This paper has two parts. The first part surveys Euler's work on the constant $\gamma=
0.57721\cdots $ bearing his name, together with some of his related work on the gamma …

We study products of random matrices in the regime where the number of terms and the size
of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of the ℓ …

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Characterizing and understanding the stability of Stochastic Gradient Descent (SGD)
remains an open problem in deep learning. A common method is to utilize the convergence …

Due to common architecture designs, symmetries exist extensively in contemporary neural
networks. In this work, we unveil the importance of the loss function symmetries in affecting …

This book is aimed at students in communications and signal processing who want to extend
their skills in the energy area. It describes power systems and why these backgrounds are …

Products of M iid random matrices of size N× N are related to classical limit theorems in
probability theory (N= 1 and large M), to Lyapunov exponents in dynamical systems (finite N …

The goal of this article is to contribute towards the conceptual and quantitative
understanding of the evolutionary benefits for (microbial) populations to maintain a seed …

We consider random products of SL (2, R) matrices that depend on a parameter in a non-
uniformly hyperbolic regime. We show that if the dependence on the parameter is monotone …

Just as phenotypic plasticity can evolve when developing individuals get informational cues
about their future adult environment, deterministic maternal effects, where offspring trait …