An asset and liability management model incorporating uncertainty

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Asset and Liability Management (ALIvI) is a well-established method, which enables companies to match future liabilities with future cash flow streams of assets. The first stage is to develop a deterministic model with forecast cash flow streams. In reality this can lead to results that are often volatile to deviations of future cash flows from their predicted values. There are two main stages to this problem. Firstly, there is the issue of representing the future uncertainties. To this end we have developed a scenario generator that forecasts alternative realizations of future cash flows streams of different assets using alternative scenarios about a financial Index and the Capital Asset Pricing Model (CAPM). Considering this with the deterministic model leads to the creation of ALM models which incorporate uncertainty. Having represented the uncertainty, we use an optimisation model to generate the current decisions concerning acquisition and disposal of assets. This model is a two stage stochastic programming model that aims to achieve targeted cash flows for each future year. Risk is represented in the form of assigning shares to different risk groups. In this thesis we describe our models of randomness and how they are captured in the two-stage stochastic programming model. We compare our model to a mean-variance representation. Both models are simulated through time. Backtesting is used to investigate the quality of both approaches

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit ($R_{ISCO}$), the rotation frequency $\Omega\equiv\frac{d\phi}{dt}$ and the epicyclic frequencies $\Omega_{\rho},\;\Omega_z$. Finally we present some results of the comparison.Comment: Contribution at the 13th Conference on Recent Developments in Gravity (NEB XIII), corrected typo in $M_4$ of eq. 5 of the published versio

Synthesis and characterization of organophosphazene and porous carbon materials for energy storage applications

The developments in energy storage systems in the last two decades, resulted in a series of interdependent events in consumer’s habits; the modern commercial devices became thinner, smaller and lighter with enhanced portability. Hence, the way in which users relate with electronic gadgets changed and this has derived in the invention of new applications. These developments within the electronic industry have demanded new materials and formulations in order to fulfil the growing requirements of new technologies and, especially in the last years, the electrification of transport. The need to pursue research to develop safe, environmental friendly, recyclable and low-cost materials is, in this context, a pressing issue. While hybrid materials offer unique properties for the development of advanced energy storage systems such as hydrogen and solar cells, lithium-ion batteries and capacitors, these are usually expensive and entail serious environmental hazards. This thesis advances scientific analyses on the cyclomatrix organophosphazenes synthesis that could be applied for the development of low-cost and eco-friendly industrial processes for the production of electrode materials. In Chapter 1, a brief introduction on the fundamental chemistry of phosphazene materials is presented followed by an outline description of the Li-ion batteries and dielectric materials and their current trends for the improvement of their efficiency. The research aim and objectives of this thesis are then presented. Chapter 2 deals with the synthesis of cyclomatrix organophosphazene (OPZ) nanospheres. The effects of the solvent, organic base, and organic co-monomer on the morphology of the nanoparticles are studied. The morphology of the nanospheres was highly dependent on the polarity of the solvent, pKa of the base and solubility of the produced salt during the reaction. A new design for the scale up synthesis of OPZs was developed based on distillation and reuse of the solvent and organic base. The dependence of the morphology on the polarity of the solvent is further investigated in detail in Chapter 3 where a self-template-direct formation of hollow OPZs is described. The presence of water in the reaction mixture promoted the formation of nanospheres with a single hole on their surface while the reactions at higher water contents resulted in the formation of hollow nanospheres and semi-shells. The subject of heteroatom-doped carbon nanospheres (CNS) as anode electrodes in Li-ion batteries is described in Chapter 4. A detailed analysis and discussion of the microporous structure and the heteroatom-doping carbon is presented in order to understand the structure-to-electrochemical properties of the CNS as anode materials. The ternary heteroatom doping had significant impact on the microporous structure of the CNS and their electrochemical performance. CNS with high pyridinic-N content and abundant micropores, showed impressive charge/discharge cycling stability for over 1100 cycles, delivering 130 mA h g−1. The facile OPZ chemistry is further applied in the presence of BaTiO3 nanoparticles in order to produce electron insulating OPZ@BaTiO3 and electron conducting C@BaTiO3 core-shell hybrid nanoparticles. The successful growth of OPZ as a thin layer/coating is based on the substrate-independency of the method. The morphology and structural characteristics of obtained core-shell particles is discussed in detail, along with the results from the impedance spectroscopy characterisation. A stable relative permittivity (εr ~ 35) and low dielectric loss over a wide range of frequency was achieved by adjusting the OPZ shell thickness. The initial insulating OPZ shell was transformed to e- conducting carbon shell, by a pyrolysis step at 700 °C and the resulted C@BaTiO3 showed a relatively high ac conductivity and specific surface area. The research outcome of this project together with suggestions for future directions are summarised in Chapter 6

Spectral mapping of brain functional connectivity from diffusion imaging.

Understanding the relationship between the dynamics of neural processes and the anatomical substrate of the brain is a central question in neuroscience. On the one hand, modern neuroimaging technologies, such as diffusion tensor imaging, can be used to construct structural graphs representing the architecture of white matter streamlines linking cortical and subcortical structures. On the other hand, temporal patterns of neural activity can be used to construct functional graphs representing temporal correlations between brain regions. Although some studies provide evidence that whole-brain functional connectivity is shaped by the underlying anatomy, the observed relationship between function and structure is weak, and the rules by which anatomy constrains brain dynamics remain elusive. In this article, we introduce a methodology to map the functional connectivity of a subject at rest from his or her structural graph. Using our methodology, we are able to systematically account for the role of structural walks in the formation of functional correlations. Furthermore, in our empirical evaluations, we observe that the eigenmodes of the mapped functional connectivity are associated with activity patterns associated with different cognitive systems