Mathematical methods for radio pulsar searching and applications

Since the dawn of civilization, mathematics has been a key tool that humans have used to try and understand the laws of nature and the world that surrounded them. The very first foundations of mathematics were laid by the ancient civilizations of Sumerians, Egyptians and Babylonias, which used mathematics as an instrument to quantify and describe their world. The Greeks further revolutionized this field, with Euclid and Pythagoras formalizing the mathematical thought into axioms and the- orems that are still valid today. A major cornerstone, which consecrated the role of mathematics for our understanding of the universe, was the development of the sci- entific method, with Galileo Galilei being one of its greatest representatives. Galileo’s empirical observations and innovative experiments laid the groundwork for modern physics. In particular, his use of the telescope to study celestial bodies, and his sub- sequent support for the heliocentric model, exemplified the power of mathematical precision and the scientific method in challenging long-held beliefs. Galileo’s legacy is a testament to the key role of mathematics in our ability to understand the universe, and is the foundation of the scientific research method that we currently use. The last few decades have witnessed yet another pivotal change in the way science is made: the technological revolution. The advent of computers, with their ability of doing computations extraordinarily fast, has opened up entire new possibilities that were simply inconceivable even just a few years ago. Besides allowing to numerically solve complex equations and non-linear systems that would have been impossible to solve otherwise, the exponential growth in the computing power has also led to the massive application of innovative techniques, such Artificial Intelligence algorithms, to all aspects of our lives, including science itself. In this PhD thesis, we will focus on the applications of mathematical algorithms in astrophysics, specifically those used to search for radio pulsar signals in radio astronomical data. These algorithms are notoriously computationally extremely expensive, so we will also discuss their implementation on modern high-performance-computing systems, as well as possible ways to improve their efficiency.