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We observe the presence of infinitely fine-scaled alternations within the performance landscape of reservoir computers aimed for chaotic data forecasting. We investigate the emergence of the observed structures by means of variations of the transversal stability of the synchronization manifold relating the observational and internal dynamical states. Finally, we deduce a simple calibration method in order to attenuate the thus evidenced performance uncertainty.

The purpose of this study was to investigate whether the combination of dual-energy X-ray absorptiometry (DXA)-based bone mass and magnetic resonance imaging (MRI)-based cortical and trabecular structural measures improves the prediction of radial bone strength. Thirty-eight left forearms were harvested from formalin-fixed human cadavers. Bone mineral content (BMC) and bone mineral density (BMD) of the distal radius were measured using DXA. Cortical and trabecular structural measures of the distal radius were computed in high-resolution 1.5T MR images. Cortical measures included average cortical thickness and cross-sectional area. Trabecular measures included morphometric and texture parameters. The forearms were biomechanically tested in a fall simulation to measure absolute radial bone strength (failure load). Relative radial bone strength was determined by dividing radial failure loads by age, body mass index, radius length, and average radius cross-sectional area, respectively. DXA derived BMC and BMD showed statistically significant (p < 0.05) correlations with absolute and relative radial bone strength (r ≤ 0.78). Correlation coefficients for cortical and trabecular structural measures with absolute and relative radial bone strength amounted up to r = 0.59 and r = 0.74, respectively, (p < 0.05). In combination with DXA-based bone mass, trabecular but not, cortical structural measures, added in multiple regression models significant (p < 0.05) information in predicting absolute and relative radial bone strength (up to Radj = 0.88). Thus, a combination of DXA-based bone mass and MRI-based trabecular structural measures most accurately predicted absolute and relative radial bone strength, whereas structural measures of the cortex did not provide significant additional information in combination with DXA.

We study the onset and characteristics of vortices in complex (dusty) plasmas using two-dimensional simulations in a setup modeled after the PK-3 Plus laboratory. A small number of microparticles initially self-arranges in a monolayer around the void. As additional particles are introduced, an extended system of vortices develops due to a non-zero curl of the plasma forces. We demonstrate a shear-thinning effect in the vortices. Velocity structure functions and the energy and enstrophy spectra show that vortex flow turbulence is present that is in essence of the "classical" Kolmogorov type., 5 pages, 6 figures

Recent technical improvements have made it possible to determine trabecular bone structure parameters of the spine using clinical multi-detector computed tomography (MDCT). Therefore, the purpose of this study was to analyze trabecular bone structure parameters obtained from clinical MDCT in relation to high resolution peripheral quantitative computed tomography (HR-pQCT) as a standard of reference and to investigate whether clinical MDCT can predict vertebral bone strength. Fourteen functional spinal segment units between T7 and L3 were harvested from 14 formalin-fixed human cadavers (11 women and 3 men; age 84 ± 10 years). All functional spinal segment units were examined using HR-pQCT (isotropic voxel size of 41 μm(3)) and a clinical whole-body MDCT (interpolated voxel size of 146 × 146 × 300 μm(3)). Trabecular bone structure analyses (histomorphometric and texture measures) were performed in the HR-pQCT as well as MDCT images. Vertebral failure load (FL) of the functional spinal segment units was determined in an uniaxial biomechanical test. The HR-pQCT and MDCT derived trabecular bone structure parameters showed correlations ranging from r = 0.60 to r = 0.90 (p0.05). Correlations between trabecular bone structure parameters and FL amounted up to r = 0.86 (p0.05) using the HR-pQCT images, and up to r = 0.79 (p0.05) using the MDCT images. Correlation coefficients of FL versus trabecular bone structure parameters obtained with HR-pQCT and MDCT were not significantly different (p0.05). In this cadaver model, the spatial resolution of clinically available whole-body MDCT scanners was suitable for trabecular bone structure analysis of the spine and to predict vertebral bone strength.

