Results 41 to 50 of about 19,164 (129)
Variants of a theorem of Macbeath in finite‐dimensional normed spaces
Mathematika, Volume 72, Issue 2, April 2026.Abstract A classical theorem of Macbeath states that for any integers d⩾2$d \geqslant 2$, n⩾d+1$n \geqslant d+1$, d$d$‐dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with n$n$ vertices.
Zsolt Lángi, Shanshan Wang
wiley +1 more source
An example of Bruns-Gubeladze K-theory defined by three dimensional polytope
Publications de l'Institut Mathematique, 2015 For the Bruns-Gubeladze polytopal K-theory, we describe a new series of three dimensional balanced Col-divisible polytopes. Also we calculate the corresponding elementary groups and as a corollary obtain an expression of the polytopal K-groups in terms of the Quillen K-groups.
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Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2135-2160, 15 March 2026.ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
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Polytopes of Minimum Positive Semidefinite Rank
, 2013 The positive semidefinite (psd) rank of a polytope is the smallest $k$ for which the cone of $k \times k$ real symmetric psd matrices admits an affine slice that projects onto the polytope.
Gouveia, João +2 more
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Osculating geometry and higher‐order distance Loci
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first‐order tangency. We focus on the data locus of points possessing at least one critical point of the distance function ...
Sandra Di Rocco +2 more
wiley +1 more source
Mathematics and Computers in SimulationAgglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel Geometrical Deep Learning-based algorithm that can exploit the geometrical and physical information of the underlying ...
Paola F. Antonietti +2 more
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Convex hulls of spheres and convex hulls of convex polytopes lying on parallel hyperplanes [PDF]
, 2011 Given a set $\Sigma$ of spheres in $\mathbb{E}^d$, with $d\ge{}3$ and $d$ odd, having a fixed number of $m$ distinct radii $\rho_1,\rho_2,...,\rho_m$, we show that the worst-case combinatorial complexity of the convex hull $CH_d(\Sigma)$ of $\Sigma$ is $\
Karavelas, Menelaos I., Tzanaki, Eleni
core
Weather and Climate Extremes: Simplex, Dynamical Systems and Hull Clustering
Journal of Geophysical Research: Atmospheres, Volume 131, Issue 4, 28 February 2026.Abstract A novel method is developed and applied to identify high‐dimensional weather and climate extremes located on the envelope of the data set within its state space. The method is based on formulating and integrating dynamical systems whose attractive set, that is, stable fixed points, is constituted of extreme states residing on the convex hull ...
A. Hannachi +6 more
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polyDB: A Database for Polytopes and Related Objects
, 2017 polyDB is a database for discrete geometric objects. The database is accessible via web and an interface from the software package polymake. It contains various datasets from the area of lattice polytopes, combinatorial polytopes, matroids and tropical ...
Paffenholz, Andreas
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The DNA of Calabi–Yau Hypersurfaces
Fortschritte der Physik, Volume 74, Issue 2, February 2026.Abstract Genetic Algorithms are implemented for triangulations of four‐dimensional reflexive polytopes, which induce Calabi–Yau threefold hypersurfaces via Batyrev's construction. These algorithms are shown to efficiently optimize physical observables such as axion decay constants or axion–photon couplings in string theory compactifications.
Nate MacFadden +2 more
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