| 1. |
- Aartsen, M. G., et al.
(författare)
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Constraints on Minute-Scale Transient Astrophysical Neutrino Sources
- 2019
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Ingår i: Physical Review Letters. - : AMER PHYSICAL SOC. - 0031-9007 .- 1079-7114. ; 122:5
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Tidskriftsartikel (refereegranskat)abstract
- High-energy neutrino emission has been predicted for several short-lived astrophysical transients including gamma-ray bursts (GRBs), core-collapse supernovae with choked jets, and neutron star mergers. IceCube's optical and x-ray follow-up program searches for such transient sources by looking for two or more muon neutrino candidates in directional coincidence and arriving within 100 s. The measured rate of neutrino alerts is consistent with the expected rate of chance coincidences of atmospheric background events and no likely electromagnetic counterparts have been identified in Swift follow-up observations. Here, we calculate generic bounds on the neutrino flux of short-lived transient sources. Assuming an E-2.5 neutrino spectrum, we find that the neutrino flux of rare sources, like long gamma-ray bursts, is constrained to < 5% of the detected astrophysical flux and the energy released in neutrinos (100 GeV to 10 PeV) by a median bright GRB-like source is < 10(52.5) erg. For a harder E-2.13 neutrino spectrum up to 30% of the flux could be produced by GRBs and the allowed median source energy is < 10(52) erg. A hypothetical population of transient sources has to be more common than 10(-5) Mpc(-3) yr(-1) (5 x 10(-8) Mpc(-3) yr(-1) for the E-2.13 spectrum) to account for the complete astrophysical neutrino flux.
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| 2. |
- Aartsen, M. G., et al.
(författare)
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Measurements using the inelasticity distribution of multi-TeV neutrino interactions in IceCube
- 2019
-
Ingår i: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 99:3
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Tidskriftsartikel (refereegranskat)abstract
- Inelasticity, the fraction of a neutrino's energy transferred to hadrons, is a quantity of interest in the study of astrophysical and atmospheric neutrino interactions at multi-TeV energies with IceCube. In this work, a sample of contained neutrino interactions in IceCube is obtained from five years of data and classified as 2650 tracks and 965 cascades. Tracks arise predominantly from charged-current nu(mu) interactions, and we demonstrate that we can reconstruct their energy and inelasticity. The inelasticity distribution is found to be consistent with the calculation of Cooper-Sarkar et al. across the energy range from similar to 1 to similar to 100 TeV. Along with cascades from neutrinos of all flavors, we also perform a fit over the energy, zenith angle, and inelasticity distribution to characterize the flux of astrophysical and atmospheric neutrinos. The energy spectrum of diffuse astrophysical neutrinos is described well by a power law in both track and cascade samples, and a best-fit index gamma = 2.62 +/- 0.07 is found in the energy range from 3.5 TeV to 2.6 PeV. Limits are set on the astrophysical flavor composition and are compatible with a ratio of (1/3 : 1/3 : 1/3)(circle plus). Exploiting the distinct inelasticity distribution of nu(mu) and (nu) over bar (mu) interactions, the atmospheric nu(mu) to (nu) over bar (mu) flux ratio in the energy range from 770 GeV to 21 TeV is found to be 0.77(-0.25)(+0.44) times the calculation by Honda et al. Lastly, the inelasticity distribution is also sensitive to neutrino charged-current charm production. The data are consistent with a leading-order calculation, with zero charm production excluded at 91% confidence level. Future analyses of inelasticity distributions may probe new physics that affects neutrino interactions both in and beyond the Standard Model.
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| 3. |
- Aartsen, M. G., et al.
