Topic: random matrix theory

The question of the origin of homochirality of living matter, or the dominance of one handedness for all molecules of life across the entire biosphere, is a long-standing puzzle in the research on the Origin of Life. In the fifties, Frank proposed a mechanism to explain homochirality based on the properties of a simple autocatalytic network containing only a few chemical species. Following this work, chemists struggled to find experimental realizations of this model, possibly due to a lack of proper methods to identify autocatalysis [1]. In any case, a model based on a few chemical species see

Recurrent neural networks (RNNs) are powerful dynamical models, widely used in machine learning (ML) for processing sequential data, and also in neuroscience, to understand the emergent properties of networks of real neurons. Prior theoretical work in understanding the properties of RNNs has focused on models with additive interactions. However, real neurons can have gating i.e. multiplicative interactions, and gating is also a central feature of the best performing RNNs in machine learning. Here, we develop a dynamical mean-field theory (DMFT) to study the consequences of gating in RNNs. We u