Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Cayley numbers

In this work certain aspects of Functional Analysis are considered in the setting of linear spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are given. Questions concerning linear functionals, the Hahn-Banach Theorem and Reflexivity are considered. The Stone-Weierstrass Theorem is proven for functions with values in a real Cayley Dickson algebra of dimension n. The concepts of inner product spaces and Hilbert spaces over the Quaternions and the Cayley algebra are developed. An extensive study of Hilbert spaces over the Quaternions is carried out. In the case of Hilbert spaces over the Quaternions, the Riesz-Representation Theorem and the Jordan-von Neumann Theorem are proven. In addition, spectral theorems for both self-adjoint and normal operators are proven for finite dimensional Hilbert spaces. These results are extended to infinite dimensional spaces for the cases of compact self-adjoint operators and compact normal operators. The spectrum of an arbitrary bounded Hermitian operator on a Hilbert space over the Quaternions is shown to be non-void. A generalization of the Fourier Transform for functions in L[1 over Q](-infinity, infinity) and L[2 over Q]( ](-infinity, infinity) is given. The Plancherel Theorem is proven for functions in L[2 over Q](-infinity, infinity). Finally, the Jordan-von Neumann theorem is proven for a Hilbert space over the Cayley algebra --Abstract, pages ii-iii

Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space.Comment: 20 pages, to appear in Israel Journal of Mathematic

Novel sulI binary vectors enable an inexpensive foliar selection method in Arabidopsis

<p>Abstract</p> <p>Background</p> <p>Sulfonamide resistance is conferred by the <it>sul</it>I gene found on many <it>Enterobacteriaceae </it>R plasmids and Tn21 type transposons. The <it>sul</it>I gene encodes a sulfonamide insensitive dihydropteroate synthase enzyme required for folate biosynthesis. Transformation of tobacco, potato or <it>Arabidopsis </it>using <it>sul</it>I as a selectable marker generates sulfadiazine-resistant plants. Typically <it>sul</it>I-based selection of transgenic plants is performed on tissue culture media under sterile conditions.</p> <p>Findings</p> <p>A set of novel binary vectors containing a <it>sul</it>I selectable marker expression cassette were constructed and used to generate transgenic <it>Arabidopsis</it>. We demonstrate that the <it>sul</it>I selectable marker can be utilized for direct selection of plants grown in soil with a simple foliar spray application procedure. A highly effective and inexpensive high throughput screening strategy to identify transgenic <it>Arabidopsis </it>without use of tissue culture was developed.</p> <p>Conclusion</p> <p>Novel <it>sul</it>I-containing <it>Agrobacterium </it>binary vectors designed to over-express a gene of interest or to characterize a test promoter in transgenic plants have been constructed. These new vector tools combined with the various beneficial attributes of sulfonamide selection and the simple foliar screening strategy provide an advantageous alternative for plant biotechnology researchers. The set of binary vectors is freely available upon request.</p

Integrated HIV Testing, Malaria, and Diarrhea Prevention Campaign in Kenya: Modeled Health Impact and Cost-Effectiveness

Efficiently delivered interventions to reduce HIV, malaria, and diarrhea are essential to accelerating global health efforts. A 2008 community integrated prevention campaign in Western Province, Kenya, reached 47,000 individuals over 7 days, providing HIV testing and counseling, water filters, insecticide-treated bed nets, condoms, and for HIV-infected individuals cotrimoxazole prophylaxis and referral for ongoing care. We modeled the potential cost-effectiveness of a scaled-up integrated prevention campaign.We estimated averted deaths and disability-adjusted life years (DALYs) based on published data on baseline mortality and morbidity and on the protective effect of interventions, including antiretroviral therapy. We incorporate a previously estimated scaled-up campaign cost. We used published costs of medical care to estimate savings from averted illness (for all three diseases) and the added costs of initiating treatment earlier in the course of HIV disease.Per 1000 participants, projected reductions in cases of diarrhea, malaria, and HIV infection avert an estimated 16.3 deaths, 359 DALYs and $85,113 in medical care costs. Earlier care for HIV-infected persons adds an estimated 82 DALYs averted (to a total of 442), at a cost of$37,097 (reducing total averted costs to $48,015). Accounting for the estimated campaign cost of$32,000, the campaign saves an estimated $16,015 per 1000 participants. In multivariate sensitivity analyses, 83$20.A mass, rapidly implemented campaign for HIV testing, safe water, and malaria control appears economically attractive

Personal and Societal Health Quality Lost to Tuberculosis

BACKGROUND: In developed countries, tuberculosis is considered a disease with little loss of Quality-Adjusted Life Years (QALYs). Tuberculosis treatment is predominantly ambulatory and death from tuberculosis is rare. Research has shown that there are chronic pulmonary sequelae in a majority of patients who have completed treatment for pulmonary tuberculosis (PTB). This and other health effects of tuberculosis have not been considered in QALY calculations. Consequently both the burden of tuberculosis on the individual and the value of tuberculosis prevention to society are underestimated. We estimated QALYs lost to pulmonary TB patients from all known sources, and estimated health loss to prevalent TB disease. METHODOLOGY/PRINCIPAL FINDINGS: We calculated values for health during illness and treatment, pulmonary impairment after tuberculosis (PIAT), death rates, years-of-life-lost to death, and normal population health. We then compared the lifetime expected QALYs for a cohort of tuberculosis patients with that expected for comparison populations with latent tuberculosis infection and without tuberculosis infection. Persons with culture-confirmed tuberculosis accrued fewer lifetime QALYs than those without tuberculosis. Acute tuberculosis morbidity cost 0.046 QALYs (4% of total) per individual. Chronic morbidity accounted for an average of 0.96 QALYs (78% of total). Mortality accounted for 0.22 QALYs lost (18% of total). The net benefit to society of averting one case of PTB was about 1.4 QALYs. CONCLUSIONS/SIGNIFICANCE: Tuberculosis, a preventable disease, results in QALYs lost owing to illness, impairment, and death. The majority of QALYs lost from tuberculosis resulted from impairment after microbiologic cure. Successful TB prevention efforts yield more health quality than previously thought and should be given high priority by health policy makers. (Refer to Abstracto S1 for Spanish language abstract)

