Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

A model of the geochemical and physical fluctuations of the lava lake at Erebus volcano, Antarctica

Erebus volcano, Antarctica, exhibits periodical surface fluctuations of both geochemical and physical nature. Modeling the physics driving the lake oscillation is a challenge, even with a relatively simple theoretical framework. We present a quantitative analysis that aims to reconcile both lake level and gas geochemical cycles. Our model is based on the assumption that the periodicity is caused by the regular release of magma batches and/or core annular flow that have a fixed volume of melt and ascend and degas in equilibrium. Results suggest that cycles are not caused by the mixing between magma residing in the lake and a deep magma but by two distinct deep sources that rise separately. These sources of bubbly magma come from at most 2–3 km depth and rise buoyantly. Individual batches detach from the rising magmas at depths of 20–250 m. The two batch types can coexist in a single conduit up to a depth of ~ 30 m, above which they rise alternately to release respectively 19 and 23 kg/s of gas at the lake surface every 10 min. The temperature of the descending flow is between 890 and 950 °C, which is roughly 100 °C colder than the ascending currents. Batch pairs have shapes likely constrained by the conduit width. Regardless of their shapes, the pairs reach very high porosities near the surface and have diameters of 4–14 m that are consistent with video observations showing spreading waves at the lake surface. The alternating arrival of these large batches suggests a lava lake mostly filled with gas-rich magma.This work is part of the first author's PhD thesis, which was funded by the 7th Framework Program of the EC (ERC grant 202844) and by Senescyt under the Prometeo Program (Ecuador). CO acknowledges support from the Isaac Newton Trust (project “Physical constraints for the interpretation of open-vent volcanism”) and the Natural Environment Research Council (National Centre for Earth Observation: COMET).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jvolgeores.2015.10.02

Controls on magma permeability in the volcanic conduit during the climactic phase of the Kos Plateau Tuff eruption (Aegean Arc)

X-ray computed microtomography (µCT) was applied to pumices from the largest Quaternary explosive eruption of the active South Aegean Arc (the Kos Plateau Tuff; KPT) in order to better understand magma permeability within volcanic conduits. Two different types of pumices (one with highly elongated bubbles, tube pumice; and the other with near spherical bubbles, frothy pumice) produced synchronously and with identical chemical composition were selected for µCT imaging to obtain porosity, tortuosity, bubble size and throat size distributions. Tortuosity drops on average from 2.2 in frothy pumice to 1.5 in tube pumice. Bubble size and throat size distributions provide estimates for mean bubble size (~93-98μm) and mean throat size (~23-29μm). Using a modified Kozeny-Carman equation, variations in porosity, tortuosity, and throat size observed in KPT pumices explain the spread found in laboratory measurements of the Darcian permeability. Measured difference in inertial permeability between tube and frothy pumices can also be partly explained by the same variables but require an additional parameter related to the internal roughness of the porous medium (friction factor f 0 ). Constitutive equations for both types of permeability allow the quantification of laminar and turbulent gas escape during ascent of rhyolitic magma in volcanic conduit

Transient degassing events at the lava lake of Erebus volcano, Antarctica: Chemistry and mechanisms

We report here on the chemical signature of degassing at Erebus lava lake associated with intermittent explosions and the return to passive conditions. Explosions caused by bubble bursts were frequent during the 2013 field season, providing the first opportunity to observe such activity since 2005-2006. Several of the explosions were captured by multiple instruments including an open-path Fourier transform infrared spectrometer. Explosive bubble bursts and other transient degassing events are associated with gas compositions that are distinct from the usual range of passive degassing compositions. We set out to compare the chemical signature of explosive degassing during the 2005-06 and 2013 episodes, and to characterise the chemistry of gases emitted during the period of lake refilling after explosions. We found little change in the explosive gas chemistry between 2005-06 and 2013, suggesting reactivation of a common mechanism of gas segregation. Bubbles can be distinguished by their size and composition, the ranges of which are likely modified during ascent by gas-melt interaction and adiabatic expansion. The proportions of water, SO2, and HCl in the emitted gas plume increase during the refill of the lake after explosions, as the lake is recharged by a combination of magma that has already partially degassed, and that vesiculates rapidly in response to the drop in magmastatic pressure at the lake.TI acknowledges doctoral grants from the AXA Research Fund and the William Georgetti trust. Fieldwork was carried out with the support of the G-081 Erebus team and the US Antarctic Program, funded by NSF grant ANT1142083. The original FTIR retrieval code was written by Mike Burton with modifications made by Georgina Sawyer. Thermal IR images and lake velocity data were supplied by Nial Peters. Support was also received from grant 202844 from the European Research Council under the European FP7 and the NERC Centre for the Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET), part of the NERC-funded National Centre for Earth Observation (http://comet.nerc.ac.uk/).This is the final version. It first appeared at http://www.sciencedirect.com/science/article/pii/S2214242815000327

