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pro vyhledávání: '"Duncan, Christian"'
Unordered feature sets are a nonstandard data structure that traditional neural networks are incapable of addressing in a principled manner. Providing a concatenation of features in an arbitrary order may lead to the learning of spurious patterns or
Externí odkaz:
http://arxiv.org/abs/1709.03019
Autor:
Pears, Nick, Duncan, Christian
Three-dimensional models of craniofacial variation over the general population are useful for assessing pre- and post-operative head shape when treating various craniofacial conditions, such as craniosynostosis. We present a new method of automatical
Externí odkaz:
http://arxiv.org/abs/1601.05593
Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. In this paper we develop a set-theoretic interpretation
Externí odkaz:
http://arxiv.org/abs/1510.02833
Akademický článek
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Autor:
Duncan, Christian A., Eppstein, David, Goodrich, Michael T., Kobourov, Stephen G., Löffler, Maarten
Publikováno v:
J. Computational Geometry 9 (1): 328-355, 2018
In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We
Externí odkaz:
http://arxiv.org/abs/1109.0345
In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that
Externí odkaz:
http://arxiv.org/abs/1104.1482
Autor:
Duncan, Christian A., Eppstein, David, Goodrich, Michael T., Kobourov, Stephen G., Nöllenburg, Martin
Publikováno v:
Discrete Comput. Geom. 49 (2): 157-182, 2013
We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\pi}/d(v). We show: 1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area. 2
Externí odkaz:
http://arxiv.org/abs/1009.0581
Autor:
Duncan, Christian A., Eppstein, David, Goodrich, Michael T., Kobourov, Stephen G., Nöllenburg, Martin
Publikováno v:
J. Graph Algorithms and Applications 16(1):85-108, 2012 (special issue for GD 2010)
We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular res
Externí odkaz:
http://arxiv.org/abs/1009.0579
In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R^2, with a bounding face defined by a polygonal schema P for S.
Externí odkaz:
http://arxiv.org/abs/0908.1608