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We describe the asymptotic behaviour of large degrees in random hyperbolic graphs, for all values of the curvature parameter $ \alpha$. We prove that, with high probability, the node degrees satisfy the following ordering property: the…

We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of…

In the field of complex networks, hypergraph models have so far received significantly less attention than graphs. However, many real-life networks feature multiary relations (co-authorship, protein reactions) may therefore be modeled way…

The white-matter (micro-)structural architecture of the brain promotes synchrony among neuronal populations, giving rise to richly patterned functional connections. A fundamental problem for systems neuroscience is determining the best way…

With the rise of big data analytics, multi-layer neural networks have surfaced as one of the most powerful machine learning methods. However, their theoretical mathematical properties are still not fully understood. Training a neural…

Neuropeptides, members of a large and evolutionarily ancient family of proteinaceous cell-cell signaling molecules, are widely recognized as extremely potent regulators of brain function and behavior. At the cellular level, neuropeptides…

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems…

The polymerization of actin via branching at a cell membrane containing nucleation-promoting factors is simulated using a stochastic-growth methodology. The polymerized-actin distribution displays three types of behavior: a) traveling…

We study the voter dynamics model on heterogeneous graphs. We exploit the non-conservation of the magnetization to characterize how consensus is reached on networks with different connectivity patterns. For a network of N sites with an…

Experimental evidence suggests that epidermal growth factor receptor (EGFR)-mediated activation of the signaling protein phospholipase C gamma plays a critical role in a cancer cell's phenotypic decision to either proliferate or to migrate…

Network representations of the nervous system have been useful for the understanding of brain phenomena such as perception, motor coordination, and memory. Although brains are composed of both neurons and glial cells, neuron-glial networks…

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behaviour: These avalanches are characterized by a power law distribution for the size and…

Efficient pattern separation in dentate gyrus plays an important role in storing information in the hippocampus. Current knowledge of the structure and function of the hippocampus, entorhinal cortex and dentate gyrus, in pattern separation…

We propose a novel discrete model of central pattern generators (CPG), neuronal ensembles generating rhythmic activity. The model emphasizes the role of nonsynaptic interactions and the diversity of electrical properties in nervous systems.…

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…

Genes are fundamental for analyzing biological systems and many recent works proposed to utilize gene expression for various biological tasks by deep learning models. Despite their promising performance, it is hard for deep neural networks…

Graph Neural Networks (GNNs) update node representations through message passing, which is primarily based on the homophily principle, assuming that adjacent nodes share similar features. However, in real-world graphs with long-tailed…

This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the…

A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…

It has been observed that mutualistic bipartite networks have a nested structure of interactions. In addition, the degree distributions associated with the two guilds involved in such networks (e.g. plants & pollinators or plants & seed…