Related papers: Comparison between an exact and a heuristic neural…
Recently, low-dimensional models of neuronal activity have been exactly derived for large networks of deterministic, Quadratic Integrate-and-Fire (QIF) neurons. Such firing rate models (FRM) describe the emergence of fast collective…
Exact firing rate models, also known as next-generation neural mass models (NG-NMMs), provide a rigorous description of the dynamics of neural populations. While in its simplest form a single population only displays fixed-point activity,…
A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of…
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis.…
Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect…
Neural mass models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by…
The dominant modeling framework for understanding cortical computations are heuristic firing rate models. Despite their success, these models fall short to capture spike synchronization effects, to link to biophysical parameters and to…
Neuroscience theory posits that the brain's visual system coarsely identifies broad object categories via neural activation patterns, with similar objects producing similar neural responses. Artificial neural networks also have internal…
Neural mass models describe the mean-field dynamics of populations of neurons. In this work we illustrate how fundamental ideas of physics, such as energy and conserved quantities, can be explored for such models. We show that…
Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled…
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;…
A population of firing neurons is expected to carry not only mean firing rate but also its fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three kinds of…
Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…
Collective dynamics of spiking networks of neurons has been of central interest to both computation neuroscience and network science. Over the past years a new generation of neural population models based on exact reductions (ER) of spiking…
A population of firing neurons is expected to carry information not only by mean firing rate but also by fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three…
Recent research has been focused on two different approaches to studying neural networks training in the limit of infinite width (1) a mean-field (MF) and (2) a constant neural tangent kernel (NTK) approximations. These two approaches have…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
Neural networks are based on a simplified model of the brain. In this project, we wanted to relax the simplifying assumptions of a traditional neural network by making a model that more closely emulates the low level interactions of…
Mathematical modelling of the macroscopic electrical activity of the brain is highly non-trivial and requires a detailed understanding of not only the associated mathematical techniques, but also the underlying physiology and anatomy.…
Learning-based methods have made significant progress in physics simulation, typically approximating dynamics with a monolithic end-to-end optimized neural network. Although these models offer an effective way to simulation, they may lose…