(författare)
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Neutrino interferometry for high-precision tests of Lorentz symmetry with IceCube
- 2018
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Ingår i: Nature Physics. - : NATURE PUBLISHING GROUP. - 1745-2473 .- 1745-2481. ; 14:9, s. 961-966
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Tidskriftsartikel (refereegranskat)abstract
- Lorentz symmetry is a fundamental spacetime symmetry underlying both the standard model of particle physics and general relativity. This symmetry guarantees that physical phenomena are observed to be the same by all inertial observers. However, unified theories, such as string theory, allow for violation of this symmetry by inducing new spacetime structure at the quantum gravity scale. Thus, the discovery of Lorentz symmetry violation could be the first hint of these theories in nature. Here we report the results of the most precise test of spacetime symmetry in the neutrino sector to date. We use high-energy atmospheric neutrinos observed at the IceCube Neutrino Observatory to search for anomalous neutrino oscillations as signals of Lorentz violation. We find no evidence for such phenomena. This allows us to constrain the size of the dimension-four operator in the standard-model extension for Lorentz violation to the 10(-28) level and to set limits on higher-dimensional operators in this framework. These are among the most stringent limits on Lorentz violation set by any physical experiment.
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| 4. |
- Aartsen, M. G., et al.
(författare)
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Search for nonstandard neutrino interactions with IceCube DeepCore
- 2018
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Ingår i: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 97:7
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Tidskriftsartikel (refereegranskat)abstract
- As atmospheric neutrinos propagate through the Earth, vacuumlike oscillations are modified by Standard Model neutral-and charged-current interactions with electrons. Theories beyond the Standard Model introduce heavy, TeV-scale bosons that can produce nonstandard neutrino interactions. These additional interactions may modify the Standard Model matter effect producing a measurable deviation from the prediction for atmospheric neutrino oscillations. The result described in this paper constrains nonstandard interaction parameters, building upon a previous analysis of atmospheric muon-neutrino disappearance with three years of IceCube DeepCore data. The best fit for the muon to tau flavor changing term is epsilon(mu tau) = -0.0005, with a 90% C.L. allowed range of -0.0067 < epsilon(mu tau) < 0.0081. This result is more restrictive than recent limits from other experiments for.mu t. Furthermore, our result is complementary to a recent constraint on epsilon(mu tau) using another publicly available IceCube high-energy event selection. Together, they constitute the world's best limits on nonstandard interactions in the mu - tau sector.
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| 5. |
- Aartsen, M. G., et al.
(författare)
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A Search for Neutrino Emission from Fast Radio Bursts with Six Years of IceCube Data
- 2018
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Ingår i: Astrophysical Journal. - : American Astronomical Society. - 0004-637X .- 1538-4357. ; 857:2
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Tidskriftsartikel (refereegranskat)abstract
- We present a search for coincidence between IceCube TeV neutrinos and fast radio bursts (FRBs). During the search period from 2010 May 31 to 2016 May 12, a total of 29 FRBs with 13 unique locations have been detected in the whole sky. An unbinned maximum likelihood method was used to search for spatial and temporal coincidence between neutrinos and FRBs in expanding time windows, in both the northern and southern hemispheres. No significant correlation was found in six years of IceCube data. Therefore, we set upper limits on neutrino fluence emitted by FRBs as a function of time window duration. We set the most stringent limit obtained to date on neutrino fluence from FRBs with an E-2 energy spectrum assumed, which is 0.0021 GeV cm(-2) per burst for emission timescales up to similar to 10(2) s from the northern hemisphere stacking search.
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| 6. |
- Aartsen, M. G., et al.
(författare)
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Differential limit on the extremely-high-energy cosmic neutrino flux in the presence of astrophysical background from nine years of IceCube data
- 2018
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Ingår i: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 98:6
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Tidskriftsartikel (refereegranskat)abstract
- We report a quasidifferential upper limit on the extremely-high-energy (EHE) neutrino flux above 5 x 10(6) GeV based on an analysis of nine years of IceCube data. The astrophysical neutrino flux measured by IceCube extends to PeV energies, and it is a background flux when searching for an independent signal flux at higher energies, such as the cosmogenic neutrino signal. We have developed a new method to place robust limits on the EHE neutrino flux in the presence of an astrophysical background, whose spectrum has yet to be understood with high precision at PeV energies. A distinct event with a deposited energy above 10(6) GeV was found in the new two-year sample, in addition to the one event previously found in the seven-year EHE neutrino search. These two events represent a neutrino flux that is incompatible with predictions for a cosmogenic neutrino flux and are considered to be an astrophysical background in the current study. The obtained limit is the most stringent to date in the energy range between 5 x 10(6) and 2 x 10(10) GeV. This result constrains neutrino models predicting a three-flavor neutrino flux of E-nu(2)phi(nu e+nu mu+nu tau) similar or equal to 2 x 10(-8) GeV/cm(2) sec sr at 10(9) GeV. A significant part of the parameter space for EHE neutrino production scenarios assuming a proton-dominated composition of ultra-high-energy cosmic rays is disfavored independently of uncertain models of the extragalactic background light which previous IceCube constraints partially relied on.
