Seifert surfaces in the 4-ball

We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in $S^3$ that do not become isotopic when their interiors are pushed into $B^4$. In particular, we identify examples where the surfaces are not even topologically isotopic in $B^4$, examples that are topologically but not smoothly isotopic, and examples of infinite families of surfaces that are distinct only up to isotopy rel. boundary. Our main proofs distinguish surfaces using the cobordism maps on Khovanov homology, and our calculations demonstrate the stability and computability of these maps under certain satellite operations.Comment: 31 pages + bibliography, 28 figures. Some computational details available in ancillary file. Compared to v1, we added Theorems 1.4 and 1.5 producing infinite families of Seifert surfaces that are pairwise not isotopic rel. boundary in B^4. (In v3, just corrected floats in Fig. 27.

Stable and Radiogenic Isotope Studies of Iron-oxides as Paleoenvironmental and Tectonic Archives

Geochemical records of continental weathering environments are limited despite their critical value to understanding how past climates functioned. This thesis seeks to address this limitation by drawing together innovative lines of research in geochronology, stable isotope geochemistry, and chemical weathering. Two distinct projects are described; each project designed to provide new insight into the paleoenvironmental and tectonic history of continental weathering environments. These projects, though distinct in their methods and samples, are unified by their goal: to use the stable, radiogenic, and nucleogenic isotopic composition of iron oxides to provide new constraints on the geologic history of continental weathering environments. The weathering of Fe-bearing rocks, coupled with the extreme insolubility of iron in moderately acidic to alkaline oxic waters, causes both goethite and hematite to be abundant chemical precipitates in near-surface environments. Goethite is favored in lower temperature and more acidic or alkaline conditions, while hematite precipitates more readily in near-neutral environments. These minerals are found in soils; spring, bog, and stream deposits; oxidized chemical sediments; and hydrothermal deposits. In many cases, substantial crystalline masses occur, which can take the form of nodules, pisoliths, botryoidal, stalactitic, and radiating masses, fibrous needles, pseudomorph, veneers, or as aggregates of flakes, tabular, or anhedral crystals. Time and temperature are arguably the two most fundamental variables we as geologists seek to constrain, and iron oxide deposits can provide a valuable archive of information on low-temperature, near-surface planetary processes. The first project investigates how the stable oxygen isotopic composition of goethite, when combined with direct He dating on the same texturally resolved scales as stable isotope analyses, can be used to interpret water sources (Chapter 1) and formation temperatures (Chapter 2). The first chapter creates a record of the paleolatitudinal gradient in the oxygen isotope composition of meteoric water. The major finding of this study is the consistency in this gradient over geologic time. This second chapter proposes a new geothermometer using the intracrystalline oxygen isotopic composition of goethite. While stable isotopic compositions of goethite have long been utilized as a tool for reconstructing paleoenvironmental conditions, previous studies have focused on the bulk concentration of stable isotopes within this phase. Since goethite has two structurally non-equivalent oxygen sites, we show it is possible to extract two isotopically unique populations of oxygen, the composition of which we interpret to be dependent on temperature at time of mineral formation. In combination with the ability to directly date goethite by the (U-Th)/He method, we may utilize goethite to constrain both the temperature and timing of goethite formation, providing a valuable archive for information on continental paleoenvironments. The second project utilized the paired He-Ne chronometer and 4He/3He method in hematite to produce thermal histories of the ancient Kaapvaal Craton over billion-year timescales. We applied these methods to hematite ore hosted within the Transvaal Supergroup in the Griqualand West (Chapter 3) and Transvaal Basin region (Chapter 4) of the ancient Kaapvaal Craton, South Africa. The application of hematite geo- and thermochronometry to these multi-billion year-old deposits represents the most challenging environments these methods have yet been applied to. We found, in some localities, hematite He-Ne ages provided further support of existing indirect age constraints on the timing of ore formation. In other localities, we found hematite He-Ne ages are uncorrelated with known tectono-thermal events. Modeled time-temperature histories indicate the Kaapvaal Craton has experienced exceptionally slow erosion rates over the last billion years, providing further evidence for the extreme tectonic stability of cratonic interiors over geologic timescales. This slow erosion took place over vast intervals of time, during which the craton was undergoing oxidative weathering, offering an additional constraint on understanding the history of atmospheric O2 during Proterozoic time.</p

Brunnian exotic surface links in the 4-ball

This paper investigates the exotic phenomena exhibited by links of disconnected surfaces with boundary that are properly embedded in the 4-ball. Our main results provide two different constructions of exotic pairs of surface links that are Brunnian, meaning that all proper sublinks of the surface are trivial. We then modify these core constructions to vary the number of components in the exotic links, the genera of the components, and the number of components that must be removed before the surfaces become unlinked. Our arguments extend two tools from 3-dimensional knot theory into the 4-dimensional setting: satellite operations, especially Bing doubling, and covering links in branched covers.Comment: 37 pages, 36 figures, 2 appendices, 1 footnote, 1 stanz

