Unraveling Complexity: Delving into a Novel Pigmented Epithelioid Melanocytoma Case.

Pigmented epithelioid melanocytoma (PEM) is a rare and diagnostically challenging skin neoplasm. Differentiating this lesion from melanoma is challenging due to overlapping clinical, histopathological, and immunohistochemical features. Some PEMs have a benign course, while others may be associated with more aggressive behaviour and have potential for local recurrence or distant metastasis.

Topological measures of order for imperfect two-dimensional Bravais lattices.

Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point distributions, are the key components for defining these measures. The measures generalize previous measures of order using persistent homology that were applicable only to imperfect hexagonal lattices in two dimensions.

Theory of the nanoscale surface ripples produced by ion irradiation of a miscut (001) gallium arsenide surface.

We develop a theory for the surface ripples produced by near-normal-incidence ion bombardment of a (001) GaAs surface with a small miscut along the [110] direction. We restrict our attention to the case in which the energy of the incident ions is below the sputter yield threshold and the sample temperature is just above the recrystallization temperature. Highly ordered, faceted ripples with their wave vector aligned with the [110] direction form when the ion beam is normally incident and there is no miscut.

Nanoscale pattern formation on solid surfaces bombarded by two broad ion beams in the regime in which sputtering is negligible.

We study nanoscale pattern formation on the surface of a solid that is bombarded with two diametrically opposed, broad ion beams for ion energies low enough that sputtering can be neglected. We focus on the case in which the angle of ion incidence is just above the threshold angle for pattern formation. The equation of motion at sufficiently long times is derived using a generalized crater function formalism.