published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

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The dissertation describes a study of the instructional validity of the Arizona Instrument to Measure Standards (AIMS), a standards-based assessment. The study addresses the third- and fifth-grade mathematics portion of the 2005 AIMS test, focusing on two performance objectives per grade level. The study centers on the following questions: Can variation in students' mathematics achievement on AIMS be explained by instructional validity measures, namely: (1) alignment between test items and instructional characteristics and (2) by the degree of teacher emphasis on the two skills of interest to the study? Does the relationship between these measures and AIMS performance differ across grade levels? What possible explanations exist to account for grade level differences? Is there a relationship between the instructional validity measures and performance on the objectives of interest to this study?The dissertation discusses the evolution of thinking about instructional validity as standardized testing has changed. The study methods, including developing alignment measures from interview transcripts and classroom assessment examples collected from 16 third-grade teachers and 20 fifth-grade teachers in one school district are also described. Findings include that, although the method of using qualitative data to gauge instructional validity yields rich information about instructional practice, there was little instructional variation between classrooms in the district studied. This may have occurred because the district requires teachers to provide instruction exactly as specified in the district-adopted mathematics text. Some between-grade level differences do exist in the curricular alignment with AIMS. Teachers attempted to overcome this in their instruction despite district mandates to the contrary. Results support the instructional sensitivity of AIMS at third grade, but not at fifth grade. Differences in instructional sensitivity across grade levels might be linked to curricular differences; some third-grade teachers reported supplementing the curriculum to address the state standards while fifth-grade teachers largely reported that this was not necessary. Interestingly, the degree of alignment at third- and fifth-grade did not vary, although fifth-grade teachers placed more emphasis the study objectives. This speaks to third-grade teacher commitment to address the standards, and the challenges in emphasizing them when district-adopted curricula are not well-aligned with state standards.

In this thesis we make progress toward establishing the observational method of 21 cm intensity mapping as a sensitive and efficient method for mapping the large-scale structure of the Universe. In Part I we undertake theoretical studies to better understand the potential of intensity mapping. This includes forecasting the ability of intensity mapping experiments to constrain alternative explanations to dark energy for the Universe's accelerated expansion. We also considered how 21 cm observations of the neutral gas in the early Universe (after recombination but before reionization) could be used to detect primordial gravity waves, thus providing a window into cosmological inflation. Finally we showed that scientifically interesting measurements could in principle be performed using intensity mapping in the near term, using existing telescopes in pilot surveys or prototypes for larger dedicated surveys. Part II describes observational efforts to perform some of the first measurements using 21 cm intensity mapping. We develop a general data analysis pipeline for analyzing intensity mapping data from single dish radio telescopes. We then apply the pipeline to observations using the Green Bank Telescope. By cross-correlating the intensity mapping survey with a traditional galaxy redshift survey we put a lower bound on the amplitude of the 21 cm signal. The auto-correlation provides an upper bound on the signal amplitude and we thus constrain the signal from both above and below. This pilot survey represents a pioneering effort in establishing 21 cm intensity mapping as a probe of the Universe.

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Timing and electrical verification is an essential part of the design of VLSI digital MOS circuits. It consists of determining the maximum operating frequency of a circuit, and verifying that the circuit will always produce the expected logical behavior at or under this frequency. This complex task requires considerable computer and human resources. / The classical simulation approach cannot be used to insure the timing and electrical correctness of the large circuits that are now being designed. The huge number of possible states in large circuits renders this method impractical. Worst-case analysis tools alleviate the problem by restricting the analysis to a limited set of states which correspond to the worst-case operating conditions. However, existing worst-case analysis tools for MOS circuits present several problems. Their accuracy is inherently limited since they use a switch-level model. Also, these procedures have a high computational complexity because they resort to path enumeration to find the latest path in each transistor group. Finally, they lack the ability to analyze circuits with arbitrarily complex clocking schemes. / In this text, a new procedure for circuit-level timing analysis is presented. Because it works at electronic circuit level, the procedure can detect electrical errors, and attains an accuracy that is impossible to attain by other means. Efficient algorithms, based on graph theory, have been developed to partition the circuits in a novel way, and to recognize series and parallel combinations. This enables the efficient computation of worst-case, earliest and latest, waveforms in the circuit, using specially designed algorithms. The new procedure extracts automatically the timing requirements from these waveforms and can compute the clocking parameters, including the maximum clock frequency, for arbitrarily complex clocking schemes. / A computer program was written to demonstrate the effectiveness of the new procedure and algorithms developed. It has been used to determine the clocking parameters of circuits using different clocking schemes. The accuracy obtained on these parameters is around 5 to 10% when compared with circuit-level simulations. The analysis time grows linearly with the circuit size and is approximately 0.5s per transistor, on a microVAX II computer. This makes the program suitable for VLSI circuits.

In this thesis we make progress toward establishing the observational method of 21 cm intensity mapping as a sensitive and efficient method for mapping the large-scale structure of the Universe. In Part I we undertake theoretical studies to better understand the potential of intensity mapping. This includes forecasting the ability of intensity mapping experiments to constrain alternative explanations to dark energy for the Universe's accelerated expansion. We also considered how 21 cm observations of the neutral gas in the early Universe (after recombination but before reionization) could be used to detect primordial gravity waves, thus providing a window into cosmological inflation. Finally we showed that scientifically interesting measurements could in principle be performed using intensity mapping in the near term, using existing telescopes in pilot surveys or prototypes for larger dedicated surveys. Part II describes observational efforts to perform some of the first measurements using 21 cm intensity mapping. We develop a general data analysis pipeline for analyzing intensity mapping data from single dish radio telescopes. We then apply the pipeline to observations using the Green Bank Telescope. By cross-correlating the intensity mapping survey with a traditional galaxy redshift survey we put a lower bound on the amplitude of the 21 cm signal. The auto-correlation provides an upper bound on the signal amplitude and we thus constrain the signal from both above and below. This pilot survey represents a pioneering effort in establishing 21 cm intensity mapping as a probe of the Universe.

No description available.