Multi-triangulations as complexes of star polygons

Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of looking at $k$-triangulations, namely as complexes of star polygons. With this tool we give new, direct, proofs of the fundamental properties of $k$-triangulations, as well as some new results. This interpretation also opens-up new avenues of research, that we briefly explore in the last section.Comment: 40 pages, 24 figures; added references, update Section

Algorithms for 3D rigidity analysis and a first order percolation transition

A fast computer algorithm, the pebble game, has been used successfully to study rigidity percolation on 2D elastic networks, as well as on a special class of 3D networks, the bond-bending networks. Application of the pebble game approach to general 3D networks has been hindered by the fact that the underlying mathematical theory is, strictly speaking, invalid in this case. We construct an approximate pebble game algorithm for general 3D networks, as well as a slower but exact algorithm, the relaxation algorithm, that we use for testing the new pebble game. Based on the results of these tests and additional considerations, we argue that in the particular case of randomly diluted central-force networks on BCC and FCC lattices, the pebble game is essentially exact. Using the pebble game, we observe an extremely sharp jump in the largest rigid cluster size in bond-diluted central-force networks in 3D, with the percolating cluster appearing and taking up most of the network after a single bond addition. This strongly suggests a first order rigidity percolation transition, which is in contrast to the second order transitions found previously for the 2D central-force and 3D bond-bending networks. While a first order rigidity transition has been observed for Bethe lattices and networks with ``chemical order'', this is the first time it has been seen for a regular randomly diluted network. In the case of site dilution, the transition is also first order for BCC, but results for FCC suggest a second order transition. Even in bond-diluted lattices, while the transition appears massively first order in the order parameter (the percolating cluster size), it is continuous in the elastic moduli. This, and the apparent non-universality, make this phase transition highly unusual.Comment: 28 pages, 19 figure

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Acute Surgical Pulmonary Embolectomy: A 9-Year Retrospective Analysis

Acute pulmonary embolism is a substantial cause of morbidity and death. Although the American College of Chest Physicians Evidence-Based Clinical Practice Guidelines recommend surgical pulmonary embolectomy in patients with acute pulmonary embolism associated with hypotension, there are few reports of 30-day mortality rates. We performed a retrospective review of acute pulmonary embolectomy procedures performed in 96 consecutive patients who had severe, globally hypokinetic right ventricular dysfunction as determined by transthoracic echocardiography. Data on patients who were treated from January 2003 through December 2011 were derived from health system databases of the New York State Cardiac Surgery Reporting System and the Society of Thoracic Surgeons. The data represent procedures performed at 3 tertiary care facilities within a large health system operating in the New York City metropolitan area. The overall 30-day mortality rate was 4.2%. Most patients (68 [73.9%]) were discharged home or to rehabilitation facilities (23 [25%]). Hemodynamically stable patients with severe, globally hypokinetic right ventricular dysfunction had a 30-day mortality rate of 1.4%, with a postoperative mean length of stay of 9.1 days. Comparable findings for hemodynamically unstable patients were 12.5% and 13.4 days, respectively. Acute pulmonary embolectomy can be a viable procedure for patients with severe, globally hypokinetic right ventricular dysfunction, with or without hemodynamic compromise; however, caution is warranted. Our outcomes might be dependent upon institutional capability, experience, surgical ability, and careful patient selection

The First HET Planet: A Companion to HD 37605

We report the first detection of a planetary-mass companion to a star using the High Resolution Spectrograph (HRS) of the Hobby-Eberly Telescope (HET). The HET-HRS now gives routine radial velocity precision of 2-3 m/s for high SNR observations of quiescent stars. The planetary-mass companion to the metal-rich K0V star HD37605 has an orbital period of 54.23 days, an orbital eccentricity of 0.737, and a minimum mass of 2.84 Jupiter masses. The queue-scheduled operation of the Hobby-Eberly Telescope enabled us to discovery of this relatively short-period planet with a total observation time span of just two orbital periods. The ability of queue-scheduled large-aperture telescopes to respond quickly to interesting and important results demonstrates the power of this new approach in searching for extra-solar planets as well as in other ares of research requiring rapid response time critical observations.Comment: 4 Pages, 2 figures. Accepted in Astrophysical Journal Letters, http://austral.as.utexas.edu/planets/hd37605/hd37605.htm

Predictors of long-term pain and disability in patients with low back pain investigated by magnetic resonance imaging: A longitudinal study

