858 research outputs found
Inside Magazine, January 2011
Iowa Department of Transportation Newsletter. INSIDE Magazine is developed to help keep all Iowa DOT employees informed about critical issues affecting them, recognize DOT employees for their excellent service and share interesting aspects in the lives of our co-workers
Locked Polyomino Tilings
A locked -omino tiling is a grid tiling by -ominoes such that, if you
remove any pair of tiles, the only way to fill in the remaining grid cells
with -ominoes is to use the same two tiles in the exact same configuration
as before. We exclude degenerate cases where there is only one tiling overall
due to small dimensions. It is a classic (and straightforward) result that
finite grids do not admit locked 2-omino tilings. In this paper, we construct
explicit locked -omino tilings for on grids of various
dimensions. Most notably, we show that locked 3- and 4-omino tilings exist on
finite square grids of arbitrarily large size, and locked -omino tilings of
the infinite grid exist for arbitrarily large . The result for 4-omino
tilings in particular is remarkable because they are so rare and difficult to
construct: Only a single tiling is known to exist on any grid up to size .
Locked -omino tilings arise as obstructions to widely used political
redistricting algorithms in a model of redistricting where the underlying
census geography is a grid graph. Most prominent is the ReCom Markov chain,
which takes a random walk on the space of redistricting plans by iteratively
merging and splitting pairs of districts (tiles) at a time. Locked -omino
tilings are isolated states in the state space of ReCom. The constructions in
this paper are counterexamples to the meta-conjecture that ReCom is irreducible
on graphs of practical interest
An Economic Analysis of Privacy Protection and Statistical Accuracy as Social Choices
Statistical agencies face a dual mandate to publish accurate statistics while protecting respondent privacy. Increasing privacy protection requires decreased accuracy. Recognizing this as a resource allocation problem, we propose an economic solution: operate where the marginal cost of increasing privacy equals the marginal benefit. Our model of production, from computer science, assumes data are published using an efficient differentially private algorithm. Optimal choice weighs the demand for accurate statistics against the demand for privacy. Examples from U.S. statistical programs show how our framework can guide decision-making. Further progress requires a better understanding of willingness-to-pay for privacy and statistical accuracy
Discrete geometry for electoral geography
We discuss the "compactness," or shape analysis, of electoral districts,
focusing on some of the most popular definitions in the political science
literature, which compare area to perimeter. We identify four problems that are
present in these and all contour-based scores of district geometry. To address
these issues, we set the stage for {\em discrete} versions of classical shape
scores, laying out definitions, goals, and questions for a promising new fusion
of combinatorics and discrete geometry with electoral geography.Comment: 18 page
Confidentiality Protection in the 2020 US Census of Population and Housing
In an era where external data and computational capabilities far exceed
statistical agencies' own resources and capabilities, they face the renewed
challenge of protecting the confidentiality of underlying microdata when
publishing statistics in very granular form and ensuring that these granular
data are used for statistical purposes only. Conventional statistical
disclosure limitation methods are too fragile to address this new challenge.
This article discusses the deployment of a differential privacy framework for
the 2020 US Census that was customized to protect confidentiality, particularly
the most detailed geographic and demographic categories, and deliver controlled
accuracy across the full geographic hierarchy.Comment: Version 2 corrects a few transcription errors in Tables 2, 3 and 5.
Version 3 adds final journal copy edits to the preprin
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