No description available.

In this thesis we will consider two mathematical models on malaria transmission and patho- genesis. The transmission model is a human-mosquito interaction model that describes the development of malaria in a human population. It accounts for the various phases of the disease in humans and mosquitoes, together with treatment of both sick and partially im- mune humans. The partially immune humans (termed asymptomatic) have recovered from the worst of the symptoms, but can still transmit the disease. We will present a mathematical model consisting of a system of ordinary differential equations that describes the evolution of humans and mosquitoes in a range of malarial states. A new feature, in what turns out to be a key class, is the consideration of reinfected asymptomatic humans. The analysis will include establishment of the basic reproduction number, R0, and asymptotic analysis to draw out the major timescale of events in the process of malaria becoming non-endemic to endemic in a region following introduction of a few infected mosquitoes. We will study the model to ascertain possible time scale in which intervention programmes may yield better results. We will also show through our analysis of the model some evidence of disease control and possible eradication. The model on malaria pathogenesis describes the evolution of the disease in the human host. We model the effect of immune response on the interaction between malaria parasites and erythrocytes with a system of delay differential equations in which there is time lag between the advent of malaria merozoites in the blood and the training of adaptive immune cells. We will study the model to ascertain whether or not a single successful bite of an infected mosquito would result in death in the absence of innate and adaptive immune response. Stability analysis will be carried out on the parasite free state in both the immune and non immune cases. We will also do numerical simulations on the model to track the development of adaptive immunity and use asymptotic methods, assuming a small delay to study the evolution of the disease in a naive individual following the injection of small amount of merozoites into the blood stream. The effect of different levels of innate immune response to the pathogenesis of the disease will be considered in the simulations to elicit a possible immune level that can serve as a guide to producing a vaccine with high efficacy level.

Rainfall data are usually gathered at daily timescales due to the availability of daily rain-gauges throughout the world. However, rainfall data at fine timescale are required for certain hydrologic modellings such as crop simulation modelling, erosion modelling etc. Limited availability of such data leads to the option of daily rainfall disaggregation. This research investigates the use of a stochastic rainfall disaggregation model on a regional basis to disaggregate daily rainfall into any desired fine timescale in the State of Queensland, Australia. With the incorporation of seasonality into the variance relationship and capping of the fine timescale maximum intensities, the model was found to be a useful tool for disaggregating daily rainfall in the regions of Queensland. The degree of model complexity in terms of binary chain parameter calibration was also reduced by using only three parameters for Queensland. The resulting rainfall Intensity-Frequency-Duration (IFD) curves better predicted the intensities at fine timescale durations compared with the existing Australian Rainfall and Runoff (ARR) approach. The model has also been linked to the SILO Data Drill synthetic data to disaggregate daily rainfall at sites where limited or no fine timescale observed data are available. This research has analysed the fine timescale rainfall properties at various sites in Queensland and established sufficient confidence in using the model for Queensland.

Coastal wetlands are globally important environments for biogeochemical cycling and are the object of intensive research related to the sequestration and exchange of carbon with oceans, continents, and the atmosphere. Wetland soil core records of organic carbon (OC) provide insights about future ecosystem responses to global change by identifying temporal variability in the context of environmental changes including sea level rise (SLR), anthropogenic reductions in freshwater flow, and landscape-scale disturbance events. My studies of Gulf of Mexico mangroves involved the use of radiometrically-dated soil cores to identify spatial and temporal accumulation trends of various constituents including organic and carbonate carbon, and macro-nutrients. My dissertation includes a literature review to assess the timescales of these processes and refine global perspectives on coastal wetland vulnerability. The contributions of organic and mineral matter to soil accretion (mm yr-1) was measured to (a) quantify how the supply of each may allow regional mangroves to keep pace with various SLR scenarios and, (b) assess wetland carbon sink capacity and stability in southwest Florida and the Yucatan Peninsula of Mexico. Mangroves in this region are largely devoid of terrigenous mineral sediments, and it has been hypothesized that storm surge-driven accretion of marine sediments could improve the capability of these locations to keep pace with SLR. Rates of accretion and organic matter accumulation were statistically similar across all four study regions, whereas mineral deposition rates ranged over two orders of magnitude. The volumetric contribution of mineral sediment to accretion is minimized by its high density. Organic matter, whose porous structures allow for highly variable densities, can contribute to a wide range of accretion rates and is a strong predictor of accretion. Future sustainability of these wetlands is more strongly dependent on the balance between soil organic matter production and preservation than the provision of storm-derived mineral sediments. To understand how OC sequestration will respond to SLR, the spatial and temporal variability of OC burial rates (g m-2 yr-1) were examined across ecosystem gradients in salinity, nutrient availability and mangrove productivity in the coastal Everglades. Results showed relatively little spatial variability and indicated that OC burial in the region is slow compared to rates in mangroves globally. However, significant regional differences in OC burial were observed in the context of primary productivity. Over a centennial timescale, mid-stream sites sequestered roughly 22% of annual net primary production and upstream sites preserved less than 10%. Least efficient sequestration occurs in the oligohaline ecotone, where increases in groundwater salinities and the potential for sulfate reduction have been recorded in the past decade. These findings indicate a significant slowdown in OC burial, and suggest that accelerating SLR will cause a substantial loss of historically sequestered carbon. The loss and potential out-welling of this carbon (including particulate and dissolved organic matter, dissolved CO2, and carbonate alkalinity) has important and complex implications for neighboring marine ecosystems including coral reefs and seagrass meadows. Several recent high-profile publications have used 5–15 years of soil accumulation rates to model wetland SLR-vulnerability outcomes over the next 50–100 years. To provide perspectives on these models, data that were generated from observations on multiple timescales (sub-annual to millennial) around the globe were used in a meta-analysis to determine the role of observational timescale on assessment outcomes. This analysis focused on rates of accretion and elevation change because of the wide availability of these data. Results demonstrate that rates of soil-body change exhibit a dependence on the length of time over which observations are made. Timescale hierarchies are driven by post-depositional diagenesis, ecosystem state changes, and regional effects primarily related to hydrology and sediment supply. Longer periods of observation utilizing multiple geochronological methods are needed to differentiate trend-changes from apparent changes that, in fact, may be due to regular periodicity. A conceptual model is presented that categorizes and explains timescale hierarchies in a soil’s geochemical history.

