Table 6. The best optimal theoretical fractional volumes and related parameters in the cortex for the combined “wire min + spine max” principle with control parameter f = 0.9.

The optimal fractions correspond to the minimal Mahalanobis distance (MD) between theory and data.

Principle type/spine distr.	Optimal parameters									MD
	x	y	s	g	c	$\overline{u}$	P	r	γ 2
Wire length min + spine max (γ 1 = 2/3)
Exponential	0.414	0.414	0.172	0.000	0.000	22077.8	1.000	1.00	0.10	18.45
Gamma (n = 1)	0.489	0.489	0.001	0.020	0.000	0.086	0.005	1.00	6.40	18.33
Gamma (n = 2)	0.484	0.484	0.003	0.029	0.000	0.118	0.012	1.00	6.20	17.88
Rayleigh	0.471	0.471	0.008	0.050	0.000	0.157	0.038	1.00	6.10	16.69
Log-logistic	0.414	0.414	0.172	0.000	0.000	22073.2	1.000	1.00	0.10	18.45
Log-normal	0.401	0.340	0.093	0.151	0.014	0.332	0.684	0.35	5.50	2.751
Wire surface min + spine max (γ 1 = 1/3)
Exponential	0.487	0.487	0.001	0.025	0.000	0.060	0.005	1.00	5.20	18.13
Gamma (n = 1)	0.478	0.478	0.004	0.040	0.000	0.107	0.018	1.00	4.90	17.38
Gamma (n = 2)	0.468	0.468	0.009	0.054	0.001	0.146	0.040	1.00	4.65	16.51
Rayleigh	0.454	0.454	0.017	0.074	0.001	0.181	0.084	1.00	4.60	15.07
Log-logistic	0.402	0.339	0.095	0.150	0.014	0.341	0.696	0.75	4.20	2.622
Log-normal	0.402	0.347	0.092	0.145	0.013	0.348	0.664	0.85	3.80	2.670
Wire volume min + spine max (γ 1 = 0)
Exponential	0.398	0.398	0.097	0.099	0.010	0.651	0.611	1.00	1.10	5.886
Gamma (n = 1)	0.386	0.386	0.108	0.109	0.012	0.628	0.728	1.00	1.20	3.591
Gamma (n = 2)	0.404	0.355	0.112	0.115	0.013	0.601	0.783	0.95	1.20	2.401
Rayleigh	0.403	0.354	0.111	0.119	0.013	0.568	0.779	0.95	1.00	2.126
Log-logistic	0.394	0.350	0.114	0.127	0.015	0.529	0.829	0.95	1.60	1.311
Log-normal	0.396	0.349	0.109	0.132	0.014	0.472	0.788	0.95	0.70	1.447
Delays min + spine max (γ 1 = 5/6)
Exponential	0.425	0.403	0.171	0.001	0.000	2095.2	1.000	0.50	0.10	18.37
Gamma (n = 1)	0.425	0.403	0.171	0.001	0.000	2091.7	1.000	0.50	0.10	18.37
Gamma (n = 2)	0.487	0.487	0.002	0.024	0.000	0.111	0.008	1.00	6.70	18.15
Rayleigh	0.475	0.475	0.006	0.043	0.000	0.151	0.029	1.00	6.70	17.11
Log-logistic	0.425	0.403	0.171	0.001	0.000	2091.7	1.000	0.50	0.10	18.37
Log-normal	0.401	0.340	0.093	0.151	0.014	0.332	0.684	0.40	5.60	2.751

All the results correspond to θ = 0.321.