We undertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli. Recalling and extending results from the literature, we compute phase response curves (PRCs) valid near bifurcations to periodic firing for Hindmarsh-Rose, Hodgkin-Huxley, FitzHugh-Nagumo, and Morris-Lecar models, encompassing the four generic (codimension one) bifurcatio...

How does attention alter neural responses? Decades of electrophysiological measurements in non-human primates as well as human EEG and fMRI studies have shown that spatial attention modulates firing rates across the visual cortex, but the computations that drive this process are still unclear. Further, while it is well known that attention affects perception, we have only a limited understandin...

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, mean rate, variance, and autocorrelation function of the network activity. The model is applicable to any network where the probability of firing of a neuron in...

The pyramidal neuron is the principal cell type in the mammalian forebrain, but its function remains poorly understood. Using a detailed compartmental model of a hippocampal CA1 pyramidal cell, we recorded responses to complex stimuli consisting of dozens of high-frequency activated synapses distributed throughout the apical dendrites. We found the cell's firing rate could be predicted by a sim...

46 Synchronous neural oscillations are found throughout the brain and are thought to contribute to neural coding 47 and the propagation of activity. Several proposed mechanisms of synchronization have gained support through 48 combined theoretical and experimental investigation, including mechanisms based on coupling and correlated 49 input. Here, we ask how correlation-induced synchrony is aff...

As important as the intrinsic properties of an individual nervous cell stands the network of neurons in which it is embedded and by virtue of which it acquires great part of its responsiveness and functionality. In this study we have explored how the topological properties and conduction delays of several classes of neural networks affect the capacity of their constituent cells to establish wel...

Hebbian changes of excitatory synapses are driven by and enhance correlations between pre- and postsynaptic neuronal activations, forming a positive feedback loop that can lead to instability in simulated neural networks. Because Hebbian learning may occur on time scales of seconds to minutes, it is conjectured that some form of fast stabilization of neural firing is necessary to avoid runaway ...

Neural Activity During Motor Planning CS229 Final Project – Fall 2005 Afsheen “the Plumber” Afshar and John “the Whale” Cunningham Introduction Patterns of neural activity in certain brain areas are understood to drive motor behavior. In the time immediately preceding a movement, there is a period of preparatory neural activity, called the "plan period." This activity can be measured as cell fi...

While recent recordings from neural populations show beyond-pairwise, or higher-order, correlations (HOC), we have little understanding of how HOC arise from network interactions and of how they impact encoded information. Here, we show that input nonlinearities imply HOC in spin-glass-type statistical models. We then discuss one such model with parametrized pairwise- and higher-order interacti...

Stochastic accumulator models account for response time in perceptual decision-making tasks by assuming that perceptual evidence accumulates to a threshold. The present investigation mapped the firing rate of frontal eye field (FEF) visual neurons onto perceptual evidence and the firing rate of FEF movement neurons onto evidence accumulation to test alternative models of how evidence is combine...