In this thesis, I present two methods of fast variable elimination in stochastic systems. Their application to models of population dynamics from ecology, epidemiology and population genetics, is explored. In each application, care is taken to develop the models at the microscale, in terms of interactions between individuals. Such an approach leads to well-defined stochastic systems for finite population sizes. These systems are then approximated at the mesoscale, and expressed as stochastic differential equations. It is in this setting the elimination techniques are developed. In each model a deterministically stable state is assumed to exist, about which the system is linearised. The eigenvalues of the system's Jacobian are used to identify the existence of a separation of timescales. The fast and slow directions are then given locally by the associated eigenvectors. These are used as approximations for the fast and slow directions in the full non-linear system. The general aim is then to remove these fast degrees of freedom and thus arrive at an approximate, reduced-variable description of the dynamics on a slow subspace of the full system. In the first of the methods introduced, the conditioning method, the noise of the system is constrained so that it cannot leave the slow subspace. The technique is applied to an ecological model and a susceptible-exposed-infectious-recovered epidemiological model, in both instances providing a reduced system which preserves the behaviour of the full model to high precision. The second method is referred to as the projection matrix method. It isolates the components of the noise on the slow subspace to provide its reduced description. The method is applied to a generalised Moran model of population genetics on islands, between which there is migration. The model is successfully reduced from a system in as many variables as there are islands, to an effective description in a single variable. The same methodology is later applied to the Lotka-Volterra competition model, which is found under certain conditions to behave as a Moran model. In both cases the agreement between the reduced system and stochastic simulations of the full model is excellent. It is stressed that the ideas behind both the conditioning and projection matrix methods are simple, their application systematic, and the results in very good agreement with simulations for a range of parameter values. When the methods are compared however, the projection matrix method is found in general to provide better results.

The aggregation of amyloid-beta by self-assembly into oligomers or amyloids is a central event in Alzheimer’s disease. In this dissertation, I propose a mathematical model as a set of coupled kinetic equations that governs the self-assembly of amyloid-beta filaments in the presence of transition-metal ions. Metal ions have been hypothesized as an important factor in the pathogenesis of AD. There is a considerable literature supporting the impact of metal ions such as copper (Cu), zinc (Zn) and iron (Fe) in many critical aspects of AD and other neurodegenerative diseases. Our study includes Cu and Zn as main transition-metal ions, where their coordination to amyloid-beta regulates the aggregation process in vivo. Metal ions mostly affect the nucleation phase and change both the structure and the charge of amyloid-beta. Our model describes the general features of the kinetics of fragmenting filamentous structures. The numerical simulations reveal a four timescale dynamics related to three important events, which are the formation of the amyloid-metal, the homogeneous aggregation of the filaments and the non-homogeneous aggregation of the protein-metal. The method of singular perturbation is used to discern between these timescales. These results are studied in the framework of slowast systems. We also compare the metal with the non-metal dynamics and apply optimization theory for realistic values of reaction rates. Simulations shows that in certain cases the presence of metal accelerates the aggregation of filaments in a drastic way.

