Computation of saddle type slow manifolds using iterative methods

This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that require mesh refinements to ensure uniform convergence with respect to $\epsilon$, appropriate estimates are directly attainable using the method of this paper. The method is applied to several examples including: A model for a pair of neurons coupled by reciprocal inhibition with two slow and two fast variables and to the computation of homoclinic connections in the FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System

A model sensitivity study of the impact of clouds on satellite detection and retrieval of volcanic ash

Volcanic ash is commonly observed by infrared detectors on board Earth-orbiting satellites. In the presence of ice and/or liquid-water clouds, the detected volcanic ash signature may be altered. In this paper the sensitivity of detection and retrieval of volcanic ash to the presence of ice and liquid-water clouds was quantified by simulating synthetic equivalents to satellite infrared images with a 3-D radiative transfer model. The sensitivity study was made for the two recent eruptions of Eyjafjallajokull (2010) and Grimsvotn (2011) using realistic water and ice clouds and volcanic ash clouds. The water and ice clouds were taken from European Centre for Medium-RangeWeather Forecast (ECMWF) analysis data and the volcanic ash cloud fields from simulations by the Lagrangian particle dispersion model FLEXPART. The radiative transfer simulations were made both with and without ice and liquid-water clouds for the geometry and channels of the Spinning Enhanced Visible and Infrared Imager (SEVIRI). The synthetic SEVIRI images were used as input to standard reverse absorption ash detection and retrieval methods. Ice and liquid-water clouds were on average found to reduce the number of detected ash-affected pixels by 6-12 %. However, the effect was highly variable and for individual scenes up to 40% of pixels with mass loading > 0 : 2 gm 2 could not be detected due to the presence of water and ice clouds. For coincident pixels, i. e. pixels where ash was both present in the FLEXPART (hereafter referred to as "Flexpart") simulation and detected by the algorithm, the presence of clouds overall increased the retrieved mean mass loading for the Eyjafjallajokull (2010) eruption by about 13 %,while for the Grimsvotn (2011) eruption ash-mass loadings the effect was a 4% decrease of the retrieved ash-mass loading. However, larger differences were seen between scenes (standard deviations of +/- 30 and +/- 20% for Eyjafjallajokull and Grimsvotn, respectively) and even larger ones within scenes. The impact of ice and liquid-water clouds on the detection and retrieval of volcanic ash, implies that to fully appreciate the location and amount of ash, hyperspectral and spectral band measurements by satellite instruments should be combined with ash dispersion modelling

Using data insertion with the NAME model to simulate the 8 May 2010 Eyjafjallajökull volcanic ash cloud

A data insertion method, where a dispersion model is initialized from ash properties derived from a series of satellite observations, is used to model the 8 May 2010 Eyjafjallajökull volcanic ash cloud which extended from Iceland to northern Spain. We also briefly discuss the application of this method to the April 2010 phase of the Eyjafjallajökull eruption and the May 2011 Grímsvötn eruption. An advantage of this method is that very little knowledge about the eruption itself is required because some of the usual eruption source parameters are not used. The method may therefore be useful for remote volcanoes where good satellite observations of the erupted material are available, but little is known about the properties of the actual eruption. It does, however, have a number of limitations related to the quality and availability of the observations. We demonstrate that, using certain configurations, the data insertion method is able to capture the structure of a thin filament of ash extending over northern Spain that is not fully captured by other modeling methods. It also verifies well against the satellite observations according to the quantitative object-based quality metric, SAL—structure, amplitude, location, and the spatial coverage metric, Figure of Merit in Space

Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree.

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether a given graph G allows a homomorphism to a given graph H that is locally bijective, surjective, or injective, respectively, are NP-complete, even when G has pathwidth at most 5, 4 or 2, respectively, or when both G and H have maximum degree 3. We complement these hardness results by showing that the three problems are polynomial-time solvable if G has bounded treewidth and in addition G or H has bounded maximum degree

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

The 2019 Raikoke volcanic eruption - Part 1: Dispersion model simulations and satellite retrievals of volcanic sulfur dioxide

