In this thesis, we consider real matrix functions that depend on two parameters and study the problem of how to detect and approximate parameters' values where the singular values coalesce. We prove several results connecting the existence of coalescing points to the periodic structure of the smooth singular values decomposition computed around the boundary of a domain enclosing the points. This is further used to develop algorithms for the detection and approximation of coalescing points in planar regions. Finally, we present techniques for continuing curves of coalescing singular values of matrices depending on three parameters, and illustrate how these techniques can be used to locate coalescing singular values of complex-valued matrices depending on three parameters.

Bibliography: p. 69-81. / 81, [52] p., [16] leaves of plates : ill. (chiefly col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis demonstrates that string (a homologue of the mitotic initiator cdc 25 from Schizosaccharomyces pombe) is a downstream target of the patterning genes, making a direct connection between patterning information and morphogenesis, which suggests that mitotic timing forms an independent and important part of morphogenesis. / Thesis (Ph.D.)--University of Adelaide, Depts. of Biochemistry and Genetics, 1997

The unemployment is one of the main economic indicators. Thanks to time series analysis and predicting values, we can take measures of eliminating negative aspects of the unemployment in the economy. This thesis is concentrated on connection between theory of unemployment with time series analysis of unemployment rate, especially based on Box-Jenkins methodology.

M.Sc. (Geology) / Please refer to full text to view abstract

Red grouper (Epinephelus morio) are long-lived, commercially important, soniferous fish belonging to the family Epinephelidae. Found throughout the western North Atlantic and Gulf of Mexico, they are protogynous hermaphrodites, and peak spawning occurs from March through May. Unlike many grouper species, red grouper do not form large spawning aggregations; rather, they form small polygynous groups, and remain in relatively close proximity to rocky depressions excavated in the sandy bottom by males. This excavation activity creates structure and habitat for a wide variety of species, and as a result, red grouper are a keystone species on the West Florida Shelf. While extensive life-history information exists, largely from fishery catches, little is known about sound production or behavior of red grouper in their natural environment. Passive acoustic recordings combined with simultaneous digital video recordings were used to investigate sonic activity and behavior of red grouper on the Steamboat Lumps and Madison-Swanson marine reserves on the West Florida Shelf. Red grouper were found to produce a unique series of low-frequency (180 Hz peak) pulses, consisting of 1-4 brief (0.15 s) broadband pulses and a 0.5-2 s down-swept "buzz" (i.e., short call); occasionally these were followed by a rapid series of 10-50 broadband pulses (i.e., pulse train). Sound production was observed throughout the day and night, but most sounds occurred between sunrise and sunset, with a noticeable increase during late afternoon. Behaviors associated with sound production included territorial displays and courtship interactions, indicating that sound production is likely related to spawning activity. Thus, monitoring red grouper using passive acoustics could be an effective tool in fisheries management and conservation efforts.

A new macroscopic ovarian reproductive maturity index for haddock, Melanogrammus aeglefinus L, was developed to improve field collection of reproductive stage data. The index was tested, validated and revised based on a comparison with a laboratory histological staging method. The comparison of field and histological observations helped to improve the field index and methodologies and provided useful insight into the reproductive biology of Haddock. Although laboratory staging based on histology is inherently more accurate than any macroscopic field staging method, field observations can reveal weaknesses in the laboratory approach due to sampling bias. The revised field index includes three new macroscopic stages that represent a progression in final oocyte maturation from early to late, which were found to be reliable for staging spawning readiness in the field. This index was then used to study a population of Haddock in the Gulf of Maine to determine if it exhibits diel spawning periodicity. Commercial fishing vessels were chartered for 25 dedicated longlining trips to collect sexually mature haddock in the Southwestern Gulf of Maine at locations identified by commercial fishers as having spawning aggregations. In order to examine diel effects on haddock reproduction, the change in catch per unit effort and percentage of male and female haddock of all reproductive maturity stages together with the gonadosomatic index were observed across a 24 hour diel cycle. Only females in hydration stage 3 (defined as late final oocyte maturation stage ovaries with 50-75% of oocytes hydrated) were significantly affected by time of day with significant increases in both catch per unit effort and percentage of hydration stage 3 haddock during the night. Because H3 is the most advanced reproductive stage observed prior to a spawning event and therefore the best indicator of imminent spawning these results demonstrate that female haddock in Southwestern Gulf of Maine primarily spawn during night hours with a peak between 2100 and 0100 hours. No diel trend was observed for any male reproductive stages. Additionally, no diel trend was observed in male or female reproductive stages unrelated to spawning including immature, spent and resting.

