*21.10.2020*

## Backstreet’s back, Numerical Mathematics & Game Theory

The beginning of this month was mostly spent learning about the wonderful world of Numerical Mathematics in order to pass one of my last exams in my bachelor degree course, so I wasn’t really exploring new stuff (except all kinds of matrix decompositions) to share with you guys…

One very interesting concept I’ve learned about is an eigenvalue algorithm called power iteration. It’s a pretty straight forward way to calculate the (according to amount) biggest eigenvalue of a matrix. You can then use the Rayleigh quotient for getting the corresponding eigenvector. Shifting and/or inverting both, the matrix *and* its spectrum, in order to shake out the other eigenvalues and -vectors is known as inverse iteration and just continues being admirably simple.

I also felt a bit sick over the last few days (no Corona though, I guess), but I’m feeling a lot better today, so I’m back at doing some light studying. Today: Game theory! This paper seems like a pretty good (but very brief) introduction to me, although I was very confused at first by some of the notation used; some elements are given the same name as the sets they’re from?! One thing I found particularly interesting is that you can draw little arrows across each dimension of the table of a game in normal form and they always point into the direction of an equilibrium (cycles mean there is none)!

## Fail2ban & Free tips for intruders

While going through my log files, I just noticed there were automated attacks on this server all around the clock, so I decided to upgrade my security a bit:

I think installing and enabling Fail2ban is a good first measure and should stop the vanilla script kiddies from performing those attacks. I don’t think knowing about this new security measure will help anyone bypassing it without using disproportionately larger guns (Note for intruders: you’d have to distribute your simpleminded brute-force attack – see, I’m even cooperative!); they probably won’t even take the time to read all those free tips I’m giving here…

P.S.: As a result of trying out the new defense mechanism, I now have to wait a while before I can update this log. But it works!

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