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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 _apply_correction_on_genes(genes, pathway_column_names, pathway_definitions):
 """Helper function to create the gene-to-pathway membership matrix and apply crosstalk correction on that matrix. Returns the crosstalk-corrected pathway definitions for the input `genes.` """

    gene_row_names = index_element_map(genes)
    membership_matrix = initialize_membership_matrix(
        genes, pathway_definitions)
    crosstalk_corrected_index_map = maximum_impact_estimation(
        membership_matrix)

    updated_pathway_definitions = _update_pathway_definitions(
        crosstalk_corrected_index_map,
        gene_row_names, pathway_column_names)
    return updated_pathway_definitions