Integrated Network Architecture for NASA's Orion Missions

NASA is planning a series of short and long duration human and robotic missions to explore the Moon and then Mars. The series of missions will begin with a new crew exploration vehicle (called Orion) that will initially provide crew exchange and cargo supply support to the International Space Station (ISS) and then become a human conveyance for travel to the Moon. The Orion vehicle will be mounted atop the Ares I launch vehicle for a series of pre-launch tests and then launched and inserted into low Earth orbit (LEO) for crew exchange missions to the ISS. The Orion and Ares I comprise the initial vehicles in the Constellation system of systems that later includes Ares V, Earth departure stage, lunar lander, and other lunar surface systems for the lunar exploration missions. These key systems will enable the lunar surface exploration missions to be initiated in 2018. The complexity of the Constellation system of systems and missions will require a communication and navigation infrastructure to provide low and high rate forward and return communication services, tracking services, and ground network services. The infrastructure must provide robust, reliable, safe, sustainable, and autonomous operations at minimum cost while maximizing the exploration capabilities and science return. The infrastructure will be based on a network of networks architecture that will integrate NASA legacy communication, modified elements, and navigation systems. New networks will be added to extend communication, navigation, and timing services for the Moon missions. Internet protocol (IP) and network management systems within the networks will enable interoperability throughout the Constellation system of systems. An integrated network architecture has developed based on the emerging Constellation requirements for Orion missions. The architecture, as presented in this paper, addresses the early Orion missions to the ISS with communication, navigation, and network services over five phases of a mission: pre-launch, launch from T0 to T+6.5 min, launch from T+6.5 min to 12 min, in LEO for rendezvous and docking with ISS, and return to Earth. The network of networks that supports the mission during each of these phases and the concepts of operations during those phases are developed as a high level operational concepts graphic called OV-1, an architecture diagram type described in the Department of Defense Architecture Framework (DoDAF). Additional operational views on organizational relationships (OV-4), operational activities (OV-5), and operational node connectivity (OV-2) are also discussed. The system interfaces view (SV-1) that provides the communication and navigation services to Orion is also included and described. The challenges of architecting integrated network architecture for the NASA Orion missions are highlighted

Distance Geometry for Kissing Spheres

A kissing sphere is a sphere that is tangent to a fixed reference ball. We develop in this paper a distance geometry for kissing spheres, which turns out to be a generalization of the classical Euclidean distance geometry.Comment: 11 pages, 2 picture

Intracrystalline site preference of oxygen isotopes in goethite: A single-mineral paleothermometer

The crystal structure of goethite, FeO(OH), has two distinct oxygen sites, one with exclusively Fe-O bonds, the other with bonds to both iron and hydrogen. We developed a method to assess the oxygen isotope contrast between these sites by measuring both the bulk goethite and the oxygen released in the conversion of goethite to hematite. The method involves collecting the water released by dehydroxylation, fluorinating that population of extracted atoms, and measuring the resulting oxygen isotope composition (extracted δO¹⁸). Then, on a separate aliquot, all structural oxygen is fluorinated and measured (bulk δO¹⁸). Using synthetic goethite precipitates grown under controlled environmental conditions, we found significant temperature-dependent fractionation, ε_(bulk-extracted)=(5.51±0.26)×(10⁶/T²)−(44.5±2.8); T in Kelvin). This intracrystalline fractionation forms the basis of a single-phase paleothermometer with an estimated uncertainty of ∼2-3°C. The temperature dependence appears to be independent of the isotopic composition of the parent fluid from which the goethite formed and the pH of that fluid. This intracrystalline thermometer can be used to simultaneously determine the formation temperature of a goethite and the isotopic composition of the water from which it formed. Natural goethites analyzed with this technique yield geologically reasonable formation temperatures of between 15 and 41°C

The single-nucleotide polymorphism (GPX4c718t) in the glutathione peroxidase 4 gene influences endothelial cell function : Interaction with selenium and fatty acids

© 2013 The Authors. Molecular Nutrition & Food Research published by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.Peer reviewedPublisher PD

Architecting the Communication and Navigation Networks for NASA's Space Exploration Systems

NASA is planning a series of short and long duration human and robotic missions to explore the Moon and then Mars. A key objective of the missions is to grow, through a series of launches, a system of systems communication, navigation, and timing infrastructure at minimum cost while providing a network-centric infrastructure that maximizes the exploration capabilities and science return. There is a strong need to use architecting processes in the mission pre-formulation stage to describe the systems, interfaces, and interoperability needed to implement multiple space communication systems that are deployed over time, yet support interoperability with each deployment phase and with 20 years of legacy systems. In this paper we present a process for defining the architecture of the communications, navigation, and networks needed to support future space explorers with the best adaptable and evolable network-centric space exploration infrastructure. The process steps presented are: 1) Architecture decomposition, 2) Defining mission systems and their interfaces, 3) Developing the communication, navigation, networking architecture, and 4) Integrating systems, operational and technical views and viewpoints. We demonstrate the process through the architecture development of the communication network for upcoming NASA space exploration missions