Table 2.

The parametric timing and time delay dispersion indices (σ) corresponding to the circular distributions of the datasets across conditioning sessions, and for three different durations of the inter-stimulus interval (ISI).

Mean angle (in radians)		Mean timing (in milliseconds)		Mean radius of the centroid		Circular kurtosis index		Time-dispersion index
ISI = 270 ms (CS–US INTERVAL, IN THE SUB-SECONDS RANGE)
${\overline{\Omega }}_{\text{MN}}$	5.0202	${\overline{T}}_{\text{MN}}$	215.7259	${\overline{C}}_{\text{MN}}$	0.0832	ρMN	0.4199	σMN	41.9183
${\overline{\Omega }}_{\text{CR}}$	1.3434	${\overline{T}}_{\text{CR}}$	57.7294	${\overline{C}}_{\text{CR}}$	0.0962	ρCR	0.8539	σCR	7.8896
${\overline{\Omega }}_{\text{IP}}$	1.6228	${\overline{T}}_{\text{IP}}$	69.7354	${\overline{C}}_{\text{IP}}$	0.0972	ρIP	0.8910	σIP	5.7710
$\overline{\Omega }0$	1.8227	$\overline{T}0$	78.3229	$\overline{C}0$	0.0850	ρ0	0.4864	σ0	35.5164
$\overline{\Omega }1$	1.4978	$\overline{T}1$	64.3623	$\overline{C}1$	0.0962	ρ1	0.8536	σ1	7.9113
$\overline{\Omega }2$	1.2120	$\overline{T}2$	52.0832	$\overline{C}2$	0.0962	ρ2	0.8551	σ2	7.8237
$\overline{\Omega }3$	1.7772	$\overline{T}3$	76.3711	$\overline{C}3$	0.0948	ρ3	0.8017	σ3	11.0338
$\overline{\Omega }4$	2.1122	$\overline{T}4$	90.7634	$\overline{C}4$	0.0949	ρ4	0.8049	σ4	10.8351
$\overline{\Omega }5$	1.7645	$\overline{T}5$	75.8225	$\overline{C}5$	0.0941	ρ5	0.7775	σ5	12.5633
$\overline{\Omega }6$	2.2227	$\overline{T}6$	95.5117	$\overline{C}6$	0.0937	ρ6	0.7628	σ6	13.5142
*ISI = 360 ms (CS–US INTERVAL, IN THE SUB-SECONDS RANGE)
${\overline{\Omega }}_{\text{MN}}$	3.7658	${\overline{T}}_{\text{MN}}$	215.7643	${\overline{C}}_{\text{MN}}$	0.0903	ρMN	0.6441	σMN	21.8045
${\overline{\Omega }}_{\text{CR}}$	1.0081	${\overline{T}}_{\text{CR}}$	57.7627	${\overline{C}}_{\text{CR}}$	0.0979	ρCR	0.9161	σCR	4.3784
${\overline{\Omega }}_{\text{IP}}$	1.2176	${\overline{T}}_{\text{IP}}$	69.7624	${\overline{C}}_{\text{IP}}$	0.0984	ρIP	0.9376	σIP	3.2203
$\overline{\Omega }0$	1.3720	$\overline{T}0$	78.6083	$\overline{C}0$	0.0914	ρ0	0.6838	σ0	18.9297
$\overline{\Omega }1$	1.1239	$\overline{T}1$	64.3936	$\overline{C}1$	0.0979	ρ1	0.9159	σ1	4.3923
$\overline{\Omega }2$	0.9096	$\overline{T}2$	52.1186	$\overline{C}2$	0.0979	ρ2	0.9168	σ2	4.3442
$\overline{\Omega }3$	1.3337	$\overline{T}3$	76.4144	$\overline{C}3$	0.0971	ρ3	0.8853	σ3	6.0854
$\overline{\Omega }4$	1.5849	$\overline{T}4$	90.8055	$\overline{C}4$	0.0971	ρ4	0.8871	σ4	5.9854
$\overline{\Omega }5$	1.3244	$\overline{T}5$	75.8846	$\overline{C}5$	0.0967	ρ5	0.8705	σ5	6.9279
$\overline{\Omega }6$	1.6681	$\overline{T}6$	95.5762	$\overline{C}6$	0.0964	ρ6	0.8616	σ6	7.4427
*ISI = 450 ms (CS–US INTERVAL, IN THE SUB-SECONDS RANGE)
${\overline{\Omega }}_{\text{MN}}$	3.0129	${\overline{T}}_{\text{MN}}$	215.7805	${\overline{C}}_{\text{MN}}$	0.0938	ρMN	0.7630	σMN	13.4836
${\overline{\Omega }}_{\text{CR}}$	0.8067	${\overline{T}}_{\text{CR}}$	57.7778	${\overline{C}}_{\text{CR}}$	0.0986	ρCR	0.9458	σCR	2.7848
${\overline{\Omega }}_{\text{IP}}$	0.9742	${\overline{T}}_{\text{IP}}$	69.7748	${\overline{C}}_{\text{IP}}$	0.0990	ρIP	0.9598	σIP	2.0534
$\overline{\Omega }0$	1.0993	$\overline{T}0$	78.7320	$\overline{C}0$	0.0944	ρ0	0.7891	σ0	11.8251
$\overline{\Omega }1$	0.8993	$\overline{T}1$	64.4079	$\overline{C}1$	0.0986	ρ1	0.9456	σ1	2.7942
$\overline{\Omega }2$	0.7279	$\overline{T}2$	52.1347	$\overline{C}2$	0.0986	ρ2	0.9462	σ2	2.7637
$\overline{\Omega }3$	1.0672	$\overline{T}3$	76.4339	$\overline{C}3$	0.0981	ρ3	0.9257	σ3	3.8596
$\overline{\Omega }4$	1.2681	$\overline{T}4$	90.8245	$\overline{C}4$	0.0981	ρ4	0.9268	σ4	3.7990
$\overline{\Omega }5$	1.0599	$\overline{T}5$	75.9126	$\overline{C}5$	0.0979	ρ5	0.9159	σ5	4.3936
$\overline{\Omega }6$	1.3349	$\overline{T}6$	95.6053	$\overline{C}6$	0.0977	ρ6	0.9099	σ6	4.7174

These results are in correspondence with the two circumstances described in Section “Circular Statistics to Analyze Time-Dispersion Patterns During Motor Learning,” with the first row of circles in Figure 5A, and with the circular sectors in Figures 5B–7B. The ISI = 270 ms is the actual CS–US interval and both ^*ISI = 360 ms and ^*ISI = 450 ms are the simulated time conditions for studying the simulated dispersion patterns of the same dataset distribution. Here, the matrix of intensity/strength components has been substituted by a matrix of those to fit their values to the unitary circle. Note that for all the distributions the time-dispersion indices satisfy the mathematical relationship σ (270 ms) > σ (360 ms) > σ (450 ms).