In many scientific fields including neuroscience, climatology or physics, complex relationships can be described most parsimoniously by non-linear mechanics. Despite their relevance, many ...

This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger equation. These breathers belong to the family of solitons on a non-vanishing and constant ...

Representation theory was initially dismissed. Today, it’s central to much of mathematics. When representation theory emerged in the late 19th century, many mathematicians questioned its worth. In ...

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data.

Analysis of variance (ANOVA) is a usual way for analysing experiments. However, depending on the design and/or the analysis scheme, it can be a hard task. ExpDes, acronym for Experimental Designs, is ...

Least-squares fitting has permeated the sciences and engineering after its introduction over two centuries ago (see, for example, ref. 1 for a brief historical review). Linear least-squares regression ...

I was asked to say more about the FRS theorem. Here is a rough account. For more details see the existing literature (→ \to). from some n n-dimensional cobordism category to some flavor of the ...