Which companies have maintained or increased their rate of innovation after they were acquired? 

Several companies have maintained or even increased their rate of innovation after being acquired. Here are a few notable examples:

1. **YouTube (Acquired by Google)**: Google acquired YouTube in 2006, and since then, YouTube has continued to innovate and expand its platform significantly. Under Google's ownership, YouTube has introduced features such as live streaming, VR videos, 360-degree videos, and various monetization options for creators.

2. **Instagram (Acquired by Facebook)**: Facebook acquired Instagram in 2012, and despite initial concerns about the acquisition stifling innovation, Instagram has continued to innovate and grow rapidly. Features such as Instagram Stories, IGTV, Reels, and shopping integrations have been introduced post-acquisition, contributing to the platform's success.

3. **GitHub (Acquired by Microsoft)**: Microsoft's acquisition of GitHub in 2018 was met with some skepticism, but GitHub has maintained its position as the leading platform for software development collaboration and version control. Under Microsoft's ownership, GitHub has introduced new features such as Actions, Packages, and Codespaces, while continuing to support a vibrant open-source community.

4. **Pixar (Acquired by Disney)**: Disney acquired Pixar in 2006, but allowed it to operate as a separate entity. Pixar has continued to produce groundbreaking animated films and maintain its reputation for innovation in storytelling, animation technology, and visual effects.

5. **WhatsApp (Acquired by Facebook)**: Facebook acquired WhatsApp in 2014, and despite concerns about privacy and independence, WhatsApp has continued to innovate in the messaging space. Features such as end-to-end encryption, voice calling, video calling, and WhatsApp Business have been introduced post-acquisition.

These examples demonstrate that, under the right circumstances and with proper management, companies can maintain or even enhance their rate of innovation after being acquired.