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Pareto Front

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111–116 of 116 posts

Re: Pareto Front

#111

Earlier quoted context omitted.

I feel like there should be a GUI tool to bake in any alternates into the font itself.

You mean like Commit Mono does? https://commitmono.com/

Something like that! But for any font.

I think fontTools instancer could work here, though it’s a CLI: https://fonttools.readthedocs.io/en/latest/varLib/instancer....

Re: Pareto Front

#114

I have a weightlifting spreadsheet with weight on the vertical axis and reps on the horizontal axis. The value of each cell is the estimated 1 rep max if I accomplish that lift. In theory if my e1RM is 100kg then I can lift any permutation of (weight,reps) that have the same e1RM. This is akin to knowing Pareto Frontier of my current strength. I use conditional formatting to color cells according to the probability t…

I wrote this app as a SPA! It uses a curve formulation similar to Brzycki, except I added a “shape” parameter (an exponent gamma between 0 and 1) that slopes the 1rm downwards at the right side. My main finding for “pick whatever weight you want today” was that picking a lot of different weights made the curve less identifiable, so my latest iteration encourages you to pick a ladder for a few sentinel exercises per m…

You both sound young. Shouldn't time be in there too?

Re: Pareto Front

#115
In the formula given in the Definition, what is the point of including the y'' /= y' condition, given that y'' >- y'? Could a solution ever Pareto-dominate itself? If we know that A dominates B, do we not know that they are distinct?

Re: Pareto Front

#116

I have a weightlifting spreadsheet with weight on the vertical axis and reps on the horizontal axis. The value of each cell is the estimated 1 rep max if I accomplish that lift. In theory if my e1RM is 100kg then I can lift any permutation of (weight,reps) that have the same e1RM. This is akin to knowing Pareto Frontier of my current strength. I use conditional formatting to color cells according to the probability t…

I wouldn't call this a Pareto Frontier, but simple isolines through a 2d function.

There are weight x rep combinations that have a e1rm of 80kg, 85kg, 90kg, and so on.

These are just equal elevation contours through the e1rm(x, y) function.

The Pareto concept doesn't require that we calculate a function of all the dimensions and find contours; that sort of thing is not involved.

But we could apply it here like this. Suppose we conduct a weight lifting contest as follows: contestants can lift any weight any number of times, and record the weight and reps.

Then, how do we rank the results to find a winner, or winners? We have multiple dimensions, not a single dimension like "seconds to run 10 km".

We can find the Pareto front set of the performances by eliminating all that have been dominated. A lift is dominated if another lift is no worse (no less weight, and no fewer reps), and strictly better: eight the weight is higher, or there are more reps, or both.

We then end up with undominated winners, e.g. there could be three like this: { (100kg, 1), (80kg, 2), (70kg, 5) } but (70kg, 4) would not belong, due to being dominated by the third one, and (90kg, 1) would not due to being dominated by the first. The middle one is not dominated by either: though it's less weight than the 100kg, it is more reps, and though it is fewer reps than the 70kg, it is more weight.

Given the Pareto front set, if we want to determine a single winner, we need a function to reduce the parameters to a single value. (The function should be such that if we included the eliminated losers under that function, none of them would emerge winner over the Pareto front set). This e1rm function looks like it fits the bill.

If we have this function, we don't need the Pareto concept; we just run all the results through the function and pick the contestant(s) that maximize it.

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