Equidistribution of Algebraic Numbers of Norm One in Quadratic Number Fields

Given a fixed quadratic extension K of Q, we consider the distribution of elements in K of norm 1 (denoted N). When K is an imaginary quadratic extension, N is naturally embedded in the unit circle in C and we show that it is equidistributed with respect to inclusion as ordered by the absolute Weil height. By Hilbert's Theorem 90, an element in N can be written as \alpha/\bar{\alpha} for some \alpha \in O_K, which yields another ordering of \mathcal N given by the minimal norm of the associated algebraic integers. When K is imaginary we also show that N is equidistributed in the unit circle under this norm ordering. When K is a real quadratic extension, we show that N is equidistributed with respect to norm, under the map \beta \mapsto \log| \beta | \bmod{\log | \epsilon^2 |} where \epsilon is a fundamental unit of O_K.Comment: 19 pages, 2 figures, comments welcome

Equidistribution of Elements of Norm 1 in Cyclic Extensions

Upon quotienting by units, the elements of norm 1 in a number field $K$ form a countable subset of a torus of dimension $r_1 + r_2 - 1$ where $r_1$ and $r_2$ are the numbers of real and pairs of complex embeddings. When $K$ is Galois with cyclic Galois group we demonstrate that this countable set is equidistributed in this torus with respect to a natural partial ordering.Comment: 7 page

Amphibians and Reptiles of United States Department of Defense Installations

The U.S. Department of Defense (DoD) occupies approximately 10.1 million ha of land within the U.S. spanning most ecosystems contained therein. To date, no comprehensive agency-wide inventory of amphibian and reptile species has been compiled. We developed an amphibian and reptile species inventory for 415 DoD installations/sites and evaluated species diversity. The amphibian and reptile species confirmed present on DoD sites represent 66% of the total native species documented in the continental U.S. Snakes are the most widespread group found on DoD lands. Of the military services, Army sites have the greatest number of confirmed species, federally listed, state-listed, and At-risk species. There are 24 federally listed (threatened or endangered), 55 state- listed, and 70 At-risk species confirmed present on DoD sites. Thirty non-native and native transplant amphibian and reptile species/subspecies are also confirmed present on DoD sites. Lastly, we verified that approximately half of the military sites evaluated in this study have at least one venomous snake species confirmed present. Our study results assist directly with ongoing management and conservation of amphibian and reptile species on DoD lands and confirm military lands comprise a significant contribution to biodiversity conservation

Advances in Underactuated Spacecraft Control

This dissertation addresses the control of a spacecraft which either becomes underactuated due to onboard failures or is made underactuated by design. Successfully controlling an underactuated spacecraft can extend spacecraft operational life in orbit and improve the robustness of space missions. The novel contributions of the dissertation include the following. Firstly, switching feedback controllers are developed for the attitude control of an underactuated spacecraft equipped with two pairs of thrusters, or two reaction wheels (RWs), or two control moment gyros (CMGs). The problem is challenging; e.g., even in the zero total angular momentum case, no smooth or even continuous time-invariant feedback law for stabilizing a desired orientation exists. The method exploits the separation of the system into inner-loop base variables and outer-loop fiber variables. The base variables track periodic reference trajectories, the amplitude of which is governed by parameters that are adjusted to induce an appropriate change in the fiber variables towards the desired pointing configuration. Secondly, nonlinear Model Predictive Control (MPC) is applied to the attitude dynamics of an underactuated spacecraft with two RWs and zero angular momentum. MPC has the remarkable ability to generate control laws that are discontinuous in the state. By utilizing nonlinear MPC, the obstruction to stabilizability is overcome and attitude maneuvers can be performed while enforcing constraints. Thirdly, an unconventional pathway is discussed for recovering the linear controllability of an underactuated spacecraft with two RWs by accounting for the effects of solar radiation pressure (SRP) in the spacecraft attitude model. Necessary and sufficient conditions for recovering linear controllability are given, and with linear controllability restored, conventional controllers can be designed for underactuated spacecraft. Lastly, two sets of coupled translational and rotational equations of motion for a spacecraft in a central gravity field are derived. The spacecraft is assumed to have only internal attitude actuators and the equations of motion are relative with respect to an equilibrium orbit. Under reasonable assumptions on the spacecraft configuration and equilibrium orbit, the coupled dynamics are small-time locally controllable (STLC), which opens a path to utilizing conventional control techniques to move translationally in space by employing attitude control only.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133430/1/cdpete_1.pd

The effect of suitcase concealment on the insect colonisation: A pilot study in Western Australia

Knowing and understanding the stages involved in the decomposition process of a cadaver is crucial in the ability to accurately estimate the post-mortem interval (PMI) or time since death (TSD). A large amount of information about the PMI can be provided by the state of decomposition as well as the fauna colonizing the body. This is the case if decomposition is treated as a semi-continuous variable and used in conjunction with accumulated degree days (ADD) and by the successional waves of the insects and other arthropods consuming the body. PMI is a pivotal information in forensic investigations as it can be used in homicide cases by personnel of law enforcement for crime scene reconstruction and for the exclusion of potential perpetrators as well as to support witness testimony. Establishing the range of natural events and environmental conditions that were likely to have affected the remains with the passing of seasons can also be aided by knowing the PMI, permitting a more thorough taphonomic analysis. However, the use of a method to conceal a body (such as burials, wrapping, suitcases) may affect changes within a body and the associated entomological activity that are different to bodies that are exposed to the environment. Therefore, it is necessary to understand the unique taphonomic processes that occur when a body is concealed. While numerous types of concealment have been researched and investigated in the past, minimal research has been specifically related to concealment within a suitcase. This literature review aims to address the effects of different concealment methods, with main focus on suitcase concealment, on the decomposition rate and entomological activity of a cadaver. KEYWORDS: forensic science, forensic entomology, taphonomy, decomposition, accumulated degree days, post-mortem interval, concealmen

