Related papers: Revisiting Compactness for District Plans
Prior proposals for cumulative statistics suggest making tiny random perturbations to the scores (independent variables in a regression) in order to ensure the scores' uniqueness. Uniqueness means that no score for any member of the…
A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^(n)) from sample data is designed. This method is based on gradually varied functions and the classical finite difference method.…
We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive…
This paper presents some applications of using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain…
Multi-agent planning (MAP) approaches have been typically conceived for independent or loosely-coupled problems to enhance the benefits of distributed planning between autonomous agents as solving this type of problems require less…
The rapid development of 3D technology and computer vision applications have motivated a thrust of methodologies for depth acquisition and estimation. However, most existing hardware and software methods have limited performance due to poor…
Future large scale structure surveys will measure the locations and shapes of billions of galaxies. The precision of such catalogs will require meticulous treatment of systematic contamination of the observed fields. We compare several…
We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a data completion scheme to reconstruct missing boundary…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
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…
Meshless methods are often used in numerical simulations of systems of partial differential equations (PDEs), particularly those which involve complex geometries or free surfaces. Here we present a novel compact scheme based on the local…
We consider the notions of agreement, diversity, and polarization in ordinal elections (that is, in elections where voters rank the candidates). While (computational) social choice offers good measures of agreement between the voters, such…
A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…
In this paper, we propose a new global geometry constraint for depth completion. By assuming depth maps often lay on low dimensional subspaces, a dense depth map can be approximated by a weighted sum of full-resolution principal depth…
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…
In this investigation we focus on the problem of mapping the ground reflectivity with multiple laser scanners mounted on mobile robots/vehicles. The problem originates because regions of the ground become populated with a varying number of…
This paper presents an enhanced version of the Interactive Voting-Based Map Matching algorithm, designed to efficiently process trajectories with varying sampling rates. The main aim is to reconstruct GPS trajectories with high accuracy,…
Algorithmic and statistical approaches to congressional redistricting are becoming increasingly valuable tools in courts and redistricting commissions for quantifying gerrymandering in the United States. While there is existing literature…
Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…
We analyze the coordinate descent method with a new coordinate selection strategy, called volume sampling. This strategy prescribes selecting subsets of variables of certain size proportionally to the determinants of principal submatrices…