Wireless Sensor Networks (WSNs) have enticed a strong attention in the research community due to the broad range of applications and services they support. WSNs are composed of intelligent sensor nodes that have the capabilities to monitor different types of environmental phenomena or critical activities. Sensor nodes operate under stringent requirements of scarce power resources, limited storage capacities, limited processing capabilities, and hostile environmental surroundings. However, conserving sensor nodes’ power resources is the top priority requirement in the design of a WSN as it has a direct impact on its lifetime. The IEEE 802.15.4 standard defines a set of specifications for both the PHY layer and the MAC sub-layer that abide by the distinguished requirements of WSNs. The standard’s MAC protocol employs an intelligent backoff algorithm, called the Binary Exponent Backoff (BEB), that minimizes the drainage of power in these networks. In this thesis we present an in-depth study of the IEEE 802.15.4 MAC protocol to highlight both its strong and weak aspects. We show that we have enticing opportunities to improve the performance of this protocol in the context of WSNs. We propose three new backoff algorithms, namely, the Standby-BEB (SB-BEB), the Adaptive Backoff Algorithm (ABA), and the Priority-Based BEB (PB-BEB), to replace the standard BEB. The main contribution of the thesis is that it develops a new design concept that drives the design of efficient backoff algorithms for the IEEE 802.15.4-based WSNs. The concept dictates that controlling the algorithms parameters probabilistically has a direct impact on enhancing the backoff algorithm’s performance. We provide detailed discrete-time Markov-based models (for AB-BEB and ABA) and extensive simulation studies (for the three algorithms) to prove the superiority of our new algorithms over the standard BEB.

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The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational points on certain algebraic varieties in function fields. The aim is to establish asymptotic relations that are relatively robust to changes in the characteristic of the base finite field. More notably, in the case when the characteristic is "small", the results are sharper than their integer analogues.

As applications like IPTV and VoD (Video on demand) are gaining popularity, it is becoming more important to study the behavior of video signals in the Internet access infrastructures such as ADSL and cable networks. Average delay, average jitter and packet loss in these networks affect the quality of service, hence transmission and access speeds need to be determined such that these parameters are minimized. In this study the behavior of the above mentioned IP networks under variable bit rate (VBR) video traffic is investigated. ns-2 simulator is used for this purpose and actual as well as artificially generated signals are applied to the networks under test. Variable bit rate (VBR) traffic is generated synthetically using ON/OFF sources with ON/OFF times taken from exponential or Pareto distributions. As VBR video shows long range dependence with a Hurst parameter between 0.5 and 1, this parameter was used as a metric to measure the accuracy of the synthetic sources. Two different topologies were simulated in this study: one similar to ADSL access networks and the other behaving like cable distribution network. The performance of the networks (delay, jitter and packet loss) under VBR video traffic and different access speeds were measured. According to the obtained results, minimum access speeds in order achieve acceptable quality video delivery to the customers were suggested.

In this study, the aim was to investigate the effects of exponential feeding strategy on benzaldehyde lyase (BAL) production by recombinant Escherichia coli BL21. For this purpose, the effects of medium components were investigated to optimize the initial medium composition of the fed-batch fermentations. For the batch bioreactor operations, the highest cell concentration and BAL activity were achieved in a media containing 30 g L-1 pretreated molasses, and 5 g L-1 (NH4)2HPO4 as 5.07 g L-1, and 1611 U ml-1 at t=8 h, respectively. Thereafter, in order to increase the cell growth and BAL production while avoiding acetate accumulation, fed-batch bioreactor operations were conducted with exponential feeding at different specific growth rates namely, 0.1 h-1 (mu-0.1), 0.15 h-1 (mu-0.15), and 0.2 h-1 (mu-0.2), and a combined exponential and constant feeding (mu-0.2+) strategy. In the experiments, 9 hours of batch-wise operation with the optimized production medium was followed by a fed-batch operation phase using the pre-determined exponential feeding profiles and for mu-0.2+ operation after 10 hours of exponential feeding as mu-0.2, where the feed rate was kept constant at 21.6 g h-1. Additionally, the plasmid stability was investigated using the feeding method of mu-0.2+ operation with antibiotics in the feed solution, and it was observed that the plasmid was stable. Among the three exponential feeding conditions, the highest cell concentration and BAL activity were determined in

