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The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.
Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.
Enzyme-catalyzed reactions have been designed to mimic various Boolean logic gates in the general framework of unconventional biomolecular computing. While some of the logic gates, particularly OR, AND, are easy to realize with biocatalytic reactions and have been reported in numerous publications, some other, like NXOR, are very challenging and have not been realized yet with enzyme reactions. The paper reports on a novel approach to mimicking the NXOR logic gate using the bell-shaped enzyme activity dependent on pH values. Shifting pH from the optimum value to the acidic or basic values by using acid or base inputs (meaning 1,0 and 0,1 inputs) inhibits the enzyme reaction, while keeping the optimum pH (assuming 0,0 and 1,1 input combinations) preserves a high enzyme activity. The challenging part of the present approach is the selection of an enzyme with a well-demonstrated bell-shape activity dependence on the pH value. While many enzymes can satisfy this condition, we selected pyrroloquinoline quinone (PQQ)-dependent glucose dehydrogenase as this enzyme has the optimum pH center-located on the pH scale allowing the enzyme activity change by the acidic and basic pH shift from the optimum value corresponding to the highest activity. The present NXOR gate is added to the biomolecular “toolbox” as a new example of Boolean logic gates based on enzyme reactions.
Wie sieht das unbemannte Flugzeug von Übermorgen aus? Dieser Frage stellen sich Forscher an der Fachhochschule Aachen. Die weltweit rasant fortschreitende Entwicklung des Marktes für unbemannte Fluggeräte (UAVs - „Unmanned Aerial Vehicles“) bietet großes Potenzial für Wachstum und Wertschöpfung. Unbemannte fliegende Systeme können – für bestimmte Anwendungsgebiete – wesentlich günstiger, kleiner und effizienter ausgelegt werden als bemannte Lösungen. Dabei sind sich viele Unternehmen über das mögliche Potential dieser Technologie noch gar nicht bewusst.