Multidimensional isotonic regression and estimation of the threshold value

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Extension of CART using multiple splits under order restrictions

CART was introduced by Breiman et al. (1984) as a classification tool. It divides the whole sample recursively in two subpopulations by finding the best possible split with respect to a optimisation criterion. This method, restricted up to date to binary splits, is extended in this paper for allowing also multiple splits. The main problem with this extension is related to the optimal number of splits and the location of the corresponding cutpoints. In order to reduce the computational effort and enhance parsimony, the reduced isotonic regression was used in order to solve this problem. The extended CART method was tested in a simulation study and was compared with the classical approach in an epidemiological study. In both studies the extended CART turned out to be a useful and reliable alternative

Modelling Under Order Restrictions

Order restricted effects of predictors can be represented in models by the monotonic transformation fitted by the pooled adjacent violators algorithm as described by T. Robertson et al. In the context of multivariate modelling, this paper aims to introduce next to additive monotonic models a multidimensional approach. The corresponding permutations test to assess significance for the predictors is described and some feeble points of the approach are discussed. We also introduce a procedure to improve the parsimony of the model by reducing the resulting level sets. The use of monotonic regression in connection with the threshold value estimation problematic is outlined and two similar approaches to assess it are discussed

Modelling time-varying effects in Cox model under order restrictions

The violation of the proportional hazards assumption in Cox model occurs quite often in studies concerning solid tumours or leukaemia. Then the time varying coefficients model is its most popular extension used. The function f(t) that measures the time variation of a covariate, can be assessed through several smoothing techniques, such as cubic splines. However, for practical propose, it is more convenient to assess f(t) by a step function. The main drawback of this approach is the lack of stability since there is no standard method of defining the cutpoints of the underlined step function. The variation in the effect of a predictor can be assumed to be monotonic during the observational period. In these cases, we propose a method to estimate f(t) based on the isotonic regression framework. Applying the idea of Grambsch and Therneau, where smoothing the Schoenfeld residuals plotted against time reveal the shape of the underlined f(t) function, we use the Pooled Adjacent Violators Algorithm as smoother. As a result a set of cutpoints is returned without any a priori information about their location. Subsequently, the corresponding step function is introduced in the model and the standard likelihood-based method is applied to estimate it while adjusting for other covariates. This approach presents the advantage that additional decisions that can effect the result, as the number of knots in cubic splines, do not need to be taken. The performance of the provided PH test and the stability of the method are explored in a simulation study

The Electron Cyclotron Resonance Light Source Assembly of PTB - ELISA

In the radiometry laboratory of the Physikalisch-Technische,Bundesanstalt at the Berlin electron storage ring BESSY I, radiation sources for radiometric applications in industry and basic research in the vacuum ultraviolet (VUV) spectral range are developed, characterized and calibrated. Established sources such as deuterium lamps, Penning and hollow cathode discharge sources have limited spectral ranges and in particular their stability and life time suffers from the erosion of the cathode material. To overcome these limitations we have developed a radiation source based on the principle of the electron cyclotron resonance ion source. ELISA is a 10 GHz monomode source with a compact design featuring a tunable cavity and axially positionable permanent magnets. The radiation emission of the source can be detected simultaneously in the VUV and X-ray spectral range via a toroidal grating monochromator and a Si(Li)-detector. The special design of the source allows spectroscopic investigations of the plasma in dependence on the cavity tuning and magnet position. A marked influence of tuning and magnet position on the radiant intensity of the VUV and X-ray emission was observed. Using the tuning potential of ELISA krypton plasmas with highly charged ions and intense VUV radiation are generated by very low power consumption in comparison to other VUV radiation sources

Double Counting in LDA+DMFT - The Example of NiO

An intrinsic issue of the LDA+DMFT approach is the so called double counting of interaction terms. How to choose the double-counting potential in a manner that is both physically sound and consistent is unknown. We have conducted an extensive study of the charge transfer system NiO in the LDA+DMFT framework using quantum Monte Carlo and exact diagonalization as impurity solvers. By explicitly treating the double-counting correction as an adjustable parameter we systematically investigated the effects of different choices for the double counting on the spectral function. Different methods for fixing the double counting can drive the result from Mott insulating to almost metallic. We propose a reasonable scheme for the determination of double-counting corrections for insulating systems.Comment: 7 pages, 6 figure

