2018, Sohmen, Lucia, Charbonnier, Jean, Blümel, Ina, Wartena, Christian, Heller, Lambert, Méndez, E., Crestani, F., Ribeiro, C., David, G., Lopes, J.

This paper summarizes the results of a comprehensive statistical analysis on a corpus of open access articles and contained figures. It gives an insight into quantitative relationships between illustrations or types of illustrations, caption lengths, subjects, publishers, author affiliations, article citations and others.

2015, Schildknecht, Konstantin, Tabelow, Karsten, Dickhaus, Thorsten

Signal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multiplicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into disjoint subsets or families, e. g., by a-priori knowledge on the functionality of certain regions of interest. If the proportion of true null hypotheses differs between families, this structural information can be used to increase statistical power. We propose a two-stage multiple test procedure which first excludes those families from the analysis for which there is no strong evidence for containing true alternatives. We show control of the family-wise error rate at this first stage of testing. Then, at the second stage, we proceed to test the hypotheses within each non-excluded family and obtain asymptotic control of the FDR within each family in this second stage. Our main mathematical result is that this two-stage strategy implies asymptotic control of the FDR with respect to all hypotheses. In simulations we demonstrate the increased power of this new procedure in comparison with established procedures in situations with highly unbalanced families. Finally, we apply the proposed method to simulated and to real fMRI data.

2015, Schildknecht, Konstantin, Olek, Sven, Dickhaus, Thorsten

Epigenetic research leads to complex data structures. Since parametric model assumptions for the distribution of epigenetic data are hard to verify we introduce in the present work a nonparametric statistical framework for two-group comparisons. Furthermore, epigenetic analyses are often performed at various genetic loci simultaneously. Hence, in order to be able to draw valid conclusions for specific loci, an appropriate multiple testing correction is necessary. Finally, with technologies available for the simultaneous assessment of many interrelated biological parameters (such as gene arrays), statistical approaches also need to deal with a possibly unknown dependency structure in the data. Our statistical approach to the nonparametric comparison of two samples with independent multivariate observables is based on recently developed multivariate multiple permutation tests. We adapt their theory in order to cope with families of hypotheses regarding relative effects. Our results indicate that the multivariate multiple permutation test keeps the pre-assigned type I error level for the global null hypothesis. In combination with the closure principle, the family-wise error rate for the simultaneous test of the corresponding locus/parameter-specific null hypotheses can be controlled. In applications we demonstrate that group differences in epigenetic data can be detected reliably with our methodology.

2015, Deliano, Matthias, Tabelow, Karsten, König, Reinhard, Polzehl, Jörg

Estimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. In this approach, it is tacitly assumed that learning performance is constant within the moving windows, which, however, is often not the case. In the present study we demonstrate that violations of this assumption lead to systematic errors in the analysis of learning curves, and we explored the dependency of these errors on window size, different statistical models, and learning phase. To reduce these errors for single subjects as well as on the population level, we propose adequate statistical methods for the estimation of learning curves and the construction of confidence intervals, trial by trial. Applied to data from a shuttle-box avoidance experiment with Mongolian gerbils, our approach revealed performance changes occurring at multiple temporal scales within and across training sessions which were otherwise obscured in the conventional analysis. The proper assessment of the behavioral dynamics of learning at a high temporal resolution clarified and extended current descriptions of the process of avoidance learning. It further disambiguated the interpretation of neurophysiological signal changes recorded during training in relation to learning.

2014, Reichelt, Sina

We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms, and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1, other species may diffuse much slower, namely, with order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and we prove that the error of its solution to the original solution is of order 1/2.

2019, Naji, Ahmed, Krause, Beate, Pötschke, Petra, Ameli, Amir

Here, we report multifunctional polycarbonate (PC)-based conductive polymer composites (CPCs) with outstanding performance manufactured by a simple extrusion process and intended for use in bipolar plate (BPP) applications in polymer electrolyte membrane (PEM) fuel cells. CPCs were developed using a ternary conductive filler system containing carbon nanotube (CNT), carbon fiber (CF), and graphite (G) and by introducing di-allyl phthalate (DAP) as a plasticizer to PC matrix. The samples were fabricated using twin-screw extrusion followed by compression molding and the microstructure, electrical conductivity, thermal conductivity, and mechanical properties were investigated. The results showed a good dispersion of the fillers with some degree of interconnection between dissimilar fillers. The addition of DAP enhanced the electrical conductivity and tensile strength of the CPCs. Due to its plasticizing effect, DAP reduced the processing temperature by 75 °C and facilitated the extrusion of CPCs with filler loads as high as 63 wt% (3 wt% CNT, 30 wt% CF, 30 wt% G). Consequently, CPCs with the through-plane electrical, in-plane electrical and thermal conductivities and tensile strength of 4.2 S cm-1, 34.3 S cm-1, 2.9 W m-1 K-1, and 75.4 MPa, respectively, were achieved. This combination of properties indicates the potential of PC-based composites enriched with hybrid fillers and plasticizers as an alternative material for BPP application.

2014, Pimenov, Alexander, Rachinskii, Dmitrii

We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.

2014, Klein, Olaf, Recupero, Vincenzo

Sweeping processes are a class of evolution differential inclusions arising in elastoplasticity and were introduced by J.J. Moreau in the early seventies. The solution operator of the sweeping processes represents a relevant example of emphrate independent operator containing as a particular case the so called emphplay operator which is widely used in hysteresis. The continuity properties of these operators were studied in several works. In this note we address the continuity with respect to the strict metric in the space of functions of bounded variation with values in the metric space of closed convex subsets of a Hilbert space. We provide a counterexample showing that the solution operator of the sweeping process is not continuous when its domain is endowed with the strict topology of BV and its codomain is endowed with the L1-topology. This is at variance with the case of the play operator which instead is continuous in this sense.

2012, Krause, Beate, Mende, Mandy, Petzold, Gudrun, Boldt, Regine, Pötschke, Petra

Two main properties of carbon nanotube (CNT) materials are discussed in this contribution. First, a method to characterize the dispersability of CNT materials in aqueous surfactant solutions in presented, which also allows conclusions towards the dispersability in other media, like polymer melts. On the other hand it is shown, how the length of CNTs before and after processing, e.g., after melt mixing with thermoplastics, can be quantified. Both methods are illustrated with examples and the practical relevance is shown. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

2013, Caffarelli, Luis, Savin, Ovidiu, Valdinoci, Enrico

We consider a minimization problem that combines the Dirichlet energy with the nonlocal perimeter of a level set. We obtain regularity results for the minimizers and for their free boundaries using blow-up analysis, density estimates, monotonicity formulas, Euler-Lagrange equations and extension problems.