No description available.

<p>We investigate the function ρ_<em>d</em>(<em>n</em>) = max { <em>r</em>(<em><strong>x</strong></em>) | <em><strong>x</strong></em> is a (<em>d</em>, <em>n</em>)-string } where <em>r</em>(<em><strong>x</strong></em>) is the number of runs in the string <em><strong>x</strong></em>, and a (<em>d</em>, <em>n</em>)-string is a string with length <em>n</em> and exactly <em>d</em> distinct symbols. Our investigation is motivated by the conjecture that ρ_<em>d</em>(<em>n</em>) ≤ <em>n</em>-<em>d</em>. We present and discuss fundamental properties of the ρ_<em>d</em>(<em>n</em>) function. The values of ρ_<em>d</em>(<em>n</em>) are presented in the (<em>d</em>, <em>n</em>-<em>d</em>)-table with rows indexed by <em>d</em> and columns indexed by <em>n</em>-<em>d</em> which reveals the regularities of the function. We introduce the concepts of the r-cover and core vector of a string, yielding a novel computational framework for determining ρ_<em>d</em>(<em>n</em>) values. The computation of the previously intractable instances is achieved via first computing a lower bound, and then using the structural properties to limit our exhaustive search only to strings that can possibly exceed this number of runs. Using this approach, we extended the known maximum number of runs in binary string from 60 to 74. In doing so, we find the first examples of run-maximal strings containing four consecutive identical symbols. Our framework is also applied for an arbitrary number of distinct symbols, <em>d</em>. For example, we are able to determine that the maximum number of runs in a string with 23 distinct symbols and length 46 is 23. Further, we discuss the structural properties of a shortest (<em>d</em>, <em>n</em>)-string <em><strong>x</strong></em> such that <em>r</em>(<em><strong>x</strong></em>) > <em>n</em>-<em>d</em>, should such a string exist.</p> / Doctor of Philosophy (PhD)

