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

Abstract: In this article, the controllability is investigated for nonlinear impulsive and switching systems with input delay. Using the fixed point method, two controllability conditions are ...

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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.

There is no disputing the importance of statistical analysis in biological research, but too often it is considered only after an experiment is completed, when it may be too late. This collection ...

On a spring afternoon in 2014, Brisha Borden was running late to pick up her god-sister from school when she spotted an unlocked kid’s blue Huffy bicycle and a silver Razor scooter. Borden and a ...

Abstract: Neural recordings, returns from radars and sonars, images in astronomy and single-molecule microscopy can be modeled as a linear superposition of a small number of scaled and delayed copies ...

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 ...