A.I. Explanation:

First sentence: Why this is the first line? This paragraph is the first line because it introduces the main topic. It talks about the discovery of gravitational waves. This is a new idea and does not need other sentences for context. It does not use any pronouns or definite articles that refer to previous ideas. Why other lines are not chosen? Paragraph 2 starts with "Allan Adams" which is a specific name and needs context. Paragraph 3 starts with "His talk" which uses a pronoun. Paragraph 4 starts with "Before joining" which is a phrase that needs more context. Paragraph 5 starts with "His talk" which also uses a pronoun.

Concluding sentence: Why this is the last line? This paragraph is the last line because it wraps up the information about Allan Adams. It shows the impact of his work and concludes the discussion about gravitational waves.

Paragraph pairs:

• Pair 1 (Paragraph 1 → Paragraph 2): Paragraph 2 connects with Paragraph 1 because it uses the connector "this discovery". It talks about the same topic of gravitational waves and explains why it is important.
• Pair 2 (Paragraph 2 → Paragraph 3): Paragraph 3 connects with Paragraph 2 because it talks about Allan Adams. It gives more information about who he is, which is a logical flow from the previous sentence.
• Pair 3 (Paragraph 3 → Paragraph 4): Paragraph 4 connects with Paragraph 3 because it continues to talk about Allan Adams. It gives background information about his education, which is related to his role as a professor.
• Pair 4 (Paragraph 4 → Paragraph 5): Paragraph 5 connects with Paragraph 4 because it talks about Adams' talk. It shows the result of his work and education, linking back to the topic of gravitational waves.