@article{banks_browning_2005, title={Time domain electromagnetic scattering using finite elements and perfectly matched layers}, volume={194}, ISSN={["0045-7825"]}, DOI={10.1016/j.cma.2004.06.013}, abstractNote={We consider a model for the interrogation of a planar Debye medium by a non-harmonic microwave pulse from an antenna source in free space, and we compute the reflected solution using finite elements in the spatial variables and finite differences in the time variable. Perfectly matched layers (PMLs) and an absorbing boundary condition are used to damp waves interacting with artificial boundaries imposed to allow finite computational domains. We present simulation results showing that numerical reflections from interfaces at PML boundaries can be controlled.}, number={2-5}, journal={COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING}, author={Banks, HT and Browning, BL}, year={2005}, pages={149–168} }
 @article{browning_browning_2002, title={On reducing the statespace of hidden Markov models for the identity by descent process}, volume={62}, ISSN={["0040-5809"]}, DOI={10.1006/tpbi.2002.1583}, abstractNote={Important methods for calculating likelihoods of genealogical relationships and mapping genes are based on hidden Markov models for the process of identity by descent along chromosomes. The computational time for the algorithms depends critically on the size of the statespace of the hidden Markov model. We describe the maximal grouping together of states of the model to reduce the size of the statespace. This grouping is based on pedigree symmetries. We also present an efficient algorithm for finding the maximal grouping.}, number={1}, journal={THEORETICAL POPULATION BIOLOGY}, author={Browning, S and Browning, BL}, year={2002}, month={Aug}, pages={1–8} }
 @article{browning_2000, title={Time and frequency domain scattering for the one-dimensional wave equation}, volume={16}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/16/5/315}, abstractNote={We give a constructive method for extending time domain data for the inverse scattering problem for the one-dimensional wave equation. We show that a reflection operator on L2(-T,T) with T finite is essentially a Hankel operator and then modify the Nehari extension of the kernel of the reflection operator to obtain a reflection operator on L2(ℝ) that is consistent with conservation of energy. This extension result allows frequency domain techniques to be used when the time domain data are only available for finite time, and we demonstrate this by using the frequency domain characterization of reflection coefficients to obtain a new proof of the characterization of reflection operators on L2(-T,T). We also give an a priori estimate for the operator norm of the reflection operator on L2(-T,T) and use the theory of Toeplitz operators to show how the singular values of these reflection operators are related to the reflection coefficient.}, number={5}, journal={INVERSE PROBLEMS}, author={Browning, BL}, year={2000}, month={Oct}, pages={1377–1403} }