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| 7. |
- Aartsen, M. G., et al.
(författare)
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Measurement of Atmospheric Neutrino Oscillations at 6-56 GeV with IceCube DeepCore
- 2018
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Ingår i: Physical Review Letters. - : AMER PHYSICAL SOC. - 0031-9007 .- 1079-7114. ; 120:7
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Tidskriftsartikel (refereegranskat)abstract
- We present a measurement of the atmospheric neutrino oscillation parameters using three years of data from the IceCube Neutrino Observatory. The DeepCore infill array in the center of IceCube enables the detection and reconstruction of neutrinos produced by the interaction of cosmic rays in Earth's atmosphere at energies as low as similar to 5 GeV. That energy threshold permits measurements of muon neutrino disappearance, over a range of baselines up to the diameter of the Earth, probing the same range of L/E-v. as long-baseline experiments but with substantially higher- energy neutrinos. This analysis uses neutrinos from the full sky with reconstructed energies from 5.6 to 56 GeV. We measure Delta m(32)(2) = 2.31(-0.13)(+0.11) x 10(-3) eV(2) and sin(2) theta(23) = 0.51(- 0.09)(+0.07), assuming normal neutrino mass ordering. These results are consistent with, and of similar precision to, those from accelerator- and reactor-based experiments.
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| 8. |
- Aartsen, M. G., et al.
(författare)
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Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert
- 2018
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Ingår i: Science. - : American Association for the Advancement of Science (AAAS). - 0036-8075 .- 1095-9203. ; 361:6398, s. 147-151
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Tidskriftsartikel (refereegranskat)abstract
- A high-energy neutrino event detected by IceCube on 22 September 2017 was coincident in direction and time with a gamma-ray flare from the blazar TXS 0506+056. Prompted by this association, we investigated 9.5 years of IceCube neutrino observations to search for excess emission at the position of the blazar. We found an excess of high-energy neutrino events, with respect to atmospheric backgrounds, at that position between September 2014 and March 2015. Allowing for time-variable flux, this constitutes 3.5 sigma evidence for neutrino emission from the direction of TXS 0506+056, independent of and prior to the 2017 flaring episode. This suggests that blazars are identifiable sources of the high-energy astrophysical neutrino flux.
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| 9. |
- Aartsen, M. G., et al.
(författare)
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Detection of the Temporal Variation of the Sun's Cosmic Ray Shadow with the IceCube Detector
- 2019
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Ingår i: Astrophysical Journal. - : IOP PUBLISHING LTD. - 0004-637X .- 1538-4357. ; 872:2
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Tidskriftsartikel (refereegranskat)abstract
- We report on the observation of a deficit in the cosmic ray flux from the directions of the Moon and Sun with five years of data taken by the IceCube Neutrino Observatory. Between 2010 May and 2011 May the IceCube detector operated with 79 strings deployed in the glacial ice at the South Pole, and with 86 strings between 2011 May and 2015 May. A binned analysis is used to measure the relative deficit and significance of the cosmic ray shadows. Both the cosmic ray Moon and Sun shadows are detected with high statistical significance (>10σ) for each year. The results for the Moon shadow are consistent with previous analyses and verify the stability of the IceCube detector over time. This work represents the first observation of the Sun shadow with the IceCube detector. We show that the cosmic ray shadow of the Sun varies with time. These results make it possible to study cosmic ray transport near the Sun with future data from IceCube.
