notes_from_hari.md

In bc/stfeasibility: The Feasibility Theory of Time-Varying Isometric Force Trajectories

sampling from a log-concave; gaussian; a bit more general - take logarithm of the density to get a concave distribution uniform: is a special case - assumes that all points are equally likely

lipschitz constraint

the lipschitz norm has to be less than \delta

finds the value of highest delta for a given muscle

the outliers can be expressed as the lipshitz norm:

|x2 - x1| lp norm is the approach Norm(x, p=2) lipschitz_norm <- f() max(abs(x2 -x1),abs(x3 -x2),... abs(x7 -x6))

4x7 per moment 7 moments

49 dimensional subspace to sample from

A_1 x_1 <= b_1 0 < a_i < 1

A_1 x_1 <= b_1 A_2 x_2 <= b_2 A_3 x_3 <= b_3 0 < a_i < 1

Product distribution - this is what you get when you append many polytopes together into higher dimensions

A_1 x_1 <= b_1 A_2 x_2 <= b_2 A_3 x_3 <= b_3 0 < a_i < 1

spatiotemporal constraints |muscle 1 in moment 2 - muscle1 in moment 1| < \delta

in case where theta is 1: becomes a redundant constraint. not a degenerate case'; not-further-constrained case

reason why we can't sample ind: there's a it's a property of high dimensional spaces picking a point on a ball, very likely to pick something very very close to the surface.

31 muscles 6 dimensions of out wrench

3,3,3, (len 31) 'each of these situations are unlikely. when you take a product they become very very unlikely.'

n=7 muscles num tasks = 7 x \in [0,1]n*numtasks HAR --> x

x_0 does your seed point affect downstream distributions? how does a seed point affect the polytope's structure

A_1 x_1 <= b x_1 == (0.5,0.5,0.5,...) # this is the stationary measure A_i x_i <= b_i lipschitz constraints x \in [0,1]

what is the downstream probability? the stationary measure you'd assign to the starting point. It's a small probabbility, but it is a positive one

task, number of points it took to get to 100 valid solution, p x_2,s98 more p)

constrained_set <- intersection of the box from the given point, with (polytope at i + 1)

Get volume of the constrained set / polytope at i + 1

Ben Cousins

relationship of volumes

https://link.springer.com/article/10.1007/s12532-015-0097-z

bc/stfeasibility documentation built on May 25, 2022, 6:04 a.m.