On acyclic and unicyclic graphs whose minimum rank equals the diameter

AbstractThe minimum rank of a graph G is defined as the smallest possible rank over all symmetric matrices governed by G. It is well known that the minimum rank of a connected graph is at least the diameter of that graph. In this paper, we investigate the graphs for which equality holds between minimum rank and diameter, and completely describe the acyclic and unicyclic graphs for which this equality holds

Eigenvalue location for nonnegative and Z-matrices

AbstractLet Lk0 denote the class of n × n Z-matrices A = tl − B with B ⩾ 0 and ϱk(B) ⩽ t < ϱk + 1(B), where ϱk(B) denotes the maximum spectral radius of k × k principal submatrices of B. Bounds are determined on the number of eigenvalues with positive real parts for A ϵ Lk0, where k satisfies, ⌊n2⌋ ⩽ k ⩽ n − 1. For these classes, when k = n − 1 and n − 2, wedges are identified that contain only the unqiue negative eigenvalue of A. These results lead to new eigenvalue location regions for nonnegative matrices

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde

Genetic testing of children for adult-onset conditions: opinions of the British adult population and implications for clinical practice

This study set out to explore the attitudes of a representative sample of the British public towards genetic testing in children to predict disease in the future. We sought opinions about genetic testing for adult-onset conditions for which no prevention/treatment is available during childhood, and about genetic 'carrier' status to assess future reproductive risks. The study also examined participants' level of agreement with the reasons professional organisations give in favour of deferring such testing. Participants (n=2998) completed a specially designed questionnaire, distributed by email. Nearly half of the sample (47%) agreed that parents should be able to test their child for adult-onset conditions, even if there is no treatment or prevention at time of testing. This runs contrary to professional guidance about genetic testing in children. Testing for carrier status was supported by a larger proportion (60%). A child's future ability to decide for her/himself if and when to be tested was the least supported argument in favour of deferring testing.European Journal of Human Genetics advance online publication, 5 November 2014; doi:10.1038/ejhg.2014.221

The cost-effectiveness of early noninvasive ventilation for ALS patients

BACKGROUND: Optimal timing of noninvasive positive pressure ventilation (NIPPV) initiation in patients with amyotrophic lateral sclerosis (ALS) is unknown, but NIPPV appears to benefit ALS patients who are symptomatic from pulmonary insufficiency. This has prompted research proposals of earlier NIPPV initiation in the ALS disease course in an attempt to further improve ALS patient quality of life and perhaps survival. We therefore used a cost-utility analysis to determine a priori what magnitude of health-related quality of life (HRQL) improvement early NIPPV initiation would need to achieve to be cost-effective in a future clinical trial. METHODS: Using a Markov decision analytic model we calculated the benefit in health-state utility that NIPPV initiated at ALS diagnosis must achieve to be cost-effective. The primary outcome was the percent utility gained through NIPPV in relation to two common willingness-to-pay thresholds: $50,000 and$100,000 per quality-adjusted life year (QALY). RESULTS: Our results indicate that if NIPPV begun at the time of diagnosis improves ALS patient HRQL as little as 13.5%, it would be a cost-effective treatment. Tolerance of NIPPV (assuming a 20% improvement in HRQL) would only need to exceed 18% in our model for treatment to remain cost-effective using a conservative willingness-to-pay threshold of $50,000 per QALY. CONCLUSION: If early use of NIPPV in ALS patients is shown to improve HRQL in future studies, it is likely to be a cost-effective treatment. Clinical trials of NIPPV begun at the time of ALS diagnosis are therefore warranted from a cost-effectiveness standpoint

Mechanism of injury and special considerations as predictive of serious injury: A systematic review.

Objectives: The Centers for Disease Control and Prevention\u27s field triage guidelines (FTG) are routinely used by emergency medical services personnel for triaging injured patients. The most recent (2011) FTG contains physiologic, anatomic, mechanism, and special consideration steps. Our objective was to systematically review the criteria in the mechanism and special consideration steps that might be predictive of serious injury or need for a trauma center. Methods: We conducted a systematic review of the predictive utility of mechanism and special consideration criteria for predicting serious injury. A research librarian searched in Ovid Medline, EMBASE, and the Cochrane databases for studies published between January 2011 and February 2021. Eligible studies were identified using a priori inclusion and exclusion criteria. Studies were excluded if they lacked an outcome for serious injury, such as measures of resource use, injury severity scores, mortality, or composite measures using a combination of outcomes. Given the heterogeneity in populations, measures, and outcomes, results were synthesized qualitatively focusing on positive likelihood ratios (LR+) whenever these could be calculated from presented data or adjusted odds ratios (aOR

Understanding the Operative Experience of the Practicing Pediatric Surgeon: Implications for Training and Maintaining Competency

Importance The number of practicing pediatric surgeons has increased rapidly in the past 4 decades, without a significant increase in the incidence of rare diseases specific to the field. Maintenance of competency in the index procedures for these rare diseases is essential to the future of the profession. Objective To describe the demographic characteristics and operative experiences of practicing pediatric surgeons using Pediatric Surgery Board recertification case log data. Design, Setting, and Participants We performed a retrospective review of 5 years of pediatric surgery certification renewal applications submitted to the Pediatric Surgery Board between 2009 and 2013. A surgeon’s location was defined by population as urban, large rural, small rural, or isolated. Case log data were examined to determine case volume by category and type of procedures. Surgeons were categorized according to recertification at 10, 20, or 30 years. Main Outcome and Measure Number of index cases during the preceding year. Results Of 308 recertifying pediatric surgeons, 249 (80.8%) were men, and 143 (46.4%) were 46 to 55 years of age. Most of the pediatric surgeons (304 of 308 [98.7%]) practiced in urban areas (ie, with a population >50 000 people). All recertifying applicants were clinically active. An appendectomy was the most commonly performed procedure (with a mean [SD] number of 49.3 [35.0] procedures per year), nonoperative trauma management came in second (with 20.0 [33.0] procedures per year), and inguinal hernia repair for children younger than 6 months of age came in third (with 14.7 [13.8] procedures per year). In 6 of 10 “rare” pediatric surgery cases, the mean number of procedures was less than 2. Of 308 surgeons, 193 (62.7%) had performed a neuroblastoma resection, 170 (55.2%) a kidney tumor resection, and 123 (39.9%) an operation to treat biliary atresia or choledochal cyst in the preceding year. Laparoscopy was more frequently performed in the 10-year recertification group for Nissen fundoplication, appendectomy, splenectomy, gastrostomy/jejunostomy, orchidopexy, and cholecystectomy (P < .05) but not lung resection (P = .70). It was more frequently used by surgeons recertifying in the 10-year group (used in 11 375 of 14 456 procedures [78.7%]) than by surgeons recertifying in the 20-year (used in 6214 of 8712 procedures [71.3%]) or 30-year group (used in 2022 of 3805 procedures [53.1%]). Conclusions and Relevance Practicing pediatric surgeons receive limited exposure to index cases after training. With regard to maintaining competency in an era in which health care outcomes have become increasingly important, these results are concerning