Generalized Involution Models for Wreath Products

We prove that if a finite group $H$ has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product $H \wr S_n$ also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gelfand model for wreath products of the form $A \wr S_n$ with $A$ abelian, and give an alternate proof of a recent result due to Adin, Postnikov, and Roichman describing a particularly elegant Gelfand model for the wreath product \ZZ_r \wr S_n. We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Roichman, and Postnikov's.Comment: 29 page

Transitive and Gallai colorings

A Gallai coloring of the complete graph is an edge-coloring with no rainbow triangle. This concept first appeared in the study of comparability graphs and anti-Ramsey theory. We introduce a transitive analogue for acyclic directed graphs, and generalize both notions to Coxeter systems, matroids and commutative algebras. It is shown that for any finite matroid (or oriented matroid), the maximal number of colors is equal to the matroid rank. This generalizes a result of Erd\H{o}s-Simonovits-S\'os for complete graphs. The number of Gallai (or transitive) colorings of the matroid that use at most $k$ colors is a polynomial in $k$. Also, for any acyclic oriented matroid, represented over the real numbers, the number of transitive colorings using at most 2 colors is equal to the number of chambers in the dual hyperplane arrangement. We count Gallai and transitive colorings of the root system of type A using the maximal number of colors, and show that, when equipped with a natural descent set map, the resulting quasisymmetric function is symmetric and Schur-positive.Comment: 31 pages, 5 figure

Determination of Inter-Phase Line Tension in Langmuir Films

A Langmuir film is a molecularly thin film on the surface of a fluid; we study the evolution of a Langmuir film with two co-existing fluid phases driven by an inter-phase line tension and damped by the viscous drag of the underlying subfluid. Experimentally, we study an 8CB Langmuir film via digitally-imaged Brewster Angle Microscopy (BAM) in a four-roll mill setup which applies a transient strain and images the response. When a compact domain is stretched by the imposed strain, it first assumes a bola shape with two tear-drop shaped reservoirs connected by a thin tether which then slowly relaxes to a circular domain which minimizes the interfacial energy of the system. We process the digital images of the experiment to extract the domain shapes. We then use one of these shapes as an initial condition for the numerical solution of a boundary-integral model of the underlying hydrodynamics and compare the subsequent images of the experiment to the numerical simulation. The numerical evolutions first verify that our hydrodynamical model can reproduce the observed dynamics. They also allow us to deduce the magnitude of the line tension in the system, often to within 1%. We find line tensions in the range of 200-600 pN; we hypothesize that this variation is due to differences in the layer depths of the 8CB fluid phases.Comment: See (http://www.math.hmc.edu/~ajb/bola/) for related movie

Domain Relaxation in Langmuir Films

We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly to the minimum-energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is wide. We model these experiments by taking previous descriptions of the full hydrodynamics, identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem for an inviscid Langmuir film whose motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. Using this model we derive relaxation rates for perturbations of a uniform strip and a circular patch. We also derive a boundary integral formulation which allows an efficient numerical solution of the problem. Numerically this model replicates the formation of a bola and the subsequent relaxation observed in the experiments. Finally, we suggest physical properties of the system (such as line tension) that can be deduced by comparison of the theory and numerical simulations to the experiment. Two movies are available with the online version of the paper

Value of Emergent Neurovascular Imaging for Seat Belt Injury : A Multi-institutional Study

BACKGROUND AND PURPOSE: Screening for blunt cerebrovascular injury in patients after motor vehicle collision (MVC) solely based on the presence of cervical seat belt sign has been debated in the literature without consensus. Our aim was to assess the value of emergent neurovascular imaging in patients after an MVC who present with a seat belt sign through a large-scale multi-institutional study. MATERIALS AND METHODS: The electronic medical records of patients admitted to the emergency department with CTA/MRAs performed with an indication of seat belt injury of the neck were retrospectively reviewed at 5 participating institutions. Logistic regression analysis was used to determine the association among age, sex, and additional trauma-related findings with blunt cerebrovascular injury. RESULTS: Five hundred thirty-five adult and 32 pediatric patients from June 2003 until March 2020 were identified. CTA findings were positive in 12/567 (2.1%) patients for the presence of blunt cerebrovascular injury of the vertebral ( CONCLUSIONS: The risk of vascular injury in the presence of the cervical seat belt sign is small, and most patients diagnosed with blunt cerebrovascular injury have other associated findings. Therefore, CTA based solely on this sign has limited value (3/567 =  a 0.5% positivity rate). We suggest that in the absence of other clinical findings, the seat belt sign does not independently justify neck CTA in patients after trauma

Idiopathic pulmonary fibrosis: Prognostic value of changes in physiology and six minute hallwalk.

Rationale and Hypothesis: Idiopathic pulmonary fibrosis is a fatal disease with a variable rate of progression. We hypothesized that changes in distance walked and quantity of desaturation during a six-minute-walk test (6MWT) would add prognostic information to changes in FVC or diffusing capacity for carbon monoxide. Methods: One hundred ninety-seven patients with idiopathic pulmonary fibrosis were evaluated. Desaturation during the 6MWT was associated with increased mortality even if a threshold of 88% was not reached. Baseline walk distance predicted subsequent walk distance but was not a reliable predictor of subsequent mortality in multivariate survival models. The predictive ability of serial changes in physiology varied when patients were stratified by the presence/absence of desaturation 88% during a baseline 6MWT. For patients with a baseline saturation 88% during a 6MWT, the strongest observed predictor of mortality was serial change in diffusing capacity for carbon monoxide. For patients with saturation 88% during their baseline walk test, serial decreases in FVC and increases in desaturation area significantly predicted subsequent mortality, whereas decreases in walk distance and in diffusing capacity for carbon monoxide displayed less consistent statistical evidence of increasing mortality in our patients. Conclusion: These data highlight the importance of stratifying patients by degree of desaturation during a 6MWT before attributing prognostic value to serial changes in other physiologic variables.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91940/1/2006 AJRCCM Idiopathic pulmonary fibrosis - Prognostic value of changes in physiology and six minute hallwalk.pd

Hydrogen bond arrangement is shown to differ in coexisting phases of aqueous two-phase systems

Analysis by attenuated total reflection-Fourier transform infrared spectroscopy shows that each coexisting phase in aqueous two-phase systems has a different arrangement of hydrogen bonds. Specific arrangements vary for systems formed by different solutes. The hydrogen bond arrangement is shown to correlate with differences in hydrophobic and electrostatic properties of the different phases of five specific systems, four formed by two polymers and one by a single polymer and salt. The results presented here suggest that the arrangement of hydrogen bonds may be an important factor in phase separation.P.P.M. acknowledges University of Aveiro, CICECO-Aveiro Institute of Materials for funding in the framework of the project UIDB/5011/2020 and UIDP/50011/2020, financed by national funds through the FCT/MEC contract foreseen in the numbers 4, 5, and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Law 57/2017, of July 19.publishe