SUMMARY The stereotyped features of neuronal circuits are those most likely to explain the remarkable capacity of the brain to process information and govern behaviors, yet it has not been possible to comprehensively quantify neuronal distributions across animals or genders due to the size and complexity of the mammalian brain. Here we apply our quantitative brain-wide (qBrain) mapping platform to document the stereotyped distributions of mainly inhibitory cell types. We discover an unexpected cortical organizing principle: sensory-motor areas are dominated by output-modulating parvalbumin-positive interneurons, whereas association, including frontal, areas are dominated by input-modulating somatostatin-positive interneurons. Furthermore, we identify local cell type distributions with more cells in the female brain in seven out of eight sexually dimorphic subcortical areas, in contrast to the overall larger brains in males. The qBrain resource can be further mined to link stereotyped aspects of neuronal distributions to known and unknown functions of diverse brain regions.

Pyramidal cells and interneurons expressing parvalbumin (PV), somatostatin (SST), and vasoactive intestinal peptide (VIP) show cell-type-specific connectivity patterns leading to a canonical microcircuit across cortex. Experiments recording from this circuit often report counterintuitive and seemingly contradictory findings. For example, the response of SST cells in mouse V1 to top-down behavioral modulation can change its sign when the visual input changes, a phenomenon that we call response reversal. We developed a theoretical framework to explain these seemingly contradictory effects as emerging phenomena in circuits with two key features: interactions between multiple neural populations and a nonlinear neuronal input-output relationship. Furthermore, we built a cortical circuit model which reproduces counterintuitive dynamics observed in mouse V1. Our analytical calculations pinpoint connection properties critical to response reversal, and predict additional novel types of complex dynamics that could be tested in future experiments.

Characterizing the influence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states. This transition cannot be explained only through the analysis of the spectral density of the connectivity matrix. We provide a low-dimensional approximation that shows the role of both the structure and disorder in the dynamics.

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The zero-range process is a stochastic interacting particle system that exhibits a condensation transition under certain conditions on the dynamics. It has recently been found that a small perturbation of a generic class of jump rates leads to a drastic change of the phase diagram and prevents condensation in an extended parameter range. We complement this study with rigorous results on a finite critical density and quenched free energy in the thermodynamic limit, as well as quantitative heuristic results for small and large noise which are supported by detailed simulation data. While our new results support the initial findings, they also shed new light on the actual (limited) relevance in large finite systems, which we discuss via fundamental diagrams obtained from exact numerics for finite systems.

In this article, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced by Sompolinsky et al. [Phys. Rev. Lett. 61(3), 259-262 (1988)] in the context of random neural networks. When system size is infinite, it is known that increasing the disorder parameter induces a phase transition leading to chaotic dynamics. We observe and investigate here a novel phenomenon in the sub-critical regime for finite size systems: the probability of observing complex dynamics is maximal for an intermediate system size when the disorder is close enough to criticality. We give a more general explanation of this type of system size resonance in the framework of extreme values theory for eigenvalues of random matrices.

We reconsider the multivariate Kyle model in a risk-neutral setting with a single, perfectly informed rational insider and a rational competitive market maker, setting the price of n correlated securities. We prove the unicity of a symmetric, positive definite solution for the impact matrix and provide insights on its interpretation. We explore its implications from the perspective of empirical market microstructure, and argue that it provides a sensible inference procedure to cure some pathologies encountered in recent attempts to calibrate cross-impact matrices. As an illustration, we determine the empirical cross impact matrix of US Treasuries, and compare the results with recent alternative calibration methods.