1) In the paragraph above the "Persistence Diagram Window" heading:
As the line moves, the both the barcode in the Line Selection Window and its persistence diagram representation in the Persistence Diagram Window are updated in real time.
2) Second paragraph:
a <= b should mean a_1 <= b_1 and a_2 <= b_2, but you say a_1 <= b_2.
1) In the paragraph above the "Persistence Diagram Window" heading:
As the line moves, the both the barcode in the Line Selection Window and its persistence diagram representation in the Persistence Diagram Window are updated in real time.
2) Second paragraph:
a <= b should mean a_1 <= b_1 and a_2 <= b_2, but you say a_1 <= b_2.