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In this article we study the treewidth of the \emph{display graph}, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display…
Synaptic pruning in biological brains removes weak connections to improve efficiency. In contrast, dropout regularization in artificial neural networks randomly deactivates neurons without considering activity-dependent pruning. We propose…
From the proliferative mechanisms generating neurons from progenitor cells to neuron migration and synaptic connection formation, several vicissitudes culminate in the mature brain. Both component loss and gain remain ubiquitous during…
Researchers have proposed that deep learning, which is providing important progress in a wide range of high complexity tasks, might inspire new insights into learning in the brain. However, the methods used for deep learning by artificial…
Neuronal morphology is an essential element for brain activity and function. We take advantage of current availability of brain-wide neuron digital reconstructions of the Pyramidal cells from a mouse brain, and analyze several emergent…
We perform the renormalization-group-like numerical analysis of geographically embedded complex networks on the two-dimensional square lattice. At each step of coarsegraining procedure, the four vertices on each $2 \times 2$ square box are…
Recursive structures are a core property of human language, yet little is known about how children with autism spectrum disorder (ASD) process complex recursion. This ERP study investigated the online processing of two-level recursive…
The minimal number of rooted subtree prune and regraft (rSPR) operations needed to transform one phylogenetic tree into another one induces a metric on phylogenetic trees - the rSPR-distance. The rSPR-distance between two phylogenetic trees…
A rearrangement operation makes a small graph-theoretical change to a phylogenetic network to transform it into another one. For unrooted phylogenetic trees and networks, popular rearrangement operations are tree bisection and reconnection…
We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown {\it in vitro}. We infer connectivity between two…
This paper studies Random and Evolving Apollonian networks (RANs and EANs), in d dimension for any d>=2, i.e. dynamically evolving random d dimensional simplices looked as graphs inside an initial d-dimensional simplex. We determine the…
For deep neural network accelerators, memory movement is both energetically expensive and can bound computation. Therefore, optimal mapping of tensors to memory hierarchies is critical to performance. The growing complexity of neural…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
We study the mean length $\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes representing the human brain's structure or function, and obtained using…
The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the…
In many biological systems, the network of interactions between the elements can only be inferred from experimental measurements. In neuroscience, non-invasive imaging tools are extensively used to derive either structural or functional…
The cortex is a very large network characterized by a complex connectivity including at least two scales: a microscopic scale at which the interconnections are non-specific and very dense, while macroscopic connectivity patterns connecting…
We demonstrate that a tree-based theory for various dynamical processes yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance…