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I installed heartbeat on a new 7.8 site and enabled the "site activity" block on the home page. It shows fine for the admin but a visitor or another authenticated user gets this message:
PDOException: You cannot serialize or unserialize PDO instances in DrupalDatabaseCache->set() (line 418 of .../includes/cache.inc).
I have enabled the permissions to view the streams.
Enabling the useractivity block causes the same error for the same roles.