The metric dimension and metric independence of a graph

A vertex x of a graph G resolves two vertices u and v of G if the distance from x to u does not equal the distance from x to v. A set S of vertices of G is a resolving set for G if every two distinct vertices of G are resolved by some vertex of S. The minimum cardinality of a resolving set for G is called the metric dimension of G. The problem of nding the metric dimension of a graph is formulated as an integer pro- gramming problem. It is shown how a relaxation of this problem leads to a linear programming problem and hence to a fractional version of the metric dimension of a graph. The linear programming dual of this problem is considered and the solution to the corresponding integer programming problem is called the metric independence of the graph. It is shown that the problem of deciding whether, for a given graph G, the metric dimension of G equals its metric independence is NP- complete. Trees with equal metric dimension and metric independence are characterized. The metric independence number is established for various classes of graphs.Preprin

Inserting professionals and professional organizations in studies of wrongdoing : the nature, antecedents and consequences of professional misconduct

Professional misconduct has become seemingly ubiquitous in recent decades. However, to date there has been little sustained effort to theorize the phenomenon of professional misconduct, how this relates to professional organizations, and how this may contribute to broader patterns of corruption and wrongdoing. In response to this gap, in this contribution we discuss the theoretical and empirical implications of analyses that focus on the nature, antecedents and consequences of professional misconduct. In particular, we discuss how the nature of professional misconduct can be quite variegated and nuanced, how boundaries between and within professions can be either too weak or too strong and lead to professional misconduct, and how the consequences of professional misconduct can be less straightforward than normally assumed. We also illuminate how some important questions about professional misconduct are still pending, including: how we define its different organizational forms; how it is instigated by the changing nature of professional boundaries; and how its consequences are responded to in professional organizations and society more widely

Cylindrical surface profile and diameter measuring tool and method

A tool is shown having a cross beam assembly made of beams joined by a center box structure. The assembly is adapted to be mounted by brackets to the outer end of a cylindrical case. The center box structure has a vertical shaft rotatably mounted therein and extending beneath the assembly. Secured to the vertical shaft is a radius arm which is adapted to rotate with the shaft. On the longer end of the radius arm is a measuring tip which contacts the cylindrical surface to be measured and which provides an electric signal representing the radius of the cylindrical surface from the center of rotation of the radius arm. An electric servomotor rotates the vertical shaft and an electronic resolver provides an electric signal representing the angle of rotation of the shaft. The electric signals are provided to a computer station which has software for its computer to calculate and print out the continuous circumference profile of the cylindrical surface, and give its true diameter and the deviations from the ideal circle

The model of mortality with incident cirrhosis (MoMIC) and the model of long-term outlook of mortality in dcirrhosis (LOMiC)

The purpose of this study was to produce two statistical survival models in those with cirrhosis utilising only routine parameters, including non-liver-related clinical factors that influence survival. The first model identified and utilised factors impacting short-term survival to 90-days post incident diagnosis, and a further model characterised factors that impacted survival following this acute phase. Data were from the Clinical Practice Research Datalink linked with Hospital Episode Statistics. Incident cases in patients ≥18 years were identified between 1998 and 2014. Patients that had prior history of cancer or had received liver transplants prior were excluded. Model-1 used a logistic regression model to predict mortality. Model-2 used data from those patients who survived 90 days, and used an extension of the Cox regression model, adjusting for time-dependent covariables. At 90 days, 23% of patients had died. Overall median survival was 3.7 years. Model-1: numerous predictors, prior comorbidities and decompensating events were incorporated. All comorbidities contributed to increased odds of death, with renal disease having the largest adjusted odds ratio (OR = 3.35, 95%CI 2.97–3.77). Model-2: covariables included cumulative admissions for liver disease-related events and admissions for infections. Significant covariates were renal disease (adjusted hazard ratio (HR = 2.89, 2.47–3.38)), elevated bilirubin levels (aHR = 1.38, 1.26–1.51) and low sodium levels (aHR = 2.26, 1.84–2.78). An internal validation demonstrated reliability of both models. In conclusion: two survival models that included parameters commonly recorded in routine clinical practice were generated that reliably forecast the risk of death in patients with cirrhosis: in the acute, post diagnosis phase, and following this critical, 90 day phase. This has implications for practice and helps better forecast the risk of mortality from cirrhosis using routinely recorded parameters without inputs from specialists

A framework for evaluating image segmentation algorithms

The purpose of this paper is to describe a framework for evaluating image segmentation algorithms. Image segmentation consists of object recognition and delineation. For evaluating segmentation methods, three factors—precision (reliability), accuracy (validity), and efficiency (viability)—need to be considered for both recognition and delineation. To assess precision, we need to choose a figure of merit, repeat segmentation considering all sources of variation, and determine variations in figure of merit via statistical analysis. It is impossible usually to establish true segmentation. Hence, to assess accuracy, we need to choose a surrogate of true segmentation and proceed as for precision. In determining accuracy, it may be important to consider different 'landmark' areas of the structure to be segmented depending on the application. To assess efficiency, both the computational and the user time required for algorithm training and for algorithm execution should be measured and analyzed. Precision, accuracy, and efficiency factors have an influence on one another. It is difficult to improve one factor without affecting others. Segmentation methods must be compared based on all three factors, as illustrated in an example wherein two methods are compared in a particular application domain. The weight given to each factor depends on application

