Related papers: Towards Dead Time Inclusion in Neuronal Modeling

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…

Analyzing temporal data (e.g., wearable device data) requires a decision about how to combine information from the recent and distant past. In the context of classifying sleep status from actigraphy, Webster's rescoring rules offer one…

We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is…

Recurrent Neural Networks (RNNs) have achieved remarkable performance on a range of tasks. A key step to further empowering RNN-based approaches is improving their explainability and interpretability. In this work we present MEME: a model…

In a generic neuron model, we present the linear response theory for the firing rate in response to both time dependent input currents and noise amplitudes. In both cases the signal transmission is strongly attenuated for frequencies above…

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines,…

We study Replica Mean Field limits for a neural system of infinitely many neurons with both inhibitory and excitatory interactions. As a result we obtain an analytical characterisation of the invariant state. In particular we focus on the…

This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the…

This paper describes a framework for modeling the interface between perception and memory on the algorithmic level of analysis. It is consistent with phenomena associated with many different brain regions. These include view-dependence (and…

Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider…

Recurrent Neural Networks (RNNs) have shown great success in modeling time-dependent patterns, but there is limited research on their learned representations of latent temporal features and the emergence of these representations during…

We demonstrate that the information contained in the spike occurrence times of a population of neurons can be broken up into a series of terms, each of which reflect something about potential coding mechanisms. This is possible in the…

As the third generation of neural networks, spiking neural networks (SNNs) have recently gained widespread attention for their biological plausibility, energy efficiency, and effectiveness in processing neuromorphic datasets. To better…

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward…

We use mean field theory to study the response properties of a simple randomly-connected model cortical network of leaky integrate-and-fire neurons with balanced excitation and inhibition. The formulation permits arbitrary temporal…

In this paper, a novel deep learning framework is proposed for temporal super-resolution simulation of blood vessel flows, in which a high-temporal-resolution time-varying blood vessel flow simulation is generated from a…

We investigate the three-dimensional formulation of a recently proposed operational arrival-time model. It is shown that within typical conditions for optical transitions the results of the simple one-dimensional version are generally…

We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed…

The size of a website's active user base directly affects its value. Thus, it is important to monitor and influence a user's likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art…