Which firewall are you using?
The first dll seems legit, it's from Logitech Mouseware. But why it's being asked to connect by ashmaisv.exe?
The second, maybe you can google to find more info.
Seems that 'shared components' are trying to connect and, that time, the program that made the 'first' request was avast mail service, probably because you're downloading emails.
Oh, another question, did you change, recently, the Logitech drivers for your mouse?