Evolution geography takes a systems approach to the study of evolution. The interconnected systems include: the gravitational and thermodynamic solar system in which the Earth was formed and resides; the cosmic, solar, electrical, chemical, radioactive and thermal energy flows of Earth; the Earth’s ever-changing biogeochemistry; the dynamic geography of the Earth (deep space); the energy gradients of living matter, which have reciprocally shaped and been shaped by their physical environment for at least 3400 million years (“deep time”); and hominid cultures and civilizations and their ramifications for the Earth's surface over at least the last 60,000 years. We humans are largely unaware of our place or time of evolutionary appearance on Earth. We have had a growing impact on Earth over the last seven centuries. Our over-reliance on reductionism affects the search for knowledge, proliferates and distorts worldviews extrapolated from within narrow disciplines, stifles debate and suppresses novel hypotheses. Data must be mapped into history and context where it can be challenged by other fields, be seen in the context of the evolution of the dynamical Earth system (Gaia). Can humanity trust any worldview to be the basis of good judgment absent the context of Gaia? The evidence is obvious and overwhelming that the answer is “no”.

This research focuses on advancing our understanding of flame stability in supersonic non-premixed flames by employing experimental data to develop a flame stability correlation parameter (SCP). Experimental data were acquired from a generalized supersonic cavity flameholder combustor equipped with converging-diverging (CD) nozzles, generating Mach 1.8-3 flow at the combustor inlet. The study encompassed both upstream and direct cavity fuel injection methods, considering diverse flameholder geometries, including axisymmetric and rectangular configurations, and utilizing ethylene and propane fuels. To address the flame stability challenge, the critical physical parameters impacting SCP were systematically identified, categorizing them into two distinct domains: the flow timescale and the chemical timescale, delineated by the Damköhler number. Flow timescale parameters were assessed by modifying flow rate to account for compressibility effects. These parameters were found to be significantly influenced by density variations attributed to high-speed aerodynamics. Pressure increases and velocity reductions at the flame shear layer were observed, arising from cavity geometry, upstream fuel jet dynamics, and flame presence. As the Mach number increased or pressure decreased, the flow timescale exhibited a proportional increase. The chemical timescale parameters were investigated through similarity, showing sensitivity to thermal diffusivity, flame speed, and flame shear layer thickness. These were further deconstructed into physical parameters such as pressure and temperature. It was observed that the chemical timescale decreased with rising temperature and pressure. Empirical relationships were derived for both flow and chemical timescales, enabling the consolidation of flame stability data onto a unified curve. This research significantly advances the understanding of flame stability mechanisms in supersonic combustion. All data was generously provided by the Air Force Research Lab (AFRL).

Electrical activity is omnipresent throughout the brain, and it varies dependant on the brain region. Areal hierarchy has been suggested to be one of the main principles of the organization of the brain, but there is not a lot of evidence available related to the specialization of the brain’s regions in the temporal domain, that is, how the activity evolves over time. It has been suggested that there is a relationship between spatial location and timescale [1] and that the timescales of neuronal activity in rodents change according to the hierarchical position (derived from anatomical connectivity measurements) of the brain region [2]. Timescale is related to to the capability of a neuron to maintain the same firing rate over a time period. This firing rate can be measured as decay time constant of an auto-correlation matrix of spiking activity, referred to as the timescale of a single neuron [3]. In this thesis, timescales of spontaneous brain activity were measured in eight regions of the mouse prefrontal cortex (PFC) (data obtained in the Carlén Laboratory) and compared to the timescales of eight visual areas (Neuropixels Visual Coding dataset, Allen Institute for Brain Science) [4]. The results showed that cortical regions hold varying timescales, but that there is no clear correspondence of the timescales of spontaneous activity to the anatomical hierarchies. Instead, we show that the PFC regions have a greater variability in their respective timescales compared to visual cortical regions. The analysis was done using two different approaches, where for some regions the measured timescales significantly differs, due to the difference in the use of the magnitudes of the correlation. This work highlights how neuronal timescales measurements can be approached in cortical regions and used for the future work investigating their functional role and the mechanisms of generation of distinct neuronal timescales in the brain. / Elektrisk aktivitet är allestädes närvarande i hela hjärnan, och den varierar beroende på hjärnregionen. Arealhierarki har föreslagits vara en av huvudprinciperna för hjärnans organisation, men det finns inte mycket bevis tillgängligt relaterat till specialiseringen av hjärnans regioner i den temporala domänen, det vill säga hur aktiviteten utvecklas över tiden . Det har föreslagits att det finns ett samband mellan rumslig plats och tidsskala [1] och att tidsskalorna för neuronal aktivitet hos gnagare ändras beroende på den hierarkiska positionen (härledd från anatomiska anslutningsmätningar) i hjärnregionen [2]. Tidsskala är relaterat till förmågan hos ett neuron att bibehålla samma fyrningshastighet under en tidsperiod. Denna avfyrningshastighet kan mätas som fallstidskonstant för en autokorrelationsmatris av spikaktivitet, kallad tidsskalan för en enda neuron [3]. I denna avhandling mättes tidsskalor för spontan hjärnaktivitet i åtta regioner i musens prefrontala kortex (PFC) (data erhållen av Carlén Laboratory) och jämfört med tidsskalorna för åtta visuella områden (Neuropixels Visual Coding dataset, Allen Institute for Brain Science) [4]. Resultaten visade att kortikala regioner har olika tidsskalor, men att det inte finns någon tydlig överensstämmelse mellan tidsskalorna för spontan aktivitet med de anatomiska hierarkierna. Istället visar vi att PFC-regionerna har större variation i sina respektive tidsskalor jämfört med visuella kortikala regioner. Analysen gjordes med hjälp av två olika tillvägagångssätt, där de uppmätta tidsskalorna för vissa regioner skiljer sig avsevärt på grund av skillnaden i användning av storleken på korrelationen. Detta arbete belyser hur neuronala tidsskalemätningar kan beaktas i kortikala regioner och användas för det framtida arbetet med att undersöka deras funktionella roll och mekanismerna för generering av distinkta neuronala tidsskalor i hjärnan.

