Sentence examples for manifolds in a from inspiring English sources

We investigate firing threshold manifolds in a mathematical model of an excitable neuron.

We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary trajectory.

It is possible to define an analysis on manifolds in a coordinate- and metric-free manner and independent of the dimension.

First, anisotropic heat kernel is computed by constructing an image pyramid and embedding multi-level image properties into 2D manifolds in a divide-and-conquer way, consequently, multi-scale structure-preserving image decomposition can be accommodated.

Similar dynamics in systems without rotational symmetry were described in [22, 23] using a map-based model in two dimensions, and in [20] by examining the intersections of invariant manifolds in a continuous-time model in three dimensions.

In conservative cases, it is shown that normal form theory allows one to compute all NNMs, as well as the attendant dynamics onto the manifolds, in a single operation.

Riemann's basic scheme makes allowance for much greater generality than he actually reaches for; but, in his judgment, it should be enough for the time being to characterize the geometry of continuous manifolds in such a way that it agrees optimally with Euclidean geometry on a small neighborhood of each point.

By structuring high-dimensional, multimodal information into a set of distinct sub-manifolds in a fully unsupervised way, it performs a substantial dimensionality reduction by providing both a symbolic representation of data and a fine discrimination between two similar stimuli.

In the modified propofol model, we are able to explain both spiking transitions through identification of the firing threshold manifold in a 4-fast/2-slow time-scale separation setting the threshold manifold being the folded saddle canard.

If the manifold in a Coat-hanger die is not properly designed, the exit velocity distribution may be not uniform; this can affect the thickness across the width of the die.

Smith says that by subcontracting some of the work abroad for example, the intake manifold in a car's air system these contractors can add 20 points to that gross margin, and that's after paying Smith his fee of 5% to 7% of the foreign invoices.