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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 _initalize_tree(self, position, momentum, slice_var, stepsize):
 """ Initalizes root node of the tree, i.e depth = 0 """


        position_bar, momentum_bar, _ = self.simulate_dynamics(self.model, position, momentum, stepsize,
                                                               self.grad_log_pdf).get_proposed_values()

        _, logp_bar = self.grad_log_pdf(position_bar, self.model).get_gradient_log_pdf()

        hamiltonian = logp_bar - 0.5 * np.dot(momentum_bar, momentum_bar)

        candidate_set_size = slice_var < np.exp(hamiltonian)
        accept_set_bool = hamiltonian > np.log(slice_var) - 10000  # delta_max = 10000

        return position_bar, momentum_bar, candidate_set_size, accept_set_bool