Page Rank Let $G = (V, E)$ be a web graph. Each node $v \in V$ represents a web page, while there is a directed edge from $u \in V$ to $v \in V$ if $u$ has a hyperlink to $v$. The importance of $v$ is proportional to the importance of nodes linking to $v$. Let $\delta_\text{in}(v)$ and $\delta_\text{out}(v)$ be the in and out degrees of $v$ in $G$. Then we can define the matrix $M$ as follows:...

The problem For some time, I’ve had the premium subscription of Spotify and it has been great. However, often times there are songs that I wish I could listen to which are simply not available in Spotify’s library. Fortunately for us, Spotify has this nice feature where you can use its client to listen to local files. In other words, we can listen to music that is not available on Spotify by simply downloading and importing it....

Warning If the LaTeX below does not render correctly, please refresh the page. Also, do not forget to set the math renderer in MathJax configurations, as shown in the figure below. The configurations window can be accessed by right-clicking on any LaTeX element. Introduction Currently the exponential advance of technology is no longer a surprise, but rather an inherent characteristic of the modern world. Even though this evolution constantly enhances devices, it does not do so in a homogeneous way, creating a world where the distribution of computational power is asymmetric....