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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.
Betrifft Design : von historischen Zukunftsperspektiven zu gegenwärtigen Vergangenheitssehnsüchten
(2019)
Human induced pluripotent stem cells (hiPSCs) have shown to be promising in disease studies and drug screenings [1]. Cardiomyocytes derived from hiPSCs have been extensively investigated using patch-clamping and optical methods to compare their electromechanical behaviour relative to fully matured adult cells. Mathematical models can be used for translating findings on hiPSCCMs to adult cells [2] or to better understand the mechanisms of various ion channels when a drug is applied [3,4]. Paci et al. (2013) [3] developed the first model of hiPSC-CMs, which they later refined based on new data [3]. The model is based on iCells® (Fujifilm Cellular Dynamics, Inc. (FCDI), Madison WI, USA) but major differences among several cell lines and even within a single cell line have been found and motivate an approach for creating sample-specific models. We have developed an optimisation algorithm that parameterises the conductances (in S/F=Siemens/Farad) of the latest Paci et al. model (2018) [5] using current-voltage data obtained in individual patch-clamp experiments derived from an automated patch clamp system (Patchliner, Nanion Technologies GmbH, Munich).
The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach.
Hypertension describes the pathological increase of blood pressure, which is most commonly associated with the increase of vascular wall stiffness [1]. Referring to the “Deutsche Bluthochdruck Liga” this pathology shows a growing trend in our aging society. In order to find novel pharmacological and probably personalized treatments, we want to present a functional approach to study biomechanical properties of a human aortic vascular model.
In this method review we will give an overview of recent studies which were carried out with the CellDrum technology [2] and underline the added value to already existing standard procedures known from the field of physiology.
Herein described CellDrum technology is a system to measure functional mechanical properties of cell monolayers and thin tissue constructs in-vitro. Additionally, the CellDrum enables to elucidate the mechanical response of cells to pharmacological drugs, toxins and vasoactive agents. Due to its highly flexible polymer support, cells can also be mechanically stimulated by steady and cyclic biaxial stretching.