Edge covering with budget constrains

We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms). Goldschmidt and Hochbaum \cite{GH97} show that the mvms problem is NP-hard and they give a 3-approximation algorithm for the problem. We improve \cite{GH97} by giving a ratio of 2. A 2(1+\epsilon)-approximation for the problem follows from the work of Carnes and Shmoys \cite{CS08}. We improve the approximation ratio to 2. algorithm for the problem. We show that the natural LP for \kmin has an integrality gap of 2-o(1). We improve the NP-completeness of \cite{GH97} by proving the pronlem are APX-hard unless a well-known instance of the dense k-subgraph admits a constant ratio. The best approximation guarantee known for this instance of dense k-subgraph is O(n^{2/9}) \cite{BCCFV}. We show that for any constant \rho>1, an approximation guarantee of \rho for the \kmin problem implies a \rho(1+o(1)) approximation for \mwms. Finally, we define we give an exact algorithm for the density version of kmin.Comment: 17 page

Risk Factors Associated With Infection in Open Fractures of the Upper and Lower Extremities

Introduction: Open fractures are associated with a high risk of infection. The prevention of infection is the single most important goal, influencing perioperative care of patients with open fractures. Using data from 2,500 participants with open fracture wounds enrolled in the Fluid Lavage of Open Wounds trial, we conducted a multivariable analysis to determine the factors that are associated with infections 12 months postfracture. Methods: Eighteen predictor variables were identified for infection a priori from baseline data, fracture characteristics, and surgical data from the Fluid Lavage of Open Wounds trial. Twelve predictor variables were identified for deep infection, which included both surgically and nonoperatively managed infections.We used multivariable Cox proportional hazards regression analyses to identify the factors associated with infection. Irrigation solution and pressure were included as variables in the analysis. The results were reported as adjusted hazard ratios (HRs), 95% confidence intervals (CIs), and associated P values. All tests were two tailed with alpha = 0.05. Results: Factors associated with any infection were fracture location (tibia: HR 5.13 versus upper extremity, 95% CI 3.28 to 8.02; other lower extremity: HR 3.63 versus upper extremity, 95% CI 2.38 to 5.55; overall P\u3c 0.001), low energy injury (HR 1.64, 95% CI 1.08 to 2.46; P = 0.019), degree of wound contamination (severe: HR 2.12 versus mild, 95% CI 1.35 to 3.32; moderate: HR 1.08 versus mild, 95% CI 0.78 to 1.49; overall P = 0.004), and need for flap coverage (HR 1.82, 95% CI 1.11 to 2.99; P = 0.017). Discussion: The results of this study provide a better understanding of which factors are associated with a greater risk of infection in open fractures. In addition, it can allow for surgeons to better counsel patients regarding prognosis, helping patients to understand their individual risk of infection

Risk Factors Associated With Infection in Open Fractures of the Upper and Lower Extremities

Introduction: Open fractures are associated with a high risk of infection. The prevention of infection is the single most important goal, influencing perioperative care of patients with open fractures. Using data from 2,500 participants with open fracture wounds enrolled in the Fluid Lavage of Open Wounds trial, we conducted a multivariable analysis to determine the factors that are associated with infections 12 months postfracture. Methods: Eighteen predictor variables were identified for infection a priori from baseline data, fracture characteristics, and surgical data from the Fluid Lavage of Open Wounds trial. Twelve predictor variables were identified for deep infection, which included both surgically and nonoperatively managed infections.We used multivariable Cox proportional hazards regression analyses to identify the factors associated with infection. Irrigation solution and pressure were included as variables in the analysis. The results were reported as adjusted hazard ratios (HRs), 95% confidence intervals (CIs), and associated P values. All tests were two tailed with alpha = 0.05. Results: Factors associated with any infection were fracture location (tibia: HR 5.13 versus upper extremity, 95% CI 3.28 to 8.02; other lower extremity: HR 3.63 versus upper extremity, 95% CI 2.38 to 5.55; overall P\u3c 0.001), low energy injury (HR 1.64, 95% CI 1.08 to 2.46; P = 0.019), degree of wound contamination (severe: HR 2.12 versus mild, 95% CI 1.35 to 3.32; moderate: HR 1.08 versus mild, 95% CI 0.78 to 1.49; overall P = 0.004), and need for flap coverage (HR 1.82, 95% CI 1.11 to 2.99; P = 0.017). Discussion: The results of this study provide a better understanding of which factors are associated with a greater risk of infection in open fractures. In addition, it can allow for surgeons to better counsel patients regarding prognosis, helping patients to understand their individual risk of infection

