Sentence examples for random dimensions from inspiring English sources
It was found that the modified algorithm produces a more accurate estimator over the range of random dimensions studied.
In the case of multiple random dimensions, n ≥ 2, sparse integration methods have to be applied in order to reduce the curse of dimensionality.
A unique highlight of the MSP procedure is that it can address heterogeneous sparsity in the spatial domain for different random dimensions.
If we use N points in each of D random dimensions, the number of neurons we need to simulate is N D. One way around this problem is to use sparse grids [33, 34], as introduced by Smolyak [35].
Selection of basis functions is particularly important for high-dimensional stochastic problems because the number of polynomial chaos basis functions required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases.
To illustrate this, we consider as an example the model, Equations 1 and 2 with I app uniformly spread between 17.5 and 32.5; the g Na uniformly spread between 2.55 and 3.05; V syn uniformly spread between −1 and 1; and V Na uniformly spread between 49 and 51, i.e. 4 independent random dimensions.
Its comical weapons make a little too much difference, especially in single-player mode, which lends proceedings an unwelcomely random dimension.
"And we wanted those discoveries to be meaningful in the sense that they could be shared with other players, all of whom existed in the exact same universe, rather than inside their own random dimension".
This characteristic behavior is attributed to the continually increasing frequency of the process in the random dimension.
A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form.
The idea in spectral stochastic formulations is to add an extra dimension, a random dimension, to the problem where the stochastic variability of the input parameters (and outputs of interest) can be modeled.
