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 …

The observed architecture of ecological and socio-economic networks differssignificantly
from that of random networks. From a network science standpoint, non-random structural …

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 …

Classical theory shows that large communities are destabilized by random interactions
among species pairs, creating an upper bound on ecosystem diversity. However, species …

The field of random matrix theory has seen an explosion of activity in recent years, with
connections to many areas of mathematics and physics. However, this makes the current …

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 …

Networks composed of distinct, densely connected subsystems are called modular. In
ecology, it has been posited that a modular organization of species interactions would …

The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

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 …

The diversity of life and its organization in networks of interacting species has been a long-
standing theoretical puzzle for ecologists. Ever since May's provocative paper challenging …