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Table 3:

Summary of the

L_{1}

-Wasserstein Distances of ISI Distributions for Langevin Type Hodgkin-Huxley Models Compared to the MC Model.

Model	Variables V+M+N	$S$ Matrix	Noise Dimensions Na+K	$L_{1}$ Norm (msec.) (Wasserstein Dist.)	Run Time (sec.)
MC	1+8+5	n/a	20+8	$2.27 e- 4 \pm 7.15 e- 5$	3790
Fox94	1+7+4	$S = \sqrt{D}$	7+4	$4.74 e- 2 \pm 1.93 e- 4$	2436
Fox97	1+2+1	n/a	3	$8.01 e- 1 \pm 9.48 e- 4$	67
Dangerfield	1+8+5	$S_{EF}$	10+4	$2.18 e- 1 \pm 2.14 e- 4$	655
Goldwyn	1+8+5	$S = \sqrt{D}$	8+5	$1.83 e- 1 \pm 1.93 e- 4$	2363
Orio	1+8+5	$S_{paired}$	10+4	$4.52 e- 2 \pm 2.08 e- 4$	577
$14 \times 28$ D	1+8+5	$S_{single}$	20+8	$4.93 e- 2 \pm 1.94 e- 4$	605
SS	1+8+5	$S_{ss}$	4+2	$7.62 e- 2 \pm 7.57 e- 5$	73

Model	Variables V+M+N	$S$ Matrix	Noise Dimensions Na+K	$L_{1}$ Norm (msec.) (Wasserstein Dist.)	Run Time (sec.)
MC	1+8+5	n/a	20+8	$2.27 e- 4 \pm 7.15 e- 5$	3790
Fox94	1+7+4	$S = \sqrt{D}$	7+4	$4.74 e- 2 \pm 1.93 e- 4$	2436
Fox97	1+2+1	n/a	3	$8.01 e- 1 \pm 9.48 e- 4$	67
Dangerfield	1+8+5	$S_{EF}$	10+4	$2.18 e- 1 \pm 2.14 e- 4$	655
Goldwyn	1+8+5	$S = \sqrt{D}$	8+5	$1.83 e- 1 \pm 1.93 e- 4$	2363
Orio	1+8+5	$S_{paired}$	10+4	$4.52 e- 2 \pm 2.08 e- 4$	577
$14 \times 28$ D	1+8+5	$S_{single}$	20+8	$4.93 e- 2 \pm 1.94 e- 4$	605
SS	1+8+5	$S_{ss}$	4+2	$7.62 e- 2 \pm 7.57 e- 5$	73

Notes: Model (see text for details): MC: Markov chain. Fox94; From Fox and Lu (1994). Fox97: Fox (1997). Goldwyn: Goldwyn and Shea-Brown (2011). Dangerfield: Dangerfield et al. (2010, 2012). $14 \times 28$ D: model proposed in section 3.2. SS: stochastic-shielding model (see section 3.3). Variables: number of degrees of freedom in Langevin equation representing voltage, sodium gates, and potassium gates, respectively. $S$ Matrix: Form of the noise coefficient matrix in equations 1.1 to 1.3. Noise dimensions: number of independent gaussian white noise sources represented for sodium and potassium, respectively. $L_{1}$ Norm: Empirically estimated $L_{1}$ -Wasserstein distance between the model's ISI distribution and the MC model's ISI distribution. For MC versus MC, independent trials were compared. $a \pm b$ ⁠: mean $\pm$ standard deviation. Run time (in seconds): see text for details.

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