Heating the Early Universe : Numerical Methods and Their Analysis

During the epoch when the first collapsed structures formed (6<z<50) our Universe went through an extended period of changes. Some of the radiation from the first stars and accreting black holes in those structures escaped and changed the state of the Intergalactic Medium (IGM). The era of this global phase change in which the state of the IGM was transformed from cold and neutral to warm and ionized, is called the Epoch of Reionization.In this thesis we focus on numerical methods to calculate the effects of this escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-Ray. We find that although this code efficiently and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to improve the code. The first element, an adaptive time step algorithm, quickly determines an optimal time step by only considering the computational cells relevant for this determination. The second element, asynchronous evolution, allows different cells to evolve with different time steps. An important constituent of methods to calculate the effects of ionizing radiation is the transport of photons through the computational domain or ``ray-tracing''. We devise a novel ray tracing method called PYRAMID which uses a new geometry - the pyramidal geometry. This geometry shares properties with both the standard Cartesian and spherical geometries. This makes it on the one hand easy to use in conjunction with a Cartesian grid and on the other hand ideally suited to trace radiation from a radially emitting source. A time-dependent photoionization calculation not only requires tracing the path of photons but also solving the coupled set of photoionization and thermal equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-Ray generally performs best.

Time domain decomposition for European options in financial modelling

Finance is one of the fastest growing areas in modern applied mathematics with real world applications. The interest of this branch of applied mathematics is best described by an example involving shares. Shareholders of a company receive dividends which come from the profit made by the company. The proceeds of the company, once it is taken over or wound up, will also be distributed to shareholders. Therefore shares have a value that reflects the views of investors about the likely dividend payments and capital growth of the company. Obviously such value will be quantified by the share price on stock exchanges. Therefore financial modelling serves to understand the correlations between asset and movements of buy/sell in order to reduce risk. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. There are other financial activities and it is not an intention of this paper to discuss all of these activities. The main concern of this paper is to propose a parallel algorithm for the numerical solution of an European option. This paper is organised as follows. First, a brief introduction is given of a simple mathematical model for European options and possible numerical schemes of solving such mathematical model. Second, Laplace transform is applied to the mathematical model which leads to a set of parametric equations where solutions of different parametric equations may be found concurrently. Numerical inverse Laplace transform is done by means of an inversion algorithm developed by Stehfast. The scalability of the algorithm in a distributed environment is demonstrated. Third, a performance analysis of the present algorithm is compared with a spatial domain decomposition developed particularly for time-dependent heat equation. Finally, a number of issues are discussed and future work suggested.

