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fix problems with naming the Gibson-Bruck Next Reaction Method
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docs/cell_modeling/simulation/index.rst

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@@ -121,15 +121,15 @@ Rather than sampling the time to the next reaction and then selecting the next r
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copy_numbers += reaction_stochiometries[:, i_reaction]
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Gibson-Bruck next reaction method
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Gibson-Bruck Next Reaction Method
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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`The Gibson-Bruck first reaction method <http://doi.org/10.1021/jp993732q>`_ is a computational optimization of the Gillespie first reaction method which uses (a) a dependency graph to only recalculate rate laws and resample putative next reaction times when necessary, namely when the participants in the rate law are updated and (b) an `indexed priority queue` to minimize the computational cost of identifying the reaction with the lowest putative next reaction time and updating the data structure which stores these putative next reaction times.
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`The Gibson-Bruck Next Reaction Method <http://doi.org/10.1021/jp993732q>`_ is a computational optimization of the Gillespie first reaction method which uses (a) a dependency graph to only recalculate rate laws and resample putative next reaction times when necessary, namely when the participants in the rate law are updated and (b) an `indexed priority queue` to minimize the computational cost of identifying the reaction with the lowest putative next reaction time and updating the data structure which stores these putative next reaction times.
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An indexed priority queue is a data structure that provides efficient identification (:math:`O(1)`) of the minimum value of the list and efficient updating of the list (:math:`O(\log{n})`. Indexed priority queues are implemented by the Python ``pqdict`` package. See the `pqdict documentation <http://pqdict.readthedocs.io/en/latest/intro.html#what-is-an-indexed-priority-queue>`_ for more information about indexed priority queues.
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Note, the Gibson-Bruck first reaction method is mathematically equivalent to the Gillespie direct and Gillespie first reaction methods.
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Note, the Gibson-Bruck Next Reaction Method is mathematically equivalent to the Gillespie direct and Gillespie first reaction methods.
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Below is pseudo code for the Gibson-Bruck next reaction method::
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Below is pseudo code for the Gibson-Bruck Next Reaction Method::
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import numpy
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import pqdict

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