In this thesis we investigate thinning of the renewal process. After multinomial thinning from a renewal process A, we obtain the k thinned processes, A_i , i =1,¡K, k. Based on some characterizations of the Poisson process as a renewal process, we give another characterizations of the Poisson process from some relations of expectation, variance, covariance, residual life of the k thinned processes. Secondly, we consider that at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the i-th new atom assigned to the process D_i , i =1,¡K, k. We also have characterizations of the Poisson process from some relations of expectation, variance of the process D_i , i =1,¡K, k.

We discuss two-sample problems and the implementation of a new two-sample data analysis procedure. The proposed procedure is based on the concepts of mid-distribution, design of score functions, components, comparison distribution, comparison density and exponential model. Assume that we have a random sample X1, . . . ,Xm from a continuous distribution F(y) = P(Xi y), i = 1, . . . ,m and a random sample Y1, . . . ,Yn from a continuous distribution G(y) = P(Yi y), i = 1, . . . ,n. Also assume independence of the two samples. The two-sample problem tests homogeneity of two samples and formally can be stated as H0 : F = G. To solve the two-sample problem, a number of tests have been proposed by statisticians in various contexts. Two typical tests are the two-sample t?test and the Wilcoxon's rank sum test. However, since they are testing differences in locations, they do not extract more information from the data as well as a test of the homogeneity of the distribution functions. Even though the Kolmogorov-Smirnov test statistic or Anderson-Darling tests can be used for the test of H0 : F = G, those statistics give no indication of the actual relation of F to G when H0 : F = G is rejected. Our goal is to learn why it was rejected. Our approach gives an answer using graphical tools which is a main property of our approach. Our approach is functional in the sense that the parameters to be estimated are probability density functions. Compared with other statistical tools for two-sample problems such as the t-test or the Wilcoxon rank-sum test, density estimation makes us understand the data more fully, which is essential in data analysis. Our approach to density estimation works with small sample sizes, too. Also our methodology makes almost no assumptions on two continuous distributions F and G. In that sense, our approach is nonparametric. Our approach gives graphical elements in two-sample problem where exist not many graphical elements typically. Furthermore, our procedure will help researchers to make a conclusion as to why two populations are different when H0 is rejected and to give an explanation to describe the relation between F and G in a graphical way.

A high resolution speedy delivery time domain reflectometer (SD/TDR) has been developed in the Electrical Engineering department at The University of Texas at Austin. The SD/TDR uses a novel non-sinusoidal signal that does not undergo dispersion during transmission in a lossy media. SD/TDR is used to estimate the length and detect the location of faults in the transmission lines. Time of flight (TOF) is one of the critical parameters of SD/TDR and a function of several temperature dependent factors. Given the TOF and length of a transmission line, signal delay can be computed. This research presents an empirical study of the effect of temperature on the TOF in a plenum grade coaxial cable for temperatures ranging from -3 °C to 60 °C. We also study the effect of temperature on characteristic impedance of the coaxial cable. Finally, a SD double exponential waveform is used to estimate TOF for calibrated short and open terminations. / text

We prove several inequalities involving the Fourier transform of functions which are compactly supported. The constraint that the functions have compact support is a simplifying feature which is desirable in applications, but there is a trade-off in control of other relevant quantities-- such as the mass of the function. With applications in mind, we prove inequalities which quantify these types of trade-offs. / text

It is essential for the managers to make investment on hardware based on the utilization information of the equipment. From December 2014, a pool of hardware and a scheduling and resource sharing system is implemented by one of the software testing sections in Ericsson. To monitor the efficiency of these equipment and the workflow, a model of non-homogeneous M/M/c queue is developed that successfully captures the main aspects of the system. The model is decomposed into arrival, service, failure and each part is estimated. Mixture exponential is estimated with EM algorithm and the impact of scheduling change is also examined. Finally a simulation of workflow is done with Python module and the optimized number of hardware is proposed based on this M/M/c queue system.