Due to its significant advantage in spectral efficiency, multiple-antenna communication technology will undoubtedly be a major component in future wireless system implementations. However, the full exploitation of this technology also requires perfect feedback of channel state information (CSI) to the transmitter-- something that is not practically feasible. This motivates the study of limited feedback systems, where CSI feedback is rate limited. This thesis focuses on the optimal design of limited feedback systems for three types of communication channels: the relay channel, the single-user point-to-point channel, and the multiuser broadcast channel. For the relay channel, we prove the efficiency of the Grassmannian codebooks as the source and relay beamforming codebooks, and propose a method for CSI exchange between the relay and the destination when global CSI is not available at destination. For the single-user point-to-point channel, we study the joint power control and beamforming problem and address the channel magnitude and direction quantization codebook design problem. It is shown that uniform quantization of the channel magnitude (in dB scale) is asymptotically optimal regardless of the channel distribution. The analysis further derives the optimal split of feedback bandwidth between the magnitude and direction quantization codebooks. For the multiuser broadcast channel, we first prove the sufficiency of a product magnitude-direction quantization codebook for managing the multiuser interference. We then derive the optimal split of feedback bandwidth across the users and their magnitude and direction codebooks. The optimization results reveal an inherent structural difference between the single-user and multiuser quantization codebooks: a multiuser codebook should have a finer direction quantization resolution as compared to a single-user codebook. It is further shown that the users expecting higher rates and requiring more reliable communication should provide a finer quantization of their CSI. Finally, we determine the minimum required total feedback rate based on users' quality-of-service constraints and derive the scaling of the system performance with the total feedback rate.

Many U.S. students do not perform well on mathematics assessments with respect to algebra topics such as linear functions, a building-block for other functions. Poor achievement of U.S. middle school students in this topic is a problem. U.S. eighth graders have had average mathematics scores on international comparison tests such as Third International Mathematics Science Study, later known as Trends in Mathematics and Science Study, (TIMSS)-1995, -99, -03, while Singapore students have had highest average scores. U.S. eighth grade average mathematics scores improved on TIMMS-2007 and held steady onTIMMS-2011. Results from national assessments, PISA 2009 and 2012 and National Assessment of Educational Progress of 2007, 2009, and 2013, showed a lack of proficiency in algebra. Results of curriculum studies involving nations in TIMSS suggest that elementary textbooks in high-scoring countries were different than elementary textbooks and middle grades texts were different with respect to general features in the U.S. The purpose of this study was to compare treatments of linear functions in Singapore and U.S. middle grades mathematics textbooks. Results revealed features currently in textbooks. Findings should be valuable to constituencies who wish to improve U.S. mathematics achievement. Portions of eight Singapore and nine U.S. middle school student texts pertaining to linear functions were compared with respect to 22 features in three categories: (a) background features, (b) general features of problems, and (c) specific characterizations of problem practices, problem-solving competency types, and transfer of representation. Features were coded using a codebook developed by the researcher. Tallies and percentages were reported. Welch's t-tests and chi-square tests were used, respectively, to determine whether texts differed significantly for the features and if codes were independent of country. U.S. and Singapore textbooks differed in page appearance and number of pages, problems, and images. Texts were similar in problem appearance. Differences in problems related to assessment of conceptual learning. U.S. texts contained more problems requiring (a) use of definitions, (b) single computation, (c) interpreting, and (d) multiple responses. These differences may stem from cultural differences seen in attitudes toward education. Future studies should focus on density of page, spiral approach, and multiple response problems.

This thesis deals with content based automatic photo categorization. The aim of the work is to experiment with advanced techniques of image represenatation and to create a classifier which is able to process large image dataset with sufficient accuracy and computation speed. A traditional solution based on using visual codebooks is enhanced by computing color features, soft assignment of visual words to extracted feature vectors, usage of image segmentation in process of visual codebook creation and dividing picture into cells. These cells are processed separately. Linear SVM classifier with explicit data embeding is used for its efficiency. Finally, results of experiments with above mentioned techniques of the image categorization are discussed.

This diploma’s thesis discourses the cryptographic systems and ciphers, whose function, usage and practical implementation are analysed. In the first chapter basic cryptographic terms, symmetric and asymetric cryptographic algorithms and are mentioned. Also usage and reliability are analysed. Following chapters mention substitution, transposition, block and stream ciphers, which are elementary for most cryptographic algorithms. There are also mentioned the modes, which the ciphers work in. In the fourth chapter are described the principles of some chosen cryptographic algorithms. The objective is to make clear the essence of the algorithms’ behavior. When describing some more difficult algorithms the block scheme is added. At the end of each algorithm’s description the example of practical usage is written. The chapter no. five discusses the hardware implementation. Hardware and software implementation is compared from the practical point of view. Several design instruments are described and different hardware design programming languages with their progress, advantages and disadvantages are mentioned. Chapter six discourses the hardware implementation design of chosen ciphers. Concretely the design of stream cipher with pseudo-random sequence generator is designed in VHDL and also in Matlab. As the second design was chosen the block cipher GOST, which was designed in VHDL too. Both designs were tested and verified and then the results were summarized.