Adopting some key ideas of the AdS/CFT correspondence, such as the geometrization of the RG formalism and having an AdS background spacetime, mappings of the 1D and 2D Ising model onto a network...Show moreAdopting some key ideas of the AdS/CFT correspondence, such as the geometrization of the RG formalism and having an AdS background spacetime, mappings of the 1D and 2D Ising model onto a network model were developed. The mappings primarily serve to engineer a 2D phase transition into a higher dimensional tree network and show what holographic properties are obtained by merely invoking some conceptual ’ingredients’ from the holographic duality. The networks were studied by MC simulation of the Ising model and subsequent construction. This thesis then further reports on efforts to describe the network ensemble seeded off the Ising model independently, by a(n) (exponential) random graph model.Show less
Many systems can be studied by representing them as multilayer networks. Multilayer networks are mathematical structures consisting of a set of objects with multiple kinds of possible relations...Show moreMany systems can be studied by representing them as multilayer networks. Multilayer networks are mathematical structures consisting of a set of objects with multiple kinds of possible relations between the objects. The study of various multilayer networks such as the network of international trade using statistical models with the assumption that the layers are independent leads to the observed overlap in the network being significantly different from the overlap predicted by the model. In an attempt to solve this issue we introduced interdependencies between the layers of a multilayer network in the model by explicitly including the overlap in our model. We then analytically derived the maximum likelihood equations for this model. Using numerical methods, we tested the validity of these obtained equations which proved to be highly accurate when compared to the numerical simulation data. Additionally, we have shown that the overlap of a network for a given number of links can be increased by either increasing the heterogeneity of the network or the value of the coupling parameter that we have introduced into the model. This allows us to create multiplexes with a specific amount of overlap for a given of number of links, given that it is within the theoretical limits. Finally, we conclude that the empirical overlap in the network of international trade is not merely a result of the correlation between the degrees of the different layers but requires a nonzero coupling between the layers in its modeling.Show less
This work examines the network structure of illicit marketplaces that operate on the darknet. These on-line marketplaces are crawled to obtain data of inter-user communications and this data is...Show moreThis work examines the network structure of illicit marketplaces that operate on the darknet. These on-line marketplaces are crawled to obtain data of inter-user communications and this data is parsed in a network structure and its physical properties are analysed. The Configuration Model is used as a null model to investigate the patterns in these networks to reveal information about their topology. This information is applied to interpret the behaviour of users within these illegal marketplaces.Show less
Financial market events can have a large impact in trading performance, but are difficult to classify in large datasets. This thesis presents a statistical method for finding financial market...Show moreFinancial market events can have a large impact in trading performance, but are difficult to classify in large datasets. This thesis presents a statistical method for finding financial market events using a maximum entropy model. A maximum entropy approach is presented to model an empirical matrix of daily stock returns while retaining its non-stationarity and heterogeneity. All speci cations of this maximum entropy model can be expressed in terms of the measurable properties of the matrix of daily stock returns. Closed form solutions of the expected moments, auto- and cross-correlations of the time series in the model, as well as the expected eigenvalue of the correlation matrix, are calculated. Using the maximum entropy model a method is constructed to detect financial market events. Here, a binary classifier is used based on the statistical significance of the empirical data calculated using the probability distribution function of the maximum entropy model. We find that the method is able to distinguish financial market events from non-events in historical data.Show less
In order to filter out unwanted noise or known factors from correlation matrices, we use maximum entropy models to generate spectra of correlation matrices, which we utilise for this purpose....Show moreIn order to filter out unwanted noise or known factors from correlation matrices, we use maximum entropy models to generate spectra of correlation matrices, which we utilise for this purpose. Furthermore, we relate them to widely used one-factor models justifying their use and presenting ways to relate the postulated one-factor models to empirical data. We improve further by adding signatures of sign projections of rectangular matrices and present a method to compare them to their corresponding weighted signatures. Finally, we make a small step towards a new definition of covariances that would filter out new types of noise.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
