San Francisco—Twitter Inc. is rolling out a new notification service that sends direct-message recommendations to users' smartphones about interesting tweets and Twitter accounts they may want to follow. Twitter users will begin seeing personalized recommendations on their phones when multiple people in their Twitter networks follow the same user or favorite, or retweet the same tweet, Twitter said on its blog. The service is intended to make Twitter more relevant to users by finding activity that is drawing the attention of the people they follow. The service is available on iPhones and Android-powered phones. Twitter users can turn off the message notifications at any time, the company said.