A classic problem in the field of pattern recognition is that of handwritten digit recognition. The heart of the problem lies within the ability to design an efficient algorithm that can recognize digits written and submitted by users via a tablet, scanner, and other digital devices. Previous studies have shown that the digits can be modeled as points in a high dimensional space which can adequately approximated by linear structures. In Chapters 2 and 3, we present two previously established algorithms rooted in two distinct geometric frameworks. In Chapter 4, we introduce a novel approach to the problem based on the linear structure that arises for the Grassmann manifold. From this framework, we developed three separate algorithms. We then tested our algorithms on the publicly available MNIST database and benchmarked our results with the algorithm described in Chapters 2 and 3. Without any preprocessing of the images, one of the Grassmann-based algorithms simultaneously achieved the highest classification rate and one of the fastest processing times.

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Tuberculosis is still a significant health and economic problem in Central Asia, despite some recent progress that may be due to improvements of the overall economic situation in these countries, and partial adoption of the DOTS Strategy recommended by WHO. Over 50,000 new cases have been detected in 2003 and over 7,000 people died due to TB in the four countries studied. This study has confirmed that it is highly unlikely that these Central Asian republics will succeed in achieving the global targets for tuberculosis control in the short term, particularly with regard to case detection. In the meantime, the epidemic continues to have a serious epidemiological impact and affects the economies of these countries, which incur productivity losses and indirect costs that are estimated to range from 0.5 to 0.8 percent of GDP annually. 'Stopping Tuberculosis in Central Asia' reviews the epidemiological situation, control efforts, and financing of tuberculosis programs in Kazakhstan, Kyrgyz Republic, Tajikistan, and Uzbekistan. It was based on a review of existing statistics and reports, and on consultation with key stakeholders Governments, NGOs, and donors in Central Asia. This work contributes an agenda for action to address the impending epidemiological crisis that has been posed by the sudden increase in cases of HIV/AIDS infection combined with a prevalent epidemic of TB."