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| 10. |
- Aartsen, M. G., et al.
(författare)
-
Measurement of atmospheric tau neutrino appearance with IceCube DeepCore
- 2019
-
Ingår i: Physical Review D. - : AMER PHYSICAL SOC. - 2470-0010 .- 2470-0029. ; 99:3
-
Tidskriftsartikel (refereegranskat)abstract
- We present a measurement of atmospheric tau neutrino appearance from oscillations with three years of data from the DeepCore subarray of the IceCube Neutrino Observatory. This analysis uses atmospheric neutrinos from the full sky with reconstructed energies between 5.6 and 56 GeV to search for a statistical excess of cascadelike neutrino events which are the signature of nu(tau) interactions. For CC thorn NC (CC-only) interactions, we measure the tau neutrino normalization to be 0.73(-0.24)(+0.30) (0.57(-0.30)(+0.36)) and exclude the absence of tau neutrino oscillations at a significance of 3.2 sigma (2.0 sigma) These results are consistent with, and of similar precision to, a confirmatory IceCube analysis also presented, as well as measurements performed by other experiments.
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| 11. |
- Aartsen, M. G., et al.
(författare)
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Measurement of the multi-TeV neutrino interaction cross-section with IceCube using Earth absorption
- 2017
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Ingår i: Nature. - : Springer Science and Business Media LLC. - 0028-0836 .- 1476-4687. ; 551:7682, s. 596-600
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Tidskriftsartikel (refereegranskat)abstract
- Neutrinos interact only very weakly, so they are extremely penetrating. The theoretical neutrino-nucleon interaction cross-section, however, increases with increasing neutrino energy, and neutrinos with energies above 40 teraelectronvolts (TeV) are expected to be absorbed as they pass through the Earth. Experimentally, the cross-section has been determined only at the relatively low energies (below 0.4 TeV) that are available at neutrino beams fromaccelerators(1,2). Here we report a measurement of neutrino absorption by the Earth using a sample of 10,784 energetic upward-going neutrino-induced muons. The flux of high-energy neutrinos transiting long paths through the Earth is attenuated compared to a reference sample that follows shorter trajectories. Using a fit to the two-dimensional distribution of muon energy and zenith angle, we determine the neutrino-nucleon interaction cross-section for neutrino energies 6.3-980 TeV, more than an order of magnitude higher than previous measurements. The measured cross-section is about 1.3 times the prediction of the standard model(3), consistent with the expectations for charged-and neutral-current interactions. We do not observe a large increase in the crosssection with neutrino energy, in contrast with the predictions of some theoretical models, including those invoking more compact spatial dimensions(4) or the production of leptoquarks(5). This cross-section measurement can be used to set limits on the existence of some hypothesized beyond-standard-model particles, including leptoquarks.
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| 12. |
- Aartsen, M. G., et al.
(författare)
-
Constraints on Galactic Neutrino Emission with Seven Years of IceCube Data
- 2017
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Ingår i: Astrophysical Journal. - : American Astronomical Society. - 0004-637X .- 1538-4357. ; 849:1
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Tidskriftsartikel (refereegranskat)abstract
- The origins of high-energy astrophysical neutrinos remain a mystery despite extensive searches for their sources. We present constraints from seven years of IceCube Neutrino Observatory muon data on the neutrino flux coming from the Galactic plane. This flux is expected from cosmic-ray interactions with the interstellar medium or near localized sources. Two methods were developed to test for a spatially extended flux from the entire plane, both of which are maximum likelihood fits but with different signal and background modeling techniques. We consider three templates for Galactic neutrino emission based primarily on gamma-ray observations and models that cover a wide range of possibilities. Based on these templates and in the benchmark case of an unbroken E-2.5 power-law energy spectrum, we set 90% confidence level upper limits, constraining the possible Galactic contribution to the diffuse neutrino flux to be relatively small, less than 14% of the flux reported in Aartsen et al. above 1 TeV. A stacking method is also used to test catalogs of known high-energy Galactic gamma-ray sources.
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| 13. |
- Aartsen, M. G., et al.
