Gaussian samples, regular simplices, and exchangeability
نویسندگان
چکیده
منابع مشابه
Regular Simplices Passing through Holes
What is the smallest circular or square wall hole that a regular tetrahedron can pass? This problem was solved by Itoh–Tanoue– Zamfirescu [8]. Then, we settled the case of equilateral triangular hole in [1]. Motivated by these results, we consider the corresponding problems in higher dimensions. Among other results, we determine the minimum (n−1)-dimensional ball hole that a unit regular n-simp...
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Picture three points at the vertices of an equilateral triangle in two dimensions, or four points at the vertices of a regular tetrahedron in three dimensions. Thought of as scatterings of data they wouldn’t seem to reveal strong linear associations between the coordinates. There are no clear axes of elongation in the scatterplots, which would suggest that change in some variable is predictable...
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We prove that the n-dimensional unit hypercube contains an n-dimensional regular simplex of edge length c √ n, where c > 0 is a constant independent of n. Let l∆n be the n-dimensional regular simplex of edge length l, and let lQn be the n-dimensional hypercube of edge length l. For simplicity, we omit l if l= 1, e.g., Qn denotes the unit hypercube. We are interested in the maximum edge length o...
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Volumetric samples on Cartesian lattices are less efficient than samples on body-centred cubic (BCC) lattices. We show how to construct isosurfaces on BCC lattices using several different algorithms. Since the mesh that arises from BCC lattices involves a large number of cells, we show two alternate methods of reducing the number of cells by clumping tetrahedra into either octahedra or hexahedr...
متن کاملExchangeability and regression models
Sir David Cox’s statistical career and his lifelong interest in the theory and application of stochastic processes began with problems in the wool industry. The problem of drafting a strand of wool yarn to near uniform width is not an auspicious starting point, but an impressive array of temporal and spectral methods from stationary time series were brought to bear on the problem in Cox (1949)....
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1997
ISSN: 0179-5376,1432-0444
DOI: 10.1007/pl00009292