The Gravity Collective: A Search for the Electromagnetic Counterpart to the Neutron Star-Black Hole Merger GW190814

We present optical follow-up imaging obtained with the Katzman Automatic Imaging Telescope, Las Cumbres Observatory Global Telescope Network, Nickel Telescope, Swope Telescope, and Thacher Telescope of the LIGO/Virgo gravitational wave (GW) signal from the neutron star-black hole (NSBH) merger GW190814. We searched the GW190814 localization region (19 deg$^{2}$ for the 90th percentile best localization), covering a total of 51 deg$^{2}$ and 94.6% of the two-dimensional localization region. Analyzing the properties of 189 transients that we consider as candidate counterparts to the NSBH merger, including their localizations, discovery times from merger, optical spectra, likely host-galaxy redshifts, and photometric evolution, we conclude that none of these objects are likely to be associated with GW190814. Based on this finding, we consider the likely optical properties of an electromagnetic counterpart to GW190814, including possible kilonovae and short gamma-ray burst afterglows. Using the joint limits from our follow-up imaging, we conclude that a counterpart with an $r$-band decline rate of 0.68 mag day$^{-1}$, similar to the kilonova AT 2017gfo, could peak at an absolute magnitude of at most $-17.8$ mag (50% confidence). Our data are not constraining for ''red'' kilonovae and rule out ''blue'' kilonovae with $M>0.5 M_{\odot}$ (30% confidence). We strongly rule out all known types of short gamma-ray burst afterglows with viewing angles $<$17$^{\circ}$ assuming an initial jet opening angle of $\sim$$5.2^{\circ}$ and explosion energies and circumburst densities similar to afterglows explored in the literature. Finally, we explore the possibility that GW190814 merged in the disk of an active galactic nucleus, of which we find four in the localization region, but we do not find any candidate counterparts among these sources.Comment: 86 pages, 9 figure

Rapid and objective assessment of neural function in autism spectrum disorder using transient visual evoked potentials

OBJECTIVE: There is a critical need to identify biomarkers and objective outcome measures that can be used to understand underlying neural mechanisms in autism spectrum disorder (ASD). Visual evoked potentials (VEPs) offer a noninvasive technique to evaluate the functional integrity of neural mechanisms, specifically visual pathways, while probing for disease pathophysiology. METHODS: Transient VEPs (tVEPs) were obtained from 96 unmedicated children, including 37 children with ASD, 36 typically developing (TD) children, and 23 unaffected siblings (SIBS). A conventional contrast-reversing checkerboard condition was compared to a novel short-duration condition, which was developed to enable objective data collection from severely affected populations who are often excluded from electroencephalographic (EEG) studies. RESULTS: Children with ASD showed significantly smaller amplitudes compared to TD children at two of the earliest critical VEP components, P60-N75 and N75-P100. SIBS showed intermediate responses relative to ASD and TD groups. There were no group differences in response latency. Frequency band analyses indicated significantly weaker responses for the ASD group in bands encompassing gamma-wave activity. Ninety-two percent of children with ASD were able to complete the short-duration condition compared to 68% for the standard condition. CONCLUSIONS: The current study establishes the utility of a short-duration tVEP test for use in children at varying levels of functioning and describes neural abnormalities in children with idiopathic ASD. Implications for excitatory/inhibitory balance as well as the potential application of VEP for use in clinical trials are discussed

Origins Space Telescope: Baseline mission concept

The Origins Space Telescope will trace the history of our origins from the time dust and heavy elements permanently altered the cosmic landscape to present-day life. How did galaxies evolve from the earliest galactic systems to those found in the Universe today? How do habitable planets form? How common are life-bearing worlds? To answer these alluring questions, Origins will operate at mid-and far-infrared (IR) wavelengths and offer powerful spectroscopic instruments and sensitivity three orders of magnitude better than that of the Herschel Space Observatory, the largest telescope flown in space to date. We describe the baseline concept for Origins recommended to the 2020 US Decadal Survey in Astronomy and Astrophysics. The baseline design includes a 5.9-m diameter telescope cryocooled to 4.5 K and equipped with three scientific instruments. A mid-infrared instrument (Mid-Infrared Spectrometer and Camera Transit spectrometer) will measure the spectra of transiting exoplanets in the 2.8 to 20 μm wavelength range and offer unprecedented spectrophotometric precision, enabling definitive exoplanet biosignature detections. The far-IR imager polarimeter will be able to survey thousands of square degrees with broadband imaging at 50 and 250 μm. The Origins Survey Spectrometer will cover wavelengths from 25 to 588 μm, making wide-area and deep spectroscopic surveys with spectral resolving power R ∼ 300, and pointed observations at R ∼ 40,000 and 300,000 with selectable instrument modes. Origins was designed to minimize complexity. The architecture is similar to that of the Spitzer Space Telescope and requires very few deployments after launch, while the cryothermal system design leverages James Webb Space Telescope technology and experience. A combination of current-state-of-the-art cryocoolers and next-generation detector technology will enable Origins\u27 natural background-limited sensitivity