Related papers: Pairing cellular and synaptic dynamics into buildi…
Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks…
We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…
The relationship of network structure and dynamics is one of most extensively investigated problems in the theory of complex systems of the last years. Understanding this relationship is of relevance to a range of disciplines -- from…
When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Networks built in this manner are required for gamete production in many…
The regulatory mechanisms driving progression of the yeast cell cycle appears to be comprised of an interacting network of transcription factors (TFs), cyclin-dependent kinases (CDK) and ubiquitin ligases. From a systems perspective the…
Despite evidence for a hydrodynamic origin of flagellar synchronization between different eukaryotic cells, recent experiments have shown that in single multi-flagellated organisms, coordination hinges instead on direct basal body…
We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock…
In this work, we perform an exploratory study on synthesizing deep neural networks using biological synaptic strength distributions, and the potential influence of different distributions on modelling performance particularly for the…
The lateral diffusion and trapping of protein receptors within the postsynaptic membrane of a neuron plays a key role in determining the strength of synaptic connections and their regulation during learning and memory. In this paper we…
This tutorial is intended as an accessible but rigorous first reference for someone interested in learning how to model and analyze cellular network performance using stochastic geometry. In particular, we focus on computing the…
The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…
Many mathematical models of synaptic plasticity have been proposed to explain the diversity of plasticity phenomena observed in biological organisms. These models range from simple interpretations of Hebb's postulate, which suggests that…
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…
Synchronization of coupled dynamical systems is a widespread phenomenon in both biological and engineered networks, and understanding this behavior is crucial for controlling such systems. Considerable research has been dedicated to…
Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the…
We study the homogenization of a novel microscopic tridomain system, allowing for a more detailed analysis of the properties of cardiac conduction than the classical bidomain and monodomain models. In (Acta Appl.Math. 179 (2022) 1--35), we…
Hierarchically modular organization is a canonical network topology that is evolutionarily conserved in the nervous systems of animals. Within the network, neurons form directional connections defined by the growth of their axonal…
Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a…
Social systems are in a constant state of flux with dynamics spanning from minute-by-minute changes to patterns present on the timescale of years. Accurate models of social dynamics are important for understanding spreading of influence or…
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…