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We present a mean-field model of the cortex that attempts to describe the gross changes in brain electrical activity for the cycles of natural sleep. We incorporate within the model two major sleep modulatory effects: slow changes in both synaptic efficiency and in neuron resting voltage caused by the ∼90-min cycling in acetylcholine, together with even(More)
One of the grand puzzles in neuroscience is establishing the link between cognition and the disparate patterns of spontaneous and task-induced brain activity that can be measured clinically using a wide range of detection modalities such as scalp electrodes and imaging tomography. High-level brain function is not a single-neuron property, yet emerges as a(More)
We use a mean-field macrocolumn model of the cerebral cortex to offer an interpretation of the K-complex of the electroencephalogram to complement those of more detailed neuron-by-neuron models. We interpret the K-complex as a momentary excursion of the cortex from a stable low-firing state to an unstable high-firing state, and hypothesize that the related(More)
Understanding the structure and purpose of sleep remains one of the grand challenges of neurobiology. Here we use a mean-field linearized theory of the sleeping cortex to derive statistics for synaptic learning and memory erasure. The growth in correlated low-frequency high-amplitude voltage fluctuations during slow-wave sleep (SWS) is characterized by a(More)
When the brain is in its noncognitive "idling" state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations (∼0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across(More)
We argue that spatial patterns of cortical activation observed with EEG, MEG and fMRI might arise from spontaneous self-organisation of interacting populations of excitatory and inhibitory neurons. We examine the dynamical behavior of a mean-field cortical model that includes chemical and electrical (gap-junction) synapses, focusing on two limiting cases:(More)
We present mathematical and simulation analyses of the below-threshold noisy response of two biophysically motivated models for excitable membrane due to H. R. Wilson: a squid axon ("resonator") and a human cortical neuron ("integrator"). When stimulated with a low-intensity white noise superimposed on a dc control current, both membrane types generate(More)
We study the dynamics of the transition between the low- and high-firing states of the cortical slow oscillation by using intracellular recordings of the membrane potential from cortical neurons of rats. We investigate the evidence for a bistability in assemblies of cortical neurons playing a major role in the maintenance of this oscillation. We show that(More)
We use Hamilton's equations of classical mechanics to investigate the behavior of a cortical neuron on the approach to an action potential. We use a two-component dynamic model of a single neuron, due to Wilson, with added noise inputs. We derive a Lagrangian for the system, from which we construct Hamilton's equations. The conjugate momenta are found to be(More)