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The Ellipsoid Factor for Quantification of Rods, Plates, and Intermediate Forms in 3D Geometries. [PDF]
Front Endocrinol (Lausanne), 2015 The Ellipsoid Factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid which fits inside ...
Doube M.
europepmc +6 more sources
Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimization [PDF]
SIAM Journal on Imaging Sciences, 2018 Consider a structured matrix factorization model where one factor is restricted to have its columns lying in the unit simplex. This simplex-structured matrix factorization (SSMF) model and the associated factorization techniques have spurred much interest in research topics over different areas, such as hyperspectral unmixing in remote sensing, topic ...
Chia-Hsiang Lin +4 more
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Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection [PDF]
INFORMS Journal on Computing, 2015 We introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic projection. It is well-known that deriving an explicit description of a projected polytope is NP-hard.
Jianzhe Zhen, Dick den Hertog
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Sharpening Geometric Inequalities using Computable Symmetry Measures [PDF]
, 2014 Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the convex body ...
Brandenberg, René, König, Stefan
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A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane [PDF]
, 2017 In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses
A Kurzhanski +27 more
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Statistical mechanics for metabolic networks during steady-state growth [PDF]
, 2017 Which properties of metabolic networks can be derived solely from stoichiometric information about the network's constituent reactions? Predictive results have been obtained by Flux Balance Analysis (FBA), by postulating that cells set metabolic fluxes ...
Andersson, Anna MC +4 more
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Bezout Inequality for Mixed volumes [PDF]
, 2016 In this paper we consider the following analog of Bezout inequality for mixed volumes: $$V(P_1,\dots,P_r,\Delta^{n-r})V_n(\Delta)^{r-1}\leq \prod_{i=1}^r V(P_i,\Delta^{n-1})\ \text{ for }2\leq r\leq n.$$ We show that the above inequality is true when ...
Soprunov, Ivan, Zvavitch, Artem
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On largest volume simplices and sub-determinants [PDF]
, 2014 We show that the problem of finding the simplex of largest volume in the convex hull of $n$ points in $\mathbb{Q}^d$ can be approximated with a factor of $O(\log d)^{d/2}$ in polynomial time.
Di Summa, Marco +3 more
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Packing ellipsoids with overlap
, 2012 The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general
Uhler, Caroline, Wright, Stephen J.
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Quantum steering ellipsoids, extremal physical states and monogamy [PDF]
, 2014 A Corrigendum for this article has been published in 2015 New J. Phys. 17 019501Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit ...
Altepeter J +14 more
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