Tropical geometry of statistical models
L Pachter, B Sturmfels - Proceedings of the National …, 2004 - National Acad Sciences
… k l 2)-dimensional zonotope associated with the complete bipartite graph Kk,l. The Newton
polytope of each coordinate fij is a line segment, and the zonotope is their Minkowski sum. …
polytope of each coordinate fij is a line segment, and the zonotope is their Minkowski sum. …
Suns in polyhedral spaces
AL Brown - Seminar of Mathematical Analysis (Malaga/Seville …, 2003 - books.google.com
… If X is of the form (4) then Sx is a zonotope and is easily seen to satisfy one and therefore
all of the six conditions, equivalent for zonotopes, of [6, Satz 5.1). …
all of the six conditions, equivalent for zonotopes, of [6, Satz 5.1). …
Volumes on normed and Finsler spaces
JCÁ Paiva, AC Thompson - A sampler of Riemann-Finsler …, 2004 - books.google.com
… A polytope in a vector space X is said to be a zonotope if all of its faces are symmetric. A
convex body is said to be az onoid if it is the limit (in the Hausdorff topology) of zonotopes. …
convex body is said to be az onoid if it is the limit (in the Hausdorff topology) of zonotopes. …
17 FACE NUMBERS OF POLYTOPES AND COMPLEXES
LJ Billera, A Björner - Handbook of Discrete and Computational …, 2004 - books.google.com
… between zonotopes and general polytopes emerges. As with general convex polytopes,
we have nonnegativity of the cd-index for zonotopes. However, the cd-index of any d-zonotope …
we have nonnegativity of the cd-index for zonotopes. However, the cd-index of any d-zonotope …
Hausdorff Measure of p-Cantor Sets
In this paper we analyze Cantor type sets constructed by the removal of open intervals whose
lengths are the terms of the p-sequence, { k - p } k = 1 ∞ . We prove that these Cantor sets …
lengths are the terms of the p-sequence, { k - p } k = 1 ∞ . We prove that these Cantor sets …
[HTML][HTML] Robust visualization of strange attractors using affine arithmetic
… zonotope enclosures that adapt themselves better to the shape and orientation of the underlying
set, thus also reducing the wrapping effect. (A zonotope is … and the zonotope enclosures …
set, thus also reducing the wrapping effect. (A zonotope is … and the zonotope enclosures …
Arrangements of hyperplanes
B Grünbaum - Convex Polytopes, 2003 - Springer
… Then we get a zonotope of dimension d +1, associated with the arrangement pi, by :e…
zonotopes, while "simple" arrangements (as defined on page 391) correspond to cubical zonotopes…
zonotopes, while "simple" arrangements (as defined on page 391) correspond to cubical zonotopes…
Non-primitive [IMG align=ABSMIDDLE alt=]tex_rm_4333_img1[/IMG]-dimensional parallelohedra of the first type: combinatorics and symbols
EA Bolshakova - Russian Mathematical Surveys, 2006 - turpion.org
Non-primitive n-dimensional parallelohedra of the first type: combinatorics and symbols
Page 1 EA Bol’shakova Non-primitive n-dimensional parallelohedra of the first type: …
Page 1 EA Bol’shakova Non-primitive n-dimensional parallelohedra of the first type: …
[PDF][PDF] On the efficiency of invariant multivariate sign and rank tests
EEP Liski, J Isotalo, J Niemelä, S Puntanen… - Festschrift for Tarmo …, 2006 - Citeseer
… The so called zonotopes and lift-zonotopes have been used to describe and investigate
the properties of a multivariate distribution, see Mosler (2002). Randles (1989) developed an …
the properties of a multivariate distribution, see Mosler (2002). Randles (1989) developed an …
Donald and the Golden Rhombohedra
M Senechal - The Coxeter Legacy: Reflections and Projections …, 2006 - books.google.com
… (Venkov and McMullen proved, independently, that a zonotope in any dimension n tiles R"
if, and only if, all of its zones have length 4 or 6.[23],[17].) If a shape tiles both periodically and …
if, and only if, all of its zones have length 4 or 6.[23],[17].) If a shape tiles both periodically and …