University of Redlands

Murmurations, Mestre–Nagao sums, and convolutional neural networks for elliptic curves

Abstract We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over $$\mathbb {Q}$$ Q and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki–Vlah, Bujanović–Kazalicki–Novak, and Pozdnyakov...

Long‐term periodontal stability following palliative management of pemphigus vulgaris: A 5‐year case report

BACKGROUND: Pemphigus vulgaris (PV) is a chronic autoimmune mucocutaneous disorder that may cause painful oral erosions, mucosal fragility, and impaired oral hygiene, complicating periodontal treatment. This case report describes a staged, minimally traumatic approach to periodon...