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Well, one way to partially prevent applications from running is to edit registry a bit.
This works only with applications started using Windows Explorer and only with specific filenames, hence partially ("Run" command from Start Menu and desktop are parts of Windows Explorer).
Go to HKEY_CURRENT_USER \ Software \ Microsoft \ Windows \ CurrentVersion \ Policies \ Explorer.
Create a key (if it doesn't exist) called DisallowRun.
Inside the key add string values of filenames you don't want Explorer to start.
As far as I know, this will then apply for every file regardless of its location, so if you for example add setup.exe there you won't be able to install many applications.