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We present exact results, as well as some illustrative Monte Carlo simulations, concerning a stochastic network with weighted connections in which the fraction of nodes that are dynamically synchronized is a parameter. This allows one to…
A rigorous bridge between spiking-level and macroscopic quantities is an on-going and well-developed story for asynchronously firing neurons, but focus has shifted to include neural populations exhibiting varying synchronous dynamics.…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal…
Cellular responses in the single cells are known to be highly heterogeneous and individualistic due to the strong influence by extrinsic and intrinsic noise. Here, we are concerned about how to model the extrinsic noise-induced…
A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory,…
In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization…
The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons…
We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered,…
A neuron transforms its input into output spikes, and this transformation is the basic unit of computation in the nervous system. The spiking response of the neuron to a complex, time-varying input can be predicted from the detailed…
We are interested in understanding the neural correlates of attentional processes using first principles. Here we apply a recently developed first principles approach that uses transmitted information in bits per joule to quantify the…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with…
We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the…
Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time…
Cortical slow oscillations occur in the mammalian brain during deep sleep and have been shown to contribute to memory consolidation, an effect that can be enhanced by electrical stimulation. As the precise underlying working mechanisms are…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
A population of firing neurons is expected to carry not only mean firing rate but also its fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three kinds of…
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the…
To understand the collective spiking activity in neuronal populations, it is essential to reveal basic circuit variables responsible for these emergent functional states. Here, I develop a mean field theory for the population coupling…
Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity,…