Zobrazeno 1 - 10
of 76
pro vyhledávání: '"WEIGHILL, THOMAS"'
Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to embed the
Externí odkaz:
http://arxiv.org/abs/2405.15959
Autor:
Weighill, Thomas
We prove that for a metric space $X$ and a finite group $G$ acting on $X$ by isometries, if $X$ coarsely embeds into a Hilbert space, then so does the quotient $X/G$. A crucial step towards our main result is to show that for any integer $k > 0$ the
Externí odkaz:
http://arxiv.org/abs/2310.09369
Autor:
Kauba, Jakini A., Weighill, Thomas
We apply persistent homology, the main method in topological data analysis, to the study of demographic data. Persistence diagrams efficiently summarize information about clusters or peaks in a region's demographic data. To illustrate how persistence
Externí odkaz:
http://arxiv.org/abs/2310.08334
Autor:
Pritchard, Neil, Weighill, Thomas
We prove an equivalence between open questions about the embeddability of the space of persistence diagrams and the space of probability distributions (i.e.~Wasserstein space). It is known that for many natural metrics, no coarse embedding of either
Externí odkaz:
http://arxiv.org/abs/2307.12884
Motivated by the problem of redistricting, we study area-preserving reconfigurations of connected subdivisions of a simple polygon. A connected subdivision of a polygon $\mathcal{R}$, called a district map, is a set of interior disjoint connected pol
Externí odkaz:
http://arxiv.org/abs/2307.00704
In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus on a classical statistic from the geography and urban sociology literature known as Moran's I, which in our language is a score associated to a real-valu
Externí odkaz:
http://arxiv.org/abs/2112.10708
Autor:
Needham, Tom, Weighill, Thomas
We introduce a method for jointly registering ensembles of partitioned datasets in a way which is both geometrically coherent and partition-aware. Once such a registration has been defined, one can group partition blocks across datasets in order to e
Externí odkaz:
http://arxiv.org/abs/2107.03460
This preprint is an exploration in how a single mathematical idea - entropy - can be applied to redistricting in a number of ways. It's meant to be read not so much as a call to action for entropy, but as a case study illustrating one of the many way
Externí odkaz:
http://arxiv.org/abs/2010.14972
Autor:
Rodden, Jonathan, Weighill, Thomas
This preprint offers a detailed look, both qualitative and quantitative, at districting with respect to recent voting patterns in one state: Pennsylvania. We investigate how much the partisan playing field is tilted by political geography. In particu
Externí odkaz:
http://arxiv.org/abs/2010.14608
We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a political districting plan with election data to produce a persistenc
Externí odkaz:
http://arxiv.org/abs/2007.02390