This paper presents a simple recursive formula to compute the Taylor polynomial of quantile for a continuous random variable. It is very easy to implement the formula in standard symbolic programming system, for example Mathematica (Wolfram, 2003). Applications of the formula to standard normal distribution and to the generation of random variables for continuous distribution with bounded support are illustrated.

Reducing power consumption is among the top concerns in Wireless Sensor Networks, as the lifetime of a Wireless Sensor Network depends on its power consumption. Directional antennas help achieve this goal contrary to the commonly used omnidirectional antennas that radiate electromagnetic power equally in all directions, by concentrating the radiated electromagnetic power only in particular directions. This enables increased communication range at no additional energy cost and reduces contention on the wireless medium. The SPIDA (SICS Parasitic Interference Directional Antenna) prototype is one of the few real-world prototypes of electronically switchable directional antennas for Wireless Sensor Networks. However, building several prototypes of SPIDA and conducting real-world experiments using them may be expensive and impractical. Modeling SPIDA based on real-world experiments avoids the expenses incurred by enabling simulation of large networks equipped with SPIDA. Such a model would then allow researchers to develop new algorithms and protocols that take advantage of the provided directional communication on existing Wireless Sensor Network simulators. In this thesis, a model of SPIDA for Wireless Sensor Networks is built based on thoroughly designed real-world experiments. The thesis builds a probabilistic model that accounts for variations in measurements, imperfections in the prototype construction, and fluctuations in experimental settings that affect the values of the measured metrics. The model can be integrated into existing Wireless Sensor Network simulators to foster the research of new algorithms and protocols that take advantage of directional communication. The model returns the values of signal strength and packet reception rate from a node equipped with SPIDA at a certain point in space given the two-dimensional distance coordinates of the point and the configuration of SPIDA as inputs. / Phone:+46765816263 Additional email: burkaja@yahoo.com

Comprehensive statistical models for non-normally distributed cancerous tumor sizes are of prime importance in epidemiological studies, whereas a long term forecasting models can facilitate in reducing complications and uncertainties of medical progress. The statistical forecasting models are critical for a better understanding of the disease and supply appropriate treatments. In addition such a model can be used for the allocations of budgets, planning, control and evaluations of ongoing efforts of prevention and early detection of the diseases. In the present study, we investigate the effects of age, demography, and race on primary brain tumor sizes using quantile regression methods to obtain a better understanding of the malignant brain tumor sizes. The study reveals that the effects of risk factors together with the probability distributions of the malignant brain tumor sizes, and plays significant role in understanding the rate of change of tumor sizes. The data that our analysis and modeling is based on was obtained from Surveillance Epidemiology and End Results (SEER) program of the United States. We also analyze the discretely observed brain cancer mortality rates using functional data analysis models, a novel approach in modeling time series data, to obtain more accurate and relevant forecast of the mortality rates for the US. We relate the cancer registries, race, age, and gender to age-adjusted brain cancer mortality rates and compare the variations of these rates during the period of the study that data was collected. Finally, in the present study we have developed effective statistical model for heterogenous and high dimensional data that forecast the hazard rates with high degree of accuracy, that will be very helpful to address subject health problems at present and in the future.

