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q^{\uparrow}_n (t) =\exp(-t/\tau_n) \cdot \left[ \ q^{\uparrow}_n (0) + \tau_n^{-1} \cdot \int_0^t \exp(s/\tau_n) \left[ \sum_m f_{nm} \ q^{\downarrow}_m(s) - \gamma_n \frac{dp_n}{ds} \right] ds \right] |
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q^{\uparrow}_n (t) =\exp(-t/\tau_n) \cdot \left[ \ q^{\uparrow}_n (0) + \tau_n^{-1} \cdot \int_0^t \exp(s/\tau_n) \left[ \sum_m f_{nm} \ q^{\downarrow}_m(s) - \gamma_n \frac{dp_n}{ds} \right] ds \right] |
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