Performance analysis in soccer: applications of player tracking technology

The aim of this thesis was threefold, firstly, to compare current player tracking technology in a single game of soccer. Secondly, to investigate the running requirements of elite women’s soccer, in particular the use and application of athlete tracking devices. Finally, how can game style be quantified and defined. Study One compared four different match analysis systems commonly used in both research and applied settings: video-based time-motion analysis, a semi-automated multiple camera based system, and two commercially available Global Positioning System (GPS) based player tracking systems at 1 Hertz (Hz) and 5 Hz respectively. A comparison was made between each of the systems when recording the same game. Total distance covered during the match for the four systems ranged from 10 830 ± 770 m (semi-automated multiple camera based system) to 9 510 ± 740m (video-based time-motion analysis). At running speeds categorised as high-intensity running (>15 km⋅h-1), the semi-automated multiple camera based system reported the highest distance of 2 650 ± 530 m with video-based time-motion analysis reporting the least amount of distance covered with 1 610 ± 370 m. At speeds considered to be sprinting (>20 km⋅h-1), the video-based time-motion analysis reported the highest value (420 ± 170 m) and 1 Hz GPS units the lowest value (230 ± 160 m). These results demonstrate there are differences in the determination of the absolute distances, and that comparison of results between match analysis systems should be made with caution. Currently, there is no criterion measure for these match analysis methods and as such it was not possible to determine if one system was more accurate than another. Study Two provided an opportunity to apply player-tracking technology (GPS) to measure activity profiles and determine the physical demands of Australian international level women soccer players. In four international women’s soccer games, data was collected on a total of 15 Australian women soccer players using a 5 Hz GPS based athlete tracking device. Results indicated that Australian women soccer players covered 9 140 ± 1 030 m during 90 min of play. The total distance covered by Australian women was less than the 10 300 m reportedly covered by female soccer players in the Danish First Division. However, there was no apparent difference in the estimated "#$%&', as measured by multi-stage shuttle tests, between these studies. This study suggests that contextual information, including the “game style” of both the team and opposition may influence physical performance in games. Study Three examined the effect the level of the opposition had on the physical output of Australian women soccer players. In total, 58 game files from 5 Hz athlete-tracking devices from 13 international matches were collected. These files were analysed to examine relationships between physical demands, represented by total distance covered, high intensity running (HIR) and distances covered sprinting, and the level of the opposition, as represented by the Fédération Internationale de Football Association (FIFA) ranking at the time of the match. Higher-ranking opponents elicited less high-speed running and greater low-speed activity compared to playing teams of similar or lower ranking. The results are important to coaches and practitioners in the preparation of players for international competition, and showed that the differing physical demands required were dependent on the level of the opponents. The results also highlighted the need for continued research in the area of integrating contextual information in team sports and demonstrated that soccer can be described as having dynamic and interactive systems. The influence of playing strategy, tactics and subsequently the overall game style was highlighted as playing a significant part in the physical demands of the players. Study Four explored the concept of game style in field sports such as soccer. The aim of this study was to provide an applied framework with suggested metrics for use by coaches, media, practitioners and sports scientists. Based on the findings of Studies 1- 3 and a systematic review of the relevant literature, a theoretical framework was developed to better understand how a team’s game style could be quantified. Soccer games can be broken into key moments of play, and for each of these moments we categorised metrics that provide insight to success or otherwise, to help quantify and measure different methods of playing styles. This study highlights that to date, there had been no clear definition of game style in team sports and as such a novel definition of game style is proposed that can be used by coaches, sport scientists, performance analysts, media and general public. Studies 1-3 outline four common methods of measuring the physical demands in soccer: video based time motion analysis, GPS at 1 Hz and at 5 Hz and semiautomated multiple camera based systems. As there are no semi-automated multiple camera based systems available in Australia, primarily due to cost and logistical reasons, GPS is widely accepted for use in team sports in tracking player movements in training and competition environments. This research identified that, although there are some limitations, GPS player-tracking technology may be a valuable tool in assessing running demands in soccer players and subsequently contribute to our understanding of game style. The results of the research undertaken also reinforce the differences between methods used to analyse player movement patterns in field sports such as soccer and demonstrate that the results from different systems such as GPS based athlete tracking devices and semi-automated multiple camera based systems cannot be used interchangeably. Indeed, the magnitude of measurement differences between methods suggests that significant measurement error is evident. This was apparent even when the same technologies are used which measure at different sampling rates, such as GPS systems using either 1 Hz or 5 Hz frequencies of measurement. It was also recognised that other factors influence how team sport athletes behave within an interactive system. These factors included the strength of the opposition and their style of play. In turn, these can impact the physical demands of players that change from game to game, and even within games depending on these contextual features. Finally, the concept of what is game style and how it might be measured was examined. Game style was defined as "the characteristic playing pattern demonstrated by a team during games. It will be regularly repeated in specific situational contexts such that measurement of variables reflecting game style will be relatively stable. Variables of importance are player and ball movements, interaction of players, and will generally involve elements of speed, time and space (location)".

A space-time hybrid hourly rainfall model for derived flood frequency analysis

For derived flood frequency analysis based on hydrological modelling long continuous precipitation time series with high temporal resolution are needed. Often, the observation network with recording rainfall gauges is poor, especially regarding the limited length of the available rainfall time series. Stochastic precipitation synthesis is a good alternative either to extend or to regionalise rainfall series to provide adequate input for long-term rainfall-runoff modelling with subsequent estimation of design floods. Here, a new two step procedure for stochastic synthesis of continuous hourly space-time rainfall is proposed and tested for the extension of short observed precipitation time series. First, a single-site alternating renewal model is presented to simulate independent hourly precipitation time series for several locations. The alternating renewal model describes wet spell durations, dry spell durations and wet spell intensities using univariate frequency distributions separately for two seasons. The dependence between wet spell intensity and duration is accounted for by 2-copulas. For disaggregation of the wet spells into hourly intensities a predefined profile is used. In the second step a multi-site resampling procedure is applied on the synthetic point rainfall event series to reproduce the spatial dependence structure of rainfall. Resampling is carried out successively on all synthetic event series using simulated annealing with an objective function considering three bivariate spatial rainfall characteristics. In a case study synthetic precipitation is generated for some locations with short observation records in two mesoscale catchments of the Bode river basin located in northern Germany. The synthetic rainfall data are then applied for derived flood frequency analysis using the hydrological model HEC-HMS. The results show good performance in reproducing average and extreme rainfall characteristics as well as in reproducing observed flood frequencies. The presented model has the potential to be used for ungauged locations through regionalisation of the model parameters.

