E.g. Matlab R2009a is shipped with Java version 1.6.0_04-b12. There have been a lot of very important bugfixes for Java since this version 6.04. I can update the Java version, but this has strange side-effects e.g. for GUI elements. And even the current Java version 7.10 is severely vulnerable.
Which security problems do I have to expect from Java under Matlab?
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My own ideas:
[EDITED, Jan] Sean's answer has disproved point 2: The builtin browser does not run Java applets. And calling Java directly from Matlab remains a security limitation.