(författare)
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Search for neutrinos from dark matter self-annihilations in the center of the Milky Way with 3 years of IceCube/DeepCore
- 2017
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Ingår i: European Physical Journal C. - : SPRINGER. - 1434-6044 .- 1434-6052. ; 77:9
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Tidskriftsartikel (refereegranskat)abstract
- We present a search for a neutrino signal from dark matter self-annihilations in the Milky Way using the Ice-Cube Neutrino Observatory (IceCube). In 1005 days of data we found no significant excess of neutrinos over the background of neutrinos produced in atmospheric air showers from cosmic ray interactions. We derive upper limits on the velocity averaged product of the darkmatter self-annihilation cross section and the relative velocity of the dark matter particles . Upper limits are set for darkmatter particle candidate masses ranging from 10GeV up to 1TeV while considering annihilation through multiple channels. This work sets the most stringent limit on a neutrino signal from dark matter with mass between 10 and 100GeV, with a limit of 1.18 . 10-23 cm(3)s(-1) for 100GeV dark matter particles self-annihilating via iota(+)iota(-) t-to neutrinos (assuming the Navarro-Frenk-White dark matter halo profile).
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| 14. |
- Aartsen, M. G., et al.
(författare)
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Search for steady point-like sources in the astrophysical muon neutrino flux with 8 years of IceCube data
- 2019
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Ingår i: European Physical Journal C. - : Springer Science and Business Media LLC. - 1434-6044 .- 1434-6052. ; 79:3
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Tidskriftsartikel (refereegranskat)abstract
- The IceCube Collaboration has observed a high-energy astrophysical neutrino flux and recently found evidence for neutrino emission from the blazar TXS 0506+056. These results open a new window into the high-energy universe. However, the source or sources of most of the observed flux of astrophysical neutrinos remains uncertain. Here, a search for steady point-like neutrino sources is performed using an unbinned likelihood analysis. The method searches for a spatial accumulation of muon-neutrino events using the very high-statistics sample of about 497,000 neutrinos recorded by IceCube between 2009 and 2017. The median angular resolution is approximate to 1 degrees at 1 TeV and improves to approximate to 0.3 degrees for neutrinos with an energy of 1 PeV. Compared to previous analyses, this search is optimized for point-like neutrino emission with the same flux-characteristics as the observed astrophysical muon-neutrino flux and introduces an improved event-reconstruction and parametrization of the background. The result is an improvement in sensitivity to the muon-neutrino flux compared to the previous analysis of approximate to 35% assuming an E-2 spectrum. The sensitivity on the muon-neutrino flux is at a level of E2dN/dE=310-13s-1. No new evidence for neutrino sources is found in a full sky scan and in an a priori candidate source list that is motivated by gamma-ray observations. Furthermore, no significant excesses above background are found from populations of sub-threshold sources. The implications of the non-observation for potential source classes are discussed.
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| 15. |
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| 16. |
- Ade, Peter, et al.
(författare)
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The Simons Observatory : science goals and forecasts
- 2019
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Ingår i: Journal of Cosmology and Astroparticle Physics. - : IOP Publishing. - 1475-7516. ; :2
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Tidskriftsartikel (refereegranskat)abstract
- The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands centered at: 27, 39, 93, 145, 225 and 280 GHz. The initial con figuration of SO will have three small-aperture 0.5-m telescopes and one large-aperture 6-m telescope, with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The small aperture telescopes will target the largest angular scales observable from Chile, mapping approximate to 10% of the sky to a white noise level of 2 mu K-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, r, at a target level of sigma(r) = 0.003. The large aperture telescope will map approximate to 40% of the sky at arcminute angular resolution to an expected white noise level of 6 mu K-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the Large Synoptic Survey Telescope sky region and partially with the Dark Energy Spectroscopic Instrument. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources.
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| 17. |
- Loughman, T., et al.