Floating wave energy converters: wave measurement & analysis techniques

The wave energy industry is entering a new phase of pre-commercial and commercial deployments of full-scale devices, so better understanding of seaway variability is critical to the successful operation of devices. The response of Wave Energy Converters to incident waves govern their operational performance and for many devices, this is highly dependent on spectral shape due to their resonant properties. Various methods of wave measurement are presented, along with analysis techniques and empirical models. Resource assessments, device performance predictions and monitoring of operational devices will often be based on summary statistics and assume a standard spectral shape such as Pierson-Moskowitz or JONSWAP. Furthermore, these are typically derived from the closest available wave data, frequently separated from the site on scales in the order of 1km. Therefore, variability of seaways from standard spectral shapes and spatial inconsistency between the measurement point and the device site will cause inaccuracies in the performance assessment. This thesis categorises time and frequency domain analysis techniques that can be used to identify changes in a sea state from record to record. Device specific issues such as dimensional scaling of sea states and power output are discussed along with potential differences that arise in estimated and actual output power of a WEC due to spectral shape variation. This is investigated using measured data from various phases of device development.

STAR Modeling of Pulmonary Tuberculosis Delay-Time in Diagnosis

Understanding what characterizes patients who suffer great delays in diagnosis of pulmonary tuberculosis is of great importance when establishing screening strategies to better control TB. Greater delays in diagnosis imply a higher chance for susceptible individuals to become infected by a bacilliferous patient. A Structured Additive Regression model is attempted in this study in order to potentially contribute to a better characterization of bacilliferous prevalence in Portugal. The main findings suggest the existence of significant regional differences in Portugal, with the fact of being female and/or alcohol dependent contributing to an increased delay-time in diagnosis, while being dependent on intravenous drugs and/or being diagnosed with HIV are factors that increase the chance of an earlier diagnosis of pulmonary TB. A decrease in 2010 to 77% on treatment success in Portugal underlines the importance of conducting more research aimed at better TB control strategies.

Frequency domain analysis of stationary time series

This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.

Análise tempo-intensidade dos estímulos doce e amargo de extrato de folhas de estévia [Stevia rebaudiana (Bert.) Bertoni] em doçura equivalente a sacarose

The extract of stevia leaves (Stevia rebaudiana Bertoni) is the only sweetener utilized in sucrose substitution which can be produced totally in Brazil. The objective of this study, was determine the temporal characteristic of sweet and bitter taste of stevia and compare with sucrose at 3 and 10% in the same equi-sweet. The time-intensity curves (T-I) for each substance were collected through the software Sistema de Coleta de Dados Tempo-Intensidade - SCDTI for Windows, where the judges recorded through of mouse the perception of each stimuli inside function of time, for each sample. The parameters of T-I curves collected were: time for intensity maxim (TImax), intensity maxim (Imax), time of decay (Td), time of plato (Platô), area under curve (Area) and total time of stimuli duration (Ttot). The parameters Td, Ttot, Area e Plato of T-I curves, for stimuli sweet in both sweetness level, were significativelly superior for stevia, while Timax e Imax were significativelly inferior (p£0,05), at differences between value for both substances were superior DESS at 10%. Sucrose didn?t present any record for simuli bitter as 3 as 10%, while stevia presented a characteristic T-I curve with intensity and total time of stimuli duration dependent of concentration.

Energy gain induced by boundary crisis

We consider a nonlinear system and show the unexpected and surprising result that, even for high dissipation, the mean energy of a particle can attain higher values than when there is no dissipation in the system. We reconsider the time-dependent annular billiard in the presence of inelastic collisions with the boundaries. For some magnitudes of dissipation, we observe the phenomenon of boundary crisis, which drives the particles to an asymptotic attractive fixed point located at a value of energy that is higher than the mean energy of the nondissipative case and so much higher than the mean energy just before the crisis. We should emphasize that the unexpected results presented here reveal the importance of a nonlinear dynamics analysis to explain the paradoxical strategy of introducing dissipation in the system in order to gain energy.

