Related papers: Inferring network structure and local dynamics fro…
Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining…
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network…
The diversity of neuron models used in contemporary theoretical neuroscience to investigate specific properties of covariances raises the question how these models relate to each other. In particular it is hard to distinguish between…
We investigate a large ensemble of Quadratic Integrate-and-Fire (QIF) neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that for a specific class of adaptation, termed quadratic spike-frequency…
Redundant information transfer in a neural network can increase the complexity of the deep learning model, thus increasing its power consumption. We introduce in this paper a novel spiking neuron, termed Variable Spiking Neuron (VSN), which…
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal…
There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the…
In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh-Nagumo neuron model (FHN) in the excitable…
Spintronic devices, such as the domain walls and skyrmions, have shown significant potential for applications in energy-efficient data storage and beyond CMOS computing architectures. In recent years, spiking neural networks have shown more…
We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing…
Spiking Neural Networks (SNNs) are valued for their ability to process spatio-temporal information efficiently, offering biological plausibility, low energy consumption, and compatibility with neuromorphic hardware. However, the commonly…
Spiking neural networks (SNNs) are promising brain-inspired energy-efficient models. Compared to conventional deep Artificial Neural Networks (ANNs), SNNs exhibit superior efficiency and capability to process temporal information. However,…
The steady-state firing rate and firing-rate response of the leaky and exponential integrate-and-fire models receiving synaptic shot noise with excitatory and inhibitory reversal potentials is examined. For the particular case where the…
We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of…
Spiking neural networks (SNNs) offer biologically inspired computation but remain underexplored for continuous regression tasks in scientific machine learning. In this work, we introduce and systematically evaluate Quadratic…
The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics. The study is preceded by a finite-size scaling analysis, carried out to identify a…
The task of the brain is to look for structure in the external input. We study a network of integrate-and-fire neurons with several types of recurrent connections that learns the structure of its time-varying feedforward input by attempting…
Over the last decade, next-generation neural mass models have become increasingly prominent in mathematical neuroscience. These models link microscopic dynamics with low-dimensional systems of so-called firing rate equations that exactly…
Neural processing systems typically represent data using leaky integrate and fire (LIF) neuron models that generate spikes or pulse trains at a rate proportional to their input amplitudes. This mechanism requires high firing rates when…
Concurrent estimation and control of robotic systems remains an ongoing challenge, where controllers rely on data extracted from states/parameters riddled with uncertainties and noises. Framework suitability hinges on task complexity and…