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The time evolution of quantum observables in the quantum states developed in the previous sections can be found by evaluating the expectation value of them.
The main obstacle lies in the complexity in evaluating the expectation in (13) which is usually done by stochastic averaging over a large number of random samples.
Substituting (37), in (39), and evaluating the expectation, the FFF can be expressed as w ( k ) = ( 1 + b ( k ) ) R xy ( k ) R yy - 1 ( k ) (40).
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Using the Price's theorem to evaluate the expectation as (54).
We will now evaluate the expectation of this random variable, and the result will be summarized as Theorem A below.
We would like to evaluate the expectation for the number of pinwheels (zeroes of z) in a given domain (mathcal {A}) of the unit disk.
With the Gaussian assumption we can evaluate the expectation values in (12). is valid, where and denote the real part and the imaginary part of a complex number, respectively.
To compute s ~ 1 , we need to evaluate the expectation E f 1 h, p ( h, Λ ) where each of the resource allocations p(h,Λ) follows from the solution of the optimization problem in (68).
The persistence (PER) model [12], the common SVM model and the linear quantile regression model are selected as the competitive models to evaluate the expectation forecast accuracy of the proposed approach.
This is an adverse property as it is intuitively clear that for a fixed number of samples, the best approximation, in terms of its ability to evaluate the expectation of a function (11), to a distribution is obtained using equal-weight samples.
Our study evaluated the expectation, experience, preference, and adherence of patients by asking matched questions.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com