adding new math part and result with dot product

[jisungyoon]

I just added a new math part without symmetry condition and relaxation cosine similarity to dot product.

And, @murrayds adds the result with dot product.

[murrayds]

Looks good! I also committed my changes throughout the draft.

I added new figures but didn't know where you wanted to include those that are relevant to the math. These figures include,

• dot product correlated with Cosine Similarity
• dot product correlated with and predicts flow
• Network visualization of the mobility network

When responding to Stasa's comments, I added text to the supporting materials so as to preserve the main structure of the current manuscript. These texts are definitely in need of editing,

• Additional motivation concerning the importance of mobility
• Explanation of mobility, how it can be defined, and what specific choices we made when defining mobility
• More detail and examples of how mobility trajectories were formed

I also made minor changes throughout the manuscript, fixing broken links and editing text where applicable. The only major changes were:

• Adjusting early text on embeddings and all SemAXis text to stress the linguistic properties of the organizational embeddings
• Added references to the new supporting materials

[murrayds]

Also please look over my changes