<p>Abstract</p> <p>Background</p> <p>It is possible that clinical outcome of low back pain (LBP) differs according to the presence or absence of spinal abnormalities on magnetic resonance imaging (MRI), in which case there could be value in using MRI findings to refine case definition of LBP in epidemiological research. We therefore conducted a longitudinal study to explore whether spinal abnormalities on MRI for LBP predict prognosis after 18 months.</p> <p>Methods</p> <p>A consecutive series of patients aged 20-64 years, who were investigated by MRI because of mechanical LBP (median duration of current episode 16.2 months), were identified from three radiology departments, and those who agreed completed self-administered questionnaires at baseline and after a mean follow-up period of 18.5 months (a mean of 22.2 months from MRI investigation). MRI scans were assessed blind to other clinical information, according to a standardised protocol. Associations of baseline MRI findings with pain and disability at follow-up, adjusted for treatment and for other potentially confounding variables, were assessed by Poisson regression and summarised by prevalence ratios (PRs) with their 95% confidence intervals (CIs).</p> <p>Results</p> <p>Questionnaires were completed by 240 (74%) of the patients who had agreed to be followed up. Among these 111 men and 129 women, 175 (73%) reported LBP in the past four weeks, 89 (37%) frequent LBP, and 72 (30%) disabling LBP. In patients with initial disc degeneration there was an increased risk of frequent (PR 1.3, 95%CI 1.0-1.9) and disabling LBP (PR 1.7, 95%CI 1.1-2.5) at follow-up. No other associations were found between MRI abnormalities and subsequent outcome.</p> <p>Conclusions</p> <p>Our findings suggest that the MRI abnormalities examined are not major predictors of outcome in patients with LBP. They give no support to the use of MRI findings as a way of refining case definition for LBP in epidemiological research.</p

Reoperations after first lumbar disc herniation surgery; a special interest on residives during a 5-year follow-up

BACKGROUND: The overall rate of operations after recurrent lumbar disc herniation has been shown to be 3–11%. However, little is known about the rate of residives. Thus the aim of this study was to explore the cumulative rates of re-operations and especially residive disc herniations at the same side and level as the primary disc herniation after first lumbar disc herniation surgery and the factors that influence the risk of re-operations over a five year follow-up study. METHODS: 166 virgin lumbar disc herniation patients (mean age 42 years, 57% males) were studied. Data on patients' initial disc operations and type and timing of re-operations during the follow-up were collected from patient files. Back and leg pain on visual analog scale and employment status were collected by questionnaires. RESULTS: The cumulative rate of re-operations for lumbar disc herniation was 10.2% (95% Cl 6.0 to 15.1). The rate of residives at initial site was 7.4% (95% Cl 3.7 to 11.3) and rate of lumbar disc herniations at other sites was 3.1% (95% Cl 0.6 to 6.2). The occurrence of residive lumbar disc herniations was evenly distributed across the 5 years. Neither age, gender, preoperative symptoms, physical activity nor employment had effect on the probability of re-operation. CONCLUSION: Seven percent of the lumbar disc patients had a residive lumbar disc operation within five years of their first operation. No specific factors influencing the risk for re-operation were found

Validation of the surgical fear questionnaire in adult patients waiting for elective surgery

Objectives: Because existing instruments for assessing surgical fear seem either too general or too limited, the Surgical Fear Questionnaire (SFQ) was developed. The aim of this study is to assess the validity and reliability of the SFQ. Methods: Based on existing literature and expert consultation the ten-item SFQ was composed. Data on the SFQ were obtained from 5 prospective studies (N = 3233) in inpatient or day surgery patients. These data were used for exploratory factor analysis (EFA), confirmatory factor analysis (CFA), reliability analysis and validity analysis. Results: EFA in Study 1 and 2 revealed a two-factor structure with one factor associated with fear of the short-term consequences of surgery (SFQ-s, item 1-4) and the other factor with fear of the long-term consequences of surgery (SFQ-l, item 5-10). However, in both studies two items of the SFQ-l had low factor loadings. Therefore in Study 3 and 4 the 2-factor structure was tested and confirmed by CFA in an eight-item version of the SFQ. Across all studies significant correlations of the SFQ with pain catastrophizing, state anxiety, and preoperative pain intensity indicated good convergent validity. Internal consistency (Cronbach's alpha) was between 0.765-0.920 (SFQ-total), 0.766-0.877 (SFQ-s), and 0.628-0.899 (SFQ-l). The SFQ proved to be sensitive to detect differences based on age, sex, education level, employment status and preoperative pain intensity. Discussion: The SFQ is a valid and reliable eight-item index of surgical fear consisting of two subscales: fear of the short-term consequences of surgery and fear of the long-term consequences.This study was conducted with departmental funding and supported by a grant from The Netherlands Organisation for Scientific Research (Zon-MW, http://www.zonmw.nl/en/), grant no. 110000007. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript