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This difficulty stems from the very complex shape of the (mathcal {S}) function once we treat (varvec{lambda }) as its arguments, which results in the joint optimization of the model parameters (w) and the set of hyperparameters ((varvec{lambda })): begin{aligned} underset{w, varvec{lambda }}{text {maximize }} mathcal {S}left( w, varvec{lambda }| left{ (x_i,y_i) right} _{i=1}^Nright).

Model parameters w i j Importance of covering O/D pair i j C i k Traveling time (cost or distance) from node i to k T Maximum permissible transportation cost (time or distance) for covering O/D pairs P Number of hubs to be established p i k Safety for the link transmitting loads between nodes i and k M A big number.

The model parameters (W :, k (m ), H k (m ), Σ (m ), α d, k (m ), π k, Z) are then learned from the data using Gibbs sampling.

The initial values of the sensitivity equations are however zero ((∂ c / ∂ w ) t 0 = 0,   (∂ c / ∂ w ) t < t 0 = 0 ), because the initial state values, c t0), are independent of model parameters w.

If the microtime data are taken in sections of real macrotime by the sliding time window, the assumption can be made that the model parameters, w, are constant for the real-time duration of the current section of the data.

Finally, we integrated the experimental data and prior information to generate 4000 distinct and executable model solutions with low errors (i.e., sets of model parameters, W ij, for which the model equations best reproduce the experimental response map) using the BP-based strategy.

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When a drug follows a one-compartment model of oral dose (1), the following non-compartment model PK parameters, w = (AUC, T max, T 1/2), are necessary to recover the one-compartment model parameters, β = (k a, k e, V). (1) (2) where, F is an assumed known bioavailability, and dose denotes the oral dose.

If a drug's pharmacokinetics follows a two-compartment model with oral dose (5), the following non-compartment model PK parameters, w = (Vd, AUC, T max, CL iv, T 1/2,slow, T 1/2,fast), are necessary to recover the two-compartment model parameters, β = (k a, k e, V 1, k 12, k 21).

(5) (6) If a drug's pharmacokinetics follows a two-compartment model with IV dose (7), the following non-compartment model PK parameters, w = (Vd, AUC, CL iv, T 1/2, slow, T 1/2, fast), are necessary to recover the two-compartment model parameters, β = (k e,V 1, k 12, k 21).

Driving the reservoir The hidden states S hidden(m, k) is updated in the light of two model parameters {W res (k), W in k)}.

In the equation, P θ (v (n)) is the probability of visible vectors in the inner model with the model parameters θ=(W, a, b).

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