Suchergebnisse

We consider the problem of political redistricting: given the locations of people in a geographical area (e.g. a US state), the goal is to decompose the area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are "compact" and "contiguous," to use the terms referred to in most US state constitutions and/or US Supreme Court rulings. We study a method that outputs a solution in which each district is the intersection of a convex polygon with the geographical area. The average number of sides per polygon is less than six. The polygons tend to be quite compact. Every two districts differ in population by at most one (so we call the solution balanced). In fact, the solution is a centroidal power diagram: each polygon has an associated center in R 3 such that • the projection of the center onto the plane z = 0 is the centroid of the locations of people assigned to the polygon, and • for each person assigned to that polygon, the polygon's center is closest among all centers. The polygons are convex because they are the intersections of 3D Voronoi cells with the plane. The solution is, in a well-defined sense, a locally optimal solution to the problem of choosing centers in the plane and choosing an assignment of people to those 2-d centers so as to minimize the sum of squared distances subject to the assignment being balanced. A practical problem with this approach is that, in real-world redistricting, exact locations of people are unknown. Instead, the input consists of polygons (census blocks) and associated populations. A real redistricting must not split census blocks. We therefore propose a second phase that perturbs the solution slightly so it does not split census blocks. In our experiments, the second phase achieves this while preserving perfect population balance. The district polygons are no longer convex at the fine scale because their boundaries must follow the boundaries of census blocks, but at a coarse scale they preserve the shape of the original polygons.

The 2D point location problem has applications in several areas, such as geographic information systems, navigation systems, motion planning, mapping, military strategy, location and tracking moves. We aim to present a new approach that expands upon current techniques and methods to locate the 2D position of a signal source sent by an emitter device. This new approach is based only on the geometric relationship between an emitter device and a system composed of m&ge ; 2 signal receiving devices. Current approaches applied to locate an emitter can be deterministic, statistical or machine-learning methods. We propose to perform this triangulation by geometric models that exploit elements of pole-polar geometry. For this purpose, we are presenting five geometric models to solve the point location problem: (1) based on centroid of points of pole-polar geometry, PPC ; (2) based on convex hull region among pole-points, CHC ; (3) based on centroid of points obtained by polar-lines intersections, PLI ; (4) based on centroid of points obtained by tangent lines intersections, TLI ; (5) based on centroid of points obtained by tangent lines intersections with minimal angles, MAI. The first one has computational cost On and whereas has the computational cost Onlognwhere n is the number of points of interest.

The 2D point location problem has applications in several areas, such as geographic information systems, navigation systems, motion planning, mapping, military strategy, location and tracking moves. We aim to present a new approach that expands upon current techniques and methods to locate the 2D position of a signal source sent by an emitter device. This new approach is based only on the geometric relationship between an emitter device and a system composed of m ≥ 2 signal receiving devices. Current approaches applied to locate an emitter can be deterministic, statistical or machine-learning methods. We propose to perform this triangulation by geometric models that exploit elements of pole-polar geometry. For this purpose, we are presenting five geometric models to solve the point location problem: (1) based on centroid of points of pole-polar geometry, PPC; (2) based on convex hull region among pole-points, CHC; (3) based on centroid of points obtained by polar-lines intersections, PLI; (4) based on centroid of points obtained by tangent lines intersections, TLI; (5) based on centroid of points obtained by tangent lines intersections with minimal angles, MAI. The first one has computational cost O(n) and whereas has the computational cost O(n log n)where n is the number of points of interest. © 2019 by the authors. Licensee MDPI, Basel, Switzerland. ; Spanish Ministry of Economy and Competitiveness TIN2016-76956-C3-2-R ; University of Seville

The papers in this volume were peer-reviewed and selected for presentation at the 29th International Meshing Roundtable (IMR), held June 21-25, 2021 as a virtual conference. The International Meshing Roundtable was started by Sandia National Laboratories in 1992 as a small meeting of organizations striving to establish a common focus for research and development in the field of mesh generation. Now after 29 years, it has become clear that the International Meshing Roundtable has become the recognized international focal point for state-of-the-art meshing research collaboration spanning research and development from universities, commercial companies, and government laboratories.