(författare)
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Analytical validation of OncoMasTR, a multigene test for predicting risk of distant recurrence in hormone receptor-positive early stage breast cancer
- 2018
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Ingår i: Annals of oncology : official journal of the European Society for Medical Oncology. - : Elsevier BV. - 1569-8041. ; 29:Suppl. 8, s. 65-65
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Background: OncoMasTR is a new multigene prognostic test that was discovered via a novel transcriptional network analysis method that identified upstream Master Transcription Regulators (MTRs), which regulate previously identified prognostic biomarkers. The optimised OncoMasTR signature incorporating clinicopathological information has been shown to be significantly prognostic for predicting distant recurrence in two independent cohorts (TransATAC & a subset of TAILORx from participating Irish centres). The analytical performance characteristics of the OncoMasTR test, comprising solely three prognostic MTRs, were determined. Methods: Relative gene expression levels were measured by RT-qPCR. Assay precision and input ranges were determined using a panel of samples representative of low and high recurrence risk tested across a number of runs incorporating different sources of variation. Serial dilutions of a pooled patient RNA sample was used to establish the linear range and efficiency of the individual gene assays. Results: The overall standard deviation of the OncoMasTR risk score was 0.15, which represents less than 2% of the 10-unit risk score range. The majority of the variability in OncoMasTR results was related to within-run variation (78.2%) with other between-run variation sources contributing relatively little (PCR instrument (0.6%), assay operator (5.2%), reagent lots (7.3%) or loading position (8.7%)). Consistent risk scores were measured for individual samples from 40ng down to < 1ng RNA per PCR reaction. Individual gene assays were linear over >500-fold RNA input range corresponding to CT values of 23 – 36, demonstrating the ability of the test to reliably detect low level expression of the OncoMasTR panel. Importantly, PCR efficiencies were similar for the individual MTR and reference gene assays which ranged from 79 – 95%. Conclusions: The OncoMasTR prognostic test displays robust analytical and clinical performance and is being launched as a CE-marked test. The concise nature of the three gene signature and a simplified workflow that can be readily adopted using standard laboratory equipment will enable convenient qualification by local laboratories for decentralised use.
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| 18. |
- Magombeyi, M. S., et al.
(författare)
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Rural food insecurity and poverty mappings and their linkage with water resources in the Limpopo River Basin
- 2016
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Ingår i: Physics and Chemistry of the Earth. - : Elsevier BV. - 1474-7065 .- 1873-5193. ; 92, s. 20-33
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Tidskriftsartikel (refereegranskat)abstract
- The mappings of poverty and food insecurity were carried out for the rural districts of the four riparian countries (Botswana, Mozambique, South Africa and Zimbabwe) of the Limpopo river basin using the results of national surveys that were conducted between 2003 and 2013. The analysis shows lower range of food insecure persons (0-40%) than poverty stricken persons (0-95%) that is attributable to enhanced government and non-government food safety networks in the basin countries, the dynamic and transitory nature of food insecurity which depends on the timings of the surveys in relation to harvests, markets and food prices, and the limited dimension of food insecurity in relation to poverty which tends to be a more structural and pervasive socio-economic condition. The usefulness of this study in influencing policies and strategies targeted at alleviating poverty and improving rural livelihoods lies with using food insecurity mappings to address short-term socio-economic conditions and poverty mappings to address more structural and long-term deprivations. Using the poverty line of $1.25/day per person (2008-2013) in the basin, Zimbabwe had the highest percentage of 68.7% of its rural population classified as poor, followed by Mozambique with 68.2%, South Africa with 56.1% and Botswana with 20%. While average poverty reduction of 6.4% was observed between 2003 and 2009 in Botswana, its population growth of 20.1% indicated no real poverty reduction. Similar observations are made about Mozambique and Zimbabwe where population growth outstripped poverty reductions. In contrast, both average poverty levels and population increased by 4.3% and 11%, respectively, in South Africa from 2007 to 2010. While areas of high food insecurity and poverty consistently coincide with low water availability, it does not indicate a simple cause-effect relationship between water, poverty and food insecurity. With limited water resources, rural folks in the basin require stronger institutions, increased investments and support to enable them generate sufficient income from their rain-fed farming livelihood to break out of the poverty cycle.
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