The phrase "instances given by" is correct and usable in written English.
It is used to refer to specific examples that are offered as proof or evidence to support an argument or statement. For example: "The psychologist provided several instances given by her clients that demonstrated the efficacy of her treatment methods."
In many past studies, the excess pressure at the sea bottom due to a tsunami is usually assumed to be given by a static contribution from the tsunami height; for instance, given by ρ0g0η, where ρ0 is the density of sea water, g0 is the gravitational constant and η is the tsunami height.
Proof Sketch 1 Sketch of the Decider Correctness Proof) To prove the correctness of the decision algorithm, the equivalence of the following two statements must be shown: A PM exists in the PMPC instance given by (mathcal {G}) and (bar {mathcal {G}}).
The codon usage pattern of a given species s is, in first instance, given by the list of the genomic frequencies of the codons, 0 ≤ C i,s ≤ 1, i = 1,2, …,64 such that ∑ i C i,s = 1.
This difference may be amplified by the number of specific instances given.
The significance p-value of observing k instances assigned by the algorithm to a given category in a set of n instances
For the same noise variance at each user, the minimum transmit power required for a particular channel instance is given by the following expression [15, 17]: p tx ( h 1, h 2, …, h K s ) = ∑ i = 1 K s γ i h i † Z i - 1 h i, (6).
A particular problem instance is given by an input sequence, or several thereof.
Discriminant value for a testing instance x given by a trained classifier is: f(x) = ∑ i α i y iK x,x i) + b.
An interesting instance is given by the phenylalanyl-tRNA synthetase, in which the α and β chains have a Clostridium and Geobacter (delta-proteobacteria) best sequence similarity match, respectively.
In most instances this was given by the first author (SDA).
