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Full-Text Articles in Physical Sciences and Mathematics
R₀ Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, Jon T. Jacobsen, M. A. Lewis
R₀ Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, Jon T. Jacobsen, M. A. Lewis
All HMC Faculty Publications and Research
Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem impacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R0 for advection-diffusion-reaction equations and on related measures. We apply the measures to population persistence in rivers under various flow regimes. This work lays …
Two-Subspace Projection Method For Coherent Overdetermined Systems, Deanna Needell, Rachel Ward
Two-Subspace Projection Method For Coherent Overdetermined Systems, Deanna Needell, Rachel Ward
CMC Faculty Publications and Research
We present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image processing. The Kaczmarz method is one of the most popular solvers for overdetermined systems of linear equations due to its speed and simplicity. Here we introduce and analyze an extension of the Kaczmarz method which iteratively projects the estimate onto a solution space given from two randomly selected rows. We show that this projection algorithm provides exponential convergence to the solution in expectation. The convergence rate significantly improves upon …