In one of my recent stories I gave a little report about Taylor expansions and its applications. In order to approximate a function by a Taylor polynomial, we need to know its derivatives. Though, in many data-driven applications we do not even know explicitly the function itself. That is, often…

The mean value theorem belongs to one of the most used and important theorems in analysis. Its statement is very intuitive and moreover surprisingly easy to prove. In this story I quickly want to describe the main idea around this theorem and to consider some of its direct applications. The mean value theorem:

No doubt, the gradient is a mathematical construct with many applications to real-world problems. Among others, it is the core tool for some optimization techniques like the ‘steepest descent’. But also, it can be used to detect edges in images, or to describe the dynamics of a heat flow. In…

Working with the Artificial bee colony algorithm — Most techniques in AI resp. Machine Learning requires solving a continuous optimization problem. Typically this optimization problem is non-linear and cannot be solved by hand. There exists a huge literature about the kind of optimization problems and possible methods to solve them efficiently. The main distinction between these methods can…

An approach using a scientific computing example — In this short article, I want to present a useful approach when you need to implement a method and keep type restrictions as generic as possible. We are looking at a simple-to-implement example, the Euler method, to solve an ordinary differential equation. Before you shrug off, no knowledge of ordinary…

You might remember my swift overview I gave about some interesting results concerning chaotic behavior of the dynamics produced from the logistic map. In this article I want to proceed with this but by looking at it from a different angle, i.e. discovering a connection to the Cantor set that…

Simplifying asynchronous communication — In this short story, I want to provide a quick glance at how Tauri supports asynchronous communication between the front end and back end. Features like these are typically needed when the back-end informs the UI about changes like progress messages of a long-running task or changes of state that…

Overloading methods is a commonly used feature in many programming languages. Before turning to further details, let me mention early, in Rust there exists no exact ‘overloading’ of functions. But nevertheless, Rust makes available some techniques that are of upmost importance to avoid code replication and at the same time…