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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def compute_csets_TRAM( connectivity, state_counts, count_matrices, equilibrium_state_counts=None, ttrajs=None, dtrajs=None, bias_trajs=None, nn=None, factor=1.0, callback=None):
 r""" Computes the largest connected sets in the produce space of Markov state and thermodynamic states for TRAM data. Parameters connectivity : string one of None, 'reversible_pathways', 'post_hoc_RE' or 'BAR_variance', 'neighbors', 'summed_count_matrix' or None. Selects the algorithm for measuring overlap between thermodynamic and Markov states. * 'reversible_pathways' : requires that every state in the connected set can be reached by following a pathway of reversible transitions. A reversible transition between two Markov states (within the same thermodynamic state k) is a pair of Markov states that belong to the same strongly connected component of the count matrix (from thermodynamic state k). A pathway of reversible transitions is a list of (i_(N-1), i_N)]. The thermodynamic state where the reversible transitions happen, is ignored in constructing the reversible pathways. This is equivalent to assuming that two ensembles overlap at some Markov state whenever there exist frames from both ensembles in that Markov state. * 'largest' : alias for reversible_pathways * 'post_hoc_RE' : similar to 'reversible_pathways' but with a more strict requirement for the overlap between thermodynamic states. It is required that every state in the connected set can be reached by following a pathway of reversible transitions or jumping between overlapping thermodynamic states while staying in the same Markov state. A reversible transition between two Markov states (within the same thermodynamic state k) is a pair of Markov states that belong to the same strongly connected component of the count matrix (from thermodynamic state k). Two thermodynamic states k and l are defined to overlap at Markov state n if a replica exchange simulation [2]_ restricted to state n would show at least one transition from k to l or one transition from from l to k. The expected number of replica exchanges is estimated from the simulation data. The minimal number required of replica exchanges per Markov state can be increased by decreasing `connectivity_factor`. * 'BAR_variance' : like 'post_hoc_RE' but with a different condition to define the thermodynamic overlap based on the variance of the BAR estimator [3]_. Two thermodynamic states k and l are defined to overlap at Markov state n if the variance of the free energy difference Delta f_{kl} computed with BAR (and restricted to conformations form Markov state n) is less or equal than one. The minimally required variance can be controlled with `connectivity_factor`. * 'neighbors' : like 'post_hoc_RE' or 'BAR_variance' but assume a overlap between "neighboring" thermodynamic states. It is assumed that the data comes from an Umbrella sampling simulation and the number of the thermodynamic state matches the position of the Umbrella along the order parameter. The overlap of thermodynamic states k and l within Markov state n is set according to the value of nn; if there are samples in both product-space states (k,n) and (l,n) and |l-n|<=nn, the states are overlapping. * 'summed_count_matrix' : all thermodynamic states are assumed to overlap. The connected set is then computed by summing the count matrices over all thermodynamic states and taking it's largest strongly connected set. Not recommended! * None : assume that everything is connected. For debugging. state_counts : numpy.ndarray((T, M), dtype=numpy.intc) Number of visits to the combinations of thermodynamic state t and Markov state m count_matrices : numpy.ndarray((T, M, M), dtype=numpy.intc) Count matrices for all T thermodynamic states. equilibrium_state_counts : numpy.dnarray((T, M)), optional Number of visits to the combinations of thermodynamic state t and Markov state m in the equilibrium data (for use with TRAMMBAR). ttrajs : list of numpy.ndarray(X_i, dtype=numpy.intc), optional List of generating thermodynamic state trajectories. dtrajs : list of numpy.ndarray(X_i, dtype=numpy.intc), optional List of configurational state trajectories (disctrajs). bias_trajs : list of numpy.ndarray((X_i, T), dtype=numpy.float64), optional List of bias energy trajectories. The last three parameters are only required for connectivity = 'post_hoc_RE' or connectivity = 'BAR_variance'. nn : int, optional Number of neighbors that are assumed to overlap when connectivity='neighbors' factor : int, default=1.0 scaling factor used for connectivity = 'post_hoc_RE' or 'BAR_variance'. Values greater than 1.0 weaken the connectivity conditions. For 'post_hoc_RE' this multiplies the number of hypothetically observed transitions. For 'BAR_variance' this scales the threshold for the minimal allowed variance of free energy differences. Returns ------- csets, projected_cset csets : list of ndarrays((X_i,), dtype=int) List indexed by thermodynamic state. Every element csets[k] is the largest connected set at thermodynamic state k. projected_cset : ndarray(M, dtype=int) The overall connected set. This is the union of the individual connected sets of the thermodynamic states. References: [1]_ Hukushima et al, Exchange Monte Carlo method and application to spin glass simulations, J. Phys. Soc. Jan. 65, 1604 (1996) [2]_ Shirts and Chodera, Statistically optimal analysis of samples from multiple equilibrium states, J. Chem. Phys. 129, 124105 (2008) """

    return _compute_csets(
        connectivity, state_counts, count_matrices, ttrajs, dtrajs, bias_trajs,
        nn=nn, equilibrium_state_counts=equilibrium_state_counts,
        factor=factor, callback=callback)