Results 1  10
of
104
Type I Membranes, Phase Resetting Curves, and Synchrony
 Neural Comput
, 1995
"... Type I membrane oscillators such as the Connor model (Connor, Walter, and McKown, 1977) and the MorrisLecar model (Morris and Lecar, 1981) admit very low frequency oscillations near the critical applied current. Hansel et.al., (1995) have numerically shown that synchrony is difficult to achieve wit ..."
Abstract

Cited by 203 (12 self)
 Add to MetaCart
Type I membrane oscillators such as the Connor model (Connor, Walter, and McKown, 1977) and the MorrisLecar model (Morris and Lecar, 1981) admit very low frequency oscillations near the critical applied current. Hansel et.al., (1995) have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive. We use singular perturbation methods and averaging to show that this is a general property of Type I membrane models. We show in a limited sense that so called type 2 resetting occurs with models that obtain rhythmicity via a Hopf bifurcation. We also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions. 1 Introduction The behavior of coupled neural oscillators has been the subject of a great deal of recent interest. In general, this behavior is quite difficult to analyze. Most of the results to date are primarily based on simulations of ...
Ionic mechanisms underlying synchronized oscillations and traveling waves in a model of ferret thalamic slices
 Sot. Neurosci. Abstr
, 1995
"... SUMMARY AND CONCLUSIONS cells, leading to waves of spindle activity as observed in experimerits. 1. A network model of thalamocortical (TC) and thalamic retic 8. The spatiotemporal properties of propagating waves in the ular (RE) neurons was developed based on electrophysiological model were highly ..."
Abstract

Cited by 47 (13 self)
 Add to MetaCart
SUMMARY AND CONCLUSIONS cells, leading to waves of spindle activity as observed in experimerits. 1. A network model of thalamocortical (TC) and thalamic retic 8. The spatiotemporal properties of propagating waves in the ular (RE) neurons was developed based on electrophysiological model were highly dependent on the intrinsic properties of TC measurements in ferret thalamic slices. Singlecompartment TC cells. The spatial pattern of spiking activity was markedly different and RE cells included voltage and calciumsensitive currents de for spindles compared with bicucullineinduced oscillations and scribed by HodgkinHuxley type of kinetics. Synaptic currents depended on the rebound burst behavior of TC cells. The upregulawere modeled by kinetic models of cramino3hydroxy5methyl tion of Ih produced a refractory period so that colliding spindle 4isoxazolepropionic acid (AMPA), yaminobutyric acidA (GA waves merged into a single oscillation and extinguished. BAA) and GABAB receptors. reducing the Ih conductance led to sustained oscillations. Finally, 2. The model reproduced successfully the characteristics of spindle and slow bicucullineinduced oscillations observed in vitro. The characteristics of these two types of oscillations depended on both the intrinsic properties of TC and RE cells and their pattern of interconnectivity.
Efficient and accurate timestepping schemes for integrateandfire neuronal networks.
 J. Comput. Neurosci.,
, 2001
"... ..."
Modeling synaptic plasticity within networks of highly accelerated
 I&F neurons,” in Circuits and Systems, 2007. ISCAS 2007. IEEE International Symposium on. IEEE Press
"... Abstract — When studying the different aspects of synaptic plasticity, the timescales involved range from milliseconds to minutes, thus covering at least seven orders of magnitude. To make this temporal dynamic range accessible to the experimentalist, we have developed a highly accelerated analog V ..."
Abstract

Cited by 29 (14 self)
 Add to MetaCart
(Show Context)
Abstract — When studying the different aspects of synaptic plasticity, the timescales involved range from milliseconds to minutes, thus covering at least seven orders of magnitude. To make this temporal dynamic range accessible to the experimentalist, we have developed a highly accelerated analog VLSI model of leaky integrate and fire neurons. It incorporates fast and slow synaptic facilitation and depression mechanisms in its conductance based synapses. By using a 180 nm process 105 synapses fit on a 25 mm2 die. A single chip can model the temporal evolution of the synaptic weights in networks of up to 384 neurons with an acceleration factor of 105 while recording the neural action potentials with a temporal resolution better than 30 µs biological time. This reduces the time needed for a 10 minute experiment to merely 6 ms, paving the way for complex parameter searches to reproduce biological findings. Due to a digital communication structure larger networks can be built from multiple chips while retaining an acceleration factor of a least 104. I.
The Cat is Out of the Bag: Cortical Simulations with 10 9 Neurons, 10 13 Synapses
"... In the quest for cognitive computing, we have built a massively parallel cortical simulator, C2, that incorporates a number of innovations in computation, memory, and communication. Using C2 on LLNL’s Dawn Blue Gene/P supercomputer with 147, 456 CPUs and 144 TB of main memory, we report two cortical ..."
Abstract

