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Approaches to predicting neuronal spike responses commonly use a Poisson learning objective. This objective quantizes responses into spike counts within a fixed summation interval, typically on the order of 10 to 100 milliseconds in…
Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive…
We investigate a network model in which a single random walker combines local diffusion with preferential resetting to previously visited nodes. Each arrival deposits one unit of stress on the target node, and threshold crossings trigger…
A central question in computational neuroscience is how structure determines function in neural networks. The emerging high-quality large-scale connectomic datasets raise the question of what general functional principles can be gleaned…
The instantaneous state of a neural network consists of both the degree of excitation of each neuron, the network is composed of, and positions of impulses in communication lines between neurons. In neurophysiological experiments, the…
Understanding the relationship between brain activity and behavior is a central goal of neuroscience. Despite significant advances, a fundamental dichotomy persists: neural activity manifests as both discrete spikes of individual neurons…
We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a…
Neural population activity often exhibits rich variability and temporal structure. This variability is thought to arise from single-neuron stochasticity, neural dynamics on short time-scales, as well as from modulations of neural firing…
One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…
Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…
The relationship between complex, brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize Maximum Caliber, a dynamical inference principle, to build a minimal, yet general model of the collective…
The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but with more…
We study a simple model for a neuron function in a collective brain system. The neural network is composed of uncorrelated random scale-free network for eliminating the degree correlation of dynamical processes. The interaction of neurons…
We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…
The plasticity of the conduction delay between neurons plays a fundamental role in learning. However, the exact underlying mechanisms in the brain for this modulation is still an open problem. Understanding the precise adjustment of…
Information measures are often used to assess the efficacy of neural networks, and learning rules can be derived through optimization procedures on such measures. In biological neural networks, computation is restricted by the amount of…
Whether an idea, information, infection, or innovation diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. Recent studies have shown that diffusion…
Understanding how recurrent neural circuits can learn to implement dynamical systems is a fundamental challenge in neuroscience. The credit assignment problem, i.e. determining the local contribution of each synapse to the network's global…
Population equations for infinitely large networks of spiking neurons have a long tradition in theoretical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form…
We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky…