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 …

Non-Hermitian band structures have gained considerable attention due to the novel
phenomena not present in their Hermitian counterparts and their connection to various …

The emergence of exceptional points (EPs) in the parameter space of a non-hermitian (2D)
eigenvalue problem has long been interest in mathematical physics, however, only in the …

Complex networks with directed, local interactions are ubiquitous in nature and often occur
with probabilistic connections due to both intrinsic stochasticity and disordered …

Inspired by works on the Anderson model on sparse graphs, we devise a method to analyze
the localization properties of sparse systems that may be solved using cavity theory. We …

The diverse roles of inhibition in neural circuits and other dynamical networks are receiving
renewed interest. Here, it is shown that increasing global inhibitory feedback leads to …

Knowing which nodes are influential in a complex network and whether the network can be
influenced by a small subset of nodes is a key part of network analysis. However, many …

Causal relationships lie at the very core of scientific description of biophysical phenomena.
Nevertheless, observable facts involving changes in system shape, dimension and …

Sequential neural activity has been observed in many parts of the brain and has been
proposed as a neural mechanism for memory. The natural world expresses temporal …

Exceptional points in non-Hermitian systems possess fascinating properties. We present an
exactly solvable attractor dynamics for the first time from the two-level time-dependent non …