Sentence examples for expanded with respect to from inspiring English sources

His formula for an option's expected utility is the same as Skyrms's assuming that U Ki & A) may be expanded with respect to a partition of factors the agent may influence, using the formula U Ki & A) = ∑j P(Cj /Ki & A U Cj & Ki & A).

Considering that the auxiliary parameters ħ1, ħ2 and ħ3 are so properly chosen that the Taylor series of f ^ η, p, θ ^ η, p and ĝ η, p expanded with respect to an embedding parameter converge at p = 1, hence Equations (17 - 19 17 - 19 f ^ η, p = f 0 η + ∑ m = 1 ∞ f m η p m, (29) θ ^ η, p = θ 0 η + ∑ m = 1 ∞ θ m η p m, (30) ĝ η, p = g 0 η + ∑ m = 1 ∞ g m η p m, (31) f m η = 1 m !

Others are expanded with respect to lifestyle, but only within individual lineages.

The NOD mouse appears to be expanded with respect to C57BL/6J, having the largest known mouse Ly49 haplotype, variation that continues to confound next-generation sequencing and assembly techniques.

Expanding with respect to the basis of the linear space of polynomials with degree at most, we get (33).

At this point, we make use of the Taylor series expansion to expand with respect to around as (48).

Let μ be the Poincaré metric on U. The polynomial (p U'rightarrow U) is strongly expanding with respect to the metric μ.

The idea here is to feign doubt as to the truth of a by removing both a and its negation from the current belief state and then implement Ramsey's recommendation of expanding with respect to the modified state.

The polynomial (p U'rightarrow U) is strongly expanding with respect to the Poincaré metric of U, i.e. there exists a constant (varepsilon<1) (which depends only on the distance between ∂U and (partial U')) such that d_{U}bigl x,x'bigr)leqvarepsilon d_{U} bigl(p(x),pbigl(x'bigr bigr).

In the era of systems biology, single-cell measurement techniques are rapidly expanding with respect to the number of cells that can be analyzed and the number of biochemical species that can be co-measured per cell.

We saw that the actin cap expands faster and to a greater extent in myosin-inhibited embryos, and observed 'streaks of actin' in the kymographs expanding outward with respect to the position of the centrosomes in both WT and myosin-inhibited embryos.