We study two data structuring problems under the bit probe model: the dynamic predecessor problem and integer representation in a manner supporting basic updates in as few bit operations as possible. The model of computation considered in this paper is the bit probe model. In this model, the complexity measure counts only the bitwise accesses to the data structure. The model ignores the cost of computation. As a result, the bit probe complexity of a data structuring problem can be considered as a fundamental measure of the problem. Lower bounds derived by this model are valid as lower bounds for any realistic, sequential model of computation. Furthermore, some of the problems are more suitable for study in this model as they can be solved using less than $w$ bit probes where $w$ is the size of a computer word. The predecessor problem is one of the fundamental problems in computer science with numerous applications and has been studied for several decades. We study the colored predecessor problem, a variation of the predecessor problem, in which each element is associated with a symbol from a finite alphabet or color. The problem is to store a subset $S$ of size $n,$ from a finite universe $U$ so that to support efficient insertion, deletion and queries to determine the color of the largest value in $S$ which is not larger than $x,$ for a given $x \in U.$ We present a data structure for the problem that requires $O(k \sqrt[k]{{\log U} \over {\log \log U}})$ bit probes for the query and $O(k^2 {{\log U} \over {\log \log U}})$ bit probes for the update operations, where $U$ is the universe size and $k$ is positive constant. We also show that the results on the colored predecessor problem can be used to solve some other related problems such as existential range query, dynamic prefix sum, segment representative, connectivity problems, etc. The second structure considered is for integer representation. We examine the problem of integer representation in a nearly minimal number of bits so that increment and decrement (and indeed addition and subtraction) can be performed using few bit inspections and fewer bit changes. In particular, we prove a new lower bound of $\Omega(\sqrt{n})$ for the increment and decrement operation, where $n$ is the minimum number of bits required to represent the number. We present several efficient data structures to represent integers that use a logarithmic number of bit inspections and a constant number of bit changes per operation.

We study two data structuring problems under the bit probe model: the dynamic predecessor problem and integer representation in a manner supporting basic updates in as few bit operations as possible. The model of computation considered in this paper is the bit probe model. In this model, the complexity measure counts only the bitwise accesses to the data structure. The model ignores the cost of computation. As a result, the bit probe complexity of a data structuring problem can be considered as a fundamental measure of the problem. Lower bounds derived by this model are valid as lower bounds for any realistic, sequential model of computation. Furthermore, some of the problems are more suitable for study in this model as they can be solved using less than $w$ bit probes where $w$ is the size of a computer word. The predecessor problem is one of the fundamental problems in computer science with numerous applications and has been studied for several decades. We study the colored predecessor problem, a variation of the predecessor problem, in which each element is associated with a symbol from a finite alphabet or color. The problem is to store a subset $S$ of size $n,$ from a finite universe $U$ so that to support efficient insertion, deletion and queries to determine the color of the largest value in $S$ which is not larger than $x,$ for a given $x \in U.$ We present a data structure for the problem that requires $O(k \sqrt[k]{{\log U} \over {\log \log U}})$ bit probes for the query and $O(k^2 {{\log U} \over {\log \log U}})$ bit probes for the update operations, where $U$ is the universe size and $k$ is positive constant. We also show that the results on the colored predecessor problem can be used to solve some other related problems such as existential range query, dynamic prefix sum, segment representative, connectivity problems, etc. The second structure considered is for integer representation. We examine the problem of integer representation in a nearly minimal number of bits so that increment and decrement (and indeed addition and subtraction) can be performed using few bit inspections and fewer bit changes. In particular, we prove a new lower bound of $\Omega(\sqrt{n})$ for the increment and decrement operation, where $n$ is the minimum number of bits required to represent the number. We present several efficient data structures to represent integers that use a logarithmic number of bit inspections and a constant number of bit changes per operation.

A novel photon flux monitor has been designed and tested for use at the Duke University High Intensity Gamma Source, where the photon beam produced is essentially mono-energetic but it is not tagged. Direct counting of the number of photons using a high-efficiency detector is not possible because of the high photon fluxes expected. Therefore, a direct counting detector with a low, accurately known efficiency was required.<p> The photon flux monitor based on a five scintillator paddle system detects recoil electrons and positrons from photoelectric, Compton and pair-production processes. It has been designed to be insensitive to gain and detector threshold changes and to be usable for photon energies above 5 MeV. It has been calibrated using direct counting with a NaI detector and its efficiency has been shown to be well predicted by a GEANT4 simulation.<p> Results of measurements, calibration and calculations required to characterize the 5-paddle photon flux monitor are presented. The photon flux monitor has met its design specifications of being able to determine the number of photons incident on it during the live time of a measurement to within a systematic error of 2%.<p> A paper based on the work for this thesis has been published in the Nuclear Instruments and Methods in Physics Research Journal.

