Sentence examples for connectivity kernel from inspiring English sources

In a neural system this connectivity kernel usually corresponds to the synaptic footprint, i.e., the connections from a neuron to others by synapses forming between its branching axon and their dendritic trees.

An interface description for this case was originally developed in [21], albeit for a special choice of synaptic connectivity kernel.

A challenge often encountered in the study of living systems is to estimate a spatial connectivity kernel w.

Our investigation here makes a smoothness assumption for the activity function f and the connectivity kernel w.

Fig. 4 A spreading pattern (C) governed by the space time model (3) and (4) with a radially symmetric synaptic connectivity kernel given by (12) and a Dirichlet boundary condition (u_{text{BC}}=0) on a domain of size ([-L,L] times [-L,L]).

In effect, by looking at the modular structure of the dominant patterns one gets an idea of the connectivity kernel.

Thus it is also of interest to consider synaptic connectivity kernels for which more explicit progress can be made.

Here we extend this approach to a far more general class of synaptic connectivity kernels, which include combinations of radially symmetric Gaussian functions (12).

The connectivity kernels (J_{ij}colon overline{varOmega}timesoverline{varOmega}mapstomathbb{R}) are assumed to be isotropic and given by J_{ij}bigl x,x'bigr)=rho_{j} eta_{ij}e^{-mu_{ij}lvert x-x'rvert}, (34) where (rho_{j}) is the density of neurons of type j, (eta_{ij}) is the maximal connection strength, and (mu_{ij}) is the spatial decay rate of the connectivity.

We shall consider radially symmetric synaptic connectivity kernels and a disc of radius D with a spot (circularly symmetric) solution of radius R. In this case (u(boldsymbol {r},t)=q(r)) with (r= vert boldsymbol {r} vert ) for all t, and (q(D =u_{text{BC}}), with (q(R)=kappa) and (q(r) > kappa ) for (r< R) and (q(r) < kappa) for (R< r< D).

Ranges of the connectivity kernels kFF, kFB, kREC and kINH are indicated in Fig. 4, and their features are explained in detail in Section 3.1.3.