In order to test for non-Gaussianities with respect to scale-dependencies we use so-called surrogate maps, in which possible phase correlations of the Fourier phases of the original WMAP data and simulations, respectively, are destroyed by applying a shuffling scheme to the maps. A statistical comparison of the original maps with the surrogate maps then allows to test for the existence of higher order correlations in the original maps, also and especially on well-defined Fourier modes. Using Minkowski functionals as an image analysis technique we calculate the deviation between the original data and 500 surrogates for different hemispheres in the sky and find ecliptic hemispherical asymmetries between northern and southern ecliptic sky. We find strong deviations from Gaussianity in the WMAP data when considering the low-l range with l = [2,20]. The analysis technique of the scaling indices leads to a slightly lower deviation. Although the underlying foreground reduction methods of the maps differ from each other, we find similar results for the WMAP 7yr ILC map and the WMAP 7yr (needlet-based) NILC map in the low-l range. Our results point once more to a cosmological nature of the signal. For a higher l range with l = [120,300] the results differ between the two image analysis techniques and between the two maps which makes an intrinsic nature of the signal on this l range less likely. When we decrease the size of the analysed sky regions for the low-l study, we do not find signatures of NG in the northern sky. In the south we find individual spots which show deviations from Gaussianity. In addition, we investigate non-Gaussian CMB simulations that depend on the f_NL parameter of the local type. These simulations cannot account for the detected signatures on the low-l range., Comment: 13 pages, 10 figures, accepted for publication in MNRAS

In this study, we investigated the scaling relations between trabecular bone volume fraction (BV/TV) and parameters of the trabecular microstructure at different skeletal sites. Cylindrical bone samples with a diameter of 8mm were harvested from different skeletal sites of 154 human donors in vitro: 87 from the distal radius, 59/69 from the thoracic/lumbar spine, 51 from the femoral neck, and 83 from the greater trochanter. μCT images were obtained with an isotropic spatial resolution of 26μm. BV/TV and trabecular microstructure parameters (TbN, TbTh, TbSp, scaling indices ( and σ of α and αz), and Minkowski Functionals (Surface, Curvature, Euler)) were computed for each sample. The regression coefficient β was determined for each skeletal site as the slope of a linear fit in the double-logarithmic representations of the correlations of BV/TV versus the respective microstructure parameter. Statistically significant correlation coefficients ranging from r=0.36 to r=0.97 were observed for BV/TV versus microstructure parameters, except for Curvature and Euler. The regression coefficients β were 0.19 to 0.23 (TbN), 0.21 to 0.30 (TbTh), -0.28 to -0.24 (TbSp), 0.58 to 0.71 (Surface) and 0.12 to 0.16 ( ), 0.07 to 0.11 ( ), -0.44 to -0.30 (σ(α)), and -0.39 to -0.14 (σ(αz)) at the different skeletal sites. The 95% confidence intervals of β overlapped for almost all microstructure parameters at the different skeletal sites. The scaling relations were independent of vertebral fracture status and similar for subjects aged 60-69, 70-79, and >79years. In conclusion, the bone volume fraction-microstructure scaling relations showed a rather universal character.

The purpose of this study was to assess and compare the reproducibility of trabecular bone structure measurements of the distal radius at 1.5 and 3.0 T magnetic resonance imaging (MRI). Root mean square reproducibility errors ranged from 0.69% to 4.94% at 1.5 T MRI and from 0.38% to 5.80% at 3.0 T MRI. Thus, reproducibility errors of trabecular bone structure measurements are overall in an acceptable range and similar at 1.5 and 3.0 T MRI.

According to Wolff's law bone remodels in response to the mechanical stresses it experiences so as to produce a minimal-weight structure that is adapted to its applied stresses. Consequently, the inner bone structure should show signs of adaptation to external forces acting on the bone. To test this paradigm, we investigate the relations between bone volume and structure for the trabecular bone using 3D μCT images taken from two different sites in the femur in vitro, namely from the femoral neck (88 specimens) and femoral trochanter (126 specimens). We determine the local structure of the trabecular network as well as its alignment with the direction of the external force acting on the bone by calculating isotropic (α) and anisotropic scaling indices (αz). Comparing global structure measures derived from the scaling indices (mean, variance) with the bone mass (BV/TV) we find that all correlations obey very accurately power laws with scaling exponents of 0.48 and 0.45 ( ), -1.45 and -1.59 (var(μz)), 0.50 and 0.44 ( ) and -1,47 and -1.32 (var(μz)) (neck and trochanter respectively). Thus, the relations for the isotropic scaling indices turn out to be siteindependent, albeit the mechanical stress to which the femoral neck is exposed is much larger than that for the trochanter. We find, however, differences in the degree of alignment of the trabeculae as reflected by the moments of the distribution of the anisotropic scaling indices. In summary, the mass-structure scaling relations of the bone probes taken from the two different sites of the femur show surprisingly small variations. Thus, a naive interpretation of Wolff's law may not universally valid.

