Models that contain the Modeling Application : Brian (web link to method) (Home Page)

( Brian is a new simulator for spiking neural networks available on almost all platforms. The motivation for this project is that a simulator should not only save the time of processors, but also the time of scientists. Brian is easy to learn and use, highly flexible and easily extensible. The Brian package itself and simulations using it are all written in the Python programming language, which is an easy, concise and highly developed language with many advanced features and development tools, excellent documentation and a large community of users providing support and extension packages.)
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    Models   Description
1.  A threshold equation for action potential initiation (Platkiewicz & Brette 2010)
"We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. ... We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. " See paper for more.
2.  Adaptive exponential integrate-and-fire model (Brette & Gerstner 2005)
"We introduce a two-dimensional integrate-and-fire model that combines an exponential spike mechanism with an adaptation equation, based on recent theoretical findings. ... The model is especially reliable in high-conductance states, typical of cortical activity in vivo, in which intrinsic conductances were found to have a reduced role in shaping spike trains. These results are promising because this simple model has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro."
3.  Fast global oscillations in networks of I&F neurons with low firing rates (Brunel and Hakim 1999)
Dynamics of a network of sparsely connected inhibitory current-based integrate-and-fire neurons. Individual neurons fire irregularly at low rate but the network is in an oscillatory global activity regime where neurons are weakly synchronized.
4.  High entrainment constrains synaptic depression in a globular bushy cell (Rudnicki & Hemmert 2017)
" ... Here we show how different levels of synaptic depression shape firing properties of GBCs in in vivo-like conditions using computer simulations. We analyzed how an interplay of synaptic depression (0 % to 70 %) and the number of auditory nerve fiber inputs (10 to 70) contributes to the variability of the experimental data from previous studies. ... Overall, this study helps to understand how synaptic properties shape temporal processing in the auditory system. It also integrates, compares, and reconciles results of various experimental studies."
5.  Impact of fast Na channel inact. on AP threshold & synaptic integration (Platkiewicz & Brette 2011)
Slope-threshold relationship with noisy inputs, in the adaptive threshold model.
6.  Late emergence of the whisker direction selectivity map in rat barrel cortex (Kremer et al. 2011)
"... We discovered that the emergence of a direction map in rat barrel cortex occurs long after all known critical periods in the somatosensory system. This map is remarkably specific, taking a pinwheel-like form centered near the barrel center and aligned to the barrel cortex somatotopy. We suggest that this map may arise from intracortical mechanisms and demonstrate by simulation that the combination of spike-timing-dependent plasticity at synapses between layer 4 and layer 2/3 and realistic pad stimulation is sufficient to produce such a map. ..."
7.  Phase locking in leaky integrate-and-fire model (Brette 2004)
"This shows the phase-locking structure of a LIF driven by a sinusoidal current. When the current crosses the threshold (a<3), the model almost always phase locks (in a measure-theoretical sense)."
8.  Reliability of spike timing is a general property of spiking model neurons (Brette & Guigon 2003)
"... Here we show, through simulations and theoretical considerations, that for a general class of spiking neuron models, which includes, in particular, the leaky integrate-and-fire model as well as nonlinear spiking models, aperiodic currents, contrary to periodic currents, induce reproducible responses, which are stable under noise, change in initial conditions and deterministic perturbations of the input. We provide a theoretical explanation for aperiodic currents that cross the threshold."
9.  Sensitivity of noisy neurons to coincident inputs (Rossant et al. 2011)
"Two distant or coincident spikes are injected into a noisy balanced leaky integrate-and-fire neuron. The PSTH of the neuron in response to these inputs is calculated along with the extra number of spikes in the two cases. This number is higher for the coincident spikes, showing the sensitivity of a noisy neuron to coincident inputs."
10.  Stable propagation of synchronous spiking in cortical neural networks (Diesmann et al 1999)
"... Here we show that precisely synchronized action potentials can propagate within a model of cortical network activity that recapitulates many of the features of biological systems. An attractor, yielding a stable spiking precision in the (sub)millisecond range, governs the dynamics of synchronization. Our results indicate that a combinatorial neural code, based on rapid associations of groups of neurons co-ordinating their activity at the single spike level, is possible within a cortical-like network."
11.  Theory of arachnid prey localization (Sturzl et al. 2000)
"Sand scorpions and many other arachnids locate their prey through highly sensitive slit sensilla at the tips (tarsi) of their eight legs. This sensor array responds to vibrations with stimulus-locked action potentials encoding the target direction. We present a neuronal model to account for stimulus angle determination using a population of second-order neurons, each receiving excitatory input from one tarsus and inhibition from a triad opposite to it. ..."
12.  Time-warp-invariant neuronal processing (Gutig & Sompolinsky 2009)
" ... Here, we report that time-warp-invariant neuronal processing can be subserved by the shunting action of synaptic conductances that automatically rescales the effective integration time of postsynaptic neurons. We propose a novel spike-based learning rule for synaptic conductances that adjusts the degree of synaptic shunting to the temporal processing requirements of a given task. Applying this general biophysical mechanism to the example of speech processing, we propose a neuronal network model for time-warp-invariant word discrimination and demonstrate its excellent performance on a standard benchmark speech-recognition task. ..."
13.  Vectorized algorithms for spiking neural network simulation (Brette and Goodman 2011)
"... We describe a set of algorithms to simulate large spiking neural networks efficiently with high-level languages using vector-based operations. These algorithms constitute the core of Brian, a spiking neural network simulator written in the Python language. Vectorized simulation makes it possible to combine the flexibility of high-level languages with the computational efficiency usually associated with compiled languages."

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