Results 41 to 50 of about 255,371 (329)
Nested Convex Bodies are Chaseable [PDF]
Algorithmica, 2018 In the Convex Body Chasing problem, we are given an initial point $v_0$ in $R^d$ and an online sequence of $n$ convex bodies $F_1, ..., F_n$. When we receive $F_i$, we are required to move inside $F_i$. Our goal is to minimize the total distance travelled. This fundamental online problem was first studied by Friedman and Linial (DCG 1993).
Bansal, Nikhil +4 more
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MATHEMATICA SCANDINAVICA, 1990 There are several ways to generalize the classical concept of affine surface area of a sufficiently smooth convex body \(K\) in \(\mathbb{R}^ n\) due to Blaschke to arbitrary convex bodies [see \textit{K. Leichtweiss}, Manuscr. Math. 56, 429-464 (1986; Zbl 0588.52011), \textit{E. Lutwak}, Adv. Math. 85, No. 1, 39-68 (1991; Zbl 0727.53016) and \textit{C.
Werner, Elisabeth, Schütt, Carsten
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Complete spherical convex bodies [PDF]
Journal of Geometry, 2020 AbstractSimilarly to the classic notion in Euclidean space, we call a set on the sphere $$S^d$$ S d complete, provided adding any extra point increases its diameter. Complete sets are convex bodies on $$S^d$$ S d . Our main theorem says that on $$S^d$$ S d complete bodies of diameter $$\delta $$ δ coincide with bodies of constant width ...
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Order Types of Convex Bodies [PDF]
Order, 2010 We give new bounds on the Erdos-Szekeres theorems for convex bodies of Bisztriczky and Fejes Toth and of Pach and Toth. We derive them from a combinatorial characterization of convex position of a family of planar convex bodies. This characterization confirms that the concept of Order Type for points can be extended to noncrossing families of convex ...
Hubard, Alfredo +3 more
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Covering cross-polytopes with smaller homothetic copies
AIMS MathematicsLet $ C_{n} $ be an $ n $-dimensional cross-polytope and $ \Gamma_{p}(C_{n}) $ be the smallest positive number $ \gamma $ such that $ C_{n} $ can be covered by $ p $ translates of $ \gamma C_{n} $.
Feifei Chen, Shenghua Gao, Senlin Wu
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On the volume of sections of a convex body by cones
, 2016 Let $K$ be a convex body in $\mathbb R^n$. We prove that in small codimensions, the sections of a convex body through the centroid are quite symmetric with respect to volume.
Fradelizi, Matthieu +2 more
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Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width
, 2011 A subset of the d-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent d-dimensional closed balls.
B.V. Dekster +25 more
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Floating and Illumination Bodies for Polytopes: Duality results
Discrete Analysis, 2019 Floating and illumination bodies for polytopes: duality results, Discrete Analysis 2019:11, 22 pp. A well-known concept in convex geometry is that of the _floating body_ of a convex body, which is defined as follows.
Elisabeth Werner, Olaf Mordhorst
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, 2018 Recently it has been demonstrated that the Shannon entropy or the von Neuman entropy are the only entropy functions that generate a local Bregman divergences as long as the state space has rank 3 or higher.
A Banerjee +15 more
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Insights Into the Antigenic Repertoire of Unclassified Synaptic Antibodies
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective We sought to characterize the sixth most common finding in our neuroimmunological laboratory practice (tissue assay‐observed unclassified neural antibodies [UNAs]), combining protein microarray and phage immunoprecipitation sequencing (PhIP‐Seq). Methods Patient specimens (258; 133 serums; 125 CSF) meeting UNA criteria were profiled;
Michael Gilligan +22 more
wiley +1 more source