Algorithm 3.

Statistical approach for choosing 〈r_opt〉

1:	inputs: Jsym ← 〈Jsym〉 averaged across jackknives, pthres, the number of random matrices to generate M
2:	initialization: calculate the vector of eigenvalues β ← eig(Jsym) arranged in descending order of magnitude, initialize empty vector ζ ← ∅, 〈ropt〉 ← 0
3:
4:	for m = 1 to M do
5:	$\widehat{\text{J}}\leftarrow$ randomly sample D(D + 1)/2 elements of ±Jsym with uniform
6:	probability and generate a D × D symmetric matrix.
7:	$\zeta \leftarrow \left[\zeta ,|min(\text{eig}(\widehat{\text{J}}))|,max(\text{eig}(\widehat{\text{J}}))\right]$                                                                             ⊳ Append magnitude of maximum and minimum eigenvalues of $\widehat{\text{J}}$
8:
9:	for k = 1 to D do
10:	$p\leftarrow \frac{1}{2M}\sum _{m=1}^{2M}H({\zeta }_m-\left|{\beta }_k\right|)$                                                                                                                               ⊳ H(·) is the Heaviside step function
11:	if p ≥ pthres then
12:	break
13:	else
14:	〈ropt〉 ← k
15:
16:	output: 〈ropt〉