The papers in this volume were peer-reviewed and selected for presentation at the 28th International Meshing Roundtable (IMR), held October 14-17, 2019 in Buffalo, New York, USA. The International Meshing Roundtable was started by Sandia National Laboratories in 1992 as a small meeting of organizations striving to establish a common focus for research and development in the field of mesh generation. Now after 28 consecutive years, it has become clear that the International Meshing Roundtable has become the recognized international focal point for state-of-the-art meshing research collaboration spanning research and development from universities, commercial companies, and government laboratories.

[EN] The recently presented software zeoGAsolver is discussed, which is based on genetic algorithms, with domain-dependent crossover and selection operators that maintain the size of the population in successive iterations while improving the average fitness. Using the density, cell parameters, and symmetry (or candidate symmetries) of a zeolite sample whose resolution can not be achieved by analysis of the XRD (X-ray diffraction) data, the software attempts to locate the coordinates of the T-atoms of the zeolite unit cell employing a function of fitness' (F), which is defined through the different contributions to the penalties' (P) as F = 1/(1 + P). While testing the software to find known zeolites such as LTA (zeolite A), AEI (SSZ-39), ITW (ITQ-12) and others, the algorithm has found not only most of the target zeolites but also seven new hypothetical zeolites whose feasibility is confirmed by energetic and structural criteria. ; G. S. thanks the Spanish government for the provision of the Severo Ochoa (SEV 2016-0683), CTQ2015-70126-R and MAT2015-71842-P projects. ; Liu, X.; Valero Cubas, S.; Argente, E.; Sastre Navarro, GI. (2018). Zeolite structure determination using genetic algorithms and geometry optimisation. Faraday Discussions. 211:103-115. https://doi.org/10.1039/C8FD00035B ; S ; 103 ; 115 ; 211 ; Liu, X., Valero, S., Argente, E., Botti, V., & Sastre, G. (2015). The importance of T⋯T⋯T angles in the feasibility of zeolites. Zeitschrift für Kristallographie - Crystalline Materials, 230(5). doi:10.1515/zkri-2014-1801 ; C. Baerlocher , L. B.McCusker and D. H.Olson , Atlas of Zeolite Framework Types , Elsevier , 6 th revised edn, 2007 , (176 structures); the web version [ www.iza-structure.org ] currently contains 232 structures ; Delgado Friedrichs, O., & Huson, D. H. (1999). Tiling Space by Platonic Solids, I. Discrete & Computational Geometry, 21(2), 299-315. doi:10.1007/pl00009423 ; Friedrichs, O. D., Dress, A. W. M., Huson, D. H., Klinowski, J., & Mackay, A. L. (1999). Systematic ...

Despite the many useful applications of power indices, the literature on power indices is raft with counterintuitive results or paradoxes, as well as real-life institutions that exhibit these behaviors. This has led to a cataloging of sorts where new and different paradoxes are calculated and then shown to exist in nature. Even though the paradoxes sound different from one another with names like the paradox of redistribution, the donor and transfer paradoxes, the paradox of quarreling members, the paradox of a new member, and the paradox of large size, they can be classified by the underlying geometric properties that induce the counterintuitive results. Perhaps surprisingly, analyzing the geometry behind the paradoxes for three voters is sufficient to understand the geometry behind the paradoxes. Voting power induces a partition on games where two games are in the same part if each player i has the same power in each game. The paradoxes are a result of three geometric ideas and how they interact with the partition: a point passing a hyperplane thereby changing parts, moving hyperplanes that change the size or number of parts in a partition, and changing the dimension of the space by adding or subtracting a voter.