Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

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

Sparse non-Hermitian random matrices arise in the study of disordered physical systems
with asymmetric local interactions, and have applications ranging from neural networks to …

These expository notes are centered around the circular law theorem, which states that the
empirical spectral distribution of an× n random matrix with iid entries of variance 1/n tends to …

Will a large economy be stable? Building on Robert May's original argument for large
ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the …

Random matrix theory successfully connects the structure of interactions of large ecological
communities to their ability to respond to perturbations. One of the most debated aspects of …

Most real networks are too large or they are not available for real time analysis. Therefore, in
practice, decisions are made based on partial information about the ground truth network. It …

Networks studied in many disciplines, including neuroscience and mathematical biology,
have connectivity that may be stochastic about some underlying mean connectivity …

Food webs have now been addressed in empirical and theoretical research for more than
50 years. Yet, even elementary foundational issues are still hotly debated. One difficulty is …

Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble
as the set of N× N real nonsymmetric matrices whose entries are independent Gaussian …