Numerical Methods for Solving Fractional Differential Equations

Department of Mathematical SciencesIn this thesis, several efficient numerical methods are proposed to solve initial value problems and boundary value problems of fractional di???erential equations. For fractional initial value problems, we propose a new type of the predictorevaluate-corrector-evaluate method based on the Caputo fractional derivative operator. Furthermore, we propose a new type of the Caputo fractional derivative operator that does not have a di???erential form of a solution. However, with some fractional orders, there are problems that a solution blows up and the scheme has a low convergence. Thus, we identify new treatments for these values. Then, we can expect a significant improvement for all fractional orders. The advantages and improvements are shown by testing various numerical examples. For fractional BVPs, we propose an explicit method that dramatically reduces the computational time for solving a dense matrix system. Moreover, by adopting high-order predictor-corrector methods which have uniform convergence rates O(h2) or O(h3) for all fractional orders [8], we propose a second-order method and a third-order method by using the Newton???s method and the Halley method, respectively. We show its advantage by testing various numerical examples.clos

AMPA experimental communications systems

The program was conducted to demonstrate the satellite communication advantages of Adaptive Phased Array Technology. A laboratory based experiment was designed and implemented to demonstrate a low earth orbit satellite communications system. Using a 32 element, L-band phased array augmented with 4 sets of weights (2 for reception and 2 for transmission) a high speed digital processing system and operating against multiple user terminals and interferers, the AMPA system demonstrated: communications with austere user terminals, frequency reuse, communications in the face of interference, and geolocation. The program and experiment objectives are described, the system hardware and software/firmware are defined, and the test performed and the resultant test data are presented

BCHS 2524- Overview of Minority Health and Health Disparities in the US

Understanding health disparities involves a critical analysis of historical, political, economic, social, cultural, and environmental conditions that have produced an inequitable health status for racial and ethnic minorities in the United States. While we also recognize that disparities exist along socio-economic status, gender, sexual orientation and other factors, this class will focus on disparities in racial and ethnic minority communities. Issues of gender, SES and other factors will be examined as they intersect race and ethnicity, and further influence disparities in health. Minority health and health disparities have gained considerable attention from the recent publication of Healthy People 2010 Report, which lists as its two goals: 1) improve the quality of life for all citizens, and 2) eliminate health disparities. The purpose of this class is to introduce basic issues that underlie health disparities. We will gain a better understanding of the relationships of social and environmental phenomena and the health of minority communities. This course will include current literature and foster discussions that will examine health disparities, explore social and environmental determinants of those disparities, critically review measurement issues, and determine public health’s response to these disparities. Students should seek to critically reflect on their personal and professional roles in eliminating health disparities. By the end of the course, students will be able to

Overview of Minority Health and Health Disparities in the US

Understanding health disparities involves a critical analysis of historical, political, economic, social, cultural, and environmental conditions that have produced an inequitable health status for racial and ethnic minorities in the United States. While we also recognize that disparities exist along socio-economic status, gender, sexual orientation and other factors, this class will focus on disparities in racial and ethnic minority communities. Issues of gender, SES and other factors will be examined as they intersect race and ethnicity, and further influence disparities in health. Minority health and health disparities have gained considerable attention from the recent publication of Healthy People 2010 Report, which lists as its two goals: 1) improve the quality of life for all citizens, and 2) eliminate health disparities. The purpose of this class is to introduce basic issues that underlie health disparities. We will gain a better understanding of the relationships of social and environmental phenomena and the health of minority communities. This course will include current literature and foster discussions that will examine health disparities, explore social and environmental determinants of those disparities, critically review measurement issues, and determine public health’s response to these disparities. Students should seek to critically reflect on their personal and professional roles in eliminating health disparities. By the end of the course, students will be able to

Adversarial Dropout for Supervised and Semi-supervised Learning

Recently, the training with adversarial examples, which are generated by adding a small but worst-case perturbation on input examples, has been proved to improve generalization performance of neural networks. In contrast to the individually biased inputs to enhance the generality, this paper introduces adversarial dropout, which is a minimal set of dropouts that maximize the divergence between the outputs from the network with the dropouts and the training supervisions. The identified adversarial dropout are used to reconfigure the neural network to train, and we demonstrated that training on the reconfigured sub-network improves the generalization performance of supervised and semi-supervised learning tasks on MNIST and CIFAR-10. We analyzed the trained model to reason the performance improvement, and we found that adversarial dropout increases the sparsity of neural networks more than the standard dropout does.Comment: submitted to AAAI-1

Optimal pricing strategies for capacity leasing based on time and volume usage in telecommunication networks

In this study, we use a monopoly pricing model to examine the optimal pricing strategies for “pay-per-time”, “pay-per-volume” and “pay-per both time and volume” based leasing of data networks. Traditionally, network capacity distribution includes short/long term bandwidth and/or usage time leasing. Each consumer has a choice to select volume based, connection-time based or both volume and connection-time based pricing. When customers choose connection-time based pricing, their optimal behavior would be utilizing the bandwidth capacity fully, which can cause network to burst. Also, offering the pay-per-volume scheme to the consumer provides the advantage of leasing the excess capacity to other potential customers serving as network providers. However, volume-based strategies are decreasing the consumers’ interest and usage, because the optimal behaviors of the customers who choose the pay-per-volume pricing scheme generally encourages them to send only enough bytes for time-fixed tasks (for real time applications), causing quality of the task to decrease, which in turn creating an opportunity cost. Choosing pay-per time and volume hybridized pricing scheme allows customers to take advantages of both pricing strategies while decreasing (minimizing) the disadvantages of each, because consumers generally have both time-fixed and size-fixed task such as batch data transactions. However, such a complex pricing policy may confuse and frighten consumers. Therefore, in this study we examined the following two issues: (i) what (if any) are the benefits to the network provider of providing the time and volume hybridized pricing scheme? and (ii) would this offering schema make an impact on the market size? The main contribution of this study is to show that pay-per both time and volume pricing is a viable and often preferable alternative to the only time and/or only volume-based offerings for a large number of customers, and that judicious use of such pricing policy is profitable to the network provider