In this task, you are given a paragraph (from a research paper) and your task is to classify each sentence of the paragraph (assume n sentence) into the following categories: Background, Purpose, Method, Finding/Contribution, or Other. Return the output in this format: 1 - category of sentence 1, 2 - category of sentence 2, ..., n - category of sentence n; where each number indicates the order of the sentence. The categories can be identified using the following questions:
Background: - Why is this problem important? - What relevant works have been done before? - What did the previous works miss? - What are the high-level research questions? - How might this help other researchers?
Purpose: - What specific things do the researchers want to do? - What specific knowledge do the researchers want to know? - What specific hypothesis do the researchers want to test?
Method: - How did the researchers do it or find it out? - What are the procedures and steps of this research?
Finding/Contribution: - What did the researchers find out? Did the proposed methods work? - Did things behave as the researchers expected?
Other: put every text fragment that does not fit into any of the categories above here. Put a sentence here if its not in English, is not part of the article, contains numbers and dates, is a caption of a figure or a table, is a formatting error, or you are not sure about it.

Cut-off Cut-off Supplementary Figure 1 | Setting cut-off to identify links and hidden source. (a) Coarse-grained distribution of element values ln(1 i )a ij times 1 in the reconstructed vector X of all nodes in a Newman-Watts small-world network (NW), where bin accumulation is implemented for the original distribution. The peak centered at zero corresponds to null connections and the other corresponds to actual links. A cut-off value can be set within the gap between the two peaks. (b) The values of ln(1 i )a ij times -1 in the reconstructed vector X for Erdos-Renyi random networks (ER), Watts-Strogatz small-world networks (WS), NW and Barabasi-Albert scale-free networks (BA), where green and yellow points correspond to existent links and null connections, respectively. All the networks share the same cut-off value of about 0.13. (c) Coarse-grained distribution of the structural variance in the NW network, where bin accumulation is exercised on the original distribution. The largest peak centered close zero corresponds to nodes of indirect neighbors of the hidden source and the large positive values of are associated with the immediate neighbors of the hidden source. A cut-off can be set within the largest gap. (d) The variance * i of element values in the reconstructed vector x of all nodes in the presence of a hidden source for ER, WS, NW and BA networks, where green and yellow points correspond to immediate neighbors and indirect neighbors of the hidden source, respectively. All the networks share the same cut-off values of about * i = 0.9. The network size in a,b is 200 and in c,d is 50, = 0.25, = 0.45, i and i are uniformly distributed in the ranges (0.2, 0.4) and (0.4, 0.6), respectively. SIS dynamics are used for the illustration. Panels a and c correspond to Fig. 2a with nt = 0.4 and Fig. 5 in the main text, respectively.
1 - background, 2 - background, 3 - background, 4 - background, 5 - background, 6 - background, 7 - background, 8 - background, 9 - background, 10 - background, 11 - background, 12 - background, 13 - finding, 14 - finding, 15 - finding, 16 - finding, 17 - finding, 18 - finding, 19 - finding, 20 - finding, 21 - finding, 22 - finding, 23 - finding, 24 - finding