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Cette thèse porte sur la modélisation 0D/1D de la combustion Diesel dans les moteurs récents. L’objectif est d’augmenter la précision des modèles tout en limitant les temps de calcul associés afin d’utiliser la simulation comme un outil dédié à la mise au point. Dans une première partie, le développement d’un modèle 0D orienté simulation système est présenté. La prise en compte de l’ensemble des phénomènes physico-chimiques se déroulant dans la chambre de combustion confère au modèle un niveau de prédictivité conséquent. Un nouveau modèle de combustion de prémélange est proposé, permettant une modélisation détaillée des combustions fortement diluées et des combustions relatives aux injections précoces. Une approche innovante permettant de quantifier les interactions entre les jets pour la multi injection est également proposée. Après calibration sur un nombre restreint d’essais moteur, les résultats du modèle global sont comparés à des mesures expérimentales pour toute la plage de fonctionnement du moteur. La seconde partie de ce travail porte sur la modélisation 1D de la combustion Diesel. Un modèle de jet Diesel est d’abord développé et validé sur des mesures expérimentales. Ce modèle est ensuite étendu à des conditions réactionnelles à l’aide d’un couplage avec un modèle de combustion. Ce dernier s’appuie sur une tabulation des mécanismes de cinétique chimique, ainsi que sur une approche Eddy Break-Up permettant de modéliser le taux de réaction lié au micro mélange. Ce modèle est ensuite intégré à un modèle de chambre de combustion et une première validation du modèle sur des essais moteur réels est entreprise. / The present thesis focuses on the 0D/1D Diesel combustion modeling of recent engines. The goal is to improve models accuracy while minimizing computation times in order to use simulation as a tool for engine pre-mapping. In the first part, a 0D model designed as a system simulation-oriented tool is proposed. The main contribution of this study is the modeling of the premixed part of the Diesel combustion. This model allows a detailed modeling of highly diluted combustion and combustion related to early injections. A new approach to quantify interactions between each spray in the case of multi injection strategies is also proposed. After calibration using a very small number of engine tests, results for the global combustion chamber model are compared with experimental measurements for the overall engine operating conditions. The second part of this work deals with the 1D Diesel combustion modeling. A Diesel spray model is at first developed and validated on experimental measurements. This model is then extended to reaction conditions using the coupling with a combustion model. The combustion model makes use of tabulated local reaction rates of fuel and is based on the Eddy Break-Up approach to describe the reaction rate related to the turbulent mixing process. The next step is the integration of the burning spray model into a Diesel engine combustion chamber model. A first validation using experimental results for a recent Diesel engine is done.

Researchers have shown that by combining multiple input multiple output (MIMO) techniques with CDMA then higher gains in capacity, reliability and data transmission speed can be attained. But a major drawback of MIMO-CDMA systems is multiple access interference (MAI) which can reduce the capacity and increase the bit error rate (BER), so statistical analysis of MAI becomes a very important factor in the performance analysis of these systems. In this thesis, a detailed analysis of MAI is performed for binary phase-shift keying (BPSK) signals with random signature sequence in Raleigh fading environment and closed from expressions for the probability density function of MAI and MAI with noise are derived. Further, probability of error is derived for the maximum Likelihood receiver. These derivations are verified through simulations and are found to reinforce the theoretical results. Since the performance of MIMO suffers significantly from MAI and inter-symbol interference (ISI), equalization is needed to mitigate these effects. It is well known from the theory of constrained optimization that the learning speed of any adaptive filtering algorithm can be increased by adding a constraint to it, as in the case of the normalized least mean squared (NLMS) algorithm. Thus, in this work both linear and non-linear decision feedback (DFE) equalizers for MIMO systems with least mean square (LMS) based constrained stochastic gradient algorithm have been designed. More specifically, an LMS algorithm has been developed , which was equipped with the knowledge of number of users, spreading sequence (SS) length, additive noise variance as well as MAI with noise (new constraint) and is named MIMO-CDMA MAI with noise constrained (MNCLMS) algorithm. Convergence and tracking analysis of the proposed algorithm are carried out in the scenario of interference and noise limited systems, and simulation results are presented to compare the performance of MIMO-CDMA MNCLMS algorithm with other adaptive algorithms.

