Sentence examples for by a sum over from inspiring English sources

The electronic density n(r) is given by a sum over occupied wave functions: n ( r ) = 2 ∑ i ∈ occ | φ i ( r ) | 2, (4).

For sexual populations, instead, each lineage is a tree of branching ratio two and the path integral describing the evolving population is given by a sum over these trees.

The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements.

The ratio of the second-order moments (lambda _2/lambda _1) can be simplified when the integration is replaced by a sum over the wavevectors (Saito et al. 2008; Shebalin et al.

Deep CNN is a bottom-up approach where an input image is subjected to multiple layers of convolutions, nonlinearities, and subsampling whereas deep deconvolutional network is a top-down appraoch where an input image is generated by a sum over convolutions of the feature maps with learned filters.

To achieve this, we apply the so-called Nyström or quadrature method (cf. [79, Chapter 4]), which amounts to replacing an integral by a sum over suitable quadrature weights and points and neglecting the error term.

The Green's function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism.

Given the probability density (p_{rho}(x_{phi},phi)) in (2), one could reconstruct the Wigner function by substituting the integration with a sum over the pairs for a sufficiently large number of data.

The Republicans claim that it will cost far more and totally reject the idea that it will cut the deficit by such a sum over the second decade.The CBO is required to score what Congress says it will do, not what it is likely will actually be done.

(11)In Equation 10, we calculate the probability distribution of H1, g, δ by taking a sum over all possible parental pairings at the previous generation that would lead to an admixture fraction q at generation g.

Ottawa says that the councils' budgets will be boosted by $280 million--but that's a sum over 3 years of flat budgets.