A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

Typically, complex systems are natural or social systems which consist of a large number of
nonlinearly interacting elements. These systems are open, they interchange information or …

The human gut harbors a large and complex community of beneficial microbes that remain
stable over long periods. This stability is considered critical for good health but is poorly …

Forty years ago, May proved, that sufficiently large or complex ecological networks have a
probability of persisting that is close to zero, contrary to previous expectations,,. May …

Random matrix theory has found many applications in physics, statistics and engineering
since its inception. Although early developments were motivated by practical experimental …

A continuous-time dynamic model of a network of N nonlinear elements interacting via
random asymmetric couplings is studied. A self-consistent mean-field theory, exact in the …

Random Matrix Theory (RMT) is applied to analyze the weight matrices of Deep Neural
Networks (DNNs), including both production quality, pre-trained models such as AlexNet …

Continuous-time analog neural networks with symmetric connections will always converge
to fixed points when the neurons have infinitely fast response, but can oscillate when a small …

Since the work of Robert May in 1972, the local asymptotic stability of large ecological
systems has been a focus of theoretical ecology. Here we review May's work in the light of …

We compute the typical number of equilibria of the generalized Lotka-Volterra equations
describing species-rich ecosystems with random, nonreciprocal interactions using the …