Sentence examples for proof of representation from inspiring English sources

Notably, cross-species representation levels may not necessarily be a proof of representation quality.

The Fourier transform of s is (derived in Appendix Appendix 2: Proof of Fourier representation of binning sampling): S ≈ ∑ λ ∈ Π Z 2 2 X α ω − λ 2 + e j ω 2 T 1 1 ⏟ unwanted filter e j λ 2 T 1 1 X β ω − λ 2 + ∑ θ ∈ Z 2 2 e j ω 2 T θ H bin ω 2 16 ⏟ unwanted filter X g ω 2 + ∑ λ ∈ Π 2 Z 4 2 ∖ 0 0 ∑ θ ∈ Z 2 2 e j ω 2 + λ T θ H bin ω 2 − λ 16 ⏟ antialias filter X g ω 2 − λ ⏟ aliasing.

A probability function and a utility function together represent a set of preferences just in case the following formula holds for all values of $A$ and $B$ in the domain of the preference relation Mathematical proofs of Representability are called representation theorems.

Our study has provided a proof-of-principle that reduced representation shotgun sequencing (RRS) [47] is a tool that can be used for nucleotide polymorphism discovery with prokaryotes.

The following technical result about real numbers (Lemma 3 in [14]) will be used in the proof of our next representation theorem.

In the course of the proofs, a representation of the Lévy process as a function on K′ is obtained and stochastic Lévy integrals are studied.

So Nativists can claim an existence proof of an innately endowed representation of objects as permanent.

(This is the substance of Goodman's proof that representation is a species of denotation).

We described a proof-of-concept semantic reasoning system for pharmacogenomics knowledge representation focused on clinical decision support.

As such, given a proof of correctness for a logical representation, it is difficult to conclude that the "actual" protocol is correct.

This work represents a proof of concept study for geometrical representation of MHC α-helices, hence, molecular dynamics simulations were performed for 250 ns.