Abstract. Volcanic eruptions can cause significant disruption to society, and numerical models are crucial for forecasting the dispersion of erupted material. Here we assess the skill and limitations of the Met Office's Numerical Atmospheric-dispersion Modelling Environment (NAME) in simulating the dispersion of the sulfur dioxide (SO2) cloud from the 21–22 June 2019 eruption of the Raikoke volcano (48.3∘ N, 153.2∘ E). The eruption emitted around 1.5±0.2 Tg of SO2, which represents the largest volcanic emission of SO2 into the stratosphere since the 2011 Nabro eruption. We simulate the temporal evolution of the volcanic SO2 cloud across the Northern Hemisphere (NH) and compare our model simulations to high-resolution SO2 measurements from the TROPOspheric Monitoring Instrument (TROPOMI) and the Infrared Atmospheric Sounding Interferometer (IASI) satellite SO2 products. We show that NAME accurately simulates the observed location and horizontal extent of the SO2 cloud during the first 2–3 weeks after the eruption but is unable, in its standard configuration, to capture the extent and precise location of the highest magnitude vertical column density (VCD) regions within the observed volcanic cloud. Using the structure–amplitude–location (SAL) score and the fractional skill score (FSS) as metrics for model skill, NAME shows skill in simulating the horizontal extent of the cloud for 12–17 d after the eruption where VCDs of SO2 (in Dobson units, DU) are above 1 DU. For SO2 VCDs above 20 DU, which are predominantly observed as small-scale features within the SO2 cloud, the model shows skill on the order of 2–4 d only. The lower skill for these high-SO2-VCD regions is partly explained by the model-simulated SO2 cloud in NAME being too diffuse compared to TROPOMI retrievals. Reducing the standard horizontal diffusion parameters used in NAME by a factor of 4 results in a slightly increased model skill during the first 5 d of the simulation, but on longer timescales the simulated SO2 cloud remains too diffuse when compared to TROPOMI measurements. The skill of NAME to simulate high SO2 VCDs and the temporal evolution of the NH-mean SO2 mass burden is dominated by the fraction of SO2 mass emitted into the lower stratosphere, which is uncertain for the 2019 Raikoke eruption. When emitting 0.9–1.1 Tg of SO2 into the lower stratosphere (11–18 km) and 0.4–0.7 Tg into the upper troposphere (8–11 km), the NAME simulations show a similar peak in SO2 mass burden to that derived from TROPOMI (1.4–1.6 Tg of SO2) with an average SO2 e-folding time of 14–15 d in the NH. Our work illustrates how the synergy between high-resolution satellite retrievals and dispersion models can identify potential limitations of dispersion models like NAME, which will ultimately help to improve dispersion modelling efforts of volcanic SO2 clouds. </jats:p

EPIC 220204960: A Quadruple Star System Containing Two Strongly Interacting Eclipsing Binaries

We present a strongly interacting quadruple system associated with the K2 target EPIC 220204960. The K2 target itself is a Kp = 12.7 magnitude star at Teff ~ 6100 K which we designate as "B-N" (blue northerly image). The host of the quadruple system, however, is a Kp = 17 magnitude star with a composite M-star spectrum, which we designate as "R-S" (red southerly image). With a 3.2" separation and similar radial velocities and photometric distances, 'B-N' is likely physically associated with 'R-S', making this a quintuple system, but that is incidental to our main claim of a strongly interacting quadruple system in 'R-S'. The two binaries in 'R-S' have orbital periods of 13.27 d and 14.41 d, respectively, and each has an inclination angle of >89 degrees. From our analysis of radial velocity measurements, and of the photometric lightcurve, we conclude that all four stars are very similar with masses close to 0.4 Msun. Both of the binaries exhibit significant ETVs where those of the primary and secondary eclipses 'diverge' by 0.05 days over the course of the 80-day observations. Via a systematic set of numerical simulations of quadruple systems consisting of two interacting binaries, we conclude that the outer orbital period is very likely to be between 300 and 500 days. If sufficient time is devoted to RV studies of this faint target, the outer orbit should be measurable within a year.Comment: 20 pages, 18 figures, 7 tables; accepted for publication in MNRA

Promoter hypermethylation of SHOX2 and SEPT9 is a potential biomarker for minimally invasive diagnosis in adenocarcinomas of the biliary tract

Clinicopathological data of the 20 biliary tract cancer cases and 100 gender- and age-matched controls included in plasma study. (XLSX 116 kb

Individual variation in levels of haptoglobin-related protein in children from Gabon

Background: Haptoglobin related protein (Hpr) is a key component of trypanosome lytic factors (TLF), a subset of highdensity lipoproteins (HDL) that form the first line of human defence against African trypanosomes. Hpr, like haptoglobin (Hp) can bind to hemoglobin (Hb) and it is the Hpr-Hb complexes which bind to these parasites allowing uptake of TLF. This unique form of innate immunity is primate-specific. To date, there have been no population studies of plasma levels of Hpr, particularly in relation to hemolysis and a high prevalence of ahaptoglobinemia as found in malaria endemic areas. Methods and Principal Findings: We developed a specific enzyme-linked immunosorbent assay to measure levels of plasma Hpr in Gabonese children sampled during a period of seasonal malaria transmission when acute phase responses (APR), malaria infection and associated hemolysis were prevalent. Median Hpr concentration was 0.28 mg/ml (range 0.03-1.1). This was 5-fold higher than that found in Caucasian children (0.049 mg/ml, range 0.002-0.26) with no evidence of an APR. A general linear model was used to investigate associations between Hpr levels, host polymorphisms, parasitological factors and the acute phase proteins, Hp, C-reactive protein (CRP) and albumin. Levels of Hpr were associated with Hp genotype, decreased with age and were higher in females. Hpr concentration was strongly correlated with that of Hp, but not CRP