Statistische Analyse des Einflusses von Herzrhythmusstörungen auf das Mortalitätsrisiko

Herzrhythmusstörungen stellen eine äußerst bedrohliche Krankheit dar und können zum plötzlichen Herztod führen. So sterben in der Bundesrepublik Deutschland pro Jahr etwa 100.000 Patienten an einem Herz-Kreislauf-Stillstand, der in 65 - 80 % durch eine Rhythmusstörung hervorgerufen wird (Trappe et al., 1996). Seit über 20 Jahren ist bekannt, daß das Ausmaß der Rhythmusstörungen wesentlich das Risiko für einen plötzlichen Herztod beeinflußt (Moss et al., 1979). Die Identifizierung von Patienten mit einem erhöhten Mortalitätsrisiko ist daher von erheblichem Interesse und nach wie vor noch nicht zufriedenstellend gelöst. Von dieser Frage hängt die Wahl der geeigneten Therapie ab. Bei Patienten mit einem erhöhten Mortalitätsrisiko ist derzeit die Implementierung eines Defibrillators die einzig wirksame Therapie. Die medikamentöse Behandlung mit sog. Antiarrhythmika war lange Zeit die Therapie der Wahl, bis Ende der 80er Jahre eine Studie aus den USA für einige Medikamente ein erhöhtes Mortalitätsrisiko nachwies (CAST-Studie, 1989). Seit dieser Zeit konzentriert sich die Forschung auf zwei Punkte, die Entwicklung neuer Medikamente und die Erkennung von besonders gefährdeten Patienten. Die einzige nicht-invasive Methode zur Erfassung der Häufigkeit der Arrhythmien ist gegenwärtig das 24 Std. Holter-EKG. Derzeit wird für die Unterteilung in verschiedene Risikogruppen nur das Ausmaß der Rhythmusstörungen, die Häufigkeit der sog. ventrikulären Extrasystolen (VES) erfaßt. Dieser Faktor ist aber nicht aussagekräftig genug. Daher liegt es nahe, die Information über die Rhythmusstörungen besser zu nutzen und vor allem die Komplexität der Arrhythmien besser zu beschreiben. Hierzu werden aus dem 24 Std. Holter-EKG alle Abstände zwischen zwei aufeinanderfolgenden Herzschlägen, die sog. RR-Intervalle, erfaßt. Wenn im Durchschnitt ein Herzschlag pro Sekunde erfolgt, liegen über 24 Stunden ca. 90 000 solcher Intervalle vor. Diese Datenmenge stellt an die Analyseverfahren eine besondere Herausforderung dar. In einem ersten Ansatz wurden Methoden aus dem Bereich der nichtlinearen Dynamik angewandt (Schmidt et al., 1996). Es ist bekannt, daß neben den Rhythmusstörungen auch die Variabilität der RR-Intervalle das Risiko beeinflussen. Mit den Ansätzen, basierend auf der nichtlinearen Dynamik, wurden aus den Daten eines 24 Std. Holter-EKG's zwei Parameter abgeleitet (alpha_VES und alpha_sin ). Der erste Parameter beschreibt die Komplexität, der zweite steht für die Variabilität. Die vorliegende Arbeit wendet statistische Verfahren aus den Bereichen Kurvenschätzung, logistische Regression, Coxsche Regression an, um besonders gefährdete Patienten zu erkennen. Für diese Analyse standen die Daten von 60 Patienten zur Verfügung. Das Ziel dieser Untersuchung ist es insbesondere, die aufwendige Methode der Bestimmung von alpha_sin , alpha_VES durch eine neue zu ersetzen, die konzeptionell und numerisch einfacher ist, die - im Unterschied zur eingeführten - vollständig algorithmisch durchgeführt werden kann und die auch - bei entsprechender Weiterentwicklung - zum Teil online erfolgen könnte

Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal

The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.Comment: 5 pages, 4 figures, supplemental material (mathematica and matlab files) available upon reques