Functional analysis of Zinc finger proteins in the arbuscular mycorrhiza symbiosis of Medicago truncatula suggests a regulatory involvement of the PALM1 transcription factor

The arbuscular mycorrhizal (AM) symbiosis is a widespread beneficial association of ~80% of vascular plant species with a variety of soil-dwelling fungi. Establishing and maintaining this symbiosis and in particular the arbuscule as its central intracellular interface requires major transcriptional reprogramming of the host cells in the root cortex. Although major efforts have been successful in identifying key members of signaling pathways contributing to the regulation of the AM symbiosis,mechanisms for finetuning the association with respect to the hormonal and nutritional status of the host plant are still largely unknown. As part of this study, four Medicago truncatula genes encoding Zinc finger (ZF) proteins were identified to be transcriptionally upregulated in roots colonized by Rhizophagus irregularis. Of these genes, MtZf1, MtZf2 and MtZf3 were not characterized prior to this study, while MtPalm1, encoding a C2H2-family transcription factor, had been identified to act as a regulator in M. truncatula compound leaf development. As part of a functional analysis, the activity of these genes was confirmed to be strongly correlated with the growth of intraradical AM fungal structures via transcript measurements and histochemical localizations. These studies also indicated the involvement of upstream/overlapping ORFs in the regulation of these genes, in particular MtPalm1. Additionally, three separate gene silencing experiments via RNA-interference demonstrated that roots deficient in MtPALM1, MtZF1 and MtZF2 were quantitatively hampered in AM fungal colonization, with functional disruption of MtPalm1 yielding average ~50% reductions in arbuscule formation. These phenotypes were confirmed for MtPalm1 and MtZf2 in stable Tnt1-insertion mutant lines and could be rescued through complementation via the introduction of a functional gene copy. Transcriptome profiles obtained from MtPALM1-deficient mycorrhized roots suggested this TF to act as a potential link between AM-symbiotic signaling involving strigolactones and other phytohormones, most crucially auxin. Conversely, heterologous protein interaction studies via a Yeast 2-Hybrid library mating suggested that the putative RING domain protein MtZF1 functions in targeted ubiquitination prior to AM fungal colonization. Furthermore, promoter-binding assays performed in a Yeast 1-Hybrid system gave indications of the position of the four ZFs studied in known AM regulatory networks, with protein-DNA interactions pointing to an involvement of key regulators such as RAM1, NSP2 and AMrelated NF-Y-proteins in the regulation of MtPalm1-, MtZf1- and MtZf3-expression. As a whole, the present thesis provides novel insights into the previously unknown contributions of ZF proteins to the fine-tuning of AM-symbiotic interactions, including the surprising role of the leaf developmental regulator MtPALM1 in modulating the level of AM-colonization, possibly by integrating hormonal signals during mycorrhization

Preseason Lower Extremity Functional Test Scores Are Not Associated With Lower Quadrant Injury - A Validation Study With Normative Data on 395 Division III Athletes

Background: Preseason performance on the lower extremity functional test (LEFT), a timed series of agility drills, has been previously reported to be associated with future risk of lower quadrant (LQ = low back and lower extremities) injury in Division III (D III) athletes.Validation studies are warranted to confirm or refute initial findings. Hypothesis/Purpose: The primary purpose of this study was to examine the ability of the LEFT to discriminate injury occurrence in D III athletes, in order to validate or refute prior findings. It was hypothesized that female and male D III athletes slower at completion of the LEFT would be at a greater risk for a non-contact time-loss injury during sport. Secondary purposes of this study are to report other potential risk factors based on athlete demographics and to present normative LEFT data based on sport participation. Methods: Two hundred and six (females = 104; males = 102) D III collegiate athletes formed a validation sample. Athletes in the validation sample completed a demographic questionnaire and performed the LEFT at the start of their sports preseason. Athletic trainers tracked non-contact time-loss LQ injuries during the season. A secondary analysis of risk based on preseason LEFT performance was conducted for a sample (n = 395) that consisted of subjects in the validation sample (n = 206) as well as athletes from a prior LEFT related study (n = 189). Study Design: Prospective cohort Results: Male athletes in the validation sample completed the LEFT [98.6 (± 8.1) seconds] significantly faster than female athletes [113.1 (± 10.4) seconds]. Male athletes, by sport, also completed the LEFT significantly faster than their female counterparts who participated in the same sport. There was no association between preseason LEFT performance and subsequent injury, by sex, in either the validation sample or the combined sample. Females who reported starting primary sport participation by age 10 were two times (OR = 2.4, 95% CI: 1.2, 4.9; p = 0.01) more likely to experience a non-contact time-loss LQ injury than female athletes who started their primary sport at age 11 or older. Males who reported greater than three hours per week of plyometric training during the six-week period prior to the start of the preseason were four times more likely (OR = 4.0, 95% CI: 1.1, 14.0; p = 0.03) to experience a foot or ankle injury than male athletes who performed three or less hours per week. Conclusions: The LEFT could not be validated as a preseason performance measure to predict future sports injury risk. The data presented in this study may aid rehabilitation professionals when evaluating an injured athlete’s ability to return to sport by comparing their LEFT score to population norms

Assimilation of GPM-Retrieved Marine Surface Meteorology Variables for Two Winter Storms

No abstract availabl