Gregory Herschlag
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View article: A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting
A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting Open
We introduce a new Markov Chain called the Cycle Walk for sampling measures of graph partitions where the partition elements have roughly equal size. Such Markov Chains are of current interest in the generation and evaluation of political …
View article: Where Data Science and the Disciplines Meet: Innovations in Linking Doctoral Students With Masters-Level Data Science Education
Where Data Science and the Disciplines Meet: Innovations in Linking Doctoral Students With Masters-Level Data Science Education Open
Although the need for data science methodological training is widely recognized across many disciplines, data science training is often absent from PhD programs. At the same time, Masters-level data science educational programs have seen i…
View article: Multiscale Parallel Tempering for Fast Sampling on Redistricting Plans
Multiscale Parallel Tempering for Fast Sampling on Redistricting Plans Open
When auditing a redistricting plan, a persuasive method is to compare the plan with an ensemble of neutrally drawn redistricting plans. Ensembles are generated via algorithms that sample distributions on balanced graph partitions. To audit…
View article: Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan
Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan Open
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 gui…
View article: Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan
Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan Open
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 gui…
View article: Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish
Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish Open
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 …
View article: A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis
A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis Open
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 tha…
View article: Analysis of GPU Data Access Patterns on Complex Geometries for the D3Q19 Lattice Boltzmann Algorithm
Analysis of GPU Data Access Patterns on Complex Geometries for the D3Q19 Lattice Boltzmann Algorithm Open
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…
View article: Optimal Legislative County Clustering in North Carolina
Optimal Legislative County Clustering in North Carolina Open
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 spl…
View article: A mechanochemical model for auto-regulation of lung airway surface layer volume
A mechanochemical model for auto-regulation of lung airway surface layer volume Open
We develop a proof-of-principle model for auto-regulation of water volume in the lung airway surface layer (ASL) by coupling biochemical kinetics, transient ASL volume, and homeostatic mechanical stresses. The model is based on the hypothe…
View article: Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting
Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting Open
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 par…
View article: Non-reversible Markov chain Monte Carlo for sampling of districting maps
Non-reversible Markov chain Monte Carlo for sampling of districting maps Open
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-pa…
View article: Quantifying Gerrymandering in North Carolina
Quantifying Gerrymandering in North Carolina Open
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 extrem…
View article: Optimal Legislative County Clustering in North Carolina
Optimal Legislative County Clustering in North Carolina Open
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 spl…
View article: A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans
A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans Open
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 grap…
View article: Metropolized Forest Recombination for Monte Carlo Sampling of Graph Partitions
Metropolized Forest Recombination for Monte Carlo Sampling of Graph Partitions Open
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 can be made reversible and able to s…
View article: Multi-physics simulations of particle tracking in arterial geometries with a scalable moving window algorithm
Multi-physics simulations of particle tracking in arterial geometries with a scalable moving window algorithm Open
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 inter…
View article: Optimal Legislative County Clustering in North Carolina
Optimal Legislative County Clustering in North Carolina Open
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 spl…
View article: Continuum-atomistic Algorithms for Dendritic Formation
Continuum-atomistic Algorithms for Dendritic Formation Open
Nanoscale patterning of materials at scales of less than 20nm remains a challenging problem. Standard techniques, such as lithography, rely on electron and photon beams to shape materials, yet these methods are difficult to employ at the s…
View article: The Signature of Gerrymandering in Rucho v. Common Cause
The Signature of Gerrymandering in Rucho v. Common Cause Open
In recent years, the U.S. mathematical community has been directing unprecedented attention to the problem of partisan gerrymandering, aided by computational advances and spurred by litigation challenging the spate of extreme partisan redi…
View article: GPU Data Access on Complex Geometries for D3Q19 Lattice Boltzmann Method
GPU Data Access on Complex Geometries for D3Q19 Lattice Boltzmann Method Open
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 typicall…
View article: Evaluating Partisan Gerrymandering in Wisconsin
Evaluating Partisan Gerrymandering in Wisconsin Open
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 …
View article: Redistricting: Drawing the Line
Redistricting: Drawing the Line Open
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…