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. Of course, using this feature has its own problems, like syncing the local files between your devices. I will not be discussing these issues here, though. ...

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. In this scenario, the ability to safely delegate hard computations to a powerful third party becomes very attractive. Studies in Verifiable Computation address this problem seeking to provide a series of important guarantees. The most important and intuitive one is that the verification must be easier than the computation of the function delegated (if this was not the case, the client should just perform the computation himself). Depending on the scheme implemented, other interesting qualities may be provided, such as public verification (in contrast, some settings may require a designated verifier that is trusted with secret information). ...