In this research, a recently proposed renormalization group approach for networks to the case of random directed graphs is being generalized: we present a scale-invariant description of directed...Show moreIn this research, a recently proposed renormalization group approach for networks to the case of random directed graphs is being generalized: we present a scale-invariant description of directed networks containing reciprocated edges. This allows us to neglect several strong assumptions that are currently necessary to renormalize directed networks such as financial transaction networks. As an application, a model of ING’s transaction data has been derived across multiple coarse-grained partitions. In this article we provide detailed information on how this particular model has been structured and how its parameters are obtained. We show how we can use this model to determine the expected cumulative degree and weight distributions of ING’s transaction network across multiple coarse-grained partitions of the network which we will compare to the empirical degree and weight distributions, respectively.Show less
Many eukaryotic organisms exhibit patterns in their DNA code that facilitate the wrapping of DNA into nucleosomes. At the same time, nucleosomes have been found to affect both interspecies DNA...Show moreMany eukaryotic organisms exhibit patterns in their DNA code that facilitate the wrapping of DNA into nucleosomes. At the same time, nucleosomes have been found to affect both interspecies DNA sequence divergence and mutational patterns in many cancer types. In my thesis I will propose a simple model capable of qualitatively reproducing all these features in a simulation. The model consists of treating the DNA code as a dynamical variable, with each specific sequence representing a state of the system. The energy required to wrap this sequence into one or more nucleosomes is the energy associated with such a state. The behaviour of the DNA sequence can then be deduced using the laws of statistical mechanics. The model turned out capable of qualitatively reproducing experimental facts.Show less
Heavy Neutral Leptons are well-motivated candidates for explaining beyond Standard Model phenomena such as dark matter, baryon asymmetry of the Universe and neutrino oscillations. A variety of...Show moreHeavy Neutral Leptons are well-motivated candidates for explaining beyond Standard Model phenomena such as dark matter, baryon asymmetry of the Universe and neutrino oscillations. A variety of probes, ranging from collider-based to cosmological, explore regions of their parameter space in a complementary way. This work will delve into the possibility that Big Bang Nucleosynthesis has to offer in constraining their lifetime based on cosmological measurements of the Helium-4 abundance. Results are derived for masses up to 100 MeV and a framework is laid for extending the analysis to higher masses.Show less
The gross domestic product is no longer as widely accepted as an indicator of economical performance as it once was, so the search for a replacement or additional indicators has begun. It was shown...Show moreThe gross domestic product is no longer as widely accepted as an indicator of economical performance as it once was, so the search for a replacement or additional indicators has begun. It was shown by Hidalgo and Hausmann, and in later research by Pietronero and others, that the network of international trade carries intrinsical information about economical competitiveness. This idea is based on the observation that strong economies have diverse production capabilities. We have been able to reproduce their results. However, we found that in deciding what trade links are relevant for the analysis, the filter of choice (the revealed comparative advantage) is flawed, as it lacks any statistical justification. We have devised a way to choose only the relevant trade links, justified by Fermi-Dirac statistics through the application of the concept of entropy on the network. With this technique, we show that although the basic idea is still valid, the results by previous authors have to be revised. More importantly, with this new statistical information, we are able to provide countries with an advice on investment strategies for particular industries.Show less