Are large clinical trials in orthopaedic trauma justified?

© 2018 The Author(s). Background: The objective of this analysis is to evaluate the necessity of large clinical trials using FLOW trial data. Methods: The FLOW pilot study and definitive trial were factorial trials evaluating the effect of different irrigation solutions and pressures on re-operation. To explore treatment effects over time, we analyzed data from the pilot and definitive trial in increments of 250 patients until the final sample size of 2447 patients was reached. At each increment we calculated the relative risk (RR) and associated 95% confidence interval (CI) for the treatment effect, and compared the results that would have been reported at the smaller enrolments with those seen in the final, adequately powered study. Results: The pilot study analysis of 89 patients and initial incremental enrolments in the FLOW definitive trial favored low pressure compared to high pressure (RR: 1.50, 95% CI: 0.75-3.04; RR: 1.39, 95% CI: 0.60-3.23, respectively), which is in contradiction to the final enrolment, which found no difference between high and low pressure (RR: 1.04, 95% CI: 0.81-1.33). In the soap versus saline comparison, the FLOW pilot study suggested that re-operation rate was similar in both the soap and saline groups (RR: 0.98, 95% CI: 0.50-1.92), whereas the FLOW definitive trial found that the re-operation rate was higher in the soap treatment arm (RR: 1.28, 95% CI: 1.04-1.57). Conclusions: Our findings suggest that studies with smaller sample sizes would have led to erroneous conclusions in the management of open fracture wounds. Trial registration: NCT01069315 (FLOW Pilot Study) Date of Registration: February 17, 2010, NCT00788398 (FLOW Definitive Trial) Date of Registration: November 10, 2008

SUDOSCAN: A Simple, Rapid, and Objective Method with Potential for Screening for Diabetic Peripheral Neuropathy.

Clinical methods of detecting diabetic peripheral neuropathy (DPN) are not objective and reproducible. We therefore evaluated if SUDOSCAN, a new method developed to provide a quick, non-invasive and quantitative assessment of sudomotor function can reliably screen for DPN. 70 subjects (45 with type 1 diabetes and 25 healthy volunteers [HV]) underwent detailed assessments including clinical, neurophysiological and 5 standard cardiovascular reflex tests (CARTs). Using the American Academy of Neurology criteria subjects were classified into DPN and No-DPN groups. Based on CARTs subjects were also divided into CAN, subclinical-CAN and no-CAN. Sudomotor function was assessed with measurement of hand and foot Electrochemical Skin Conductance (ESC) and calculation of the CAN risk score. Foot ESC (μS) was significantly lower in subjects with DPN [n = 24; 53.5(25.1)] compared to the No-DPN [77.0(7.9)] and HV [77.1(14.3)] groups (ANCOVA p<0.001). Sensitivity and specificity of foot ESC for classifying DPN were 87.5% and 76.2%, respectively. The area under the ROC curve (AUC) was 0.85. Subjects with CAN had significantly lower foot [55.0(28.2)] and hand [53.5(19.6)] ESC compared to No-CAN [foot ESC, 72.1(12.2); hand ESC 64.9(14.4)] and HV groups (ANCOVA p<0.001 and 0.001, respectively). ROC analysis of CAN risk score to correctly classify CAN revealed a sensitivity of 65.0% and specificity of 80.0%. AUC was 0.75. Both foot and hand ESC demonstrated strong correlation with individual parameters and composite scores of nerve conduction and CAN. SUDOSCAN, a non-invasive and quick test, could be used as an objective screening test for DPN in busy diabetic clinics, insuring adherence to current recommendation of annual assessments for all diabetic patients that remains unfulfilled

