Stochastic trace estimation for newbies

In this post we are going to discuss an essetially important method for estimating the trace of the inverse matrix. Our target is to overview the stochastic approach for computation of the trace inverse of large sparse matrices.


Note: this paragraph will introduce some concepts of matrix calculations. It is in no way intended to explain everything that is going on, but rather just to convey some ideas to the reader that should help them understand the rest of the entry. 

The deadlock in climate policy and the science of extreme event attribution

Climate. It is among the most discussed topics of our days: from international policy making to public demonstrations, media outlets, and even elevator small talk. There is no lack of controversy and strong opinions when climate change is on the table, but that is not exactly surprising. When concrete actions must be taken, responsibility must be assigned; and it seems to be human nature that such discussions must be hard and tiring. Naturally, even more so when people's livelihoods are affected.

Symmetry and Physics: how to explain to my grandma what I do.


15th of August. National holiday in Italy. All my family meets together to celebrate. Break between the first and the second course. Frozen ready meals - my standard menu when I'm away - seem like a distant memory. It's a beautiful day, the birds sing in the trees, the sun is bright in the sky, everything is perfect when it happens:

"But, what do you do exactly?" 

Operator Splitting Methods

    Operator splitting is a powerful method for numerical investigation of complex models. The basic idea of the operator splitting methods based on splitting of complex problem into a sequence of simpler tasks, called split sub-problems. The sub operators are usually chosen with regard to different physical process. Then instead of the original problem, a sequence of sub-models is solved, which gives rise to a splitting error. In practice, splitting procedures are associated with different numerical methods for solving the sub-problems, which also causes a certain amount of error.

Machine Learning and Physics

Machine Learning - A very short introduction

Machine Learning (ML) is a particular branch of a very broad discipline called Artificial Intelligence (AI). Whereas AI tries to solve the fundamental problem of "creating" a sentient or intelligent being from a silicon-based machine, or anything you could define as artificial in general, the problem with ML is somehow simpler.

Turing machines, Memcomputing and High Performance Computing

Many of us have seen The Imitation Game, a movie describing the life of Alan Turing, considered the father of theoretical Computer Science. In 1936 Turing wrote an incredible piece of art: a paper titled On Computable Numbers, with an Application to the Entscheidungsproblem.