Mean-field analysis

Biological neural network models with synaptic plasticity pose challenges for both theoretical and numerical analyses. The numerical bottleneck arises from the $N^2$ scaling of synapses. Additionally, the intricate coupling between neuron and synapse dynamics, along with plasticity-induced heterogeneity, hinders the use of classical tools from theory. One approach to address these challenges has been to assume plasticity to be very slow compared to neural activity and leverage slow-fast theory [1]. However, this slowness is not universally applicable in the brain, leaving unclear how to analys

Understanding the trade-off between plasticity and stability–how neural networks form new memories while avoiding runaway potentiation or fast overwriting of memories–is a fundamental problem in neuroscience. Previous theoretical studies that relied on non-plausible plasticity rules did not reproduce realistic synaptic weight distributions or neural activity statistics and predicted fast forgetting times. We revisit this problem by investigating the implications of a multiplicative calcium-based plasticity rule in a recurrent network. This rule was recently fitted to experiments done in physio

A myriad of pathological changes associated with epilepsy, including the loss of specific cell types, improper expression of individual ion channels, and synaptic sprouting, can be recast as decreases in cell and circuit heterogeneity. In recent experimental work, we demonstrated that biophysical diversity is a key characteristic of human cortical pyramidal cells, and past theoretical work has shown that neuronal heterogeneity improves a neural circuit’s ability to encode information. Viewed alongside the fact that seizure is an information-poor brain state, these findings motivate the hypothe

How can neural networks exhibit persistent activity on time scales much larger than allowed by cellular properties? We address this question in the context of larval zebrafish, a model vertebrate that is accessible to brain-scale neuronal recording and high-throughput behavioral studies. We study in particular the dynamics of a bilaterally distributed circuit, the so-called ARTR, including hundreds neurons. ARTR exhibits slow antiphasic alternations between its left and right subpopulations, which can be modulated by the water temperature, and drive the coordinated orientation of swim bouts, t