Hermite and Gegenbauer polynomials in superspace using Clifford analysis

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.Comment: 18 pages, accepted for publication in J. Phys.

A tool for subjective and interactive visual data exploration

We present SIDE, a tool for Subjective and Interactive Visual Data Exploration, which lets users explore high dimensional data via subjectively informative 2D data visualizations. Many existing visual analytics tools are either restricted to specific problems and domains or they aim to find visualizations that align with user’s belief about the data. In contrast, our generic tool computes data visualizations that are surprising given a user’s current understanding of the data. The user’s belief state is represented as a set of projection tiles. Hence, this user-awareness offers users an efficient way to interactively explore yet-unknown features of complex high dimensional datasets

Performance of seven ECG interpretation programs in identifying arrhythmia and acute cardiovascular syndrome

Background: No direct comparison of current electrocardiogram (ECG) interpretation programs exists. Objective: Assess the accuracy of ECG interpretation programs in detecting abnormal rhythms and flagging for priority review records with alterations secondary to acute coronary syndrome (ACS). Methods: More than 2,000 digital ECGs from hospitals and databases in Europe, USA, and Australia, were obtained from consecutive adult and pediatric patients and converted to 10 s analog samples that were replayed on seven electrocardiographs and classified by the manufacturers' interpretation programs. We assessed ability to distinguish sinus rhythm from non-sinus rhythm, identify atrial fibrillation/flutter and other abnormal rhythms, and accuracy in flagging results for priority review. If all seven programs' interpretation statements did not agree, cases were reviewed by experienced cardiologists. Results: All programs could distinguish well between sinus and non-sinus rhythms and could identify atrial fibrillation/flutter or other abnormal rhythms. However, false-positive rates varied from 2.1% to 5.5% for non-sinus rhythm, from 0.7% to 4.4% for atrial fibrillation/flutter, and from 1.5% to 3.0% for other abnormal rhythms. False-negative rates varied from 12.0% to 7.5%, 9.9% to 2.7%, and 55.9% to 30.5%, respectively. Flagging of ACS varied by a factor of 2.5 between programs. Physicians flagged more ECGs for prompt review, but also showed variance of around a factor of 2. False-negative values differed between programs by a factor of 2 but was high for all (>50%). Agreement between programs and majority reviewer decisions was 46–62%. Conclusions: Automatic interpretations of rhythms and ACS differ between programs. Healthcare institutions should not rely on ECG software “critical result” flags alone to decide the ACS workflow

Performance of seven ECG interpretation programs in identifying arrhythmia and acute cardiovascular syndrome

Abstract Background No direct comparison of current electrocardiogram (ECG) interpretation programs exists. Objective Assess the accuracy of ECG interpretation programs in detecting abnormal rhythms and flagging for priority review records with alterations secondary to acute coronary syndrome (ACS). Methods More than 2,000 digital ECGs from hospitals and databases in Europe, USA, and Australia, were obtained from consecutive adult and pediatric patients and converted to 10 s analog samples that were replayed on seven electrocardiographs and classified by the manufacturers' interpretation programs. We assessed ability to distinguish sinus rhythm from non-sinus rhythm, identify atrial fibrillation/flutter and other abnormal rhythms, and accuracy in flagging results for priority review. If all seven programs' interpretation statements did not agree, cases were reviewed by experienced cardiologists. Results All programs could distinguish well between sinus and non-sinus rhythms and could identify atrial fibrillation/flutter or other abnormal rhythms. However, false-positive rates varied from 2.1% to 5.5% for non-sinus rhythm, from 0.7% to 4.4% for atrial fibrillation/flutter, and from 1.5% to 3.0% for other abnormal rhythms. False-negative rates varied from 12.0% to 7.5%, 9.9% to 2.7%, and 55.9% to 30.5%, respectively. Flagging of ACS varied by a factor of 2.5 between programs. Physicians flagged more ECGs for prompt review, but also showed variance of around a factor of 2. False-negative values differed between programs by a factor of 2 but was high for all (>50%). Agreement between programs and majority reviewer decisions was 46–62%. Conclusions Automatic interpretations of rhythms and ACS differ between programs. Healthcare institutions should not rely on ECG software "critical result" flags alone to decide the ACS workflow

Fluid modeling of the conversion of CH4 in presence of O2 of CO2 into methanol and syngas in an atmospheric pressure dielectric barrier discharge

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Dielectric barrier discharges used for the conversion of greenhouse gases : modeling the plasma chemistry by fluid simulations

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Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications