Sentence examples for dimension of the underlying from inspiring English sources

It will be shown that, in theory, the computational cost of the proposed algorithm grows linearly with respect to the dimension of the underlying probability space of the system.

where C 0 is a positive constant, d is a dimension of the underlying spaces, x ∈ X, r ∈ ( 0, ∞ ).

It is precisely the requirement that such a complex structure exists, which forces the dimension of the underlying vector space to be even:.

Note that such an element cannot exist when the dimension of the underlying vector space is odd, whence from now on, we will put.

In fact, it is precisely in order to ensure that such a complex structure exists that the dimension of the underlying vector space is taken to be even.

Of note, our definition did not specify a minimal duration of dependency, since from a quality-improvement perspective the duration of dependency is not necessarily the most important dimension of the underlying TD construct.

Lost In Translation: a handbook for information systems in the 21st century explains how capturing requirements for IT solutions in terms of the values, policies, events, content and trust dimensions of the underlying information system provides IT with a personality of the desired solution that allows them to make the right technical decisions about implementation.

To evaluate the possibility that the apparently random ISI sequences are produced by a nonlinear system causing chaotic dynamics we estimated the fractal dimensions of the underlying attractor of the sequences.

Genes in a network are ordered in one dimension based on the underlying hierarchical organization of the network, making it possible to provide an overview of data for all genes in a network, with composite tracks visualized as heat maps, single continuous tracks as bar charts, and single binary tracks as barcode plots.

The method is robust in the following ways: (1) integrations of source terms on a co-dimension one surface are independent of the underlying grid and therefore stable under perturbations of the domain's boundary; (2) the method depends only on the function value of a level function, not on its derivatives.

As fisheries and aquaculture are fundamentally spatially distributed, responsible management requires a solid understanding of the underlying spatial dimension.