Hubble Space Telescope imaging of η Carinae

We present new high spatial resolution observations of the material around η Carinae obtained with the Hubble Space Telescope Wide Field/Planetary Camera. The star η Carinae is one of the most massive and luminous stars in our Galaxy, and has been episodically expelling significant quantities of gas over the last few centuries. The morphology of the bright central nebulosity (the homunculus) indicates that it is a thin shell with very well defined edges, and is clumpy on 0".2 (~10^(16)cm) scales. An extension to the northeast of the star {NN/NS using Walborn's [ApJL, 204, L17 ( 1976)] nomenclature} appears to be a stellar jet and its associated bow shock. The bow shock is notable for an intriguing series of parallel linear features across its face. The S ridge and the W arc appear to be part of a "cap" of emission located to the SW and behind the star. Together, the NE jet and the SW cap suggest that the symmetry axis for the system runs NE-SW rather than SE-NW, as previously supposed. Overall, the data indicate that the material around the star may represent an oblate shell with polar blowouts, rather than a bipolar flow

Not so Classical Mechanics - Unexpected Symmetries of Classical Motion

A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central force problem; inequivalent Lagrangians and Hamiltonians; constants of central force motion; a general discussion of higher-order Lagrangians and Hamiltonians with examples from Bohmian quantum mechanics, the Korteweg-de Vries equation and the logistic equation; gauge theories of Newtonian mechanics; classical spin, Grassmann numbers, and pseudomechanics.Comment: Einstein Centennial Review Article, 48 page

Early respiratory viral infections in infants with cystic fibrosis

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Background Viral infections contribute to morbidity in cystic fibrosis (CF), but the impact of respiratory viruses on the development of airway disease is poorly understood. Methods Infants with CF identified by newborn screening were enrolled prior to 4 months of age to participate in a prospective observational study at 4 centers. Clinical data were collected at clinic visits and weekly phone calls. Multiplex PCR assays were performed on nasopharyngeal swabs to detect respiratory viruses during routine visits and when symptomatic. Participants underwent bronchoscopy with bronchoalveolar lavage (BAL) and a subset underwent pulmonary function testing. We present findings through 8.5 months of life. Results Seventy infants were enrolled, mean age 3.1 ± 0.8 months. Rhinovirus was the most prevalent virus (66%), followed by parainfluenza (19%), and coronavirus (16%). Participants had a median of 1.5 viral positive swabs (range 0–10). Past viral infection was associated with elevated neutrophil concentrations and bacterial isolates in BAL fluid, including recovery of classic CF bacterial pathogens. When antibiotics were prescribed for respiratory-related indications, viruses were identified in 52% of those instances. Conclusions Early viral infections were associated with greater neutrophilic inflammation and bacterial pathogens. Early viral infections appear to contribute to initiation of lower airway inflammation in infants with CF. Antibiotics were commonly prescribed in the setting of a viral infection. Future investigations examining longitudinal relationships between viral infections, airway microbiome, and antibiotic use will allow us to elucidate the interplay between these factors in young children with CF

Bariatric-metabolic surgery for NHS patients with type 2 diabetes in the United Kingdom National Bariatric Surgery Registry

Aim: Bariatric-metabolic surgery is approved by the National Institute of Health and Care Excellence (NICE) for people with severe obesity and type 2 diabetes (T2DM) (including class 1 obesity after 2014). This study analysed baseline characteristics, disease severity and operations undertaken in people with obesity and T2DM undergoing bariatric-metabolic surgery in the UK National Health Service (NHS) compared to those without T2DM. Methods: Baseline characteristics, trends over time and operations undertaken were analysed for people undergoing primary bariatric-metabolic surgery in the NHS using the National Bariatric Surgical Registry (NBSR) for 11 years from 2009 to 2019. Clinical practice before and after the publication of the NICE guidance (2014) was examined. Multivariate logistic regression was used to determine associations with T2DM status and the procedure undertaken. Results: 14,948/51,715 (28.9%) participants had T2DM, with 10,626 (71.1%) on oral hypoglycaemics, 4322 (28.9%) on insulin/other injectables, and with T2DM diagnosed 10+ years before surgery in 3876 (25.9%). Participants with T2DM, compared to those without T2DM, were associated with older age (p &lt; 0.001), male sex (p &lt; 0.001), poorer functional status (p &lt; 0.001), dyslipidaemia (OR: 3.58 (CI: 3.39–3.79); p &lt; 0.001), hypertension (OR: 2.32 (2.19–2.45); p &lt; 0.001) and liver disease (OR: 1.73 (1.58–1.90); p &lt; 0.001), but no difference in body mass index was noted. Fewer people receiving bariatric-metabolic surgery after 2015 had T2DM (p &lt; 0.001), although a very small percentage increase of those with class I obesity and T2DM was noted. Gastric bypass was the commonest operation overall. T2DM status was associated with selection for gastric bypass compared to sleeve gastrectomy (p &lt; 0.001). Conclusion: NHS bariatric-metabolic surgery is used for people with T2DM much later in the disease process when it is less effective. National guidance on bariatric-metabolic surgery and data from multiple RCTs have had little impact on clinical practice.</p