimental time dependent measurements generated by a single point source or one incident plane wave. In particular, we estimate dielectric constants of those objects using the globally convergent inverse algorithm of Beilina and Klibanov. Our algorithm is tested on experimental data collected using a microwave scattering facility at the University of North Carolina at Charlotte. There are two main challenges working with this type of experimental data: (i) there is a huge misfit between these data and computationally simulated data, and (ii) the signals scattered from the targets may overlap with and be dominated by the reflection from the ground's surface. To overcome these two challenges, we propose new data preprocessing steps to make the experimental data to be approximately the same as the simulated ones, as well as to remove the reflection from the ground's surface. Results of total 25 data sets of both non blind and blind targets indicate a good accuracy.Comment: 34 page

Cellular Probabilistic Automata - A Novel Method for Uncertainty Propagation

We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve the latter. The translation is achieved by state discretization as in set oriented numerics and the use of the locality concept from cellular automata theory. We develop the method at the example of initial value uncertainties under deterministic dynamics and prove a consistency result. As an application we discuss arsenate transportation and adsorption in drinking water pipes and compare our results to Monte Carlo computations

High-dimensional learning of linear causal networks via inverse covariance estimation

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting the best-scoring graph amongst DAGs that are consistent with the moralized graph. We show that when the error variances are known or estimated to close enough precision, the true DAG is the unique minimizer of the score computed using the reweighted squared l_2-loss. Our population-level results have implications for the identifiability of linear SEMs when the error covariances are specified up to a constant multiple. On the statistical side, we establish rigorous conditions for high-dimensional consistency of our two-part algorithm, defined in terms of a "gap" between the true DAG and the next best candidate. Finally, we demonstrate that dynamic programming may be used to select the optimal DAG in linear time when the treewidth of the moralized graph is bounded.Comment: 41 pages, 7 figure