Societies in much of the Horn of Africa are affected by variability in two distinct rainy seasons: the March-May (MAM) “long” rains and the October-December (OND) “short” rains. The region is the driest area of the tropics, while its societies are heavily dependent on the rainfall cycle. Especially worrying are anomalously dry conditions, which, together with other factors, contribute to food insecurity in the region. The recent 2020-2023 5-season drought, associated with the concurrent “triple-dip” La Niña and resulting in tens of millions of people facing “high levels of food insecurity” (cf: IGAD), renewed fears of long-term and possibly anthropogenically-forced drying trends, especially during the MAM long rains. A long-term decline in the long rains beginning in the early 1980s and lasting until the 2010s had indeed been noted in studies examining historical station-based observations, satellite observations, and farmer recollections in the region, though seasonal average rainfall has since partially recovered. Consequently, global climate models (GCMs) are increasingly used to project changes in rainfall characteristics under global warming scenarios and associated impacts on societies, such as agricultural production, groundwater resources, and urban infrastructure, in addition to providing seasonal forecasts used for near-term decision-making. However, GCMs uniformly predict long-term wetting in both seasons despite observed drying trends in the long rains, an “East African Paradox” that complicates the ability of decisionmakers to plan for future rainfall conditions. Previous generations of GCMs have known biases in key dynamics of the regional hydroclimate. Decisionmakers relying on projections of future rainfall in the GHA therefore need to know whether current GCM projections are trustworthy. In other words, can we be confident in future modeled wetting trends in both the long and short rains? This thesis pursues this question in three parts. Chapter 2 seeks to understand the fundamental dynamics affecting the East African seasonal rainfall climatology, which is unique for its latitude in both its aridity and for the dynamical differences between its two rainy seasons. I explain these characteristics through the climatology of moist static stability, estimated as the difference between surface moist static energy h? and midtropospheric saturation moist static energy h*. In areas and at times when this difference, h? − h*, is higher, rainfall is more frequent and more intense. However, even during the rainy seasons, h? − h* < 0 on average and the atmosphere remains largely stable, in line with the region’s aridity. The seasonal cycle of h? − h*, to which the unique seasonal cycles of surface humidity, surface temperature, and midtropospheric temperature all contribute, helps explain the double-peaked nature of the regional hydroclimate. Despite tropospheric temperature being relatively uniform in the tropics, even small changes in h* can have substantial impacts on instability; for example, during the short rains, the annual minimum in regional h* lowers the threshold for convection and allows for instability despite surface humidity anomalies being relatively weak. This h? − h* framework can help identify the drivers of interannual variability in East African rainfall or diagnose the origin of biases in climate model simulations of the regional climate. Chapter 3 applies these results to conduct a process-based model evaluation of the ability of GCMs from the 6th phase of the Coupled Model Intercomparison Project (CMIP6, the latest GCM generation) to simulate the historical climatology and variability in the East African long and short rains. I find that key biases from the 5th phase of the Coupled Model Intercomparison Project (CMIP5) remain or are worsened, including long rains that are too short and weak and short rains that are too long and strong. Model biases are driven by a complex set of related oceanic and atmospheric factors, including simulations of the Walker Circulation. h? − h* is too high in models, requiring more instability for the same amount of rainfall than in observations. Biased wet short rains in models are connected with Indian Ocean zonal sea surface temperature (SST) gradients that are too warm in the west and convection that is too deep. Models connect equatorial African winds with the strength of the short rains, though in observations a robust connection is primarily found in the long rains. Model mean state biases in the timing of the western Indian Ocean SST seasonal cycle are associated with certain rainfall timing biases, though both biases may be due to a common source. Simulations driven by historical SSTs (so-called ‘AMIP’ runs) often have larger biases than fully coupled runs. However, models generally respond to teleconnections with the Indian Ocean Dipole and the El Niño Southern Oscillation in particular as expected, maintaining the possibility that trends in the long and short rains may also respond correctly to simulated trends in large-scale dynamics. Finally, Chapter 4 applies these results to directly tackle the East African Paradox by analyzing model trends across the entire observational record to identify under what conditions they fail to reproduce observed trends. Since even with perfect models and observational records model output may differ from observations due to internal variability, I analyze the full spread of CMIP6 output, including Large Ensembles and totalling 598 runs from 47 models. I find that while observed trends are always within the model spread if all runs from all Large Ensembles are considered, the Paradox remains in CMIP6 models, since GCMs substantially underproduce strong drying trends compared to observations. Within the observational record, the Paradox is limited to the time period with the most anomalous drying trends (especially in the years 1980-2010); the recent recovery in rainfall falls comfortably within the range of GCM simulations. The Paradox is not visible in AMIP runs forced with observed historical SSTs, suggesting that biases in simulations of SSTs may be part of the explanation, though clear causality remains elusive. The transition towards more biased trends from SST-forced to coupled runs can also be seen in output from hindcasts from seasonal forecast models, where trends calculated from short-lead-time projections (when the ocean state resembles observations) do not feature the Paradox, while lead times starting with 1.5 months do. More broadly, I show that climate model simulations of observed trends alone cannot be used to reject model predictions of increased (or decreased) precipitation under future forcings. Decision-makers relying on future projections of rainfall trends in East Africa will likely need to consider the possibility of further drying in addition to wetting trends from GCMs.

Intensity-duration-frequency (IDF) curves are widely used for peak discharge estimation in designing hydraulic structures. The traditional Gumbel probability method entails selecting annual maximum rainfall depths (intensities) conditioned on a fixed time window width (which in general will not coincide with the rainfall event duration) from a continuous record to perform a frequency analysis in terms of the marginal distribution. The digitized database contains annual maximum intensities for selected discrete durations. This method presents problems when intensities are required for arbitrary durations which are not part of the selected durations. Accurate interpolated and especially extrapolated intensity values are hard to obtain. The present study offers two methods both involving a joint probability approach to overcome the deficiencies inherent in the traditional method of IDF analysis. The first joint probability approach employs Box-Cox and modulus transformations to transform original data to near bivariate normality. The second method does not require such a transformation. Instead, it uses the closed-form bivariate Burr III cumulative distribution to fit the data. Another advantage of the joint probability approach is that it allows one to gauge the rarity of certain extreme events, such as probable maximum precipitation, in terms of the joint occurrence of its extremely high intensity and a sufficiently long duration (e.g. 24 hours). The joint probability approach is applied to three data sets. The resulting conditional probability intensity estimates are quite close to those obtained by traditional Gumbel IDF analysis. In addition, reliable interpolated and extrapolated intensities are available because the approach essentially fits a flexible surface to the discrete data with the capability of providing a complete probabilistic structure. / Master of Science