Determination of post-mortem interval using in situ tissue optical fluorescence

In this study we have used fluorescence spectroscopy to determine the post-mortem interval. Conventional methods in forensic medicine involve tissue or body fluids sampling and laboratory tests, which are often time demanding and may depend on expensive analysis. The presented method consists in using time-dependent variations on the fluorescence spectrum and its correlation with the time elapsed after regular metabolic activity cessation. This new approach addresses unmet needs for post-mortem interval determination in forensic medicine, by providing rapid and in situ measurements that shows improved time resolution relative to existing methods. (C) 2009 Optical Society of America

Time stability of soil water storage measured by neutron probe and the effects of calibration procedures in a small watershed

The knowledge of soil water storage (SWS) of soil profiles is crucial for the adoption of vegetation restoration practices. With the aim of identifying representative sites to obtain the mean SWS of a watershed, a time stability analysis of neutron probe evaluations of SWS was performed by the means of relative differences and Spearman rank correlation coefficients. At the same time, the effects of different neutron probe calibration procedures were explored on time stability analysis. mean SWS estimation. and preservation of the spatial variability of SWS. The selected watershed, with deep gullies and undulating slopes which cover an area of 20 ha, is characterized by an Ust-Sandiic Entisol and an Aeolian sandy soil. The dominant vegetation species are bunge needlegrass (Stipa bungeana Trim) and korshinsk peashrub (Carugano Korshinskii kom.). From June 11, 2007 to July 23,2008, SWS of the top1 m soil layer was evaluated for 20 dates, based on neutron probe data of 12 sampling sites. Three calibration procedures were employed: type 1, most complete, with each site having its own linear calibration equation (TrE); type II. with TrE equations extended over the whole field: and type III, with one single linear calibration curve for the whole field (UnE) and also correcting its intercept based on site specific relative difference analysis (RdE) and on linear fitting of data (RcE), both maintaining the same slope. A strong time stability of SWS estimated by TrE equations was identified. Soil particle size and soil organic matter content were recognized as the influencing factors for spatial variability of SWS. Land use influenced neither the spatial variability nor the time stability of SWS. Time stability analysis identified one site to represent the mean SWS of the whole watershed with mean absolute percentage errors of less than 10%, therefore. this site can be used as a predictor for the mean SWS of the watershed. Some equations of type II were found to be unsatisfactory to yield reliable mean SWS values or in preserving the associated soil spatial variability. Hence, it is recommended to be cautious in extending calibration equations to other sites since they might not consider the field variability. For the equations with corrected intercept (type III), which consider the spatial variability of calibration in a different way in relation to TrE, it was found that they can yield satisfactory means and standard deviation of SWS, except for the RdE equations, which largely leveled off the SWS values in the watershed. Correlation analysis showed that the neutron probe calibration was linked to soil bulk density and to organic matter content. Therefore, spatial variability of soil properties should be taken into account during the process of neutron probe calibration. This study provides useful information on the mean SWS observation with a time stable site and on distinct neutron probe calibration procedures, and it should be extended to soil water management studies with neutron probes, e.g., the process of vegetation restoration in wider area and soil types of the Loess Plateau in China. (C) 2009 Elsevier B.V. All rights reserved.

Evaluation of flow regimes in a semi-cylindrical spouted bed through statistical, mutual information, spectral and Hurst`s analysis

Hydrodynamic studies were conducted in a semi-cylindrical spouted bed column of diameter 150 mm, height 1000 mm, conical base included angle of 60 degrees and inlet orifice diameter 25 mm. Pressure transducers at several axial positions were used to obtain pressure fluctuation time series with 1.2 and 2.4 mm glass beads at U/U-ms from 0.3 to 1.6, and static bed depths from 150 to 600 mm. The conditions covered several flow regimes (fixed bed, incipient spouting, stable spouting, pulsating spouting, slugging, bubble spouting and fluidization). Images of the system dynamics were also acquired through the transparent walls with a digital camera. The data were analyzed via statistical, mutual information theory, spectral and Hurst`s Rescaled Range methods to assess the potential of these methods to characterize the spouting quality. The results indicate that these methods have potential for monitoring spouted bed operation.

