Real roots of Random Polynomials: Universality close to accumulation points

We identify the scaling region of a width O(n^{-1}) in the vicinity of the accumulation points $t=\pm 1$ of the real roots of a random Kac-like polynomial of large degree n. We argue that the density of the real roots in this region tends to a universal form shared by all polynomials with independent, identically distributed coefficients c_i, as long as the second moment \sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to the previously reported abrupt) and quite nontrivial suppression of the number of real roots for coefficients with a nonzero mean value \mu_n = E(c_i) scaled as \mu_n\sim n^{-1/2}.Comment: Some minor mistakes that crept through into publication have been removed. 10 pages, 12 eps figures. This version contains all updates, clearer pictures and some more thorough explanation

Counting zeros and critical points of random curves and surfaces

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Evaluation of a Microfluidic Device for the Electrochemical Determination of Halide Content in Ionic Liquids

A microfluidic device designed for electrochemical studies on a microliter scale has been utilized for the examination of impurity levels in ionic liquids (ILs). Halide impurities are common following IL synthesis, and this study demonstrates the ability to quantify low concentrations of halide in a range of ILs to levels of 5 ppm, even in ILs not currently measurable using other methods such as ion chromatography. To validate the mixer device, the electrochemistry of ferrocene was also examined and compared with spectroscopic and bulk electrochemistry measurements. An automated “sample preparation, delivery, and calibration” method was developed, and the chip successfully used for linear sweep, cyclic voltammetry (under both quiescent and steady-state flowing conditions), square wave voltammetry, and differential pulse voltammetry. An effective method of electrochemically cleaning the electrodes is also presented

ICare-ACS (Improving Care Processes for Patients With Suspected Acute Coronary Syndrome): A study of cross-system implementation of a national clinical pathway

Background: Efforts to safely reduce length of stay for emergency department patients with symptoms suggestive of acute coronary syndrome (ACS) have had mixed success. Few system-wide efforts affecting multiple hospital emergency departments have ever been evaluated. We evaluated the effectiveness of a nationwide implementation of clinical pathways for potential ACS in disparate hospitals. Methods: This was a multicenter pragmatic stepped-wedge before-and-after trial in 7 New Zealand acute care hospitals with 31332 patients investigated for suspected ACS with serial troponin measurements. The implementation was a clinical pathway for the assessment of patients with suspected ACS that included a clinical pathway document in paper or electronic format, structured risk stratification, specified time points for electrocardiographic and serial troponin testing within 3 hours of arrival, and directions for combining risk stratification and electrocardiographic and troponin testing in an accelerated diagnostic protocol. Implementation was monitored for \u3e4 months and compared with usual care over the preceding 6 months. The main outcome measure was the odds of discharge within 6 hours of presentation Results: There were 11529 participants in the preimplementation phase (range, 284–3465) and 19803 in the postimplementation phase (range, 395–5039). Overall, the mean 6-hour discharge rate increased from 8.3% (range, 2.7%–37.7%) to 18.4% (6.8%–43.8%). The odds of being discharged within 6 hours increased after clinical pathway implementation. The odds ratio was 2.4 (95% confidence interval, 2.3–2.6). In patients without ACS, the median length of hospital stays decreased by 2.9 hours (95% confidence interval, 2.4–3.4). For patients discharged within 6 hours, there was no change in 30-day major adverse cardiac event rates (0.52% versus 0.44%; P=0.96). In these patients, no adverse event occurred when clinical pathways were correctly followed. Conclusions: Implementation of clinical pathways for suspected ACS reduced the length of stay and increased the proportions of patients safely discharged within 6 hours. Clinical Trail Registration: URL: https://www.anzctr.org.au/ (Australian and New Zealand Clinical Trials Registry). Unique identifier: ACTRN12617000381381