Six Permutation Patterns Force Quasirandomness

A sequence $\pi_1,\pi_2,\dots$ of permutations is said to be "quasirandom" if the induced density of every permutation $\sigma$ in $\pi_n$ converges to $1/|\sigma|!$ as $n\to\infty$. We prove that $\pi_1,\pi_2,\dots$ is quasirandom if and only if the density of each permutation $\sigma$ in the set $$\{123,321,2143,3412,2413,3142\}$$ converges to $1/|\sigma|!$. Previously, the smallest cardinality of a set with this property, called a "quasirandom-forcing" set, was known to be between four and eight. In fact, we show that there is a single linear expression of the densities of the six permutations in this set which forces quasirandomness and show that this is best possible in the sense that there is no shorter linear expression of permutation densities with positive coefficients with this property. In the language of theoretical statistics, this expression provides a new nonparametric independence test for bivariate continuous distributions related to Spearman's $\rho$.Comment: 27 pages, 1 figure, 5 appendices included as ancillary file

Brillouin Scattering from Smectic Liquid Crystals

Brillouin-scattering results are reported for monodomain samples of $\beta$-methyl butyl p [(p-methoxy benzylidine)amino] cinnamate in both the smectic-A and -B phases. For both phases theoretical predictions are confirmed concerning the number and polarizations of the propagating hypersonic waves. We report quantitative measurements of various thermodynamic derivatives, including the coupling between density and smectic-layer spacing. We discuss preliminary evidence concerning one model of the smectic-B phase.Engineering and Applied Science

Extremal Bounds for Three-Neighbour Bootstrap Percolation in Dimensions Two and Three

For $r\geq1$, the $r$-neighbour bootstrap process in a graph $G$ starts with a set of infected vertices and, in each time step, every vertex with at least $r$ infected neighbours becomes infected. The initial infection percolates if every vertex of $G$ is eventually infected. We exactly determine the minimum cardinality of a set that percolates for the $3$-neighbour bootstrap process when $G$ is a $3$-dimensional grid with minimum side-length at least $11$. We also characterize the integers $a$ and $b$ for which there is a set of cardinality $\frac{ab+a+b}{3}$ that percolates for the $3$-neighbour bootstrap process in the $a\times b$ grid; this solves a problem raised by Benevides, Bermond, Lesfari and Nisse [HAL Research Report 03161419v4, 2021].Comment: 45 page

Polarized Raman Scattering Studies of Orientational Order in Uniaxial Liquid Crystalline Phases

The measurement of vibrational Raman depolarization ratios has been used to study molecular orientational order in uniaxial single domain nematic and smectic liquid crystal samples. This technique is demonstrated to obtain the same microscopic order parameter $\langle P_2 \rangle =1/2 \langle 3 cos^2\theta −1 \rangle$, where $\theta$ is the angle between a molecular long axis and the uniaxial direction, as other existing methods. In addition, the next higher moment of the orientational distribution function $\langle P_4 \rangle=1/8 \langle 35 cos^4 \theta−30 cos^2 \theta+3 \rangle$ has been measured for the first time. The physical basis, theoretical apparatus, and experimental methods necessary for the application of this technique are thoroughly detailed in this paper. Measurements are presented of the temperature dependence of $\langle P_2 \rangle$ and $\langle P_4 \rangle$ of N‐(p'‐butoxybenzylidene)‐p‐cyanoaniline (BBCA) dissolved in N‐(p'‐methoxybenzylidene)‐p‐cyanoaniline (MBBA) and of pure MBBA in the isotropic and nematic phases, and in the isotropic, nematic, smectic A, and smectic B phases of N‐(p'‐butoxybenzylidene)‐p‐n‐octylaniline (40.8). In the nematic phases the new quantitative information marks significant discrepancies with existing theories of nematic ordering. In the smectic phases the results show unambiguously the anticipated high degree of molecular orientational order.Engineering and Applied Science

Light Scattering by Deformation of the Plane Texture of Smectic and Cholesteric Liquid Crystals

Distortions of the plane texture of smectic-A and cholesteric liquid crystals are shown to combine with the uniaxial birefringence of the plane texture to produce a strong characteristic light-scattering effect. We have observed static deformations, arising from surface defects, as well as dynamic deformations arising from thermal or mechanical stress. An immediate application of this effect is to confirm theoretical speculations on the elasticity of smectic-A phases.Engineering and Applied Science

Estimating spring terminus submarine melt rates at a greenlandic tidewater glacier using satellite imagery

Oceanic forcing of the Greenland Ice Sheet is believed to promote widespread thinning at tidewater glaciers, with submarine melting proposed as a potential trigger of increased glacier calving, retreat, and subsequent acceleration. The precise mechanism(s) driving glacier instability, however, remain poorly understood, and while increasing evidence points to the importance of submarine melting, estimates of melt rates are uncertain. Here we estimate submarine melt rate by examining freeboard changes in the seasonal ice tongue of Kangiata Nunaata Sermia (KNS) at the head of Kangersuneq Fjord (KF), southwest Greenland. We calculate melt rates for March and May 2013 by differencing along-fjord surface elevation, derived from high-resolution TanDEM-X digital elevation models (DEMs), in combination with ice velocities derived from offset tracking applied to TerraSAR-X imagery. Estimated steady state melt rates reach up to 1.4 ± 0.5m d-1 near the glacier grounding line, with mean values of up to 0.8 ± 0.3 and 0.7 ± 0.3m d-1 for the eastern and western parts of the ice tongue, respectively. Melt rates decrease with distance from the ice front and vary across the fjord. This methodology reveals spatio-temporal variations in submarine melt rates (SMRs) at tidewater glaciers which develop floating termini, and can be used to improve our understanding of ice-ocean interactions and submarine melting in glacial fjords.Publisher PDFPeer reviewe

