Untangling polygons and graphs

Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at least \Omega(n^{2/3}) vertices fixed. For any graph G, we also present an upper bound on the number of fixed vertices in the worst case. The bound is a function of the number of vertices, maximum degree and diameter of G. One of its consequences is the upper bound O((n log n)^{2/3}) for all 3-vertex-connected planar graphs.Comment: 11 pages, 3 figure

Irreducible triangulations of surfaces with boundary

A triangulation of a surface is irreducible if no edge can be contracted to produce a triangulation of the same surface. In this paper, we investigate irreducible triangulations of surfaces with boundary. We prove that the number of vertices of an irreducible triangulation of a (possibly non-orientable) surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was known only for surfaces without boundary (b=0). While our technique yields a worse constant in the O(.) notation, the present proof is elementary, and simpler than the previous ones in the case of surfaces without boundary

A Prospective Analysis of Pharmacists Integration in the Patient-Centered Medical Home: Preparing for Value-Based Care

This is an unpublished manuscript of research completed in several patient centered medical homes that provide pharmacy services; presented at the 2016 American Pharmacists Association annual meeting in Baltimore, MD.Objective: The purpose of this project was to describe pharmacy services in a patient-centered medical home to demonstrate pharmacists’ involvement in the evolving delivery of primary care. Design: This was a prospective, qualitative study. Setting and Participants: This project analyzed the work of eight pharmacists employed at a National Committee for Quality Assurance tier III patient-centered medical home associated with a large, academic medical center. Outcome Measures: The primary outcome was to identify and quantify the types of services completed by pharmacists in a patient-centered medical home. Secondary outcomes included determining the percentage of pharmacist recommendations accepted by providers and patients, the percentage of pharmacist interventions submitted for third-party reimbursement, and the average time spent per encounter. Results: Eight pharmacists (representing 4.0 full-time equivalents) facilitated 581 encounters over 20 days. Mean time spent per encounter was 20 minutes (± 19). The most common types of encounters were interdisciplinary visits (31.8%) and phone/secure portal communication (30.0%). Of 918 pharmacist recommendations made to providers, 830 (90.4%) were accepted and implemented. Of 412 pharmacist recommendations made to patients, 393 (95.4%) were verbally accepted. Thirty-nine percent of encounters were eligible for direct payor billing. Conclusion: Our data show that pharmacists working in a patient-centered medical home are effectively integrated within the evolving delivery of primary care. Consistent inclusion of pharmacy services should be readily supported in future models of health care reform

Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

An experimental investigation of supersonic flow past a wedge-cylinder configuration

An experimental investigation of supersonic flow past double-wedge configurations was conducted. Over the range of geometries tested, it was found that, while theoretical solutions both for a Type V pattern and for a Type VI pattern could be generated for a particular flow condition (as defined by the geometry and the free-stream conditions), the weaker, Type VI pattern was observed experimentally. More rigorous flow-field solutions were developed for the flow along the wing leading-edge. Solutions were developed for the three-dimensional flow in the plane of symmetry of a swept cylinder (which represented the wing leading-edge) which was mounted on a wedge (which generated the "bow" shock wave). A numerical code was developed using integral techniques to calculate the flow in the shock layer upstream of the interaction region (i.e., near the wing root). Heat transfer rates were calculated for various free stream conditions. The present investigation was undertaken to examine the effects of crossflow on the resultant flow-field and to verify the flow model used in theoretical calculations

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

A mathematical basis for automated structured grid generation with close coupling to the flow solver

The first two truncation error terms resulting from finite differencing the convection terms in the two-dimensional Navier-Stokes equations are examined for the purpose of constructing two-dimensional grid generation schemes. These schemes are constructed such that the resulting grid distributions drive the error terms to zero. Two sets of equations result, one for each error term, that show promise in generating grids that provide more accurate flow solutions and possibly faster convergence. One set results in an algebraic scheme that drives the first truncation term to zero, and the other a hyperbolic scheme that drives the second term to zero. Also discussed is the possibility of using the schemes in sequentially constructing a grid in an iterative algorithm involving the flow solver. In essence, the process is envisioned to generate not only a flow field solution but the grid as well, rendering the approach a hands-off method for grid generatio

Modification of the nanostructure of lignocellulose cell walls via a non-enzymatic lignocellulose deconstruction system in brown rot wood-decay fungi

Abstract Wood decayed by brown rot fungi and wood treated with the chelator-mediated Fenton (CMF) reaction, either alone or together with a cellulose enzyme cocktail, was analyzed by small angle neutron scattering (SANS), sum frequency generation (SFG) spectroscopy, Fourier transform infrared (FTIR) analysis, X-ray diffraction (XRD), atomic force microscopy (AFM), and transmission electron microscopy (TEM). Results showed that the CMF mechanism mimicked brown rot fungal attack for both holocellulose and lignin components of the wood. Crystalline cellulose and lignin were both depolymerized by the CMF reaction. Porosity of the softwood cell wall did not increase during CMF treatment, enzymes secreted by the fungi did not penetrate the decayed wood. The enzymes in the cellulose cocktail also did not appear to alter the effects of the CMF-treated wood relative to enhancing cell wall deconstruction. This suggests a rethinking of current brown rot decay models and supports a model where monomeric sugars and oligosaccharides diffuse from the softwood cell walls during non-enzymatic action. In this regard, the CMF mechanism should not be thought of as a “pretreatment” used to permit enzymatic penetration into softwood cell walls, but instead it enhances polysaccharide components diffusing to fungal enzymes located in wood cell lumen environments during decay. SANS and other data are consistent with a model for repolymerization and aggregation of at least some portion of the lignin within the cell wall, and this is supported by AFM and TEM data. The data suggest that new approaches for conversion of wood substrates to platform chemicals in biorefineries could be achieved using the CMF mechanism with >75% solubilization of lignocellulose, but that a more selective suite of enzymes and other downstream treatments may be required to work when using CMF deconstruction technology. Strategies to enhance polysaccharide release from lignocellulose substrates for enhanced enzymatic action and fermentation of the released fraction would also aid in the efficient recovery of the more uniform modified lignin fraction that the CMF reaction generates to enhance biorefinery profitability