A nationwide study of adults admitted to hospital with diabetic ketoacidosis or hyperosmolar hyperglycaemic state and COVID‐19

AimsTo investigate characteristics of people hospitalized with coronavirus-disease-2019 (COVID-19) and diabetic ketoacidosis (DKA) or hyperosmolar hyperglycaemic state (HHS), and to identify risk factors for mortality and intensive care admission.Materials and methodsRetrospective cohort study with anonymized data from the Association of British Clinical Diabetologists nationwide audit of hospital admissions with COVID-19 and diabetes, from start of pandemic to November 2021. The primary outcome was inpatient mortality. DKA and HHS were adjudicated against national criteria. Age-adjusted odds ratios were calculated using logistic regression.ResultsIn total, 85 confirmed DKA cases, and 20 HHS, occurred among 4073 people (211 type 1 diabetes, 3748 type 2 diabetes, 114 unknown type) hospitalized with COVID-19. Mean (SD) age was 60 (18.2) years in DKA and 74 (11.8) years in HHS (p < .001). A higher proportion of patients with HHS than with DKA were of non-White ethnicity (71.4% vs 39.0% p = .038). Mortality in DKA was 36.8% (n = 57) and 3.8% (n = 26) in type 2 and type 1 diabetes respectively. Among people with type 2 diabetes and DKA, mortality was lower in insulin users compared with non-users [21.4% vs. 52.2%; age-adjusted odds ratio 0.13 (95% CI 0.03-0.60)]. Crude mortality was lower in DKA than HHS (25.9% vs. 65.0%, p = .001) and in statin users versus non-users (36.4% vs. 100%; p = .035) but these were not statistically significant after age adjustment.ConclusionsHospitalization with COVID-19 and adjudicated DKA is four times more common than HHS but both associate with substantial mortality. There is a strong association of previous insulin therapy with survival in type 2 diabetes-associated DKA

Breast cancer management pathways during the COVID-19 pandemic: outcomes from the UK ‘Alert Level 4’ phase of the B-MaP-C study

Abstract: Background: The B-MaP-C study aimed to determine alterations to breast cancer (BC) management during the peak transmission period of the UK COVID-19 pandemic and the potential impact of these treatment decisions. Methods: This was a national cohort study of patients with early BC undergoing multidisciplinary team (MDT)-guided treatment recommendations during the pandemic, designated ‘standard’ or ‘COVID-altered’, in the preoperative, operative and post-operative setting. Findings: Of 3776 patients (from 64 UK units) in the study, 2246 (59%) had ‘COVID-altered’ management. ‘Bridging’ endocrine therapy was used (n = 951) where theatre capacity was reduced. There was increasing access to COVID-19 low-risk theatres during the study period (59%). In line with national guidance, immediate breast reconstruction was avoided (n = 299). Where adjuvant chemotherapy was omitted (n = 81), the median benefit was only 3% (IQR 2–9%) using ‘NHS Predict’. There was the rapid adoption of new evidence-based hypofractionated radiotherapy (n = 781, from 46 units). Only 14 patients (1%) tested positive for SARS-CoV-2 during their treatment journey. Conclusions: The majority of ‘COVID-altered’ management decisions were largely in line with pre-COVID evidence-based guidelines, implying that breast cancer survival outcomes are unlikely to be negatively impacted by the pandemic. However, in this study, the potential impact of delays to BC presentation or diagnosis remains unknown

Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BackgroundDisorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.MethodsWe estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.FindingsGlobally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.InterpretationAs the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed