Gravitational Wave Timing Residual Models for Pulsar Timing Experiments

The ability to detect gravitational waves now gives scientists and astronomers a new way in which they can study the universe. So far, the scientific collaboration LIGO has been successful in detecting binary black hole and binary neutron star mergers. These types of sources produce gravitational waves with frequencies of the order hertz to millihertz. But there do exist other theoretical sources which would produce gravitational waves in different parts of the frequency spectrum. Of these are the theoretical mergers of supermassive black hole binaries (SMBHBs), which could occur upon the merging of two galaxies with supermassive black holes at their cores. Sources like these would produce gravitational waves generally around the nanohertz regime, and the current main effort for detecting and measuring these waves comes from pulsar timing experiments. Detection of gravitational waves in these experiments would come as small fluctuations in the otherwise extremely regular period of pulsars over a long period of time (months to decades). There are numerous goals for this dissertation. The first is to re-present much of the fundamental physics and mathematics concepts behind the calculations in this paper. While there exist many reference sources in the literature, we simply try to offer a fully self-contained explanation of the fundamentals of this research which we hope the reader will find helpful. It is often a challenge when jumping into a new field of study to quickly learn and understand the fundamentals (like the derivations of various formulae and the assumptions behind the models), so if this dissertation can help future readers to connect the dots between the blanks not filled in by other literature sources, then this goal will be accomplished. The pedantic approach to this dissertation is also helpful since much of the initial work for this dissertation was theoretical development of the mathematical models used in pulsar timing. The next goal broadly speaking has been to combine the efforts of two previous studies by Deng & Finn (2011) and Corbin & Cornish (2010) to further develop the mathematics behind the currently used pulsar timing models for detecting gravitational waves with pulsar timing experiments. Previous timing residual models have first been derived assuming that the pulsar timing array receives plane-waves coming from distant sources (with the notable exception of Deng & Finn). Then these models can either treat the SMBHB as a monochromatic gravitational wave source, or model the frequency evolution of the gravitational waves over the thousands to tens of thousands of years it takes light to travel from the pulsar to the Earth. Our research began by first generalizing these models by removing the plane-wave assumption. In Chapter 3 we classify four regimes of interest (Figure 3.5), governed by the main assumptions made when deriving each regime. Of these four regimes the plane-wave models are well established in previous literature. We add a new regime which we label Fresnel, as we will show it becomes important for significant Fresnel numbers describing the curvature of wavefronts. With these mathematical models developed, in Chapter 6 we present the first main study investigated which was to forecast the ability of future pulsar timing experiments to probe and measure these Fresnel effects. Here we show the constraints needed on the pulsar timing experiments themselves (largely explained by the discussion in Chapter 5), and the types of precision measurements which could theoretically be achieved. Then we generalize our models to a cosmologically expanding universe in Chapter 7. We show that in the fully general Fresnel frequency evolution regime, the Hubble constant enters the model and can now be measured directly. In this chapter we investigate what we will need of future experiments in order to obtain a measurement of this parameter. This offers future pulsar timing experiments the unique possibility of being able to procure a purely gravitational wave-based measurement of the Hubble constant. Finally, Chapter 8 shows the initial steps taken to extend this work in the future, specifically for Doppler tracking experiments. The main goal of the inclusion of this final section, which was not the primary focus of this dissertation, is to point out how the mathematics and models derived in Chapters 2 and 3 can be applied and extended more generally

Modeling Cost Effectiveness of Green Infrastructure at Stormwater Runoff Critical Points in Maunalua Bay Watershed, Oʻahu

Like many urbanized areas, the watersheds surrounding Maunalua Bay are highly developed with impervious surfaces and channelized waterways. This can cause issues with stormwater. Stormwater is water that flows over impermeable surfaces (roads, roofs, etc.) after heavy rain events. Stormwater can pick up pollutants as is flows down slope, negatively impacting the health of water bodies. It can also cause flood events impacting infrastructure and lives Green Infrastructure (G.I.) techniques can be implemented to improve conventional infrastructure and stormwater management. Green infrastructure is an approach to stormwater management that tries to mimic the natural water cycle. Most green infrastructure traps and treats water from a storm event and then slowly releases it back into the environment allowing for more control on the quantity of water being released. We created a map that identifies areas in Maunalua that have the highest potential for stormwater mitigation via G.I. Using existing maps on land cover, slope , soil permeability and storm drain density, we created a model that ranks each map attribute in terms of stormwater risk. This map can assist regional stakeholders in prioritizing and evaluating the costs and benefits of adopting G.I. techniques.Our model identified two stormwater "hotspots" within the Kamilo Iki watershed. One "hotspot" validated the model with existing green infrastructure already present. The other "hotspot" lacked green infrastructure. Using the EPA stormwater calculator we identified the most cost effective green infrastructure for a residential neighborhood.Malama Maunalu

Is There a Relationship Between Mathematics Background and Conception of Proof?

