Customized Jupyter environments on Google Cloud

Kaggle docker images come with a huge list of pre-installed packages for machine-learning, including the support of GPU computing. They run within a container as a Jupyter application accessed by users through its web interface. Running a custom image boils down to these steps Below we can see how it looks like The following test …

Repairing user-managed notebooks on Google Cloud

In this note, I am sharing a case study on debugging and fixing jupyter-lab access issues. The diagnostic script can be run on a VM instance as shown below: Jupyter service runs from a container, but it somehow stopped in this case 😳 Not a problem! We can restart the container, but carefully choosing the …

Making SSH work by proxy

It is a popular misbelief that hiding encrypted connections (SSH) behind a proxy is a dark domain reserved to crime activities. You may need a Russian or Iranian proxy to get your coding job done, when firewalls of your favourite coffee place or wifi in travel forbid the use of SSH. As this happens to …

Free and robust Tweets extraction

As anticipated by many, Twitter stopped offering its (limited!) API for free ​1​. Now, what options do you have to programmatically access the public content for free?In this context, it is worth mentioning the library snscrape, a tool (well-maintained as of now) for extracting the content from social media services such as Facebook, Instagram or …

Fourier integrals vanishing on large circles

When evaluating contour integrals, it is often of interest to prove that Fourier-type integrals vanish on large enough semicircles (see the figure). This holds under the following condition: Theorem. Suppose that $$f(z)=O(|z|^{-a}), \quad a>0$$ for in the upper half-plane. Then for any \(\lambda > 0\) we have $$\int_{\gamma_R} f(z)\mathrm{e}^{i\lambda z} \rightarrow 0, \quad R\to+\infty,$$ where …

Expanding Inverse Functions

The problem of inverting the implicit function $$y=f(x)$$ in the form of power-series $$x = a + \sum_{k=1}^{\infty} b_k (y-f(a))^k$$ around a point of interest $x=a$, has a long history. Lagrange obtained a theoretical inversion formula ((https://mathworld.wolfram.com/LagrangeInversionTheorem.html)), yet efficient implementations are relatively recent ((Brent, Richard P., and Hsiang T. Kung. “Fast algorithms for manipulating formal …