Christoph Räth

Detection and quantification of breast tumor necrosis with MR imaging: Value of the necrosis-avid contrast agent Gadophrin-3

RATIONALE AND OBJECTIVES The authors evaluated the use of T1-weighted magnetic resonance (MR) imaging with Gadophrin-3 enhancement and of plain T2-weighted MR imaging to detect and quantify breast tumor necrosis. MATERIALS AND METHODS Twenty EMT-6 tumors (mouse mammary sarcoma), implanted into the mammary fat pad of BALB/c-AnNCrl mice, underwent MR imaging with plain T2-weighted and T1-weighted fast field echo sequences before and 24 hours after injection of Gadophrin-3, a new necrosis-avid contrast agent. Tumor necrosis on MR images was quantified by means of a dedicated segmentation program and was correlated with histologic findings. RESULTS In all tumors a central necrosis was revealed by histopathologic analysis, and central enhancement was seen with Gadophrin-3 on T1-weighted images. Small tumors (diameter, < 1 cm) showed an inhomogeneous central enhancement, whereas larger tumors (diameter, > 1 cm) enhanced mainly in the periphery of necrotic tissue. Plain T2-weighted images showed a hyperintense central area in only three of 20 cases with a large central necrosis. CONCLUSION Gadophrin-3-enhanced T1-weighted images are superior to plain T2-weighted images for the detection of necrosis in a murine tumor xenograft model.

A scaling index analysis of the Wilkinson Microwave Anisotropy Probe three-year data: signatures of non-Gaussianities and asymmetries in the cosmic microwave background

Local scaling properties of the co-added foreground-cleaned three-year Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted scaling in- dices α. The scaling index method (SIM) is - for the first time - adapted and applied to the case of spherical symmetric spatial data. The results are compared with 1000 Monte Carlo simulations based on Gaussian fluctuations with a best fitCDM power spectrum and WMAP-like beam and noise properties. Statistical quantities based on the scaling indices, namely the moments of the distribution and probability-based measures are determined. We find for most of the test statistics significant deviations from the Gaussian hypothesis. Using a very conservative χ 2 statistics, which aver- ages over all scales, we detect non-Gaussianity with a probability of 97.3 % regarding the Kp0-masked full sky, 98.9 % for the Kp0-masked northern and 91.6 % for the Kp0-masked southern hemisphere. When analysing different length scales separately, the detection rates increase to 99.7 % (> 99.9 % north, 97.4 % south) for the mean, 98.4 % (99.9 % north, 71.6 % south) for the standard deviation and 97.9 % (99.4 % north, 80.3 % south) for a χ 2 -combination of mean and standard deviation. We find pronounced asymmetries, which can be interpreted as a global lack of structure in the northern hemisphere, which is consistent with previous findings. Furthermore, we detect a localized anomaly in the southern hemisphere, which gives rise to highly significant signature for non-Gaussianity in the spectrum of scaling indices P(α). We identify this signature as the cold spot, which was also already detected in the first year WMAP data. Our results provide further evidence for both the presence of non- Gaussianities and asymmetries in the WMAP three-year data. More detailed band- and year-wise analyses are needed to elucidate the origin of the detected anomalies. In either case the scaling indices provide powerful nonlinear statistics to analyse CMB maps.

Analysing large-scale structure - I. Weighted scaling indices and constrained randomization

The method of constrained randomisation, which was originally developed in the field of time series analysis for testing for nonlinearities, is extended to the case of three-dimensional point distributions as they are typical in the analysis of the large scale structure of galaxy distributions in the universe. With this technique it is possible to generate for a given data set so-called surrogate data sets which have the same linear properties as the original data whereas higher order or nonlinear correlations are not preserved. The analysis of the original and surrogate data sets with measures, which are sensitive to nonlinearities, yields valuable information about the existence of nonlinear correlations in the data. On the other hand one can test whether given statistical measures are able to account for higher order or nonlinear correlations by applying them to original and surrogate data sets. We demonstrate how to generate surrogate data sets from a given point distribution, which have the same linear properties (power spectrum) as well as the same density amplitude distribution but different morphological features. We propose weighted scaling indices, which measure the local scaling properties of a point set, as a nonlinear statistical measure to quantify local morphological elements in large scale structure. Using surrogates is is shown that the data sets with the same 2-point correlation functions have slightly different void probability functions and especially a different set of weighted scaling indices. Thus a refined analysis of the large scale structure becomes possible by calculating local scaling properties whereby the method of constrained randomisation yields a vital tool for testing the performance of statistical measures in terms of sensitivity to different topological features and discriminative power.

Texture detection and texture discrimination with anisotropic scaling indices

A new method to determine specific local features of textures is proposed. Based on the idea of pointwise dimensions, the concept of isotropic and anisotropic scaling indices is developed. A new algorithm for texture detection and texture localization that makes use of level-2 statistics is introduced. The performance of the algorithm is evaluated on an example of two natural textures. The effect of noise is studied, and it is shown that the algorithm is insensitive to white noise. The global and local aspects of the detection and discrimination process within this statistical model are pointed out. Some remarks on the choice of parameters in texture discrimination algorithms are made.

