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Ultrahigh-dimensional Quadratic Discriminant Analysis Using Random Projections
Annesha Deb, Minerva Mukhopadhyay, Subhajit Dutta
https://arxiv.org/abs/2505.23324

Ultrahigh-dimensional Quadratic Discriminant Analysis Using Random Projections
This paper investigates the effectiveness of implementing the Random Projection Ensemble (RPE) approach in Quadratic Discriminant Analysis (QDA) for ultrahigh-dimensional classification problems. Classical methods such as Linear Discriminant Analysis (LDA) and QDA are widely used, but face significant challenges when the dimension of the samples (say, $p$) exceeds the sample size (say, $n$). In particular, both LDA (using the Moore-Penrose inverse for covariance matrices) and QDA (even with kno…

Ordine privo di periodicit\`a: il fascino matematico delle tassellazioni
Francesco D'Andrea
https://arxiv.org/abs/2505.21379 https://

Ordine privo di periodicità: il fascino matematico delle tassellazioni
This is a review (in Italian) on aperiodic tilings of the plane intended for a general audience. First, we recall some basic results about lattices and periodic tilings. Then, we move on to one-dimensional (domino) tilings and Wang tilings. We present a beautiful proof of the existence of an aperiodic set of Wang prototiles due to J. Kari. Next, we discuss Penrose tilings and their properties. Finally, we briefly present the recent discovery by D. Smith and his collaborators of an aperiodic mon…

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