To invest in the future of mathematics education is to invest in our future teachers. Equipping such individuals should be the utmost priority, for they will communicate mathematics to our students. Research shows that the way we work with and explain mathematics is consequential to our proof scheme; that is, the proof schemes we hold are the proof schemes we will inevitably teach. This study explores the possible proof schemes and mindsets held by ten university students studying mathematics education at Lee University--six enrolled in a geometry course and four in an algebra course. Through interviews and critical thinking exercises, we analyzed the future students\u27 proof schemes and views on mathematics. Our analysis found that participants who had encountered proof-based mathematics courses had a tendency to approach problems analytically, which implied the existence of an association between their definitions of proof and methods of problem-solving. This relationship perhaps has implications about teacher preparation and development prior to entering the classroom, thus revealing its significance to student success

Multimessenger Approaches to Supermassive Black Hole Binary Detection and Parameter Estimation II: Optimal Strategies for a Pulsar Timing Array

Pulsar timing arrays (PTAs) are Galactic-scale gravitational wave (GW) detectors consisting of precisely-timed pulsars distributed across the sky. Within the decade, PTAs are expected to detect the nanohertz GWs emitted by close-separation supermassive black hole binaries (SMBHBs), thereby opening up the low frequency end of the GW spectrum for science. Individual SMBHBs which power active galactic nuclei are also promising multi-messenger sources; they may be identified via theoretically predicted electromagnetic (EM) signatures and be followed up by PTAs for GW observations. In this work, we study the detection and parameter estimation prospects of a PTA which targets EM-selected SMBHBs. Adopting a simulated Galactic millisecond pulsar population, we envisage three different pulsar timing campaigns which observe three mock sources at different sky locations. We find that an all-sky PTA which times the best pulsars is an optimal and feasible approach to observe EM-selected SMBHBs and measure their source parameters to high precision (i.e., comparable to or better than conventional EM measurements). We discuss the implications of our findings in the context of the future PTA experiment with the planned Deep Synoptic Array-2000 and the multi-messenger studies of SMBHBs such as the well-known binary candidate OJ 287.Comment: 14 pages, 6 figures, 3 tables; ApJ accepted; data will be available with the ApJ publicatio

Spliced DNA sequences in the Paramecium germline: their properties and evolutionary potential

Despite playing a crucial role in germline-soma differentiation, the evolutionary significance of developmentally regulated genome rearrangements (DRGRs) has received scant attention. An example of DRGR is DNA splicing, a process that removes segments of DNA interrupting genic and/or intergenic sequences. Perhaps, best known for shaping immune-system genes in vertebrates, DNA splicing plays a central role in the life of ciliated protozoa, where thousands of germline DNA segments are eliminated after sexual reproduction to regenerate a functional somatic genome. Here, we identify and chronicle the properties of 5,286 sequences that putatively undergo DNA splicing (i.e., internal eliminated sequences [IESs]) across the genomes of three closely related species of the ciliate Paramecium (P. tetraurelia, P. biaurelia, and P. sexaurelia). The study reveals that these putative IESs share several physical characteristics. Although our results are consistent with excision events being largely conserved between species, episodes of differential IES retention/excision occur, may have a recent origin, and frequently involve coding regions. Our findings indicate interconversion between somatic—often coding—DNA sequences and noncoding IESs, and provide insights into the role of DNA splicing in creating potentially functional genetic innovation

Spatial patterns of Fasciola hepatica and Calicophoron daubneyi infections in ruminants in Ireland and modelling of C. daubneyi infection

peer-reviewedBackground Fasciola hepatica has always represented a threat to Irish livestock because the Irish climate is highly suitable for the main local intermediate host of the parasite, the snail Galba truncatula. The recent clinical emergence of infections due to Calicophoron daubneyi has raised the question of whether the two parasites, which share a niche during part of their life-cycles, interact in some way. Here, we used geographical information systems (GIS) to analyse the distribution of both parasites in cattle and sheep. We also developed the first predictive model of paramphistomosis in Ireland. Results Our results indicated that, in cattle, liver fluke infection is less common than rumen fluke infection and does not exhibit the same seasonal fluctuations. Overall, we found that cattle had a higher likelihood of being infected with rumen fluke than sheep (OR = 3.134, P < 0.01). In addition, infection with one parasite increased the odds of infection with the other in both host species. Rumen fluke in cattle showed the highest spatial density of infection. Environmental variables such as soil drainage, land cover and habitat appeared to be the most important risk factors for C. daubneyi infection, followed by rainfall and vegetation. Overall the risk of infection with this parasite was predicted to be higher in the west of the country. Conclusions This study shows differences between the infection rates and spatial patterns of bovine and ovine infections with F. hepatica and C. daubneyi in Ireland. Whether the reasons for this are due to susceptibility, exposure and/or management factors is yet to be determined. Furthermore, the rumen fluke model indicates distinct risk factors and predicted distribution to those of F. hepatica, suggesting potential biological differences between both parasite species.This work was supported by the European Union Horizon 2020 programme (PARAGONE: vaccines for animal parasites. H2020-EU.3.2. SOCIETAL CHALLENGES, under grant agreement No 635408), who provided funding for training and software access used in the analysis. The Department of Agriculture Food and the Marine - Research Stimulus Fund though the Flukeless Research Project (under project no 13/S/405), provided data employed in the modelling process

Supplementary data for article: Casey, W. T.; Nikodinović-Runić, J.; Fonseca Garcia, P.; Guzik, M. W.; McGrath, J. W.; Quinn, J. P.; Cagney, G.; Auxiliadora Prieto, M.; O’Connor, K. E. The Effect of Polyphosphate Kinase Gene Deletion on Polyhydroxyalkanoate Accumulation and Carbon Metabolism in Pseudomonas Putida KT2440. Environmental Microbiology Reports 2013, 5 (5), 740–746. https://doi.org/10.1111/1758-2229.12076

Supporting information for: [https://doi.org/10.1111/1758-2229.12076]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/1408]Related to accepted version: [http://cherry.chem.bg.ac.rs/handle/123456789/3553