Results 31 to 40 of about 125,665 (304)
Random hyperplane search trees in high dimensions
Journal of Computational Geometry, 2015 Given a set S of n ≥ d points in general position in Rd, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree is a binary space
Luc Devroye, James King
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Hyperplane Neural Codes and the Polar Complex
, 2019 Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane codes in terms of the {\it polar complex} of the code, a simplicial ...
Allen Hatcher +10 more
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On the freeness of hypersurface arrangements consisting of hyperplanes and spheres
Open Mathematics, 2018 Let V be a smooth variety. A hypersurface arrangement 𝓜 in V is a union of smooth hypersurfaces, which locally looks like a union of hyperplanes. We say 𝓜 is free if all these local models can be chosen to be free hyperplane arrangements.
Gao Ruimei, Dai Qun, Li Zhe
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Hyperplane Arrangements in polymake [PDF]
, 2020 Hyperplane arrangements form the latest addition to the zoo of combinatorial objects dealt with by polymake. We report on their implementation and on a algorithm to compute the associated cell decomposition. The implemented algorithm performs significantly better than brute force alternatives, as it requires less convex hulls computations.
Kastner, Lars, Panizzut, Marta
openaire +2 more sources
Multi-Objective Models for Sparse Optimization in Linear Support Vector Machine Classification
Mathematics, 2023 The design of linear Support Vector Machine (SVM) classification techniques is generally a Multi-objective Optimization Problem (MOP). These classification techniques require finding appropriate trade-offs between two objectives, such as the amount of ...
Behzad Pirouz, Behrouz Pirouz
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Poisson polyhedra in high dimensions
, 2015 The zero cell of a parametric class of random hyperplane tessellations depending on a distance exponent and an intensity parameter is investigated, as the space dimension tends to infinity.
Hoerrmann, Julia +3 more
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Financial Decisions Based on Zero-Sum Games: New Conceptual and Mathematical Outcomes
International Journal of Financial StudiesAll the n possible returns on a financial asset are the components of an element of a linear space over R. This paper shows how to transfer all these n possible returns on a one-dimensional straight line.
Pierpaolo Angelini
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Triple-Point Defective Surfaces
, 2009 In this paper we study the linear series $|L-3p|$ of hyperplane sections with a triple point $p$ on a surface $S$ embedded via a very ample line bundle $L$ for a \emph{general} point $p$. If this linear series does not have the expected dimension we call
Chiantini, Luca, Markwig, Thomas
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Unveiling the Role of Curvature in Carbon for Improved Energy Release of Ammonium Perchlorate
Advanced Materials, EarlyView.High‐curvature carbon materials identified via machine learning and simulation can enhance the heat release and combustion performance of ammonium perchlorate. ABSTRACT The catalytic role of carbon curvature in the thermal decomposition of ammonium perchlorate (AP) remains largely unexplored. To address this gap, this study employs machine learning and
Dan Liu +8 more
wiley +1 more source
A commutative algebraic approach to the fitting problem [PDF]
, 2012 Given a finite set of points $\Gamma$ in $\mathbb P^{k-1}$ not all contained in a hyperplane, the "fitting problem" asks what is the maximum number $hyp(\Gamma)$ of these points that can fit in some hyperplane and what is (are) the equation(s) of such ...
Tohaneanu, Stefan O.
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