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An improved feature extraction algorithm for EEG-based driving fatigue recognition. [PDF]
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Mathematical Notes
Let \(\mathbb{R}^n\) be the \(n\)-dimensional Euclidean space. A set \(C\subseteq\mathbb{R}^n\) is strictly convex if every non extreme point of a line segment joining two points of \(C\) is inside the topological interior of \(C\). The authors prove that if \(H\) is a hyperplane of a closed and strictly convex set \(C\subseteq \mathbb{R}^n\), then ...
Ünveren, Burak, Barokas, Guy
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Let \(\mathbb{R}^n\) be the \(n\)-dimensional Euclidean space. A set \(C\subseteq\mathbb{R}^n\) is strictly convex if every non extreme point of a line segment joining two points of \(C\) is inside the topological interior of \(C\). The authors prove that if \(H\) is a hyperplane of a closed and strictly convex set \(C\subseteq \mathbb{R}^n\), then ...
Ünveren, Burak, Barokas, Guy
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Classifying Hyperplanes in Hypercubes
SIAM Journal on Discrete Mathematics, 1996Summary: We consider hyperplanes spanned by vertices of the unit \(d\)-cube. We classify these hyperplanes by parallelism to coordinate axes, by symmetry of the \(d\)-cube vertices they avoid, as well as by so-called hull-honesty. (Hull-honest hyperplanes are those whose intersection figure with the \(d\)-cube coincides with the convex hull of the \(d\)
Aichholzer, Oswin, Aurenhammer, Franz
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Graphs and Combinatorics, 1985
A family of q-ary linear codes with length \(N=\left( \begin{matrix} n\\ m\end{matrix} \right)(q-1)^{m-1}\) and dimension n (or n-1) is constructed and the weight distribution of these codes is calculated. It is shown that they are subschemes of the hypercubic association scheme H(N,q).
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A family of q-ary linear codes with length \(N=\left( \begin{matrix} n\\ m\end{matrix} \right)(q-1)^{m-1}\) and dimension n (or n-1) is constructed and the weight distribution of these codes is calculated. It is shown that they are subschemes of the hypercubic association scheme H(N,q).
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Iterated hyperplane search for the budgeted maximum coverage problem
Expert Systems With Applications, 2023Zequn Wei, Jin-Kao Hao
exaly
Hyperplane Assisted Evolutionary Algorithm for Many-Objective Optimization Problems
IEEE Transactions on Cybernetics, 2020Huangke Chen, Ye Tian, Witold Pedrycz
exaly