In an orchestra, there are three musicians: Akira, Takeshi, and Yumi. Each musician has a mentor who helps them refine their skills. Akira's mentor is Mr. Fujimoto and Takeshi's mentor is Mrs. Watanabe. Yumi, who plays the violin, shares the same mentor as Akira. Takeshi is known for his exceptional piano skills, and he has just composed a piece that requires both violin and piano, which he plans to perform with Yumi. Explain the relationships between the musicians and their mentors. What is the role of Yumi in Takeshi's new composition? Also, indicate which musical piece or pieces Mr. Fujimoto is linked with. Provide a brief response.
Akira is mentored by Mr. Fujimoto, indicating a mentor-mentee relationship in music. Takeshi's mentor is Mrs. Watanabe, forming another mentor-mentee pair. Yumi, being a violinist who also has Mr. Fujimoto as a mentor, has the same type of relationship with her mentor as Akira does with his.

For the new composition that Takeshi has created, it requires both violin and piano, and Yumi, being a violinist, will perform the violin part while Takeshi will perform on the piano. Thus, Yumi's role is to collaborate with Takeshi as a violinist in the musical piece.

Mr. Fujimoto is connected to the pieces that his mentees are involved in since he is mentoring them to refine their skills. As Mr. Fujimoto mentors Akira and Yumi, and considering Yumi's involvement with Takeshi's new composition for violin and piano, Mr. Fujimoto is linked with any solo piece Akira might be working on and the new composition which Yumi will perform alongside Takeshi.