For the details of the comparison between the Jarzynski's equality method and the umbrella sampling method see Figure S5.
In addition, the Jarzynski's equality method can also be used to calculate the shape of one-dimensional free energy landscape [30], [59], but it needs a large number of pulling trajectories in order to reproduce the shape of free energy landscape accurately [60].
Teng et al. (2009) developed a mathematical model for an EOQ inventory with two warehouses and solved the problem by an arithmetic geometric in-equality method.
For features as phone and date, we simply used the equality comparison method - as this method appeared to us to be the most appropriate to capture the semantics between two different feature values in this particular case.
The proposed two-stage directional in-equality detection method identifies the source of test images stably in various environments: various image or video formats, cropping portion, and image or video compression.
We used the Wilcoxon signed ranks test to assess equality between methods, as the normality assumption (tested with the Shapiro-Francia test) was not satisfied.
No hypothesis of superiority of one of the methods studied, nor equality between the methods, was initially anticipated.
Google's solution, at least for now, is what they call the "equality of opportunity" method, which ensures a system doesn't accidentally discriminate based on sensitive, non-relevant data, for instance race or religion, when calculating something not directly related to them.
Also, we can prove these equalities using the method of successive approximation; see Section 4.
I've had many interactions with students where it has been hard for them to understand that the civil rights movement isn't just a thing that happened 50 years ago when Dr. Martin Luther King, Jr. gave a speech, marched for equality, and employed methods of non-violence to make the statement that "whatever affects one directly, affects all indirectly".
But in the modern era, there is no excuse for privately-owned voting machines that breed mistrust, confusing ballot designs, polling places with long lines, voter registration laws that leave nearly a third of Americans off the rolls, an Electoral College system that undercuts equality and voting methods that suppress voter choice and stifle fair representation.
