Related papers: Long-term stability of interacting Hawkes processe…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…
Neurons communicate with downstream systems via sparse and incredibly brief electrical pulses, or spikes. Using these events, they control various targets such as neuromuscular units, neurosecretory systems, and other neurons in connected…
The critical brain hypothesis posits that neural circuitry operates near criticality to reap the computational benefits of accessing a wide range of timescales. The theory of critical phenomena generally predicts heavy-tailed (power-law)…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
We consider a nonlinear multivariate Hawkes process having a variable length memory which allows to describe the activity of a neuronal network by its membrane potential. We propose a graphical construction of the process and we construct,…
We continue the study of a stochastic system of interacting neurons introduced in De Masi-Galves-L\"ocherbach-Presutti (2014). The system consists of N neurons, each spiking randomly with rate depending on its membrane potential. At its…
Identifying the spatio-temporal network structure of brain activity from multi-neuronal data streams is one of the biggest challenges in neuroscience. Repeating patterns of precisely timed activity across a group of neurons is potentially…
Spike time response curves (STRC's) are used to study the influence of synaptic stimuli on the firing times of a neuron oscillator without the assumption of weak coupling. They allow us to approximate the dynamics of synchronous state in…
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…
Recent advances in experimental techniques have allowed the simultaneous recording of populations of hundreds of neurons, allowing more comprehensive investigation into the nature of the collective structure of population neural activity.…
The Neural Tangent Kernel (NTK) offers a powerful tool to study the functional dynamics of neural networks. In the so-called lazy, or kernel regime, the NTK remains static during training and the network function is linear in the static…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…
The stability and convergence of the neural networks are the fundamental characteristics in the Hopfield type networks. Since time delay is ubiquitous in most physical and biological systems, more attention is being made for the delayed…
Temporal processing is fundamental for both biological and artificial intelligence systems, as it enables the comprehension of dynamic environments and facilitates timely responses. Spiking Neural Networks (SNNs) excel in handling such data…
We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point. Within this class, we investigate the limit behaviour, when n goes to infinity, of a…
The activity of neurons is correlated, and this correlation affects how the brain processes information. We study the neural circuit mechanisms of correlations by analyzing a network model characterized by strong and heterogeneous…