The Knife-Edge Scanning Microscope (KESM) enables imaging of an entire mouse brain at sub-micrometer resolution. By using the data sets from the KESM, we can trace the neuronal and vascular structures of the whole mouse brain. I investigated effective methods for automatic seedpoint selection on 3D data sets from the KESM. Furthermore, based on the detected seedpoints, I counted the total number of somata and traced the neuronal structures in the KESM data sets. In the first step, the acquired images from KESM were preprocessed as follows: inverting, noise filtering and contrast enhancement, merging, and stacking to create 3D volumes. Second, I used a morphological object detection algorithm to select seedpoints in the complex neuronal structures. Third, I used an interactive 3D seedpoint validation and a multi-scale approach to identify incorrectly detected somata due to the dense overlapping structures. Fourth, I counted the number of somata to investigate regional differences and morphological features of the mouse brain. Finally, I traced the neuronal structures using a local maximum intensity projection method that employs moving windows. The contributions of this work include reducing time required for setting seedpoints, decreasing the number of falsely detected somata, and improving 3D neuronal reconstruction and analysis performance.

Thesis (Ph. D.)--University of Hawaii at Manoa, 2005. / Includes bibliographical references (leaves 129-135).

No description available.

The main purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the work presented in this thesis. Also, the definitions and notation used throughout the paper are introduced here The second chapter starts with examining the product spaces of the form {1; 2; : : : ;n} × {1; 2}. That is, we begin by analyzing a two-row by n-column space for n > N. Three separate approaches are discussed, and verified, to find the total number of convex sets on the space. A general formula is presented to obtain this total for all n. In the third chapter we take the same {1; 2; : : : ;n} × {1; 2} spaces from Chapter 2 and consider all the scenarios for adding a second disjoint convex set to the space. Adding a second convex set gives a collection of two mutually disjoint sets. Again, a general formula is presented to obtain this total number of such collections for all n. The fourth chapter takes the idea from Chapter 2 and expands it to product spaces {1; 2; : : : ;n} × {1; 2; : : : ;m} consisting of more than two rows. Here the creation of convex sets having z rows from those having z − 1 rows is exploited to obtain a model that will give the total number of z-row convex sets on any n × m space, provided the set occupies z adjacent rows. Finally, the fifth chapter describes all possible scenarios for convex sets to be placed in the {1; 2; : : : ;n}×{1; 2; : : : ;m} space. This chapter then explains the process needed to acquire a count of all convex sets on any such space as well. Chapter 5 ends by walking through this process with a concrete example, breaking it down into each scenario. We conclude by briefly summarizing the results and specifying future work we would like to further investigate, in Chapter 6.

The ability to discriminate relative and absolute number has been researched widely in both human and nonhuman species. However, the full extent of numerical ability in nonhuman animals, and the nature of the underlying numerical representation, on which discriminations are based, is still unclear. The aim of the current research was to examine the performance of pigeons and humans in tasks that require the discrimination of relative number (a bisection procedure), and absolute number (in a reproduction procedure). One of the main research questions was whether numerical control over responding could be obtained, above and beyond control by temporal cues in nonhuman animals, and if so, whether it was possible to quantify the relative influences of number and time on responding. Experiment 1 examines nonhuman performance in a numerical bisection task; subjects were presented with either 2 and 6, 4 and 12, or 8 and 24 keylight flashes across three different conditions, and were required to classify these flash sequences as either a “large” or “small” number, by pecking the blue or white key, respectively. Subjects were then tested with novel values within and 2 values higher and lower than the training values. Experiments 2-4 investigate responding in a novel numerical reproduction procedure, in which pigeons were trained to match the number of responses made during a production phase to the number of keylight flashes (2, 4, or 6) in a recently completed sample phase. Experiments 2 and 2A examined discrimination performance when the temporal variables, flash rate and sample phase duration, were perfectly correlated (Experiment 2) or only weakly correlated (Experiment 2a) with flash number. Acquisition of performance in the numerical reproduction procedure was investigated in Experiment 3. For Experiments 1-3, hierarchical regression analyses showed significant control by number over responding, after controlling for temporal cues. Additionally, positive transfer to novel values both within and outside the training range was obtained when the temporal organization of test sequences was similar to baseline training. Experiment 4 investigated the effects of increasing or decreasing the retention interval (RI) on performance in the reproduction procedure, and found this produced a response bias towards larger numbers, contrary to predictions based on previous RI research, and suggested responding was not affected by memorial decay processes. The structure of the representation of number developed by subjects in the bisection and reproduction procedures was investigated using analyses of responding and response variability in Chapters 2 and 6, respectively. Bisection points obtained in Experiment 1 were located at the arithmetic, not geometric mean of all three scales, and coefficients of variation (CVs) obtained in both the bisection and reproduction experiments tended to decrease as flash number increased. Additionally, analyses of the acquisition data found differences in average response number was better fit by a linear than logarithmic scale. These results show that responding did not conform to scalar variability and is largely inconsistent with previous nonhuman research. Together these results suggest responding appeared to be based on a linear scale of number with constant generalisation between values, similar to that associated with human verbal counting, rather than a logarithmic scale with constant generalisation or a linear scale with scalar generalisation between values. Experiment 5 compared pigeons’ and humans’ verbal and nonverbal discrimination performance with numbers 1-20 in analogous bisection, reproduction and report tasks. Human verbal and nonverbal performance in the three tasks was similar and resembled nonhuman performance, although verbal discriminations were more accurate and less variable. The main findings from Experiments 1 and 2A were replicated with humans; bisection points were located at the arithmetic mean, average response number increased linearly as sample number increased, though there was a tendency to underestimate sample number, and decreasing CVs were also obtained for values less than 8. An additional, interesting finding was that CVs showed scalar variability for values greater than 8, suggesting a less exact representation and discrimination process was being used for these values. Collectively, these five experiments provide new evidence for a nonverbal ability to discriminate relative and absolute number with increasing relative accuracy resembling human verbal counting in both human and nonhumans.

