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Internet Traffic Do you have any idea how much internet traffic (volume) you need? How much do you download / upload on a usual day? I didn't have any idea, so I started recording it. In this article I will show you the results. For the context: A couple of internet providers ... Read More »

Sommerakademie Greifswald Eine Sommerakademie ist eine Veranstaltung der Studienstiftung des deutschen Volkes, bei der einige Dutzend Stipendiaten zusammenkommen und knapp zwei Wochen mit einander verbringen. Es gibt Kurse und Abendvorträge zu welchen man kommen muss, sowie einiges an Freizeitprogramm das durch die Stipendiaten organisiert wird. Sommerakademien sind eine wunderbare Möglichkeit ... Read More »

Diverging Gradient Descent When you take the function $$f(x, y) = 3x^2 + 3y^2 + 2xy$$ and start gradient descent at \(x_0 = (6, 6)\) with learning rate \(\eta = \frac{1}{2}\) it diverges. Gradient descent Gradient descent is an optimization rule which starts at a point \(x_0\) and then applies the update rule ...if (!document.getElementById('mathjaxscript_pelican_#%@#$@#')) { var align = "center", indent = "0em", linebreak = "false"; if (false) { align = (screen.width Read More »

XOR tutorial with TensorFlow The XOR-Problem is a classification problem, where you only have four data points with two features. The training set and the test set are exactly the same in this problem. So the interesting question is only if the model is able to find a decision boundary which classifies all four ... Read More »

Estimating Demand I've just had the problem that I'm helping to plan a group event, where the participants should all have bikes. There are 170 participants and 80 bikes. Some of the participants might be able to bring their own bikes. So we asked them to tell us who can ... Read More »

Optimization Basics Optimization is a subfield of mathematics / computer science which deals with finding the best solution. Typically, problems in optimization are stated like this: $$ \begin{align} &\underset{x}{\operatorname{minimize}}& & f(x) \\ &\operatorname{subject\;to} & &g_i(x) \leq 0, \quad i = 1,\dots,m \\ &&&h_i(x) = 0, \quad i = 1, \dots,p \end{align} $$ ...if (!document.getElementById('mathjaxscript_pelican_#%@#$@#')) { var align = "center", indent = "0em", linebreak = "false"; if (false) { align = (screen.width Read More »

Pythons map, reduce and filter as list comprehensions I recently was challenged to re-write Pythons map, reduce and filter as list comprehensions. Examples First of all, I want to make sure you understand what those functions do. You might also want to have a look at my old article Functional Programming in Python. map numbers = list(range(10 ... Read More »

Linear Classification In classification problems you have data points \(x \in \mathbb{R}^m\) which you want to classify into one of \(k \in \mathbb{N}_{\geq 2}\) classes. This is a supervised task. This means you have \(n\) data points for training in a matrix \(X \in \mathbb{R}^{n \times m}\) ...if (!document.getElementById('mathjaxscript_pelican_#%@#$@#')) { var align = "center", indent = "0em", linebreak = "false"; if (false) { align = (screen.width Read More »

Kalman Filter The Kalman Filter is an algorithm which helps to find a good state estimation in the presence of time series data which is uncertain. For example, when you want to track your current position, you can use GPS. However, GPS is not totally accurate as you know if you ever ... Read More »

Thoughts about Language Language is a method of communication. It is used to transport information from one individuals brain to another brain. I'm not entirely sure about it, but I think every language which is wide-spread might be complete in a sense that once you know every word of the language you ... Read More »