https://www.um.edu.mt/library/oar/handle/123456789/112401 2026-04-27T13:29:40Z 2026-04-27T13:29:40Z https://www.um.edu.mt/library/oar/handle/123456789/119998 2024-03-21T07:10:22Z 2023-01-01T00:00:00Z

Title: Identification of novel properties of metabolic systems through null-space analysis Abstract: Metabolic models provide a mathematical description of the complex network of biochemical reactions that sustain life. Among these, genome-scale models capture the entire metabolism of an organism, by encompassing all known biochemical reactions encoded by its genome. They are invaluable tools for exploring the metabolic potential of an organism, such as by predicting its response to different stimuli and identifying which reactions are essential for its survival. However, as the understanding of metabolism continues to grow, so too has the size and complexity of metabolic models, making the need for novel techniques that can simplify networks and extract specific features from them ever more important. This thesis addresses this challenge by leveraging the underlying structure of the network embodied by these models. Three different approaches are presented. Firstly, an algorithm that uses convex analysis techniques to decompose flux measurements into a set of fundamental flux pathways is developed and applied to a genome scale model of Campylobacter jejuni in order to investigate its absolute requirement for environmental oxygen. This approach aims to overcome the computational limitations associated with the traditional technique of elementary mode analysis. Secondly, a method that can reduce the size of models by removing redundancies is introduced. This method identifies alternative pathways that lead from the same start to end product and is useful for identifying systematic errors that arise from model construction and for revealing information about the network’s flexibility. Finally, a novel technique for relating metabolites based on relationships between their concentration changes, or alternatively their chemical similarity, is developed based on the invariant properties of the left null-space of the stoichiometry matrix. Although various methods for relating the composition of metabolites exist, this technique has the advantage of not requiring any information apart from the model’s structure and allowed for the development of an algorithm that can simplify models and their analysis by extracting pathways containing metabolites that have similar composition. Furthermore, a method that uses the left null-space to facilitate the identification of un-balanced reactions in models is also presented. Description: Ph.D.(Melit.)

2023-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/119419 2024-03-18T07:15:25Z 2023-01-01T00:00:00Z

Title: Feasibility and forbidden subgraphs Abstract: The topics of feasibility and forbidden subgraphs are two topics that are very well-known in the area of graph theory. This thesis aims to delve into both areas and continue to build on the results already proved, with a particular focus on the feasibility of line graphs. This thesis is sectioned into two main parts, where the first part consists of two chapters containing some basic definitions and results, as well as results on forbidden subgraphs. In the former, the definitions which will be used throughout the text are provided, as well as some basic results and concepts which are used in the theorems and examples that follow. The latter chapter consists of three parts, where the first part contains results on the forbidden subgraphs in extremal graph theory, while the second part mainly focuses on subdivisions and minors. In this part, several results are provided, most of which are also proved, such as the fact that both K5 and K3,3 are not planar, Kuratowski’s Theorem with a proof, as well as results on outerplanar graphs. The last part of this chapter introduces results on forbidden induced subgraphs. It incorporates results on the relation between chordal graphs and split graphs, results on forbidden subgraphs and line graphs, and finally, a note on Hamiltonicity, together with some theorems and conjectures related to this area, are also provided. The second part of the this thesis contains a chapter on feasibility, which essentially is the question of how many edges a graph on H vertices can have if it does not contain a forbidden induced subgraph or a family of such subgraphs. We focus in particular on the feasibility of H-free graphs, mainly paw-free graphs and H-free graphs where H is an extension of the paw graph, and conclude with a section on future work that can be done in this area of feasibility. The main results and observations in the paper Feasibility of Line Graphs, by Caro, Lauri & Zarb, which was the main inspiration behind this thesis, are presented and discussed in more detail. A technique used in this paper (the Universal Elimination Procedure construction) is complemented by a new construction (the Edge Elimination construction) to give further feasibility results, which are the main new findings of this thesis. These results are further explained with concrete examples. The last part of this thesis includes possible improvements on the results obtained in this study, as well as a conjecture on the feasibility of F-free graphs, where F is a family of at least two independent forbidden graphs. One of the independent forbidden graphs is proven to be feasible by the Universal Elimination Procedure construction, but not feasible by the Edge Elimination method, while the other graph can be solved by the Edge Elimination method but not by the Universal Elimination Procedure. Description: M.Sc.(Melit.)

2023-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/118101 2024-02-05T08:45:44Z 2023-01-01T00:00:00Z

Title: Reconstruction algorithms for electrical impedance mammography Abstract: Electrical impedance tomography (EIT) is a medical imaging method which aims to reconstruct internal electric properties, such as conductivity and permittivity, of an object from electrical measurements conducted on its boundary. Within this dissertation, we investigate the application of EIT for breast cancer detection. Initially, the focus of the work is to introduce the reader to the mathematical formulation of EIT and what makes its associated inverse problem, namely the inverse conductivity problem, both nonlinear and ill-posed. After the introductory chapters, an extension of a direct algorithm dependent on a linearized integral equation approach to the inverse conductivity problem in two dimensions is derived and tested numerically. The proposed algorithm is capable of simultaneously approximating both electrical conductivity and permittivity distributions either from single-time, time difference (tdEIT) and multiple times voltage measurements at different angular frequencies. Then, the design of a novel three-dimensional sensing head with a hemispherical geometry based on a brassiere is described. The proposed design is modelled in EIDORS and we present three-dimensional conductivity reconstructions of the interior of the hemispherical domain when it contains one or two inclusions with conductivities three times (or more) greater than the background, thereby simulating tumours in a human breast. We present novel expressions for the associated potential function related to Laplace’s equation in three dimensions, specifically, for a hemispherical domain. Two expressions for the potential function subject to two different idealized Neumann boundary conditions are obtained, first by a method which uses the Neumann Green’s function of the hemisphere and then by separation of variables. Both derived expressions are infinite series containing associated Legendre functions. A convergence analysis of the derived expressions is presented. One of the expressions is determined to be convergent in the interior of the domain but divergent on the hemispherical boundary whereas the other expression is determined to be convergent both within and on the domain. Finally, we derive a system of integral equations which, when solved, would provide an alternative approach of obtaining the three-dimensional potential function which solves the Laplace’s equation in a spherical domain. Description: M.Sc.(Melit.)

2023-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/112813 2023-09-01T09:51:19Z 2023-01-01T00:00:00Z

Title: Newton’s and quasi-Newton methods for minimising multi-variable functions Abstract: Newton’s method (also known as the Newton-Raphson method) is an optimisation method that can be used for obtaining the minimiser of objective functions. This method has superior convergence when compared to other optimisation techniques such as the method of steepest descent and the conjugate gradient method (provided the initial point is taken close to the minimiser). In this thesis, the Newton method is discussed in detail by looking at the implementation of this method to obtaining the minimiser of single variable as well as multi-variable functions. Some modifications of the method are also analysed. The applicability of this method to solving problems is exhibited through a novel application example. Some quasi-Newton methods namely, the rank-one correction, DFP and BFGS methods, are also considered in an attempt to remedy the drawbacks of Newton’s method. Algorithms implemented in MATLAB for all the methods discussed in this thesis can be found in the Appendix section of this dissertation. Description: B.Sc. (Hons)(Melit.)

2023-01-01T00:00:00Z