Table 4. The best optimal theoretical fractional volumes and related parameters in the cortex for the combined “wire min + spine max” principle with control parameter f = 0.1.

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	0.399	0.396	0.097	0.098	0.010	0.655	0.612	0.99	1.00	5.885
Gamma (n = 1)	0.395	0.377	0.107	0.110	0.012	0.612	0.717	0.90	0.95	3.558
Gamma (n = 2)	0.393	0.368	0.110	0.117	0.013	0.569	0.759	0.85	0.95	2.416
Rayleigh	0.395	0.362	0.110	0.120	0.013	0.553	0.768	0.80	0.90	2.117
Log-logistic	0.400	0.344	0.116	0.126	0.015	0.544	0.844	0.65	0.90	1.277
Log-normal	0.386	0.353	0.112	0.134	0.015	0.480	0.825	0.80	0.80	1.565
Wire surface min + spine max (γ 1 = 1/3)
Exponential	0.402	0.393	0.100	0.096	0.010	0.696	0.631	0.95	0.70	5.903
Gamma (n = 1)	0.394	0.377	0.108	0.109	0.012	0.629	0.728	0.90	0.70	3.549
Gamma (n = 2)	0.396	0.364	0.111	0.116	0.013	0.589	0.774	0.80	0.70	2.375
Rayleigh	0.399	0.358	0.111	0.118	0.013	0.576	0.784	0.75	0.65	2.105
Log-logistic	0.398	0.346	0.117	0.125	0.015	0.550	0.850	0.65	0.70	1.280
Log-normal	0.396	0.347	0.104	0.138	0.014	0.423	0.759	0.65	0.80	1.741
Wire volume min + spine max (γ 1 = 0)
Exponential	0.399	0.396	0.099	0.096	0.010	0.692	0.629	0.98	0.45	5.898
Gamma (n = 1)	0.398	0.374	0.107	0.110	0.012	0.617	0.721	0.85	0.50	3.553
Gamma (n = 2)	0.395	0.365	0.112	0.115	0.013	0.598	0.781	0.80	0.50	2.371
Rayleigh	0.397	0.359	0.113	0.117	0.013	0.590	0.792	0.75	0.45	2.111
Log-logistic	0.399	0.345	0.117	0.125	0.015	0.548	0.848	0.60	0.55	1.277
Log-normal	0.400	0.343	0.110	0.133	0.015	0.474	0.798	0.60	0.45	1.409
Delays min + spine max (γ 1 = 5/6)
Exponential	0.398	0.398	0.096	0.099	0.010	0.642	0.606	1.00	1.15	5.887
Gamma (n = 1)	0.390	0.382	0.106	0.111	0.012	0.597	0.708	0.95	1.10	3.588
Gamma (n = 2)	0.393	0.367	0.111	0.117	0.013	0.580	0.768	0.85	1.05	2.393
Rayleigh	0.392	0.366	0.108	0.121	0.013	0.537	0.755	0.85	1.05	2.164
Log-logistic	0.396	0.348	0.114	0.127	0.014	0.530	0.830	0.70	1.05	1.295
Log-normal	0.390	0.356	0.108	0.132	0.014	0.469	0.775	0.80	1.00	1.553

All the results correspond to θ = 0.321.