Related papers: Stimulus sensitivity of a spiking neural network m…

Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, neuroscience, social networks,…

We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process (PDMP) with values in ${\mathbb R}^N, $ where $ N$ is the number of neurons…

Generative models based on neural networks present a substantial challenge within deep learning. As it stands, such models are primarily limited to the domain of artificial neural networks. Spiking neural networks, as the third generation…

In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results…

Spiking neural networks play an important role in brain-like neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large scale spiking neural network is that updating all weights is…

Spiking Neural Networks (SNNs) offer biologically inspired, energy-efficient alternatives to traditional Deep Neural Networks (DNNs) for real-time control systems. However, their training presents several challenges, particularly for…

The ability to modulate brain states using targeted stimulation is increasingly being employed to treat neurological disorders and to enhance human performance. Despite the growing interest in brain stimulation as a form of neuromodulation,…

Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact…

In this work we study the detection of weak stimuli by spiking neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present…

Deep Spiking Neural Networks are becoming increasingly powerful tools for cognitive computing platforms. However, most of the existing literature on such computing models are developed with limited insights on the underlying hardware…

The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected…

We study the spatio-temporal prediction problem, which has attracted the attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the…

Criticality can be exactly demonstrated in certain models of brain activity, yet it remains challenging to identify in empirical data. We trained a fully connected deep neural network to learn the phases of an excitable model unfolding on…

We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…

Spiking neural networks (SNN) are a biologically inspired model of neural networks with certain brain-like properties. In the past few decades, this model has received increasing attention in computer science community, owing also to the…

We present a theoretical application of an optimal experiment design (OED) methodology to the development of mathematical models to describe the stimulus-response relationship of sensory neurons. Although there are a few related studies in…

A recurrent idea in the study of complex systems is that optimal information processing is to be found near bifurcation points or phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard…

A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of…

Asynchronous events on the continuous time domain, e.g., social media actions and stock transactions, occur frequently in the world. The ability to recognize occurrence patterns of event sequences is crucial to predict which typeof events…

Neural networks with equal excitatory and inhibitory feedback show high computational performance. They operate close to a critical point characterized by the joint activation of large populations of neurons. Yet, in macaque motor cortex we…