Related papers: Measuring Congressional District Meandering
In recent years, the study of various models and questions related to Liquid Democracy has been of growing interest among the community of Computational Social Choice. A concern that has been raised, is that current academic literature…
We study the problem of estimating the convex hull of the image $f(X)\subset\mathbb{R}^n$ of a compact set $X\subset\mathbb{R}^m$ with smooth boundary through a smooth function $f:\mathbb{R}^m\to\mathbb{R}^n$. Assuming that $f$ is a…
We introduce the vacillating voter model in which each voter consults two neighbors to decide its state, and changes opinion if it disagrees with either neighbor. This irresolution leads to a global bias toward zero magnetization. In…
Complex motion patterns of natural systems, such as fish schools, bird flocks, and cell groups, have attracted great attention from scientists for years. Trajectory measurement of individuals is vital for quantitative and high-throughput…
We examine how the measure and the number of vertices of the convex hull of a random sample of $n$ points from an arbitrary probability measure in $\mathbf{R}^d$ relates to the wet part of that measure. This extends classical results for…
We discuss how to use tidal streams from globular clusters to measure the mass distribution of the Milky Way. Recent proper motion determinations for globular clusters from plate measurements and Hipparcos astrometry provide several good…
Data mining is a popular concept of mined necessary data from a large set of data. Data mining using clustering is a powerful way to analyze data and gives prediction. In this paper non structural time series data is used to forecast daily…
With historic misses in the 2016 and 2020 US Presidential elections, interest in measuring polling errors has increased. The most common method for measuring directional errors and non-sampling excess variability during a postmortem for an…
Most democratic countries use election methods to transform election results into whole numbers which usually give the number of seats in a legislative body the parties obtained. Which election method does this best can be specified by…
We analyze the optimal size of a congress in a representative democracy. We take an epistemic view where voters decide on a binary issue with one ground truth outcome, and each voter votes correctly according to their competence levels in…
Recently, a proposal has been advanced to detect unconstitutional partisan gerrymandering with a simple formula called the efficiency gap. The efficiency gap is now working its way towards a possible landmark case in the Supreme Court. This…
Given a set $P$ of $n$ points in the plane, we study the computation of the probability distribution function of both the area and perimeter of the convex hull of a random subset $S$ of $P$. The random subset $S$ is formed by drawing each…
This paper presents results from the (to our knowledge) first dynamic double-directionally resolved measurement campaign at mm-wave frequencies for an outdoor microcellular scenario. The measurements are performed with USC's real-time…
Computational methods to model political bias in social media involve several challenges due to heterogeneity, high-dimensional, multiple modalities, and the scale of the data. Political bias in social media has been studied in multiple…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
In this paper, we present a novel real-time multiple-input-multiple-output (MIMO) channel sounder for the 28 GHz band. Until now, most investigations of the directional characteristics of millimeter-wave channels have used mechanically…
A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of…
We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its…
Landau, Reid, and Yershov [A Fair Division Solution to the Problem of Redistricting, \textit{Social Choice and Welfare}, 2008] propose a protocol for drawing legislative districts based on a two player fair division process, where each…
The U.S. Supreme Court is currently deliberating over whether a proposed mathematical formula should be used to detect unconstitutional partisan gerrymandering. We show that in some cases, this formula will only flag bizarrely shaped…