Related papers: Coarse-graining effect in axonal wiring databases …
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…
The wiring diagram of the mouse brain has recently been mapped at a mesoscopic scale in the Allen Mouse Brain Connectivity Atlas. Axonal projections from brain regions were traced using green fluoresent proteins. The resulting data were…
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through…
We show that the error of iteratively magnitude-pruned networks empirically follows a scaling law with interpretable coefficients that depend on the architecture and task. We functionally approximate the error of the pruned networks,…
Accurate simulations of electric fields (E-fields) in neural stimulation depend on tissue conductivity representations that link underlying microscopic tissue structure with macroscopic assumptions. Mesoscale conductivity variations can…
Quantifying the complex/multifractal organization of the brain signals is crucial to fully understanding the brain processes and structure. In this contribution, we performed the multifractal analysis of the electroencephalographic (EEG)…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
Brain connectivity analysis based on magnetic resonance imaging is crucial for understanding neurological mechanisms. However, edge-based connectivity inference faces significant challenges, particularly the curse of dimensionality when…
We explore a systematic approach to studying the dynamics of evolving networks at a coarse-grained, system level. We emphasize the importance of finding good observables (network properties) in terms of which coarse grained models can be…
We report in situ observations of an electron diffusion region (EDR) and adjacent separatrix region. We observe significant magnetic field oscillations near the lower hybrid frequency which propagate perpendicularly to the reconnection…
Alzheimer's disease is the most common neurodegenerative disease. The aim of this study is to infer structural changes in brain connectivity resulting from disease progression using cortical thickness measurements from a cohort of…
In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…
Magnetic reconnection is a fundamental plasma process that alters the magnetic field topology and releases magnetic energy. Most numerical simulations and spacecraft observations assume a two-dimensional diffusion region, with the electron…
We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…
In many far-from-equilibrium biological systems, energy injected by irreversible processes at microscopic scales propagates to larger scales to fulfill important biological functions. But given dissipative dynamics at the microscale, how…
It is shown that a Hopfield recurrent neural network exhibits a scaling regime, whose specific exponents depend on the number of parcels used and the decay length of the coupling strength. This scaling regime recovers the picture introduced…
Robotic arms are increasingly being used in collaborative environments, requiring an accurate understanding of human intentions to ensure both effectiveness and safety. Electroencephalogram (EEG) signals, which measure brain activity,…
Recent studies have shown that high disparities in effective learning rates (ELRs) across layers in deep neural networks can negatively affect trainability. We formalize how these disparities evolve over time by modeling weight dynamics…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…