The interaction between exercise and cognitive task performance has been previously examined using cycle ergometer and treadmill running tasks. The interaction between natural (non-constrained) exercise and cognitive task performance has, however, been well less examined. An example of a natural exercise task would be running outdoors on a steep trail where route selection and foot placement are critical for the runner. The performance of runners is examined in a dual trail-running and working memory task. The working memory task involved counting tones, and was performed at both a low workload, in which they were asked to count every fourth low frequency tone and a high workload in which they were asked to count every fourth low, medium and high frequency tone. In experiment 1, runners performed the tone-counting tasks both while running on a steep trail with uneven terrain and while seated (control conditions). In addition, they ran the trail without a cognitive task load. Running distance and counting accuracy significantly decreased during the dual task trials, there was a linear trend the run distance decreased as the task got harder. As the secondary cognitive task demand increased running performance decreased (linear trend). Cognitive performance was only significantly impaired while running for the hard cognitive task (for the easy cognitive task there was no statistically significant difference). Participants reported an increased workload in the dual run-counting task conditions when compared with the seated task conditions. Reports of task focus and feeling of being spent (exhausted) also varied across task conditions. In experiment 2 unconstrained running was conducted in the same manner, on a flat-even terrain track to establish if the route selection and scanning required to negotiate uneven terrain was causing the dual-task interference, or if there is a general interference effect caused by the self-regulatory demands of running, or the direct demands of running itself (exercise). The linear trend of decreased running performance with increased secondary cognitive demand was similar to experiment 1 - the more cognitive load the less distance traveled. The effect on the cognitive task was, however, not evident in experiment 2; there was no statistically significant difference between cognitive task performance in the dual and single-task conditions. The findings outlined in these experiments, demonstrate dual cognitive tasks have a negative effect on running performance, and the cognitive task may also be affected depending on running intensity, particularly where self-paced natural running over terrain is coupled with complex cognitive tasks.

SuperB is a high luminosity e+e- collider experiment that is currently being designed to explore the flavour sector of particle physics. The detector at SuperB will contain a drift chamber, a gas filled device used to measure the momentum and identity of particles produced in the collisions. Particle identification in a drift chamber uses the measured amount of ionization deposited by the particle in the cells of the chamber, which provides a measurement of the particle speed. The ionization loss is traditionally measured by integrating the total charge released by the ionization after a gas amplification avalanche process. Since such a measurement has potentially large uncertainties associated with fluctuations in the gas amplification and other processes, it is possible that measuring the number of primary clusters of ionization caused by the particle could provide an improvement in the measurement of the ionization loss. The results of experiments performed at the University of Victoria and the TRIUMF laboratory M11 test beam using a SuperB drift chamber prototype to test the feasibility of counting clusters are presented here. The ability to separate muons and pions at the momenta explored in the TRIUMF testbeam was similar to the ability to separate pions and kaons at the higher momenta of SuperB. It was found that counting the clusters provides a significant improvement to particle identification when combined with the traditional measurement of the integrated charge. / Graduate