7 research outputs found

    Teaching Differential Equations with Graphics and without Linear Algebra

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    We present our approach to teaching the Method of Eigenvectors to solve linear systems of ODEs without assuming a prerequisite course in Linear Algebra. Rather we depend heavily on a graphical approach to systems in two dimensions to motivate the eigenvalue equation

    Spectral Zeta Functions of Laplacians on Self-Similar Fractals

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    This thesis investigates the spectral zeta function of fractal differential operators such as the Laplacian on the unbounded (i.e., infinite) Sierpinski gasket and a self-similar Sturm--Liouville operator associated with a fractal self-similar measure on the half-line. In the latter case, C. Sabot discovered the relation between the spectrum of this operator and the iteration of a rational map of several complex variables, called the renormalization map. We obtain a factorization of the spectral zeta function of such an operator, expressed in terms of the Dirac delta hyperfunction, a geometric zeta function, and the zeta function associated with the dynamics of the corresponding renormalization map, viewed either as a polynomial function on the complex plane (in the first case) or (in the second case) as a polynomial on the complex projective plane. Our first main result extends to the case of the fractal Laplacian on the unbounded Sierpinski gasket a factorization formula obtained by M. Lapidus for the spectral zeta function of a fractal string and later extended by A. Teplyaev to the bounded (i.e., finite) Sierpinski gasket and some other decimable fractals. Furthermore, our second main result generalizes these factorization formulas to the renormalization maps of several complex variables associated with fractal Sturm--Liouville operators. Moreover, as a corollary, in the very special case when the underlying self-similar measure is Lebesgue measure on [0, 1], we obtain a representation of the Riemann zeta function in terms of the dynamics of a certain polynomial on the complex projective plane, thereby extending to several variables an analogous result by A. Teplyaev

    Predictive Models of Student College Commitment Decisions Using Machine Learning

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    Every year, academic institutions invest considerable effort and substantial resources to influence, predict and understand the decision-making choices of applicants who have been offered admission. In this study, we applied several supervised machine learning techniques to four years of data on 11,001 students, each with 35 associated features, admitted to a small liberal arts college in California to predict student college commitment decisions. By treating the question of whether a student offered admission will accept it as a binary classification problem, we implemented a number of different classifiers and then evaluated the performance of these algorithms using the metrics of accuracy, precision, recall, F-measure and area under the receiver operator curve. The results from this study indicate that the logistic regression classifier performed best in modeling the student college commitment decision problem, i.e., predicting whether a student will accept an admission offer, with an AUC score of 79.6%. The significance of this research is that it demonstrates that many institutions could use machine learning algorithms to improve the accuracy of their estimates of entering class sizes, thus allowing more optimal allocation of resources and better control over net tuition revenue

    Tests of CMS Hadron Forward Calorimeter Upgrade Readout Box Prototype

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    A readout box prototype for CMS Hadron Forward calorimeter upgrade is built and tested in CERN H2 beamline. The prototype is designed to enable simultaneous tests of different readout options for the four anode upgrade PMTs, new front-end electronics design and new cabling. The response of the PMTs with different readout options is uniform and the background response is minimal. Multi-channel readout options further enhance the background elimination. Passing all the electronics, mechanical and physics tests, the readout box proves to be capable of providing the forward hadron calorimeter operations requirements in the upgrade era

    Evaluation of a quality improvement intervention to reduce anastomotic leak following right colectomy (EAGLE): pragmatic, batched stepped-wedge, cluster-randomized trial in 64 countries

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    Background Anastomotic leak affects 8 per cent of patients after right colectomy with a 10-fold increased risk of postoperative death. The EAGLE study aimed to develop and test whether an international, standardized quality improvement intervention could reduce anastomotic leaks. Methods The internationally intended protocol, iteratively co-developed by a multistage Delphi process, comprised an online educational module introducing risk stratification, an intraoperative checklist, and harmonized surgical techniques. Clusters (hospital teams) were randomized to one of three arms with varied sequences of intervention/data collection by a derived stepped-wedge batch design (at least 18 hospital teams per batch). Patients were blinded to the study allocation. Low- and middle-income country enrolment was encouraged. The primary outcome (assessed by intention to treat) was anastomotic leak rate, and subgroup analyses by module completion (at least 80 per cent of surgeons, high engagement; less than 50 per cent, low engagement) were preplanned. Results A total 355 hospital teams registered, with 332 from 64 countries (39.2 per cent low and middle income) included in the final analysis. The online modules were completed by half of the surgeons (2143 of 4411). The primary analysis included 3039 of the 3268 patients recruited (206 patients had no anastomosis and 23 were lost to follow-up), with anastomotic leaks arising before and after the intervention in 10.1 and 9.6 per cent respectively (adjusted OR 0.87, 95 per cent c.i. 0.59 to 1.30; P = 0.498). The proportion of surgeons completing the educational modules was an influence: the leak rate decreased from 12.2 per cent (61 of 500) before intervention to 5.1 per cent (24 of 473) after intervention in high-engagement centres (adjusted OR 0.36, 0.20 to 0.64; P < 0.001), but this was not observed in low-engagement hospitals (8.3 per cent (59 of 714) and 13.8 per cent (61 of 443) respectively; adjusted OR 2.09, 1.31 to 3.31). Conclusion Completion of globally available digital training by engaged teams can alter anastomotic leak rates. Registration number: NCT04270721 (http://www.clinicaltrials.gov)