When is a symmetric pin-jointed framework isostatic?

Maxwell's rule from 1864 gives a necessary condition for a framework to be isostatic in 2D or in 3D. Given a framework with point group symmetry, group representation theory is exploited to provide further necessary conditions. This paper shows how, for an isostatic framework, these conditions imply very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework. In particular, it turns out that an isostatic framework in 2D can belong to one of only six point groups. Some conjectures and initial results are presented that would give sufficient conditions (in both 2D and 3D) for a framework that is realized generically for a given symmetry group to be an isostatic framework.Comment: 24 pages, 10 figures; added references, minor changes, revised last paragrap

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

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

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

Effect of defects on reaction of NiO surface with Pb-contained solution

In order to understand the role of defects in chemical reactions, we used two types of samples, which are molecular beam epitaxy (MBE) grown NiO(001) film on Mg(001) substrate as the defect free NiO prototype and NiO grown on Ni(110) single crystal as the one with defects. In-situ observations for oxide-liquid interfacial structure and surface morphology were performed for both samples in water and Pb-contained solution using high-resolution X-ray reflectivity and atomic force microscopy. For the MBE grown NiO, no significant changes were detected in the high-resolution X-ray reflectivity data with monotonic increase in roughness. Meanwhile, in the case of native grown NiO on Ni(110), significant changes in both the morphology and atomistic structure at the interface were observed when immersed in water and Pb-contained solution. Our results provide simple and direct experimental evidence of the role of the defects in chemical reaction of oxide surfaces with both water and Pb-contained solution.ope

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

Resource utilization and costs before and after total joint arthroplasty

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to compare pre- and post-surgical healthcare costs in commercially insured total joint arthroplasty (TJA) patients with osteoarthritis (OA) in the United States (U.S.).</p> <p>Methods</p> <p>Using a large healthcare claims database, we identified patients over age 39 with hip or knee OA who underwent unilateral primary TJA (hip or knee) between 1/1/2006 and 9/30/2007. Utilization of healthcare services and costs were aggregated into three periods: 12 months "pre-surgery," 91 days "peri-operative," and 3 to 15 month "follow-up," Mean total pre-surgery costs were compared with follow-up costs using Wilcoxon signed-rank test.</p> <p>Results</p> <p>14,912 patients met inclusion criteria for the study. The mean total number of outpatient visits declined from pre-surgery to follow-up (18.0 visits vs 17.1), while the percentage of patients hospitalized increased (from 7.5% to 9.8%) (both <it>p </it>< 0.01). Mean total costs during the follow-up period were 18% higher than during pre-surgery ($11,043 vs.$9,632, <it>p </it>< 0.01), largely due to an increase in the costs of inpatient care associated with hospital readmissions ($3,300 vs.$1,817, p < 0.01). Pharmacotherapy costs were similar for both periods ($2013 [follow-up] vs.$1922 [pre-surgery], p = 0.33); outpatient care costs were slightly lower in the follow-up period ($4338 vs.$4571, <it>p </it>< 0.01). Mean total costs for the peri-operative period were $36,553.</p> <p>Conclusions</p> <p>Mean total utilization of outpatient healthcare services declined slightly in the first year following TJA (exclusive of the peri-operative period), while mean total healthcare costs increased during the same time period, largely due to increased costs associated with hospital readmissions. Further study is necessary to determine whether healthcare costs decrease in subsequent years.</p

Risk factors for moderate and severe persistent pain in patients undergoing total knee and hip arthroplasty : a prospective predictive study

Persistent post-surgical pain (PPSP) is a major clinical problem with significant individual, social and health care costs. The aim of this study was to examine the joint role of demographic, clinical and psychological risk factors in the development of moderate and severe PPSP after Total Knee and Hip Arthroplasty (TKA and THA, respectively). This was a prospective study wherein a consecutive sample of 92 patients were assessed 24 hours before (T1), 48 hours after (T2) and 4-6 months (T3) after surgery. Hierarchical logistic regression analyses were performed to identify predictors of moderate and severe levels of PPSP. Four to six months after TKA and THA, 54 patients (58.7%) reported none or mild pain (Numerical Rating Scale: NRS 3). In the final multivariate hierarchical logistic regression analyses, illness representations concerning the condition leading to surgery (osteoarthritis), such as a chronic timeline perception of the disease, emerged as a significant predictor of PPSP. Additionally, post-surgical anxiety also showed a predictive role in the development of PPSP. Pre-surgical pain was the most significant clinical predictive factor and, as expected, undergoing TKA was associated with greater odds of PPSP development than THA. The findings on PPSP predictors after major joint arthroplasties can guide clinical practice in terms of considering cognitive and emotional factors, together with clinical factors, in planning acute pain management before and after surgery.This work was supported by a Project grant (PTDC/SAU-NEU/108557/2008) and by a PhD grant (SFRH/BD/36368/2007) from the Portuguese Foundation of Science and Technology, COMPETE and FEDER. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Adjunctive rifampicin for Staphylococcus aureus bacteraemia (ARREST): a multicentre, randomised, double-blind, placebo-controlled trial.

BACKGROUND: Staphylococcus aureus bacteraemia is a common cause of severe community-acquired and hospital-acquired infection worldwide. We tested the hypothesis that adjunctive rifampicin would reduce bacteriologically confirmed treatment failure or disease recurrence, or death, by enhancing early S aureus killing, sterilising infected foci and blood faster, and reducing risks of dissemination and metastatic infection. METHODS: In this multicentre, randomised, double-blind, placebo-controlled trial, adults (≥18 years) with S aureus bacteraemia who had received ≤96 h of active antibiotic therapy were recruited from 29 UK hospitals. Patients were randomly assigned (1:1) via a computer-generated sequential randomisation list to receive 2 weeks of adjunctive rifampicin (600 mg or 900 mg per day according to weight, oral or intravenous) versus identical placebo, together with standard antibiotic therapy. Randomisation was stratified by centre. Patients, investigators, and those caring for the patients were masked to group allocation. The primary outcome was time to bacteriologically confirmed treatment failure or disease recurrence, or death (all-cause), from randomisation to 12 weeks, adjudicated by an independent review committee masked to the treatment. Analysis was intention to treat. This trial was registered, number ISRCTN37666216, and is closed to new participants. FINDINGS: Between Dec 10, 2012, and Oct 25, 2016, 758 eligible participants were randomly assigned: 370 to rifampicin and 388 to placebo. 485 (64%) participants had community-acquired S aureus infections, and 132 (17%) had nosocomial S aureus infections. 47 (6%) had meticillin-resistant infections. 301 (40%) participants had an initial deep infection focus. Standard antibiotics were given for 29 (IQR 18-45) days; 619 (82%) participants received flucloxacillin. By week 12, 62 (17%) of participants who received rifampicin versus 71 (18%) who received placebo experienced treatment failure or disease recurrence, or died (absolute risk difference -1·4%, 95% CI -7·0 to 4·3; hazard ratio 0·96, 0·68-1·35, p=0·81). From randomisation to 12 weeks, no evidence of differences in serious (p=0·17) or grade 3-4 (p=0·36) adverse events were observed; however, 63 (17%) participants in the rifampicin group versus 39 (10%) in the placebo group had antibiotic or trial drug-modifying adverse events (p=0·004), and 24 (6%) versus six (2%) had drug interactions (p=0·0005). INTERPRETATION: Adjunctive rifampicin provided no overall benefit over standard antibiotic therapy in adults with S aureus bacteraemia. FUNDING: UK National Institute for Health Research Health Technology Assessment