Comparing interferon-gamma release assays with tuberculin skin test for identifying latent tuberculosis infection that progresses to active tuberculosis : systematic review and meta-analysis

Background Timely and accurate identification of people with latent tuberculosis infection (LTBI) is important for controlling Mycobacterium tuberculosis (TB). There is no gold standard for diagnosis of LTBI. Screening tests such as interferon gamma release assays (IGRAs) and tuberculin skin test (TST) provide indirect and imperfect information. This systematic review compared two types of IGRAs QuantiFERON®-TB Gold In-Tube test (QFT-GIT) and T-SPOT.TB with TST for identification of LTBI by predicting progression to a diagnosis of active TB in three subgroups: children, immunocompromised people, and those recently arrived from countries with high TB burden. Methods Cohort studies were eligible for inclusion. We searched MEDLINE, EMBASE, the Cochrane Library and other databases from December 2009 to June 2015. One reviewer screened studies, extracted data, and assessed risk of bias with cross checking by a second reviewer. Strength of association between test results and incidence of TB was summarised using cumulative incidence ratios (CIRs with 95% CIs). Summary effect measures: the ratio of CIRs (R-CIR) with 95% CIs. R-CIRs, were pooled using a random-effects model. Heterogeneity was assessed using Chi-squared and I2 statistics. Results Seventeen studies, mostly of moderate or high risk of bias (five in children, 10 in immunocompromised people, and two in those recently arrived) were included. In children, while in two studies, there was no significant difference between QFT-GIT and TST (≥5 mm) (pooled R-CIR = 1.11, 95% CI: 0.71, 1.74), two other studies showed QFT-GIT to outperform TST (≥10 mm) in identifying LTBI. In immunocompromised people, IGRA (T-SPOT.TB) was not significant different from TST (≥10 mm) for identifying LTBI, (pooled R-CIR = 1.01, 95% CI: 0.65, 1.58). The forest plot of two studies in recently arrived people from countries with high TB burden demonstrated inconsistent findings (high heterogeneity; I2 = 92%). Conclusions Prospective studies comparing IGRA testing against TST on the progression from LTBI to TB were sparse, and these results should be interpreted with caution due to uncertainty, risk of bias, and unexplained heterogeneity. Population-based studies with adequate sample size and follow-up are required to adequately compare the performance of IGRA with TST in people at high risk of TB

Single wall carbon nanotubes enter cells by endocytosis and not membrane penetration

<p>Abstract</p> <p>Background</p> <p>Carbon nanotubes are increasingly being tested for use in cellular applications. Determining the mode of entry is essential to control and regulate specific interactions with cells, to understand toxicological effects of nanotubes, and to develop nanotube-based cellular technologies. We investigated cellular uptake of Pluronic copolymer-stabilized, purified ~145 nm long single wall carbon nanotubes (SWCNTs) through a series of complementary cellular, cell-mimetic, and in vitro model membrane experiments.</p> <p>Results</p> <p>SWCNTs localized within fluorescently labeled endosomes, and confocal Raman spectroscopy showed a dramatic reduction in SWCNT uptake into cells at 4°C compared with 37°C. These data suggest energy-dependent endocytosis, as shown previously. We also examined the possibility for non-specific physical penetration of SWCNTs through the plasma membrane. Electrochemical impedance spectroscopy and Langmuir monolayer film balance measurements showed that Pluronic-stabilized SWCNTs associated with membranes but did not possess sufficient insertion energy to penetrate through the membrane. SWCNTs associated with vesicles made from plasma membranes but did not rupture the vesicles.</p> <p>Conclusions</p> <p>These measurements, combined, demonstrate that Pluronic-stabilized SWCNTs only enter cells via energy-dependent endocytosis, and association of SWCNTs to membrane likely increases uptake.</p

Single wall carbon nanotubes enter cells by endocytosis and not membrane penetration

<p>Abstract</p> <p>Background</p> <p>Carbon nanotubes are increasingly being tested for use in cellular applications. Determining the mode of entry is essential to control and regulate specific interactions with cells, to understand toxicological effects of nanotubes, and to develop nanotube-based cellular technologies. We investigated cellular uptake of Pluronic copolymer-stabilized, purified ~145 nm long single wall carbon nanotubes (SWCNTs) through a series of complementary cellular, cell-mimetic, and in vitro model membrane experiments.</p> <p>Results</p> <p>SWCNTs localized within fluorescently labeled endosomes, and confocal Raman spectroscopy showed a dramatic reduction in SWCNT uptake into cells at 4°C compared with 37°C. These data suggest energy-dependent endocytosis, as shown previously. We also examined the possibility for non-specific physical penetration of SWCNTs through the plasma membrane. Electrochemical impedance spectroscopy and Langmuir monolayer film balance measurements showed that Pluronic-stabilized SWCNTs associated with membranes but did not possess sufficient insertion energy to penetrate through the membrane. SWCNTs associated with vesicles made from plasma membranes but did not rupture the vesicles.</p> <p>Conclusions</p> <p>These measurements, combined, demonstrate that Pluronic-stabilized SWCNTs only enter cells via energy-dependent endocytosis, and association of SWCNTs to membrane likely increases uptake.</p