Related papers: Spike Train Cumulants for Linear-Nonlinear Poisson…
The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex…
Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of…
Deep learning has recently led to great successes in tasks such as image recognition (e.g Krizhevsky et al., 2012). However, deep networks are still outmatched by the power and versatility of the brain, perhaps in part due to the richer…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
Continuous-time, event-native spiking neural networks (SNNs) operate strictly on spike events, treating spike timing and ordering as the representation rather than an artifact of time discretization. This viewpoint aligns with biological…
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…
A network of propagating nonlinear oscillatory modes (waves) in the human brain is shown to generate collectively synchronized spiking activity (hypersynchronous spiking) when both amplitude and phase coupling between modes are taken into…
Despite the incredible complexity of our brains' neural networks, theoretical descriptions of neural dynamics have led to profound insights into possible network states and dynamics. It remains challenging to develop theories that apply to…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this…
We introduce a novel concept for spiking neural networks (SNNs) derived from the idea of "linear pieces" used to analyse the expressiveness and trainability of artificial neural networks (ANNs). We prove that the input domain of SNNs…
By introducing the twin concepts of reliability and precision along with the corresponding measures, Mainen and Sejnowski's seminal 1995 paper "Reliability of spike timing in neocortical neurons" (Mainen and Sejnowski, 1995) paved the way…
Background: Spike trains of multiple neurons can be analyzed following the summed population (SP) or the labeled line (LL) hypothesis. Responses to external stimuli are generated by a neuronal population as a whole or the individual neurons…
Neuronal ensemble activity, including coordinated and oscillatory patterns, exhibits hallmarks of nonequilibrium systems with time-asymmetric trajectories to maintain their organization. However, assessing time asymmetry from neuronal…
The organization of neurons into functionally related assemblies is a fundamental feature of cortical networks, yet our understanding of how these assemblies maintain distinct identities while sharing members remains limited. Here we…
Describing the collective activity of neural populations is a daunting task: the number of possible patterns grows exponentially with the number of cells, resulting in practically unlimited complexity. Recent empirical studies, however,…
Granger causality is a widely-used criterion for analyzing interactions in large-scale networks. As most physical interactions are inherently nonlinear, we consider the problem of inferring the existence of pairwise Granger causality…
Excitatory and inhibitory nonlinear noisy leaky integrate and fire models are often used to describe neural networks. Recently, new mathematical results have provided a better understanding of them. It has been proved that a fully…
Inferring the mechanisms underlying physiological and pathological processes in the brain from recorded electrical activity is challenging. Bayesian model selection and dynamic causal modelling aim to identify likely biophysical models to…
Spiking transformers achieve competitive accuracy with conventional transformers while offering $38$-$57\times$ energy efficiency on neuromorphic hardware, yet no theoretical framework guides their design. This paper establishes the first…