Stochastic analysis of different rough surfaces

This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more details. In particular we show the evidence of Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in details advantages and disadvantages of these methods.Comment: Minor text changes to be identical with the published versio

Multiscale reconstruction of time series

A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of scales. It is possible to generate complete new time series, or to model the next steps for a given sequence of data. The method itself is based on the joint probability density which can be extracted directly from given data, thus no estimation of parameters is necessary. The results of this approach are shown for a real world dataset, namely for turbulence. The unconditional and conditional probability densities of the original and reconstructed time series are compared and the ability to reproduce both is demonstrated. Therefore in the case of Markov properties the method proposed here is able to generate artificial time series with correct n-point statistics.Comment: 4 pages, 3 figure

Locoregional heterogeneity of glioblastoma entails pro- or antitumorigenic effects of tumor associated mesenchymal stem cells

Among other cell lines of the tumor microenvironment, mesenchymal stem cells play an important role in glioma progression. However, many diverging aspects were shown throughout the complex interaction between mesenchymal stem cells and tumor cells. The first part of this work investigated in the migration of injected mesenchymal stem cells in glioblastoma. Furthermore, this study aimed to model one pathologically relevant aspect of the in vivo interaction between mesenchymal stem cells and glioma cells under simplified in vitro conditions in order to analyze a potential effect on the viability of glioma cells. First, mice were intracranially inoculated with glioma cells. Once the tumor had grown for 58 days, mesenchymal stem cells were injected into the brain into the main tumor mass. After sacrificing the mice, brain sections were analyzed with regards to the mesenchymal stem cells location and blood-brain barrier integrity in glioma. Furthermore, an in vitro proliferation assay was performed studying glioma cells viability under serum-free mesenchymal stem cell conditioned medium. The in vivo experiment shows migration of mesenchymal stem cells to invasive parts of the tumor. It was demonstrated that in these regions the blood-brain barrier is widely intact. Hence, serum-derived factors larger than the size of 70 kDa do not reach the structures where mesenchymal stem cells reside. Consequently, this serum-free situation was modeled in an in vitro proliferation assay. Serum-free medium, which was conditioned by mesenchymal stem cells, enhances viability in two lines of glioma stem cells even under conditions of chemotherapy. This paper adds to our understanding of the complex interaction between mesenchymal stem cells and glioma cells. The results of the study provide evidence for mesenchymal stem cells tropism for invasive regions of glioblastoma. These invasive regions remain in the brain after neurosurgery, representing the source of tumor relapse. Taken together, these encouraging results suggest that mesenchymal stem cells are able to support tumor relapse formation by improving viability of glioma cells even under conditions of chemotherapy. This makes mesenchymal stem cells and their interaction with glioblastoma promising potential therapeutical targets to evaluate in glioblastoma therapy in the future