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

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

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

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

Ambiguous Nucleotide Calls From Population-based Sequencing of HIV-1 are a Marker for Viral Diversity and the Age of Infection

The fraction of ambiguous nucleotide calls in bulk sequencing of human immunodeficiency virus type 1 (HIV-1) carries important information on viral diversity and the age of infection. In particular, a fraction of ambiguous nucleotides of >.5% provides evidence against a recent infection event <1 year ago

Platelet degranulation and bleeding phenotype in a large cohort of Von Willebrand disease patients

Von Willebrand disease (VWD) is a bleeding disorder caused by quantitative (type 1 or 3) or qualitative (type 2A/2B/2M/2N) defects of circulating von Willebrand factor (VWF). Circulating VWF levels not always fully explain bleeding phenotypes, suggesting a role for alternative factors, like platelets. Here, we investigated platelet factor 4 (PF4) in a large cohort of patients with VWD. PF4 levels were lower in type 2B and current bleeding phenotype was significantly associated with higher PF4 levels, particularly in type 1 VWD. Based on our findings we speculate that platelet degranulation and cargo release may play a role across VWD subtypes

C–O–H–S fluids and granitic magma : how S partitions and modifies CO2 concentrations of fluid-saturated felsic melt at 200 MPa

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Contributions to Mineralogy and Petrology 162 (2011): 849-865, doi:10.1007/s00410-011-0628-1.Hydrothermal volatile-solubility and partitioning experiments were conducted with fluid-saturated haplogranitic melt, H2O, CO2, and S in an internally heated pressure vessel at 900°C and 200 MPa; three additional experiments were conducted with iron-bearing melt. The run-product glasses were analyzed by electron microprobe, FTIR, and SIMS; and they contain ≤ 0.12 wt% S, ≤ 0.097 wt.% CO2, and ≤ 6.4 wt.% H2O. Apparent values of log ƒO2 for the experiments at run conditions were computed from the [(S6+)/(S6++S2-)] ratio of the glasses, and they range from NNO-0.4 to NNO+1.4. The C-O-H-S fluid compositions at run conditions were computed by mass balance, and they contained 22-99 mol% H2O, 0-78 mol% CO2, 0-12 mol% S, and < 3 wt% alkalis. Eight S-free experiments were conducted to determine the H2O and CO2 concentrations of melt and fluid compositions and to compare them with prior experimental results for C-O-H fluid-saturated rhyolite melt, and the agreement is excellent. Sulfur partitions very strongly in favor of fluid in all experiments, and the presence of S modifies the fluid compositions, and hence, the CO2 solubilities in coexisting felsic melt. The square of the mole fraction of H2O in melt increases in a linear fashion, from 0.05-0.25, with the H2O concentration of the fluid. The mole fraction of CO2 in melt increases linearly, from 0.0003-0.0045, with the CO2 concentration of C-O-H-S fluids. Interestingly, the CO2 concentration in melts, involving relatively reduced runs (log ƒO2 ≤ NNO+0.3) that contain 2.5-7 mol% S in the fluid, decreases significantly with increasing S in the system. This response to the changing fluid composition causes the H2O and CO2 solubility curve for C-O-H-S fluid-saturated haplogranitic melts at 200 MPa to shift to values near that modeled for C-O-H fluid-saturated, S-free rhyolite melt at 150 MPa. The concentration of S in haplogranitic melt increases in a linear fashion with increasing S in C-O-H-S fluids, but these data show significant dispersion that likely reflects the strong influence of ƒO2 on S speciation in melt and fluid. Importantly, the partitioning of S between fluid and melt does not vary with the (H2O/H2O+CO2) ratio of the fluid. The fluid-melt partition coefficients for H2O, CO2, and S and the atomic (C/S) ratios of the run-product fluids are virtually identical to thermodynamic constraints on volatile partitioning and the H, S, and C contents of pre-eruptive magmatic fluids and volcanic gases for subduction-related magmatic systems thus confirming our experiments are relevant to natural eruptive systems.This research was supported in part by National Science Foundation awards EAR 0308866 and EAR-0836741 to J.D.W