Unformatted text preview: that is currently not capable of handling something other than binary states is REACT. A multi-state version is in preparation. However, in order to obtain useful performance, the computations will have to be performed in parallel on a multi-processor machine.) While Booleanization is a rather drastic transformation of the data and in many cases loses valu- able information in the data, it can still derive useful information from experimental data, as is shown in Vera-Licona et al. (2009). There, the authors use transcript data from a gene regulatory network in yeast used to compare different reverse-engineering methods Cantone et al. (2009). It is shown that the performance of REACT with a Booleanization of the data compares very favorably to the other methods tested. Example 1. Suppose that vector v = (1 , 2 , 7 , 9 , 10 , 11) is to be discretized. We start by constructing the complete weighted graph based on v . Eight edges with weights 10, 9, 9, 8, 8, 7, 6, and 5, respectively, have to be deleted to disconnect the graph into two components: one containing vertices 1 and 2 and another having vertices 7, 9, 10, and 11; this is the first iteration. Having disconnected the graph, the next task is to determine if the obtained degree of discretization is sufficient; if not, the components need to be further disconnected in a similar manner to obtain a finer discretization. A commonly occurring phenomenon, when discretizing time courses, is that the result- ing data are inconsistent with a deterministic process. This happens because a given state can transition to two different states at different times. So, when a deterministic model is desired, these inconsistencies have to be removed. A common cause of such inconsistencies is small variations among consecutive time points, so that these get discretized into the same state. Eventually, there is sufficient change in the data so that a later discrete state becomes different again. This situation is dealt with by removing all but one instance of the repeated state. This essentially amounts to a local adjustment of time scale. Since time is not represented explicitly in discrete models, this is permissible. In the case of a given state transitioning to two different states in two different time courses, we remove the state in question, disconnecting the two time courses into four shorter ones. We further assume that there are no missing (unmeasured) time points. If new data points are included, then the parameter estimation process has to be restarted at the beginning. 7 4. Parameter estimation 4.1. The minimal-sets algorithm Inferring the wiring diagram of a gene regulatory network has received lots of attention and many different methods in different contexts have been developed to address this problem. Using methods from computational algebra and algebraic geometry, we have developed an algorithm that first finds all possible minimal wiring diagrams of a gene regulatory network, and then chooses a particular model using different selection methods.regulatory network, and then chooses a particular model using different selection methods....
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