By comparing a specific redistricting plan to an ensemble of plans, we evaluate whether the translates individual votes election outcomes in unbiased fashion. Explicitly, if given exhibits extreme statistical properties compared nonpartisan plans satisfying all legal criteria. Thus, capture how interpret via state's geo-political landscape. We generate through Markov chain Monte Carlo algorithm coupled with simulated annealing based on reference distribution that does not include partisan...

We examine the extent of gerrymandering for 2010 General Assembly district map Wisconsin. find that there is substantial variability in election outcome depending on what maps are used. also found robust evidence highly gerrymandered and this likely altered partisan make up Wisconsin some elections. Compared to distribution possible redistricting plans Assembly, Wisconsin's chosen plan an outlier it yields results skewed Republicans when statewide proportion Democratic votes comprises more...

.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 Metropolis–Hastings method. Our resulting algorithm able sample from specified measure or spanning forests. Being requirement of what we consider gold standard quantifying extent which particular map gerrymander. modifies recently developed method called recombination (ReCom), draws trees joined and then randomly cuts them repartition. We improve...

GPU performance of the lattice Boltzmann method (LBM) depends heavily on memory access patterns. When LBM is advanced with GPUs complex computational domains, geometric data typically accessed indirectly, and lexicographically in Structure Array (SoA) layout. Although there are a variety existing patterns beyond typical choices, no study has yet examined relative efficacy between them. Here, we compare suite schemes via empirical testing modeling. We find strong evidence that semi-direct...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 23 March 2021Accepted: 27 August 2021Published online: 16 December 2021Keywordshierarchical sampling, Metropolis--Hastings, spanning trees, multilevel graphs, multiscale computation, redistrictingAMS Subject Headings60J10, 60J22, 05C05, 65C05, 62P25Publication DataISSN (print): 1540-3459ISSN (online): 1540-3467Publisher: Society for Industrial and Applied...

We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within is set ordinary differential equations considers correlations varying lattice distance; assumption full system will have finite thus behavior models approach system. provide evidence this convergence in context one- two-dimensional numerical examples. Lower levels consider shorter are shown be up three orders...

We derive an exact solution for Stokes flow in a channel with permeable walls. assume that at the walls, normal component of fluid velocity is described by Darcy's law and tangential no slip condition. The pressure exterior to assumed be constant. Although this problem has been well studied, typical studies permeability wall small relative other non-dimensional parameters; work relaxes assumption explores regime parameter space not yet studied. A consequence relaxation transverse longer...

GPU performance of the lattice Boltzmann method (LBM) depends heavily on memory access patterns. When implemented with GPUs complex domains, typically, geometric data is accessed indirectly and lexicographically. Although there are a variety other options, no study has examined relative efficacy between them. Here, we examine suite schemes via empirical testing modeling. We find strong evidence that semi-direct often better suited than more common indirect addressing, providing increased...

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 may undergo peristaltic pumping which is thought enhance exchange. To date, little analytic work has been done study effect of on extraction across walls. this paper, we examine model flowing through exchanged reservoir. walls are allowed contract expand uniformly, simulating mechanism....

We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The is designed to be usable as the proposal in Chain Monte Carlo (MCMC) algorithm. Sampling space of plans amounts dividing graph into partition with specified number elements which each correspond different district. districts satisfy collection hard constraints and measure may weighted regard other criteria. multi-scale algorithm similar our previously developed proposal, however, this provides improved scaling...

We develop methods to evaluate whether a political districting accurately represents the will of people. To explore and showcase our ideas, we concentrate on congressional districts for U.S. House representatives use state North Carolina its redistrictings since 2010 census. Using Monte Carlo algorithm, randomly generate over 24,000 that are non-partisan adhere criteria from proposed legislation. Applying historical voting data these random redistrictings, find number democratic republican...

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To audit political district maps for partisan gerrymandering, one may determine a baseline the expected distribution of outcomes by sampling an ensemble maps. One approach to is use redistricting policy as guide precisely codify preferences between Such give rise probability on space plans, and Metropolis-Hastings methods allow sample ensembles from specified distribution. Although these approaches have nice theoretical properties successfully detected gerrymandering in legal settings,...

When auditing a redistricting plan, persuasive method is to compare the plan with an ensemble of neutrally drawn plans. Ensembles are generated via algorithms that sample distributions on balanced graph partitions. To audit partisan difference between and given one must ensure non-partisan criteria matched so we may conclude differences come from bias rather than, for example, levels compactness or in community preservation. Certain sampling allow explicitly state policy-based probability...

Although the need for data science methodological training is widely recognized across many disciplines, often absent from PhD programs. At same time, Masters-level educational programs have seen incredible growth and investment. In 2018, Duke initiated a National Science Foundation (NSF)-funded program to determine whether that universities already invested in could be leveraged reduce education barriers doctoral students face. Doctoral Fellows diverse fields worked with teams of master's...

In arterial systems, cancer cell trajectories determine metastatic locations; similarly, particle drug delivery distribution. Predicting is challenging, as the dynamics are affected by local interactions with red blood cells, complex hemodynamic flow structure, and downstream factors such stenoses or blockages. Direct simulation not possible, a single of large domain explicit cells currently intractable on even largest supercomputers. To overcome this limitation, we present multi-physics...

Evaluating the degree of partisan districting (Gerrymandering) in a statistical framework typically requires an ensemble plans which are drawn from prescribed probability distribution that adheres to realistic and non-partisan criteria. In this article we introduce novel non-reversible Markov chain Monte-Carlo (MCMC) methods for sampling such have improved mixing properties comparison previously used (reversible) MCMC algorithms. doing so extend current construction chains on discrete spaces...