An inequality of Kostka numbers and Galois groups of Schubert problems

We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kostka numbers of two-rowed tableaux. In most cases, an easy combinatorial injection proves the inequality. For the remaining cases, we use that these Kostka numbers appear in tensor product decompositions of sl_2(C)-modules. Interpreting the tensor product as the action of certain commuting Toeplitz matrices and using a spectral analysis and Fourier series rewrites the inequality as the positivity of an integral. We establish the inequality by estimating this integral.Comment: Extended abstract for FPSAC 201

The Secant Conjecture in the real Schubert calculus

We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.Comment: 19 page

An inequality of Kostka numbers and Galois groups of Schubert problems

We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kostka numbers of two-rowed tableaux. In most cases, an easy combinatorial injection proves the inequality. For the remaining cases, we use that these Kostka numbers appear in tensor product decompositions of $\mathfrak{sl}_2\mathbb{C}$ -modules. Interpreting the tensor product as the action of certain commuting Toeplitz matrices and using a spectral analysis and Fourier series rewrites the inequality as the positivity of an integral. We establish the inequality by estimating this integral

Quantification of liquid phase faecal odourants to evaluate membrane technology for wastewater reuse from decentralised sanitation facilities

Public willingness to use decentralised sanitation facilities or arising water products is discouraged due to malodour, preventing improved sanitation practices or water reuse opportunities in low income countries Whilst odour is characterised in the gas phase, it originates in the liquid phase. Consequently, controlling odour at source could prevent gas-phase partitioning and limit produced water contamination. This study therefore developed an analytical method for the quantitation of a range of liquid phase volatile organic compounds (VOCs) classified into eight chemical groups, known to be primary indicators of faecal odour, to provide characterisation of real fluids and to permit evaluation of several potential membrane separation technologies for liquid phase odourant separation. The gas chromatography mass spectrometry method provided quantitation in the range of 0.005 mg L-1 to 100 mg L-1 with instrument detection limits ranging from 0.005 mg L-1 to 0.124 mg L-1. Linear calibration curves were achieved (r2 >0.99) with acceptable accuracy (77-115%) and precision (<15%) for quantitation in the calibration range below 1 mg L 1, and good accuracy (98-104%) and precision (<2%) determined for calibration in the range 1-100 mg L-1. Pre-concentration of real samples was facilitated via solid phase extraction. Subsequent application of the method to the evaluation of two thermally driven membranes based on hydrophilic (polyvinyl alcohol) and hydrophobic (polydimethylsiloxane) polymers evidenced contrasting separation profiles. Importantly, this study demonstrates the methods utility for liquid phase VOC determination which is of use to a range of disciplines, including healthcare professionals, taste and odour specialists and public health engineers

Thermal Emission of WASP-14b Revealed with Three Spitzer Eclipses

Exoplanet WASP-14b is a highly irradiated, transiting hot Jupiter. Joshi et al. calculate an equilibrium temperature Teq of 1866 K for zero albedo and reemission from the entire planet, a mass of 7.3 +/- 0.5 Jupiter masses and a radius of 1.28 +/- 0.08 Jupiter radii. Its mean density of 4.6 g/cm3 is one of the highest known for planets with periods less than 3 days. We obtained three secondary eclipse light curves with the Spitzer Space Telescope. The eclipse depths from the best jointly fit model are $0.224\%$ +/- $0.018\%$ at 4.5 {\mu}m and $0.181\%$ +/- $0.022\%$ at 8.0 {\mu}m. The corresponding brightness temperatures are 2212 +/- 94 K and 1590 +/- 116 K. A slight ambiguity between systematic models suggests a conservative 3.6 {\mu}m eclipse depth of $0.19\%$ +/- $0.01\%$ and brightness temperature of 2242 +/- 55 K. Although extremely irradiated, WASP-14b does not show any distinct evidence of a thermal inversion. In addition, the present data nominally favor models with day night energy redistribution less than $~30\%$. The current data are generally consistent with oxygen-rich as well as carbon-rich compositions, although an oxygen-rich composition provides a marginally better fit. We confirm a significant eccentricity of e = 0.087 +/- 0.002 and refine other orbital parameters.Comment: 16 pages, 16 figure

Genomic and panproteomic analysis of the development of infant immune responses to antigenically-diverse pneumococci

Streptococcus pneumoniae (pneumococcus) is a nasopharyngeal commensal and respiratory pathogen. This study characterises the immunoglobulin G (IgG) repertoire recognising pneumococci from birth to 24 months old (mo) in a prospectively-sampled cohort of 63 children using a panproteome array. IgG levels are highest at birth, due to transplacental transmission of maternal antibodies. The subsequent emergence of responses to individual antigens exhibit distinct kinetics across the cohort. Stable differences in the strength of individuals’ responses, correlating with maternal IgG concentrations, are established by 6 mo. By 12 mo, children develop unique antibody profiles that are boosted by re-exposure. However, some proteins only stimulate substantial responses in adults. Integrating genomic data on nasopharyngeal colonisation demonstrates rare pneumococcal antigens can elicit strong IgG levels post-exposure. Quantifying such responses to the diverse core loci (DCL) proteins is complicated by cross-immunity between variants. In particular, the conserved N terminus of DCL protein zinc metalloprotease B provokes the strongest early IgG responses. DCL proteins’ ability to inhibit mucosal immunity likely explains continued pneumococcal carriage despite hosts’ polyvalent antibody repertoire. Yet higher IgG levels are associated with reduced incidence, and severity, of pneumonia, demonstrating the importance of the heterogeneity in response strength and kinetics across antigens and individuals

Microfluidic systems for the analysis of the viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/ expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application