Galois groups of multivariate Tutte polynomials

The multivariate Tutte polynomial $\hat Z_M$ of a matroid $M$ is a generalization of the standard two-variable version, obtained by assigning a separate variable $v_e$ to each element $e$ of the ground set $E$. It encodes the full structure of $M$. Let \bv = \{v_e\}_{e\in E}, let $K$ be an arbitrary field, and suppose $M$ is connected. We show that $\hat Z_M$ is irreducible over K(\bv), and give three self-contained proofs that the Galois group of $\hat Z_M$ over K(\bv) is the symmetric group of degree $n$, where $n$ is the rank of $M$. An immediate consequence of this result is that the Galois group of the multivariate Tutte polynomial of any matroid is a direct product of symmetric groups. Finally, we conjecture a similar result for the standard Tutte polynomial of a connected matroid.Comment: 8 pages, final version, to appear in J. Alg. Comb. Substantial revisions, including the addition of two alternative proofs of the main resul

Additive models with random scaling factors: Applications to modeling price response functions

We discuss inference for additive models with random scaling factors. The additive effects are of the form (1+g)f(z) where f is a nonlinear function of the continuous covariate z modeled by P(enalized)-splines and 1+g is a random scaling factor. Additionally, monotonicity constraints on the nonlinear functions are possible. Our work is motivated by the situation of a retailer analyzing the impact of price changes on a brand's sales in its orange juice product category. Relating sales to a brand's own price as well as to the prices of competing brands in the category, we estimate own- and cross-item price response functions flexibly to represent nonlinearities and irregular pricing effects in sales response. Monotonicity constraints are imposed so that a brand's own price is inversely related and the prices of competing brands are directly related to the number of items sold, as suggested by economic theory. Unobserved store-specific heterogeneity is accounted for by allowing the price response curves to vary between different stores.@Wir behandeln additive Modelle mit zufälligen Skalierungsfaktoren. Die additive Effekte haben die Form (1 + ã)f (z). f ist eine nichtlineare Funktion der stetigen Kovariable z, modelliert mittels P(enalized)- splines und 1 + ã ist ein zufälliger Skalierungsfaktor. Den nichtlinearen Funktionen können zusätzlich Monotonierestriktionen auferlegt werden. Den Ausgangspunkt unserer Arbeit bildet die Situation eines Einzelhändlers, der den Einfluss von Preisänderungen auf den Absatz einer Orangensaftmarke in seinem Sortiment analysieren möchte. Eine entsprechende Absatzreaktionsfunktion lässt sich schätzen, indem der Absatz der betrachteten Marke als nichtlineare Funktion des eigenen Preises sowie der Preise der Konkurrenzmarken modelliert wird. Monotonierestriktionen für die Preiseffekte gewährleisten darüber hinaus einen inversen Verlauf des Absatzes bezüglich des eigenen Preises sowie eine direkte Beziehung des Absatzes zu Konkurrenzpreisen, wie es in Anlehnung an die ökonomische Preistheorie zu erwarten ist. Unbeobachtete Heterogenität wird berücksichtigt, indem die Preiseffekte über die einzelnen Geschäfte des Händlers zufällig variieren können

A systematic method of parameterisation estimation using data assimilation

In numerical weather prediction, parameterisations are used to simulate missing physics in the model. These can be due to a lack of scientific understanding or a lack of computing power available to address all the known physical processes. Parameterisations are sources of large uncertainty in a model as parameter values used in these parameterisations cannot be measured directly and hence are often not well known; and the parameterisations themselves are also approximations of the processes present in the true atmosphere. Whilst there are many efficient and effective methods for combined state/parameter estimation in data assimilation (DA), such as state augmentation, these are not effective at estimating the structure of parameterisations. A new method of parameterisation estimation is proposed that uses sequential DA methods to estimate errors in the numerical models at each space-time point for each model equation. These errors are then fitted to pre-determined functional forms of missing physics or parameterisations that are based upon prior information. We applied the method to a one-dimensional advection model with additive model error, and it is shown that the method can accurately estimate parameterisations, with consistent error estimates. Furthermore, it is shown how the method depends on the quality of the DA results. The results indicate that this new method is a powerful tool in systematic model improvement

Two-gap superconductivity with line nodes in CsCa2_2Fe4_4As4_4F2_2

We report the results of a muon-spin rotation ($\mu$SR) experiment to determine the superconducting ground state of the iron-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$ with $T_{\rm c} \approx 28.3\,$K. This compound is related to the fully-gapped superconductor CaCsFe$_4$As$_4$, but here the Ca-containing spacer layer is replaced with one containing Ca$_2$F$_2$. The temperature evolution of the penetration depth strongly suggests the presence of line nodes and is best modelled by a system consisting of both an $s$- and a $d$-wave gap. We also find a potentially magnetic phase which appears below $\approx 10\,$K but does not appear to compete with the superconductivity. This compound contains the largest alkali atom in this family of superconductors and our results yield a value for the in-plane penetration depth of $\lambda_{ab}(T=0)=423(5)\,$nm.Comment: 6 pages, 2 figure