Petrological Insights into Shifts in Eruptive Styles at Volcán Llaima (Chile)

Tephra and lava pairs from two summit eruptions (ad 2008 and 1957) and a flank fissure eruption (∼ ad 1850) are compared in terms of textures, phenocryst contents, and mineral zoning patterns to shed light on processes responsible for the shifts in eruption style during typical eruptive episodes at Volcán Llaima (Andean Southern Volcanic Zone, Chile). The mineralogy and whole-rock compositions of tephra and lavas are similar within eruptive episodes, suggesting a common magma reservoir for Strombolian paroxysms and lava effusion. The zoning profiles and textures of plagioclase record successive and discrete intrusions of volatile-rich mafic magma accompanied by mixing of these recharge magmas with the resident basaltic-andesitic crystal mushes that are commonly present at shallow levels in the Llaima system. Each recharge event destabilizes the plagioclase in equilibrium with the resident crystal mush melt and stabilizes relatively An-rich plagioclase, as is recorded by the numerous resorption zones. Lavas typically have ∼15-20 vol. % more phenocrysts than the tephra. Differences in plagioclase and olivine textures and zoning, combined with different phenocryst contents, indicate that a greater volume fraction of recharge magma is present in the explosively erupted magma than in subsequent effusively erupted magma. We propose that Strombolian paroxysms at Volcán Llaima are triggered by interactions with large volume fractions of recharge magma, which decrease the bulk viscosity and increase the volatile contents of the erupted magmas, leading to the conditions required for the fragmentation of basaltic-andesite. Lava effusion ensues from reduced interactions with the recharge magma, after it has partially degassed and crystallized, thereby impeding rapid ascent. This process could be operating at other steady-state basaltic volcanoes, wherein shallow reservoirs are periodically refilled by fresh, volatile-rich magma

Minority Quasispecies of Drug-Resistant HIV-1 That Lead to Early Therapy Failure in Treatment-Naive and -Adherent Patients

Background.Early virological failure of antiretroviral therapy associated with the selection of drug-resistant human immunodeficiency virus type 1 in treatment-naive patients is very critical, because virological failure significantly increases the risk of subsequent failures. Therefore, we evaluated the possible role of minority quasispecies of drug-resistant human immunodeficiency virus type 1, which are undetectable at baseline by population sequencing, with regard to early virological failure. Methods.We studied 4 patients who experienced early virological failure of a first-line regimen of lamivudine, tenofovir, and either efavirenz or nevirapine and 18 control patients undergoing similar treatment without virological failure. The key mutations K65R, K103N, Y181C, M184V, and M184I in the reverse transcriptase were quantified by allele-specific real-time polymerase chain reaction performed on plasma samples before and during early virological treatment failure. Results.Before treatment, none of the viruses showed any evidence of drug resistance in the standard genotype analysis. Minority quasispecies with either the M184V mutation or the M184I mutation were detected in 3 of 18 control patients. In contrast, all 4 patients whose treatment was failing had harbored drug-resistant viruses at low frequencies before treatment, with a frequency range of 0.07% 2.0%. A range of 1 4 mutations was detected in viruses from each patient. Most of the minority quasispecies were rapidly selected and represented the major virus population within weeks after the patients started antiretroviral therapy. All 4 patients showed good adherence to treatment. Nonnucleoside reverse-transcriptase inhibitor plasma concentrations were in normal ranges for all 4 patients at 2 separate assessment times. Conclusions.Minority quasispecies of drug-resistant viruses, detected at baseline, can rapidly outgrow and become the major virus population and subsequently lead to early therapy failure in treatment-naive patients who receive antiretroviral therapy regimens with a low genetic resistance barrie

