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Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
In recent years self organised critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behaviour of neuronal systems. It has been shown that dynamical synapses, as a form of short-term…
Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood.…
Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional block in the brain, how STDP shapes neural networks possibly…
The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale…
Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…
Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve…
In realistic neural circuits, both neurons and synapses are coupled in dynamics with separate time scales. The circuit functions are intimately related to these coupled dynamics. However, it remains challenging to understand the intrinsic…
We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…
A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is based…
When a neuron breaks silence, it can emit action potentials in a number of patterns. Some responses are so sudden and intense that electrophysiologists felt the need to single them out, labeling action potentials emitted at a particularly…
In recurrent networks of leaky integrate-and-fire (LIF) neurons, mean-field theory has proven successful in describing various statistical properties of neuronal activity at equilibrium, such as firing rate distributions. Mean-field theory…
The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…
We propose a model to describe the quasistatic shearing of dry granular materials, which notably captures the differences in velocity profiles recently observed in 2 and 3-D Couette flow experiments. In our scheme, the steady-state flow is…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
We apply the recent frame-invariant theory of separation spike formation to complex unsteady flows including a turbulent separation bubble, an impinging jet, and flows around a freely moving cylinder and a freely rotating ellipse. We show…
In recent years, there has been increasing interest in developing models and tools to address the complex patterns of connectivity found in brain tissue. Specifically, this is due to a need to understand how emergent properties emerge from…
Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network…
For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence…
We study an abstracted model of neuronal activity via numerical simulation, and report spatiotemporal pattern formation and critical like dynamics. A population of pulse coupled, discretised, relaxation oscillators is simulated over…