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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+NS MatrixNoise Dimensions Na+KL1 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 
14×281+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+NS MatrixNoise Dimensions Na+KL1 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 
14×281+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). 14×28D: 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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