Robustness of superconductivity to competing magnetic phases in tetragonal FeS

We have determined the superconducting and magnetic properties of a hydrothermally synthesized powder sample of tetragonal FeS using muon spin rotation ({\mu}SR). The superconducting properties are entirely consistent with those of a recently published study, showing fully gapped behavior and giving a penetration depth of {\lambda}_{ab} = 204(3) nm. However, our zero-field {\mu}SR data are rather different and indicate the presence of a small, non-superconducting magnetic phase within the sample. These results highlight that sample-to-sample variations in magnetism can arise in hydrothermally prepared phases, but interestingly the superconducting behavior is remarkably insensitive to these variations.Comment: 5 pages, 2 figure

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.Comment: 9 page

Influence of hunger on attentional engagement with and disengagement from pictorial food cues in women with a healthy weight

Because of inconsistencies in the field of attentional bias to food cues in eating behavior, this study aimed to re-examine the assumption that hungry healthy weight individuals have an attentional bias to food cues, but satiated healthy weight individuals do not. Since attentional engagement and attentional disengagement have been proposed to play a distinct role in behavior, we used a performance measure that is specifically designed to differentiate between these two attentional processes. Participants were healthy weight women who normally eat breakfast. In the satiated condition (n = 54), participants were instructed to have breakfast just before coming to the lab. In the fasted condition (n = 50), participants fasted on average 14 h before coming into the lab. Satiated women showed no stronger attentional engagement or attentional disengagement bias to food cues than to neutral cues. Fasted women did show stronger attentional engagement to food cues than to neutral cues that were shown briefly (100 ms). They showed no bias in attentional engagement to food cues that were shown longer (500 ms) or in attentional disengagement from food cues. These findings are in line with the assumption that healthy weight individuals show an attentional bias to food cues when food stimuli are motivationally salient. Furthermore, the findings point to the importance of differentiating between attentional engagement and attentional disengagement

Robustness of superconducting properties to transition metal substitution and impurity phases in Fe1-xVxSe

We have performed transverse- and zero-field muon spin rotation/relaxation experiments, as well as magnetometry measurements, on samples of Fe1-xVxSe and their Li+NH3 intercalates Li0.6(NH2)0.2(NH3)0.8 Fe1-x Vx Se. We examine the low vanadium substitution regime: x = 0.005, 0.01, and 0.02. The intercalation reaction significantly increases the critical temperature (Tc) and the superfluid stiffness for all x. The nonintercalated samples all exhibit Tc = 8.5 K while the intercalated samples all show an enhanced Tc > 40 K. Vanadium substitution has a negligible effect on Tc, but seems to suppress the superfluid stiffness for the nonintercalated samples and weakly enhance it for the intercalated materials. The optimal substitution level for the intercalated samples is found to be x = 0.01, with Tc = 41 K and {\lambda}_{ab}(0) = 0.18 {\mu}m. The nonintercalated samples can be modeled with either a single d-wave superconducting gap or with an anisotropic gap function based on recent quasiparticle imaging experiments, whereas the intercalates display multigap nodal behavior which can be fitted using s + d- or d + d-wave models. Magnetism, likely from iron impurities, appears after the intercalation reaction and coexists and competes with the superconductivity. However, it appears that the superconductivity is remarkably robust to the impurity phase, providing an avenue to stably improve the superconducting properties of transition metal substituted FeSe.Comment: 7 pages, 4 figure

Formative Evaluation of a Hepatitis C Virus Computer Assisted Instruction Tool or Communities of African Descent

Hepatitis C Virus (HCV) has become increasingly prevalent within traditionally undeserved communities. The paper describes the formative evaluation of a HCV Computer Assisted Instruction (CAI) tool. Specific aims are to describe the feasibility of a CAI tool with a high-risk population, and the use of Nigrescence Theory to develop targeted messages. Three participants, recruited at an all-male substance abuse halfway house, reviewed the CAI in a mini-focus group. A Health History/HCV Knowledge Questionnaire, The Cross Racial Identity Scale and a focus group question route were used to collect qualitative and quantitative data. The analysis plan utilized descriptive statistics, content analysis and profile analysis. Results suggested that the CAI was acceptable to this segment of the population, and Nigrescence Theory provided a context for targeting messages to differing segments of the target group. Recommendations are offered to health promotion programs targeting people of African descent