Table 3:
Summary of the $L1$-Wasserstein Distances of ISI Distributions for Langevin Type Hodgkin-Huxley Models Compared to the MC Model.
ModelVariables V+M+N$S$ MatrixNoise Dimensions Na+K$L1$ Norm (msec.) (Wasserstein Dist.)Run Time (sec.)
MC 1+8+5 n/a 20+8 $2.27e-4±7.15e-5$ 3790
Fox94 1+7+4 $S=D$ 7+4 $4.74e-2±1.93e-4$ 2436
Fox97 1+2+1 n/a $8.01e-1±9.48e-4$ 67
Dangerfield 1+8+5 $SEF$ 10+4 $2.18e-1±2.14e-4$ 655
Goldwyn 1+8+5 $S=D$ 8+5 $1.83e-1±1.93e-4$ 2363
Orio 1+8+5 $Spaired$ 10+4 $4.52e-2±2.08e-4$ 577
$14×28$1+8+5 $Ssingle$ 20+8 $4.93e-2±1.94e-4$ 605
SS 1+8+5 $Sss$ 4+2 $7.62e-2±7.57e-5$ 73
ModelVariables V+M+N$S$ MatrixNoise Dimensions Na+K$L1$ Norm (msec.) (Wasserstein Dist.)Run Time (sec.)
MC 1+8+5 n/a 20+8 $2.27e-4±7.15e-5$ 3790
Fox94 1+7+4 $S=D$ 7+4 $4.74e-2±1.93e-4$ 2436
Fox97 1+2+1 n/a $8.01e-1±9.48e-4$ 67
Dangerfield 1+8+5 $SEF$ 10+4 $2.18e-1±2.14e-4$ 655
Goldwyn 1+8+5 $S=D$ 8+5 $1.83e-1±1.93e-4$ 2363
Orio 1+8+5 $Spaired$ 10+4 $4.52e-2±2.08e-4$ 577
$14×28$1+8+5 $Ssingle$ 20+8 $4.93e-2±1.94e-4$ 605
SS 1+8+5 $Sss$ 4+2 $7.62e-2±7.57e-5$ 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). $14×28$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. $L1$ Norm: Empirically estimated $L1$-Wasserstein distance between the model's ISI distribution and the MC model's ISI distribution. For MC versus MC, independent trials were compared. $a±b$: mean$±$standard deviation. Run time (in seconds): see text for details.

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