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 ...

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 author establishes a property of supply for a competitive firm: Assuming differentiability of the production frontier, linearly independent price vectors have disjoint image sets under the supply ...