This study presents SynaptoGen, a differentiable extension of connectome models that links gene expression, protein-protein interaction probabilities, synaptic multiplicity, and synaptic weights, and ...

Various classes of analytic, quasi-analytic and other infinitely differentiable functions of a real variable are studied. The paper gives a self-contained treatment by means of an elementary real ...

We develop a partitioning lemma (see Lemma 5) for superadditive set functions satisfying certain continuity conditions. This leads to a relatively simple proof of two theorems of A. S. Besicovitch on ...

The Uncertainty-Aware Fourier Ptychography (UA-FP) framework marks a transformative milestone in computational imaging, revolutionizing the way we address system uncertainties. This innovative ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky ...