Gregory Joseph Herschlag

Journal Article SIAM 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 ... Full text Open Access Cite

Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan

Conference ACM 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 ... Full text Open Access Cite

Analysis of GPU Data Access Patterns on Complex Geometries for the D3Q19 Lattice Boltzmann Algorithm

Journal Article IEEE 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 ... Full text Cite

METROPOLIZED MULTISCALE FOREST RECOMBINATION for REDISTRICTING

Journal Article Multiscale 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 ... Full text Open Access Cite

Non-reversible Markov chain Monte Carlo for sampling of districting maps

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. ... Open Access Link to item Cite

Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting

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 ... Open Access Link to item Cite

Quantifying Gerrymandering in North Carolina

Journal Article Statistics 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 ... Full text Open Access Cite

Optimal Legislative County Clustering in North Carolina

Journal Article Statistics 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 ... Full text Open Access Cite

Optimal Legislative County Clustering in North Carolina

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 ... Open Access Link to item Cite

Multi-physics simulations of particle tracking in arterial geometries with a scalable moving window algorithm

Conference Proceedings - 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 ... Full text Cite

The Signature of Gerrymandering in Rucho v. Common Cause

Journal Article South Carolina Law Review · 2019 Open Access Cite

Multi-physics simulations of particle tracking in arterial geometries with a scalable moving window algorithm

Conference 2019 IEEE INTERNATIONAL CONFERENCE ON CLUSTER COMPUTING (CLUSTER) · January 1, 2019 Link to item Cite

GPU data access on complex geometries for D3Q19 lattice boltzmann method

Conference Proceedings - 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 ... Full text Cite

Programmable assembly of pressure sensors using pattern-forming bacteria.

Journal Article Nature biotechnology · 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 ... Full text Cite

Evaluating Partisan Gerrymandering in Wisconsin

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 ... Open Access Link to item Cite

Redistricting: Drawing the Line

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 ... Open Access Link to item Cite

Fluid extraction across pumping and permeable walls in the viscous limit

Journal Article Physics 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 ... Full text Cite

Optimal reservoir conditions for fluid extraction through permeable walls in the viscous limit

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 ... Link to item Cite

A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

Journal Article The 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 ... Full text Open Access Cite

Multiscale Parallel Tempering for Fast Sampling on Redistricting Plans

Preprint · January 30, 2024 Link to item Cite

METROPOLIZED FOREST RECOMBINATION FOR MONTE CARLO SAMPLING OF GRAPH PARTITIONS

Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan

Analysis of GPU Data Access Patterns on Complex Geometries for the D3Q19 Lattice Boltzmann Algorithm

METROPOLIZED MULTISCALE FOREST RECOMBINATION for REDISTRICTING

Non-reversible Markov chain Monte Carlo for sampling of districting maps

Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting

Quantifying Gerrymandering in North Carolina

Optimal Legislative County Clustering in North Carolina

Multi-physics simulations of particle tracking in arterial geometries with a scalable moving window algorithm

The Signature of Gerrymandering in Rucho v. Common Cause

Journal Article South Carolina Law Review · 2019 Open Access Cite

Multi-physics simulations of particle tracking in arterial geometries with a scalable moving window algorithm

Conference 2019 IEEE INTERNATIONAL CONFERENCE ON CLUSTER COMPUTING (CLUSTER) · January 1, 2019 Link to item Cite

GPU data access on complex geometries for D3Q19 lattice boltzmann method

Programmable assembly of pressure sensors using pattern-forming bacteria.

Evaluating Partisan Gerrymandering in Wisconsin

Redistricting: Drawing the Line

Fluid extraction across pumping and permeable walls in the viscous limit

Optimal reservoir conditions for fluid extraction through permeable walls in the viscous limit

A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

An exact solution for stokes flow in a channel with arbitrarily large wall permeability

Journal Article SIAM 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 ... Full text Cite

Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish

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 ... Link to item Cite

Leaf roll-up and aquaplaning in strong winds and floods

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 ... Link to item Cite

A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans

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 ... Open Access Link to item Cite