Biomolecular interaction analysis of IFN gamma-induced signaling events in whole-cell lysates: Prevalence of latent STAT1 in high-molecular weight complexes

The basic framework for the JAK/STAT pathway is well documented. Recruitment of latent cytoplasmic STAT transcription factors to tyrosine phosphorylated docking sites on cytokine receptors and their JAK-mediated phosphorylation instigates their translocation to the nucleus and their ability to bind DNA, The biochemical processes underlying recruitment and activation of this pathway have commonly been studied in reconstituted in vitro systems using previously defined recombinant signaling components. We have dissected the Interferon gamma (IFN gamma) signal transduction pathway in crude extracts from wild-type and STAT1-negative mutant cell Lines by real-time BIAcore analysis, size-exclusion (SE) chromatography and immune-detection. The data indicate that in detergent-free cell extracts: (1) the phospho-tyrosine (Y440P)-containing peptide motif of the IFN gamma-receptor ct-chain interacts directly with STAT1, or STAT1 complexes, and no other protein; (2) nonactivated STAT 1 is present in a higher molecular weight complex(es) and, at least for IFN gamma-primed cells, is available for recruitment to the activated IFN gamma-receptor from only a subset of such complexes; (3) activated STAT1 is released from the receptor as a monomer.

Tests for the hysteresis hypothesis in Brazilian industrialized exports: A threshold cointegration analysis

This paper examines the hysteresis hypothesis in the Brazilian industrialized exports using a time series analysis. This hypothesis finds an empirical representation into the nonlinear adjustments of the exported quantity to relative price changes. Thus, the threshold cointegration analysis proposed by Balke and Fomby [Balke, N.S. and Fomby, T.B. Threshold Cointegration. International Economic Review, 1997; 38; 627-645.] was used for estimating models with asymmetric adjustment of the error correction term. Amongst sixteen industrial sectors selected, there was evidence of nonlinearities in the residuals of long-run relationships of supply or demand for exports in nine of them. These nonlinearities represent asymmetric and/or discontinuous responses of exports to different representative measures of real exchange rates, in addition to other components of long-run demand or supply equations. (C) 2007 Elsevier B.V. All rights reserved.

Expression of insulin-like growth factor-II and its receptor in pediatric and adult adrenocortical tumors

Background: Adrenocortical tumors are heterogeneous neoplasms with incompletely understood pathogenesis. IGF-II overexpression has been consistently demonstrated in adult adrenocortical carcinomas. Objectives: The objective of the study was to analyze expression of IGF-II and its receptor (IGF-IR) in pediatric and adult adrenocortical tumors and the effects of a selective IGF-IR kinase inhibitor (NVP-AEW541) on adrenocortical tumor cells. Patients: Fifty-seven adrenocortical tumors (37 adenomas and 20 carcinomas) from 23 children and 34 adults were studied. Methods: Gene expression was determined by quantitative real-time PCR. Cell proliferation and apoptosis were analyzed in NCI H295 cells and a new cell line established from a pediatric adrenocortical adenoma. Results: IGF-II transcripts were overexpressed in both pediatric adrenocortical carcinomas and adenomas. Otherwise, IGF-II was mainly overexpressed in adult adrenocortical carcinomas (270.5 +/- 130.2 vs. 16.1 +/- 13.3; P = 0.0001). IGF-IR expression was significantly higher in pediatric adrenocortical carcinomas than adenomas (9.1 +/- 3.1 vs. 2.6 +/- 0.3; P = 0.0001), whereas its expression was similar in adult adrenocortical carcinomas and adenomas. IGF-IR expression was a predictor of metastases in pediatric adrenocortical tumors in univariate analysis (hazard ratio 1.84; 95% confidence interval 1.28 -2.66; P = 0.01). Furthermore, NVP-AEW541 blocked cell proliferation in a dose-and time-dependent manner in both cell lines through a significant increase of apoptosis. Conclusion: IGF-IR overexpression was a biomarker of pediatric adrenocortical carcinomas. Additionally, a selective IGF-IR kinase inhibitor had antitumor effects in adult and pediatric adrenocortical tumor cell lines, suggesting that IGF-IR inhibitors represent a promising therapy for human adrenocortical carcinoma.