Journal ArticleSIAM Journal on Applied Mathematics · August 1, 2023
We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method. Our resulting algorithm is able to sample from a specified measure on partiti ...
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ConferenceACM International Conference Proceeding Series · October 6, 2022
To audit political district maps for partisan gerrymandering, one may determine a baseline for the expected distribution of partisan outcomes by sampling an ensemble of maps. One approach to sampling is to use redistricting policy as a guide to precisely c ...
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Journal ArticleIEEE Transactions on Parallel and Distributed Systems · October 1, 2021
GPU performance of the lattice Boltzmann method (LBM) depends heavily on memory access patterns. When implemented with GPUs on complex domains, typically, geometric data is accessed indirectly and lattice data is accessed lexicographically. Although there ...
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Journal ArticleMultiscale Modeling and Simulation · January 1, 2021
We develop a Metropolized Multiscale Forest Recombination Markov Chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into a ...
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Journal Article · August 18, 2020
Evaluating the degree of partisan districting (Gerrymandering) in a
statistical framework typically requires an ensemble of districting plans which
are drawn from a prescribed probability distribution that adheres to a
realistic and non-partisan criteria. ...
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Journal Article · August 18, 2020
We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The
chain is designed to be usable as the proposal in a Markov Chain Monte Carlo
(MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into
a partition with a spe ...
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Journal ArticleStatistics and Public Policy · January 1, 2020
By comparing a specific redistricting plan to an ensemble of plans, we evaluate whether the plan translates individual votes to election outcomes in an unbiased fashion. Explicitly, we evaluate if a given redistricting plan exhibits extreme statistical pro ...
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Journal ArticleStatistics and Public Policy · January 1, 2020
North Carolina’s constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the “one person, one vote” mandate of the U.S. Supreme Court. Given that counties must be split, the North Car ...
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Internet Publication · November 22, 2019
North Carolina's constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the "one person, one vote" mandate of the U.S. Supreme Court. Given that counties must be split, the North Car ...
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Internet Publication · November 22, 2019
North Carolina's constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the "one person, one vote" mandate of the U.S. Supreme Court. Given that counties must be split, the North Car ...
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ConferenceProceedings - IEEE International Conference on Cluster Computing, ICCC · September 1, 2019
In arterial systems, cancer cell trajectories determine metastatic cancer locations; similarly, particle trajectories determine drug delivery distribution. Predicting trajectories is challenging, as the dynamics are affected by local interactions with red ...
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ConferenceProceedings - 2018 IEEE 32nd International Parallel and Distributed Processing Symposium, IPDPS 2018 · August 3, 2018
GPU performance of the lattice Boltzmann method (LBM) depends heavily on memory access patterns. When LBM is advanced with GPUS on complex computational domains, geometric data is typically accessed indirectly, and lattice data is typically accessed lexico ...
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Journal ArticleNat Biotechnol · November 2017
Biological systems can generate microstructured materials that combine organic and inorganic components and possess diverse physical and chemical properties. However, these natural processes in materials fabrication are not readily programmable. Here, we u ...
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Journal Article · September 2, 2017
We examine the extent of gerrymandering for the 2010 General Assembly
district map of Wisconsin. We find that there is substantial variability in the
election outcome depending on what maps are used. We also found robust evidence
that the district maps are ...
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Journal Article · April 9, 2017
We develop methods to evaluate whether a political districting accurately
represents the will of the people. To explore and showcase our ideas, we
concentrate on the congressional districts for the U.S. House of
representatives and use the state of North C ...
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Journal ArticlePhysics of Fluids · April 1, 2016
In biological transport mechanisms such as insect respiration and renal filtration, fluid travels along a leaky channel allowing material exchange with systems exterior to the channel. The channels in these systems may undergo peristaltic pumping which is ...
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Journal Article · November 4, 2015
In biological transport mechanisms such as insect respiration and renal
filtration, fluid travels along a leaky channel allowing exchange with systems
exterior the the channel. The channels in these systems may undergo peristaltic
pumping which is thought ...
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Journal ArticleThe Journal of chemical physics · June 2015
We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spati ...
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Journal ArticleSIAM Journal on Applied Mathematics · January 1, 2015
We derive an exact solution for Stokes flow in a channel with permeable walls. At the channel walls, the normal component of the fluid velocity is described by Darcy's law, and the tangential component of the fluid velocity is described by the no slip cond ...
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Journal Article · October 16, 2010
The Scallop Theorem states that reciprocal methods of locomotion, such as jet
propulsion or paddling, will not work in Stokes flow (Reynolds number = 0). In
nature the effective limit of jet propulsion is still in the range where
inertial forces are signif ...
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Journal Article · October 10, 2008
Flexible plants, fungi, and sessile animals are thought to reconfigure in the
wind and water to reduce the drag forces that act upon them. In strong winds,
for example, leaves roll up into cone shapes that reduce flutter and drag when
compared to paper cut ...
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Journal Article
We describe a Markov chain on redistricting plans that makes relatively global moves. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into a partitio ...
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