Check if rectangles fill a rectangular space without gaps or overlaps
Several people have hit around the solution, but haven't stated it clearly, so here it is:
Every app in OS X should be signed by the developer. This signature ensures that the contents of the application haven't been changed. The firewall verifies this signature as part of its process. When the signature verification process fails, you will receive this Allow/Deny error message every time you use the program, even if you click Allow on the dialog box.
Why is the signature verification failing? This can happen for several reasons, but primarily it is because somewhere along the line you've changed the contents of the /Applications/YourProblemApplication.app container. For example, if you use Monolingual or a similar app to remove other language files to save disk space, you've modified the contents of the app. If you've used a program like CandyBar or IconDubber to change the icon (.icns) file, you've also changed the contents of the app.
The easiest way to fix this problem is to delete the .app that is generating this error (be sure to empty the recycle bin). Reinstall the .app and this time, don't modify the contents.
BTW, the whole signature process can lead to plenty of errors in other applications, especially security conscious apps like VPNs. For example, my Cisco Unified Personal Communicator stopped working after running Monolingual (but would only generate deny errors in the Console log).
I used data from a publication but didn't cite it properly
It is hard to say from that description, but yes, that can qualify as academic dishonesty/misconduct and be grounds for removal from a program. That said, except in the most blatant and worst cases, programs, and universities, generally try and provide some other sort of punishment.
some publications in journals not of a good standard and he started accusing me of lying
I cannot see how publishing your work would be grounds for dismissal under any circumstances. Lying obviously can be related to academic misconduct and be grounds for dismissal.
got delayed in providing him with some research material and he plainly stated that he does not want to supervise me anymore.
Not meeting deadlines can be grounds for dismissal, but generally there is a procedure that most be followed. The fact that he does not want to supervise you anymore is probably the most problematic issue. Your program may require you to have a supervisor, if so, you will need to find a new supervisor.
It sounds like things are going poorly and a talk with the department chair (or head of graduate studies) is appropriate. If this is the first time you are talking to the department chair, then I highly doubt the conclusion of that meeting would be you being kicked out. The meeting might start the process of you being dismissed, but more likely, it will start the process of trying to improve your situation and resolve the issues.
As John Rennie wrote in his answer, what one should consider is not a generic $\Delta t$ but the period $\tau$ which is a positive number. However positivity also arises form coherence with other relations. In particular, in relativistic quantum mechanics $E= \sqrt{\hbar^2 \vec{k}^2 + m^2c^4}$. For $m=0$ you have $E= \hbar |\vec{k}| = \hbar \omega = h\nu$ where $\omega$ and $\nu =1/\tau$ are therefore supposed to be non negative. These numbers are trivially invariant under time reversal.