Non-Gaussian signatures in the five-year WMAP data as identified with isotropic scaling indices

We continue the analysis of non-Gaussianities in the cosmic microwave background by means of the scaling index method by applying this method on the single Q, V, W bands and the co-added VW band of the five-year data of the Wilkinson Microwave Anisotropy Probe. We compare each of the results with 1000 Monte Carlo simulations mimicking the Gaussian properties of the best fitting A cold dark matter model. Based on the scaling indices, scale-dependent empirical probability distributions, moments of these distributions and χ 2 combinations of them are calculated, obtaining similar results as in the former analysis of the three-year data: we derive evidence for non-Gaussianity with a probability of up to 97.3 per cent for the mean when regarding the KQ75-masked full sky and summing up over all considered length-scales by means of a diagonal χ 2 statistics. Looking at only the northern or southern hemisphere of the galactic coordinate system, we obtain up to 98.5 or 96.6 per cent, respectively. For the standard deviation, these results appear as 95.6 per cent for the full sky (99.7 per cent north, 89.4 per cent south) and for a χ 2 combination of both measurements as 97.4 per cent (99.1 per cent north, 95.5 per cent south). We obtain larger deviations from Gaussianity when looking at separate scale lengths. By performing an analysis of rotated hemispheres, we detect an obvious asymmetry in the data. In addition to these investigations, we present a method of filling the mask with Gaussian noise to eliminate boundary effects caused by the mask. With the help of this technique, we identify several local features on the map, of which the most significant one turns out to be the well-known cold spot. When excluding all these spots from the analysis, the deviation from Gaussianity increases, which shows that the discovered local anomalies are not the reason of the global detection of non-Gaussianity, but actually were damping the deviations on average. Our analyses per band and per year suggest, however, that it is very unlikely that the detected anomalies are due to foreground effects.

Revisiting algorithms for generating surrogate time series

The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate realizations with Fourier phase correlations leading to nondetections of nonlinearities. We argue that reliable surrogates can only be generated, if one tests separately for static and dynamic nonlinearities.

A Scaling Index Analysis of the WMAP three year data: Signatures of non-Gaussianities and Asymmetries in the CMB

Local scaling properties of the co-added foreground-cleaned three-year Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted scaling in- dices α. The scaling index method (SIM) is - for the first time - adapted and applied to the case of spherical symmetric spatial data. The results are compared with 1000 Monte Carlo simulations based on Gaussian fluctuations with a best fitCDM power spectrum and WMAP-like beam and noise properties. Statistical quantities based on the scaling indices, namely the moments of the distribution and probability-based measures are determined. We find for most of the test statistics significant deviations from the Gaussian hypothesis. Using a very conservative χ 2 statistics, which aver- ages over all scales, we detect non-Gaussianity with a probability of 97.3 % regarding the Kp0-masked full sky, 98.9 % for the Kp0-masked northern and 91.6 % for the Kp0-masked southern hemisphere. When analysing different length scales separately, the detection rates increase to 99.7 % (> 99.9 % north, 97.4 % south) for the mean, 98.4 % (99.9 % north, 71.6 % south) for the standard deviation and 97.9 % (99.4 % north, 80.3 % south) for a χ 2 -combination of mean and standard deviation. We find pronounced asymmetries, which can be interpreted as a global lack of structure in the northern hemisphere, which is consistent with previous findings. Furthermore, we detect a localized anomaly in the southern hemisphere, which gives rise to highly significant signature for non-Gaussianity in the spectrum of scaling indices P(α). We identify this signature as the cold spot, which was also already detected in the first year WMAP data. Our results provide further evidence for both the presence of non- Gaussianities and asymmetries in the WMAP three-year data. More detailed band- and year-wise analyses are needed to elucidate the origin of the detected anomalies. In either case the scaling indices provide powerful nonlinear statistics to analyse CMB maps.

On the nature of X-ray variability in Ark 564

We use data from a recent long ASCA observation of the Narrow Line Seyfert 1 galaxy Ark 564 to investigate in detail its timing properties. We show that a thorough analysis of the time series, employing techniques not generally applied to AGN light curves, can provide useful information to characterize the engines of these powerful sources. We searched for signs of non-stationarity in the data, but did not find strong evidences for it. We find that the process causing the variability is very likely nonlinear, suggesting that variability models based on many active regions, as the shot noise model, may not be applicable to Ark 564. The complex light curve can be viewed, for a limited range of time scales (as indicated by the breaks in the structure and power density spectrum), as a fractal object with non-trivial fractal dimension and statistical self-similarity. Finally, using a nonlinear statistic based on the scaling index as a tool to discriminate time series, we demonstrate that the high and low count rate states, which are indistinguishable on the basis of their autocorrelation, structure and probability density functions, are intrinsically dierent, with the high state characterized by higher complexity.

Statistics and meta-statistics in the concept of complexity

Abstract A crucial distinction between different classes of complexity measures is found to consist in their statistical structure. While first-order statistics always provides one or another kind of a measure of randomness, second-order (meta-) statistics provides more subtle measures of complexity. An example of a second-order measure is constructed and applied to specific cases. Some formal and conceptual issues concerning the general relevance of meta-statistical concepts of complexity are pointed out.

Network analysis of three-dimensional complex plasma clusters in a rotating electric field

Network analysis was used to study the structure and time evolution of driven three-dimensional complex plasma clusters. The clusters were created by suspending micron-size particles in a glass box placed on top of the rf electrode in a capacitively coupled discharge. The particles were highly charged and manipulated by an external electric field that had a constant magnitude and uniformly rotated in the horizontal plane. Depending on the frequency of the applied electric field, the clusters rotated in the direction of the electric field or remained stationary. The positions of all particles were measured using stereoscopic digital in-line holography. The network analysis revealed the interplay between two competing symmetries in the cluster. The rotating cluster was shown to be more cylindrical than the nonrotating cluster. The emergence of vertical strings of particles was also confirmed.