Megacrystals track magma convection between reservoir and surface

Active volcanoes are typically fed by magmatic reservoirs situated within the upper crust. The development of thermal and/or compositional gradients in such magma chambers may lead to vigorous convection as inferred from theoretical models and evidence for magma mixing recorded in volcanic rocks. Bi-directional flow is also inferred to prevail in the conduits of numerous persistently-active volcanoes based on observed gas and thermal emissions at the surface, as well as experiments with analogue models. However, more direct evidence for such exchange flows has hitherto been lacking. Here, we analyse the remarkable oscillatory zoning of anorthoclase feldspar megacrystals erupted from the lava lake of Erebus volcano, Antarctica. A comprehensive approach, combining phase equilibria, solubility experiments and melt inclusion and textural analyses shows that the chemical profiles are best explained as a result of multiple episodes of magma transport between a deeper reservoir and the lava lake at the surface. Individual crystals have repeatedly travelled up-and-down the plumbing system, over distances of up to several kilometers, presumably as a consequence of entrainment in the bulk magma flow. Our findings thus corroborate the model of bi-directional flow in magmatic conduits. They also imply contrasting flow regimes in reservoir and conduit, with vigorous convection in the former (regular convective cycles of ∼150 days at a speed of ∼0.5 mm s−1) and more complex cycles of exchange flow and re-entrainment in the latter. We estimate that typical, 1-cm-wide crystals should be at least 14 years old, and can record several (from 1 to 3) complete cycles between the reservoir and the lava lake via the conduit. This persistent recycling of phonolitic magma is likely sustained by CO2 fluxing, suggesting that accumulation of mafic magma in the lower crust is volumetrically more significant than that of evolved magma within the edifice.The work reported here has been partially supported by the National Science Foundation (Division of Polar Programs) under grant ANT1142083. The authors thank the Natural Environment Research Council (NERC) for access to the NERC Ion Microprobe Facility (Grant IMF453/1011) and Richard Hinton for invaluable help with SIMS analyses. Y.M. acknowledges support from the Cambridge Philosophical Society, the University of Cambridge Home and EU Scholarship Scheme, and the Philip Lake and William Vaughan Lewis funds from the Department of Geography, University of Cambridge. Y.M. also acknowledges support from ERC grant #279790.This is the final published version. It first appeared at http://www.sciencedirect.com/science/article/pii/S0012821X14007833#

Redox evolution of a degassing magma rising to the surface.

Volatiles carried by magmas, either dissolved or exsolved, have a fundamental effect on a variety of geological phenomena, such as magma dynamics1–5 and the composition of the Earth's atmosphere 6. In particular, the redox state of volcanic gases emanating at the Earth's surface is widely believed to mirror that of the magma source, and is thought to have exerted a first-order control on the secular evolution of atmospheric oxygen6,7. Oxygen fugacity (fO2 ) estimated from lava or related gas chemistry, however, may vary by as much as one log unit8–10, and the reason for such differences remains obscure. Here we use a coupled chemical–physical model of conduit flow to show that the redox state evolution of an ascending magma, and thus of its coexisting gas phase, is strongly dependent on both the composition and the amount of gas in the reservoir. Magmas with no sulphur show a systematic fO2 increase during ascent, by as much as 2 log units. Magmas with sulphur show also a change of redox state during ascent, but the direction of change depends on the initial fO2 in the reservoir. Our calculations closely reproduce the H2S/SO2 ratios of volcanic gases observed at convergent settings, yet the difference between fO2 in the reservoir and that at the exit of the volcanic conduit may be as much as 1.5 log units. Thus, the redox state of erupted magmas is not necessarily a good proxy of the redox state of the gases they emit. Our findings may require re-evaluation of models aimed at quantifying the role of magmatic volatiles in geological processes

Earth science: Redox state of early magmas

International audienceA study of cerium in zircon minerals has allowed an assessment of the redox conditions that prevailed when Earth's earliest magmas formed. The results suggest that the mantle became oxidized sooner than had been though

Nosocomial outbreak of multiple bloodborne viral infections

In resource-limited countries, nosocomial transmission of bloodborne pathogens is a major public health concern. After a major outbreak of human immunodeficiency virus (HIV) infection in approximately 400 children in 1998 in Libya, we tested HIV, hepatitis C virus (HCV), and hepatitis B virus (HBV) markers in 148 children and collected epidemiological data in a subgroup of 37 children and 46 parents. HIV infection was detected in all children but one, with HCV or HBV coinfection in 47% and 33%, respectively. Vertical transmission was ruled out by analysis of parents' serology. The children visited the same hospital 1-6 times; at each visit, invasive procedures with potential blood transmission of virus were performed. HIV and HCV genotypic analyses identified a HIV monophyletic group, whereas 4 clusters of HCV sequences were identified. To our knowledge, this is the largest documented outbreak of nosocomial HIV transmission