The objectives of the thesis - which comprises six parts – can be summarized in i) implementing linear and nonlinear/nonparametric approaches toward detecting, measuring and analyzing the nature and directionality of causal relationships in financial markets, ii) elaborating on modern topics in financial investment analysis, iii) probing into the role of commodity futures in constructing optimal portfolios as well as iv) investigating growth dynamics via aggregated and disaggregated indices. The first paper named “Analyzing causal interactions between sectoral equity returns and commodity futures returns in the aftermath of the global financial crisis: The case of the US and EU equity returns”, aims to explore and compare the dependence and co-movement structure between commodity and various asset classes’ returns including the USA and EU stock markets via the use of linear and non-linear causality testing in a comparative context with the additional adjustment for cointegration and conditional heteroscedasticity. The findings provide important implications for optimal asset allocation and portfolio diversification with respect to various market conditions, namely both in “good” and “bad” (crisis) times. The second paper is entitled “On the time scale behaviour of Equity-Commodity links: Implications for Portfolio Management”, and has been published in the Journal of International Financial Markets, Institutions and Money (2016). The study is co-authored with Professors S. Bekiros, D.K. Nguyen, and B. Sjö. It develops a holistic framework for the investigation of the multi-horizon and intra-frequency causal directionalities of various asset classes, by means of multi-resolution analysis. The results verify the assumption that financial markets exhibit time-varying co-movement patterns, which are fundamentally important in a) generating profitable trading strategies according to different investor horizon expectations and b) decoding the financialization mechanism across various asset classes. The third paper entitled “Business Cycle (de) Synchronization in the aftermath of the Global Financial Crisis: Implications for the Euro Area”, was published at Studies in Nonlinear Dynamics and Econometrics (2015) and is co-authored with S. Bekiros, D.K Nguyen and B. Sjö. In this work, the scale-dependent time-varying (de)synchronization effects between the Eurozone and the broad Euro area business cycles are revealed, before and after the global financial crisis. The results, which point towards an increased observed comovement during the crisis period for the Euro area, could be catalytic for the introduction of a more efficient monetary policy by EU institutions and in particular by the European Central Bank. In the fourth paper, “Do financial stress and policy uncertainty have an impact on the energy and metals markets? A quantile regression approach”, which was published in the International Review of Economics and Finance (2016) and co-authored with J.C. Reboredo, the financial and policy uncertainty is investigated in relation to the price dynamics of energy and metal commodity futures’ markets. This work lead to the analysis of the asymmetric interrelationships with respect to changes in the perceptions of various risk measures, covering various periods, i.e., “normal” vs. “turbulent” such as upward or downward market episodes. The fifth paper, co-authored with P. Andreasson, S. Bekiros and D.K. Nguyen, is entitled “The impact of speculation and economic uncertainty on commodity markets”, and is published in the International Review of Financial Analysis (2016). This paper attempts a novel methodological approach to measuring speculation in commodity markets, in particular whether market speculation drives agricultural commodity prices or viceversa. The assessment of the empirical analysis demonstrates that agricultural prices are not affected by speculation. Finally, the sixth paper “Energy and Output Dynamics in Bangladesh”, co-authored with B.P. Paul, was published in Energy Economics (2011) and explores the relationship between energy utilization and economic growth in Bangladesh. Specifically, it deals with the important issue of whether energy consumption can be reduced without affecting economic growth while at the same time implicitly may lead to poverty reduction. The findings substantiate the fact that a) energy usage has become more efficient in recent times, as well as indicate that b) fluctuations in energy consumption did not have a significant impact on economic output.