Of mice and men: Dendritic architecture differentiates human from mouse neuronal networks.

The organizational principles that distinguish the human brain from other species have been a long-standing enigma in neuroscience. Focusing on the uniquely evolved human cortical layers 2 and 3, we computationally reconstruct the cortical architecture for mice and humans. Human neurons form highly complex networks demonstrated by their increased number and simplex dimension compared to mice.

MARBLE: interpretable representations of neural population dynamics using geometric deep learning.

The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a representation learning method, MARBLE, which decomposes on-manifold dynamics into local flow fields and maps them into a common latent space using unsupervised geometric deep learning.

Modeling of Blood Flow Dynamics in Rat Somatosensory Cortex.

The cerebral microvasculature forms a dense network of interconnected blood vessels where flow is modulated partly by astrocytes. Increased neuronal activity stimulates astrocytes to release vasoactive substances at the endfeet, altering the diameters of connected vessels. Our study simulated the coupling between blood flow variations and vessel diameter changes driven by astrocytic activity in the rat somatosensory cortex.

Of mice and men: Dendritic architecture differentiates human from mice neuronal networks.

The organizational principles that distinguish the human brain from other species have been a long-standing enigma in neuroscience. Focusing on the uniquely evolved human cortical layers 2 and 3, we computationally reconstruct the cortical architecture for mice and humans. We show that human pyramidal cells form highly complex networks, demonstrated by the increased number and simplex dimension compared to mice.

Community-based reconstruction and simulation of a full-scale model of the rat hippocampus CA1 region.

The CA1 region of the hippocampus is one of the most studied regions of the rodent brain, thought to play an important role in cognitive functions such as memory and spatial navigation. Despite a wealth of experimental data on its structure and function, it has been challenging to integrate information obtained from diverse experimental approaches. To address this challenge, we present a community-based, full-scale in silico model of the rat CA1 that integrates a broad range of experimental data, from synapse to network, including the reconstruction of its principal afferents, the Schaffer collaterals, and a model of the effects that acetylcholine has on the system.

A unified framework for simplicial Kuramoto models.

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: "simple" models, "Hodge-coupled" models, and "order-coupled" (Dirac) models. Our framework is based on topology and discrete differential geometry, as well as gradient systems and frustrations, and permits a systematic analysis of their properties.

A universal workflow for creation, validation, and generalization of detailed neuronal models.

Detailed single-neuron modeling is widely used to study neuronal functions. While cellular and functional diversity across the mammalian cortex is vast, most of the available computational tools focus on a limited set of specific features characteristic of a single neuron. Here, we present a generalized automated workflow for the creation of robust electrical models and illustrate its performance by building cell models for the rat somatosensory cortex.

Controlling morpho-electrophysiological variability of neurons with detailed biophysical models.

Variability, which is known to be a universal feature among biological units such as neuronal cells, holds significant importance, as, for example, it enables a robust encoding of a high volume of information in neuronal circuits and prevents hypersynchronizations. While most computational studies on electrophysiological variability in neuronal circuits were done with single-compartment neuron models, we instead focus on the variability of detailed biophysical models of neuron multi-compartmental morphologies. We leverage a Markov chain Monte Carlo method to generate populations of electrical models reproducing the variability of experimental recordings while being compatible with a set of morphologies to faithfully represent specifi morpho-electrical type.

Sensitivity and spectral control of network lasers.

Recently, random lasing in complex networks has shown efficient lasing over more than 50 localised modes, promoted by multiple scattering over the underlying graph. If controlled, these network lasers can lead to fast-switching multifunctional light sources with synthesised spectrum. Here, we observe both in experiment and theory high sensitivity of the network laser spectrum to the spatial shape of the pump profile, with some modes for example increasing in intensity by 280% when switching off 7% of the pump beam.

Relative, local and global dimension in complex networks.

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogeneities, or to intrinsically discrete systems such as networks. To take into account locality, finiteness and discreteness, dynamical processes can be used to probe the space geometry and define its dimension.

Computational synthesis of cortical dendritic morphologies.

Neuronal morphologies provide the foundation for the electrical behavior of neurons, the connectomes they form, and the dynamical properties of the brain. Comprehensive neuron models are essential for defining cell types, discerning their functional roles, and investigating brain-disease-related dendritic alterations. However, a lack of understanding of the principles underlying neuron morphologies has hindered attempts to computationally synthesize morphologies for decades.

Digital Reconstruction of the Neuro-Glia-Vascular Architecture.

Astrocytes connect the vasculature to neurons mediating the supply of nutrients and biochemicals. They are involved in a growing number of physiological and pathophysiological processes that result from biophysical, physiological, and molecular interactions in this neuro-glia-vascular ensemble (NGV). The lack of a detailed cytoarchitecture severely restricts the understanding of how they support brain function.

Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature.

Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to specific classes of networks because incompatible metric spaces generally result in information loss. Here, we study arbitrary networks geometrically by defining a dynamic edge curvature measuring the similarity between pairs of dynamical network processes seeded at nearby nodes.

HCGA: Highly comparative graph analysis for network phenotyping.

Networks are widely used as mathematical models of complex systems across many scientific disciplines. Decades of work have produced a vast corpus of research characterizing the topological, combinatorial, statistical, and spectral properties of graphs. Each graph property can be thought of as a feature that captures important (and sometimes overlapping) characteristics of a network.

Noise and Dissipation on Coadjoint Orbits.

We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect product extension. Random attractors are found for this general class of systems when the Lie algebra is semi-simple, provided the top Lyapunov exponent is positive. We study in details two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown.

Un-reduction in field theory.

The un-reduction procedure introduced previously in the context of classical mechanics is extended to covariant field theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter). Other possibilities are also explored: nonlinear [Formula: see text]-models and the hyperbolic flows of curves.

-Strands on symmetric spaces.

We study the -strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group , and we treat in more detail examples with symmetric space (2)/ and (4)/(3).