Related papers: Coarse-graining effect in axonal wiring databases …
Studying structural brain networks has witnessed significant advancement in recent decades. Findings have revealed a geometric principle, the exponential distance rule (EDR) showing that the number of neurons decreases exponentially with…
In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization…
Very recently, a kind of spatial network constructed with power-law distance distribution and total energy constriction is proposed. Moreover, it has been pointed out that such spatial networks have the optimal exponents $\delta$ in the…
Diffusion-weighted MR imaging (DWI) is the only method we currently have to measure connections between different parts of the human brain in vivo. To elucidate the structure of these connections, algorithms for tracking bundles of axonal…
Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the…
Brain networks exhibit remarkable structural properties, including high local clustering, short path lengths, and heavy-tailed weight and degree distributions. While these features are thought to enable efficient information processing with…
The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain\'s dynamic properties at the ground level. Karbowski derived a power-law decay…
Neural circuits must balance local connectivity constraints against the need for global integration. Here we introduce a minimal wiring rule motivated by synaptic crowding: as a neuron accumulates incoming connections, each additional…
Exponential moving average (EMA) has recently gained significant popularity in training modern deep learning models, especially diffusion-based generative models. However, there have been few theoretical results explaining the effectiveness…
Networks with long-range connections obeying a distance-dependent power law of sufficiently small exponent display superdiffusion, L\'evy flights and robustness properties very different from the scale-free networks. It has been proposed…
Over the last years, increasing evidence has fuelled the hypothesis that Autism Spectrum Disorder (ASD) is a condition of altered brain functional connectivity. The great majority of these empirical studies rely on functional magnetic…
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We analyze the mathematical model…
Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However,…
We propose a model to create synthetic networks that may also serve as a narrative of a certain kind of infrastructure network evolution. It consists of an initialization phase with the network extending tree-like for minimum cost and a…
We investigated the degree distribution of brain networks extracted from functional magnetic resonance imaging of the human brain. In particular, the distributions are compared between macroscopic brain networks using region-based nodes and…
Network science has been extensively developed to characterize structural properties of complex systems, including brain networks inferred from neuroimaging data. As a result of the inference process, networks estimated from experimentally…
Cellular automata and other discrete dynamical systems have long been studied as models of emergent complexity. Recently, neural cellular automata have been proposed as models to investigate the emerge of a more general artificial…
Many real networks are embedded in space, where in some of them the links length decay as a power law distribution with distance. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we…
We develop a phenomenological coarse--graining procedure for activity in a large network of neurons, and apply this to recordings from a population of 1000+ cells in the hippocampus. Distributions of coarse--grained variables seem to…
The structural human connectome (i.e.\ the network of fiber connections in the brain) can be analyzed at ever finer spatial resolution thanks to advances in neuroimaging. Here we analyze several large data sets for the human brain network…