Tools¶

Here you find all of the tools currently in the toolbox, sorted by submodule.

The tools, which are the implementations of the contained analytical methods, are the core of NNMT. There are underscored _tools that expect all required parameters direcly as arguments, and respective wrapper tools that expect a model as argument.

Please read the overview for more details.

Approximations and assumptions¶

Analytical analyses of neuronal netoworks almost always rely on approximations and assumptions. If the network analyzed with a mean-field based tool does not fulfill the tool’s requirements, it cannot provide reliable results. These restrictions should be documented in the docstrings of the respective tools. Here, we explain a few important terms that appear in that context.

Diffusion approximation: If a neuron receives Poissonian uncorrelated input spike trains and the contribution of a single syanptic connection is small compared to the distance between reset and threshold $w \ll \left(V_\Theta - V_0\right)$ , the random input can be approximated by Gaussian white noise with mean $\mu$ and noise intensity $\sigma^2$ [Amit and Tsodyks, 1991, Tuckwell, 1988]. This approximation does not hold if the network features highly correlated activity or receives strong external input common to many neurons.
Linear response theory: Studies how populations of neurons in the stationary state respond to weak external input, ignoring non-linear interactions. Linear response theory cannot explain higher order effects like the occurence of higher harmonics.
Fast/slow synaptic regime: Parameter regime in which the synaptic time constant $\tau_\mathrm{s}$ is much shorter/longer than the membrane time constant $\tau_\mathrm{m}$ .