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

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

Longitudinal change in the BODE index predicts mortality in severe emphysema

Rationale: The predictive value of longitudinal change in BODE (Body mass index, airflow Obstruction, Dyspnea, and Exercise capacity) index has received limited attention. We hypothesized that decrease in a modified BODE (mBODE) would predict survival in National Emphysema Treatment Trial (NETT) patients. Objectives: To determine how the mBODE score changes in patients with lung volume reduction surgery versus medical therapy and correlations with survival. Methods: Clinical data were recorded using standardized instruments. The mBODE was calculated and patient-specific mBODE trajectories during 6, 12, and 24 months of follow-up were estimated using separate regressions for each patient. Patients were classified as having decreasing, stable, increasing, or missing mBODE based on their absolute change from baseline. The predictive ability of mBODE change on survival was assessed using multivariate Cox regression models. The index of concordance was used to directly compare the predictive ability of mBODE and its separate components. Measurements and Main Results: The entire cohort (610 treated medically and 608 treated surgically) was characterized by severe airflow obstruction, moderate breathlessness, and increased mBODE at baseline. A wide distribution of change in mBODE was seen at follow-up. An increase in mBODE of more than 1 point was associated with increased mortality in surgically and medically treated patients. Surgically treated patients were less likely to experience death or an increase greater than 1 in mBODE. Indices of concordance showed that mBODE change predicted survival better than its separate components.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91943/1/2008 AJRCCM Longitudinal change in the BODE index predicts mortality in severe emphysema.pd