423 research outputs found

    When does the inverse have the same sign pattern as the transpose?

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    summary:By a sign pattern (matrix) we mean an array whose entries are from the set {+,−,0}\lbrace +,-,0\rbrace . The sign patterns AA for which every real matrix with sign pattern AA has the property that its inverse has sign pattern ATA^T are characterized. Sign patterns AA for which some real matrix with sign pattern AA has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal matrices is examined

    Clinical judgement and therapeutic decision making

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    AbstractClinical decision making is under increased scrutiny due to concerns about the cost and quality of medical care. Variability in physician decision making is common, in part because of deficiencies in the knowledge base, but also due to the difference in physicians' approaches to clinical problem solving. Evaluation of patient prognosis is a critical factor in the selection of therapy, and careful attention to methodology is essential to provide reliable information.Randomized controlled clinical trials provide the most solid basis for the establishment of broad therapeutic principles. Because randomized studies cannot be performed to address every question, observational studies will continue to play a complementary role in the evaluation of therapy. Randomized studies in progress, meta analyses of existing data, and increased use of administrative and collaborative clinical data bases will improve the knowledge base for decision making in the future

    Importance of clinical measures of ischemia in the prognosis of patients with documented coronary artery disease

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    AbstractTo examine the value of clinical measures of ischemia for stratifying prognosis, 5,886 consecutive patients who had symptomatic significant (≄75% stenosis) coronary artery disease were studied. Using the Cox regression model in a randomly selected half of the patients, the prognostically independent clinical variables were weighted and arranged into a simple angina score: angina score = angina course × (1 + daily angina frequency) + ST-T changes, where angina course was equal to 3 if unstable or variant angina was present, 2 if the patient's angina was progressive with nocturnal episodes, 1 if it was progressive without nocturnal symptoms and 0 if it was stable; 6 points were added for the presence of “ischemic” ST-T changes. This angina score was then validated in an independent patient sample.The score was a more powerful predictor of prognosis than was any individual anginal descriptor. Furthermore, the angina score added significant independent prognostic information to the patient's age, sex, coronary anatomy and left ventricular function. Patients with three vessel disease and a normal ventricle (n = 1,233) had a 2 year infarction-free survival rate of 90% with an angina score of 0 and a 68% survival rate with an angina score ≄9. With an ejection fraction <50% and three vessel disease (n = 1,116), the corresponding infarction-free survival figures were 76 and 56%. Thus, a careful summarization of clinical markers of ischemia in the form of an angina score can provide a powerful prognostic tool and may aid clinicians in identifying high risk patients who are candidates for aggressive therapeutic interventions

    Sums of magnetic eigenvalues are maximal on rotationally symmetric domains

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    The sum of the first n energy levels of the planar Laplacian with constant magnetic field of given total flux is shown to be maximal among triangles for the equilateral triangle, under normalization of the ratio (moment of inertia)/(area)^3 on the domain. The result holds for both Dirichlet and Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary conditions too. The square similarly maximizes the eigenvalue sum among parallelograms, and the disk maximizes among ellipses. More generally, a domain with rotational symmetry will maximize the magnetic eigenvalue sum among all linear images of that domain. These results are new even for the ground state energy (n=1).Comment: 19 pages, 1 figur

    Case complexity scores in congenital heart surgery: A comparative study of the Aristotle Basic Complexity score and the Risk Adjustment in Congenital Heart Surgery (RACHS-1) system

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    ObjectiveThe Aristotle Basic Complexity score and the Risk Adjustment in Congenital Heart Surgery system were developed by consensus to compare outcomes of congenital cardiac surgery. We compared the predictive value of the 2 systems.MethodsOf all index congenital cardiac operations at our institution from 1982 to 2004 (n = 13,675), we were able to assign an Aristotle Basic Complexity score, a Risk Adjustment in Congenital Heart Surgery score, and both scores to 13,138 (96%), 11,533 (84%), and 11,438 (84%) operations, respectively. Models of in-hospital mortality and length of stay were generated for Aristotle Basic Complexity and Risk Adjustment in Congenital Heart Surgery using an identical data set in which both Aristotle Basic Complexity and Risk Adjustment in Congenital Heart Surgery scores were assigned. The likelihood ratio test for nested models and paired concordance statistics were used.ResultsAfter adjustment for year of operation, the odds ratios for Aristotle Basic Complexity score 3 versus 6, 9 versus 6, 12 versus 6, and 15 versus 6 were 0.29, 2.22, 7.62, and 26.54 (P < .0001). Similarly, odds ratios for Risk Adjustment in Congenital Heart Surgery categories 1 versus 2, 3 versus 2, 4 versus 2, and 5/6 versus 2 were 0.23, 1.98, 5.80, and 20.71 (P < .0001). Risk Adjustment in Congenital Heart Surgery added significant predictive value over Aristotle Basic Complexity (likelihood ratio χ2 = 162, P < .0001), whereas Aristotle Basic Complexity contributed much less predictive value over Risk Adjustment in Congenital Heart Surgery (likelihood ratio χ2 = 13.4, P = .009). Neither system fully adjusted for the child’s age. The Risk Adjustment in Congenital Heart Surgery scores were more concordant with length of stay compared with Aristotle Basic Complexity scores (P < .0001).ConclusionsThe predictive value of Risk Adjustment in Congenital Heart Surgery is higher than that of Aristotle Basic Complexity. The use of Aristotle Basic Complexity or Risk Adjustment in Congenital Heart Surgery as risk stratification and trending tools to monitor outcomes over time and to guide risk-adjusted comparisons may be valuable

    Cost effectiveness of thrombolytic therapy with tissue plasminogen activator as compared with streptokinase for acute myocardial infarction

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    BACKGROUND. Patients with acute myocardial infarction who were treated with accelerated tissue plasminogen activator (t-PA) (given over a period of 1 1/2 hours rather than the conventional 3 hours, and with two thirds of the dose given in the first 30 minutes) had a 30-day mortality that was 15 percent lower than that of pati

    Novel quasi-exactly solvable models with anharmonic singular potentials

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    We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly via the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of a set of algebraic equations.Comment: LaTex 18 pages. Updated version to appear in Annals of Physic