In this work, we propose three control strategies from different perspectives to solve the alignment problem for different optical wireless communication (OWC) systems. • Experimental modeling based strategy: we model and analyze the vibration effects on the stationary OWC system (e.g. urban free-space optical (FSO) communication system in our case). The proposed Bifurcated-Gaussian (B-G) distribution model of the receiver optical power is derived under different vibra- tion levels and link distances using the nonlinear iteration method. Besides, the UFSO channel under the effects of both vibration and atmospheric turbulence is also explored under three atmospheric turbulence conditions. Our proposed B-G distribution model helps to easily evaluate the link performance of UFSO systems and paves the way for constructing completed auxiliary control subsys- tems for robust UFSO links. • Extremum seeking control based strategy: we propose an extremum seeking control (ESC) based strategy for the mobile OWC system. Our proposed ap- proach consists of coarse alignment and fine alignment. The coarse alignment using feedback proportional-derivative (PD) control is responsible for tracking and following the receiver. For fine alignment, the perturbation-based extremum seeking control (ESC) is adopted for a continuous search for the optimal posi- tion, where the received optical power is maximum in the presence of distur- bance. The proposed approach is simple, effective, and easy to implement. • Time scale theory based strategy: we design a time scale based Kalman filter for the intermittent OWC system. First, the algorithm of Kalman filter on time scales is presented, followed by several numerical examples for interpretation and analysis. The design of Kalman filter on time scales for our simulated vibrating OWC system is then discussed, whose results are analyzed thoroughly and further validated by a reference system. The proposed strategy has great potential for solving the problem of observer design in the case of intermittent received signals (non-uniform measurements) and paves the way for further controller design. The three proposed control strategies directly or indirectly solve the beam align- ment problem for optical communication systems, supporting the development of robust optical communication link.

<div>Computational studies are performed on a Cambridge Stratified Swirl burner (SwB), a lean premixed stratified flame, by using the Reynolds Averaged Navier Stokes (RANS) model and the transported Probability Density Function (PDF) model. The SwB burner was measured</div><div>by Sweeney et al. (Combustion and Flame, 2012, 159: 2896-2911), and comprehensive data are available for model validation, e.g., the mean and root-mean-square values of velocity, temperature, and species mass fractions. The experimental data are available for sixteen different cases to investigate flames in premixed and stratified regimes, with or without swirl. In this study, we consider only non-swirling, premixed and stratified cases. Different</div><div>turbulence models are examined in the modeling studies, and the Reynolds Stress model with standard model constant values is found to perform well with the transported PDF model. A joint PDF for enthalpy and species mass fractions allows for the highly non-linear reaction term in the transport equation to be completely closed. The mixing term arising from molecular diffusion is not closed and requires modeling which is a significant challenge. For the SwB, we consider a series of mixing models including the Interaction by Exchange with the Mean (IEM) mixing model with different mixing model constants, the Modified Curl model, and two mixing models designed for premixed combustion from the literature. We first examine the models in the non-stratified/premixed case (SwB1) to isolate the effect</div><div>of other conditions from stratification on the model predictions. The stratification is then added in two levels, a moderately stratified case (SwB5) and a highly stratified case (SwB9). The predicted results are compared with the experimental data at various locations, inside and outside the recirculation zone in the burner. In general, good agreement is obtained for the velocity fields inside the recirculation zone. Good agreement is also obtained</div><div>of the predicted and measured results is obtained for the mean values of temperature and species mass fractions. The scalar fluctuations are generally underpredicted. Overall, the employed modeling method is able to capture the mean flame structure reasonably well in lean premixed stratified flames. Some limitations are noticed, e.g., the underprediction of scalar fluctuations, and overprediction of CH4 concentration in the stratified cases. These observations are useful for guiding the future research directions.</div>

We describe basic notions of functional random elements and the space of functions L2 [0, 1]. We discuss the non-existence of a probability density functional and the re- quirements for integrating in a functional space. In Chapter 2, we define distribution functionals and introduce a goodness-of-fit test which utilises them. The concept of char- acteristic functionals follows in Chapter 3, along with the latest test for Gaussianity of functional random elements. We conclude the chapter with our own new goodness-of- fit test, where we prove the distribution of its test statistic under the alternative, then under the null hypothesis, and lastly the distribution of the bootstrapped test statistic. Finally, we illustrate the theory on a simulation study of the empirical significance level and power of the goodness-of-fit tests. 1

Yes / This paper presents a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.