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## e - like everywhere

Everybody doing any kind of geometry, calculus or higher algebra will have stumbled over this number:

2.71828182845904523536028747135266249775724709369995...

More commonly it is known as $e$ , Euler's number. You may wonder, where does this number come from and why is it so important? Well... If you are like me that is: waiting for simulations to finish, having 20 minutes of spare time on your hands, and having a tenacious drive to understand things. So come along as I explain two different ways that result explain where this beautiful number comes from.

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## Workaround MATLAB's intellisense/auto-complete issues for user defined classes

This will be a short post, but a little wakeup call for myself, and others that may get annoyed by the same issue. The issue at hand is, that MATLAB does not seem to have fully functioning intellisense/auto-complete when dealing with a class definition that spans over multiple files. Let me elaborate...

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## Python and DLLs (applied to OpenDSS)

It has been a very long time since I programmed using a Dynamic Linked Library (DLL). Last time I remember was during my 3rd year for our master project to interface the xbox Kinect to our semi-autonomous drone; good old days... For my PhD we need to interface our developed energy management algorithms with a standardized simulation environment. The one we chose is OpenDSS (link), and as it seems it comes with a so called "Direct Connection Shared Library (DLL) for OpenDSS"! This far, every time we wanted to interface with OpenDSS, we had to fully install OpenDSS on our target machines in the HTCluster and let our code interface to the simulation engine via the registered COM server. Now we can achieve the same without installing OpenDSS by simply including the relevant DLLs alongside our Python code! This post addresses (and in the future will remind me) how this is done, and how some traps and errors can be prevented and fixed.

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## Independent Component Alanysis

I am trying to get my head around, and fully understand and implement, Independent Component Analysis (ICA) for my power profile analysis. Doing this is more challenging than I anticipated. Therefore I did what I always do when trying to understand challenging topics: find them in my mother tongue, i.e. German. Some of my colleagues would happily vouch for the unambiguousness of a native language when it comes, and for me this is no exception (after all, that's how I managed to truly understand Maxwell in my 2nd year). So here I go again, and found a great article written in 2005 by Dr Christoph Bergmeir during his time at the faculty of Engineering, Informatics and Psychology at Ulm University (link). His article is extremely well versed (but that may be due to the preciseness of the German language 😛 ), it covers basic stochastic fundamentals based on information theory, it highlights requirements and limitations of ICA, and it also gives well explained examples (which I hope to replicate and include in this post). By reading the article and coding it up, I finally delved beyond my superficial understanding of ICA and am extremely happy to translate the article, both for my benefit, as well as that of others. Enjoy...

Big credit goes to Dr Christoph Bergmeir, many thanks!

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## My attempt at understanding information estimation using k-nearest-neighbours

During my undergraduate studies we studied a module covering information theory. It was incredibly abstract, but very relevant and interesting. Unfortunateky, this far in my degree I have not yet found any application for this knowledge. That was until my good friends and colleagues in our Brain Embodiment Laboratory (BEL) decided to share one of their information theory issues. The question was; how one can obtain, or at least estimate, the mutual information (MI) shared between two signals using a k-nearest-neighbour (kNN) algorithm. Now this may seem absurd, but after having had that chat an extraordinary motivation to refresh my memory was sparked! Mainly because it is an incredibly interesting and challenging problem, but also because I have the strong suspicion the answer will be of huge help for my Bayesian probability scheduling issue that I got stuck on last week.

So, here is my take at making sense of information theory to explain why the link between kNN and MI exists. And as a warning, there will be equations, but I will do my best to talk around them (in the case you won't read them).

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