Cited by 28 (4 self)
 Add to MetaCart
In the quest for cognitive computing, we have built a massively parallel cortical simulator, C2, that incorporates a number of innovations in computation, memory, and communication. Using C2 on LLNL’s Dawn Blue Gene/P supercomputer with 147, 456 CPUs and 144 TB of main memory, we report two cortical simulations – at unprecedented scale – that effectively saturate the entire memory capacity and refresh it at least every simulated second. The first simulation consists of 1.6 billion neurons and 8.87 trillion synapses with experimentallymeasured gray matter thalamocortical connectivity. The second simulation has 900 million neurons and 9 trillion synapses with probabilistic connectivity. We demonstrate nearly perfect weak scaling and attractive strong scaling. The simulations, which incorporate phenomenological spiking neurons, individual learning synapses, axonal delays, and dynamic synaptic channels, exceed the scale of the cat cortex, marking the dawn of a new era in the scale of cortical simulations. 1.
Expanding NEURON's Repertoire of Mechanisms with NMODL
"... Neuronal function involves the interaction of electrical and chemical signals that are distributed in time and space. ... ..."
Abstract

Cited by 26 (10 self)
 Add to MetaCart
Neuronal function involves the interaction of electrical and chemical signals that are distributed in time and space. ...
Computational Models of Neuromodulation
, 1998
"... this article is to highlight, through a targeted review of the modeling literature, some of the basic computational roles assigned to neuromodulation and present their possible neural implementation. Due to the diversity and ubiquity of neuromodulatory phenomena, we will not provide a comprehensive ..."
Abstract

Cited by 25 (0 self)
 Add to MetaCart
this article is to highlight, through a targeted review of the modeling literature, some of the basic computational roles assigned to neuromodulation and present their possible neural implementation. Due to the diversity and ubiquity of neuromodulatory phenomena, we will not provide a comprehensive review of all neuromodulatory systems in terms of their anatomical loci, detailed biochemical pathways, and individual physiological effects. Nor will we attempt to define it; rather, we will review neuromodulation according to the computational framework provided by a chosen set of modeling studies. Our intent is not to be exhaustive. Many models not mentioned here have discussed how specific neuromodulations can be implemented and how they affect particular aspects of the neural system they consider. We include here a selection of studies that have dealt explicitly with neuromodulation and will help readers understand a specific computational role of neuromodulation.
The Analysis of Synaptically Generated Traveling Waves
 J. Comput. Neurosci
, 1998
"... Mathematical and computational models for the propagation of activity in excitatorily coupled neurons are simulated and analyzed. The basic measurable quantity, velocity, is found for a wide class of models. Numerical bifurcation techniques, asymptotic analysis, and numerical simulations are used to ..."
Abstract

Cited by 23 (2 self)
 Add to MetaCart
Mathematical and computational models for the propagation of activity in excitatorily coupled neurons are simulated and analyzed. The basic measurable quantity, velocity, is found for a wide class of models. Numerical bifurcation techniques, asymptotic analysis, and numerical simulations are used to show that there are distinct scaling laws for the velocity as a function of a variety of parameters. In particular, the obvious linear relationships between speed and spatial spread or synaptic decay rate are shown. More surprisingly, it is shown that the velocity scales as a power law with synaptic coupling strength and that the exponent is dependent only on the rising phase of the synapse. Supported in part by NSF DMS9626728 1 Introduction There has been a great deal of recent interest in the propagation of traveling waves in neural tissue (ChagnacAmitai and Connors, 1989; Kim et.al, 1995; Kleinfeld, et al, 1994; Traub et. al. 1993), The advent of voltage sensitive dyes, intrinsi...
Dynamics of Strongly Coupled Spiking Neurons
 Neural Computation
, 2000
"... We present a dynamical theory of integrateandfire neurons with strong synaptic coupling. We show how phaselocked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike interval ..."
Abstract

Cited by 21 (3 self)
 Add to MetaCart
We present a dynamical theory of integrateandfire neurons with strong synaptic coupling. We show how phaselocked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a onedimensional network of neurons with longrange interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response. 1