We analyze μ-CT tomographic images of human trabecular bone in vitro. We consider a sample consisting of 201 bone specimens harvested from six different skeletal sites with bone fraction in the range BV/TV e [0.04, 0.075]. Using the local characterization of the bone trabecular network given by isotropic and anisotropic scaling indices, we apply classification algorithms in order to reveal structural similarities in the sample. The classification procedures based on isotropic and anisotropic scaling indices lead to different clustering solutions. This comparison helps revealing interesting site specific structural features connected to the intrinsic anisotropy of the trabecular network.

The development of high-resolution visualisation techniques, such as magnetic resonance (MR) and computer tomography (CT) opens the possibility for non-destructive studies of the inner structure of the objects of different nature and origin. The deterioration of the structure with time, deformations and loss of strength under the load and other processes lead to morphological and topological changes inside materials, which require both qualitative analysis and quantitative evaluation. Assessment and proper description of the topological and morphological characteristics of materials with porous and irregular architecture is of great importance for many scientific and engineering studies. The Scaling Index Method (SIM) is a novel numerical tool for characterising the local topology of an arbitrary structure. By evaluating the local dimensionality of each point, the SIM indicates topologically different substructures: unstructured background, onedimensional (rod-like) and two-dimensional (plate-like) elements. By changing the parameters of the SIM one can distinguish the outer surface from inner points of the structure, describe structures at different scales, and include anisotropic features of the tissue. This method can be applied to both binary and greyscale multidimensional images. To demonstrate the scientific performance of the method we apply numerical techniques based on the SIM to tree-dimensional μCT images of the bone tissue engineering scaffolds (as an example of designed porous structure) and to trabecular bone specimens taken from the human vertebrae in vitro (as an example of biological tissue with very irregular and complicated structure). A proper description of the global and local structural characteristics of the trabecular bone network, which carries and redistributes mechanical load inside the bone, helps to evaluate the deterioration of bone tissue caused by osteoporosis and to predict the most frequent complications of this disease, namely spine and hip fractures. Because of the porous and very irregular architecture of the trabecular bone tissue, a detailed assessment of such a structure requires the use of many texture measures derived from different morphological, biomechanical, topological, and statistical concepts. We show that the Scaling Index Method provides complementary information to the existing wellestablished techniques.

Osteoporosis is a metabolic bone disorder in which bones become brittle and prone to fracture. According to the World Health Organization, it is characterized by the loss of bone mineral density and the deterioration of the bone micro-architecture (Prevention and Management of Osteoporosis, 2003). One of the most important factors in determining the risk of fracture is the bone strength. In clinical practice, the risk of fracture and the effects of drug therapy are assessed using only densitometric techniques as a quantitative measure (Kanis, 2002; Kanis, 2007). Modern high-resolution imaging modalities like High-Resolution Computer Tomography (HRCT) and High-Resolution Magnetic Resonance Imaging (HRMRI) open up new possibilities to improve diagnostic techniques of osteoporosis since they are able to depict the architecture of trabecular bone. In particular, recent advances in MRI technology allow us to obtain images with in-plane spatial resolution as high as 50 μm in vitro and 150 μm in vivo, and a slice thickness of 128 μm in vitro and 280 μm in vivo (Link, et al., 1999; Carballido-Gamio et al., 2006; Wehrli, 2007; Krug et al., 2006). These figures should be compared with the actual thickness of the trabeculae, which ranges from 80 to 200 μm with an average size of approximately 120 μm. It has been shown that these imaging modalities enable the assessment of image data with respect to textural properties to detect structural differences (Boutry et al., 2003; Majumdar et al., 1996; Vieth et al., 2001). HRCT is the preferred methodology to image bones. In contrast to MRI scans, CT scans can easily be calibrated using phantoms, thus rendering images with a standardize grey level distribution. In addition, CT images of the bone are free from the susceptibility artifacts and, in case of in vivo applications, have a less stringent requirement for patients to remain absolutely motionless during the scan as compared to MRI.

We analyse μ-CT tomographic images of human trabecular bone in vitro. We consider a sample consisting of 201 bone specimens harvested from six different skeletal sites within a narrow range of bone fraction values. Using the characterization of the trabecular bone network given by local Minkowski Functionals, we apply classification algorithms in order to reveal structural similarities in the sample. Clusters show some interesting specific structural features, like compact, porous, and fragmented structures. The contribution of the different skeletal sites to these clusters indicate some variability due to intrinsic structural differences of the specific skeletal site.

Dedicated experiments with strongly coupled complex plasmas in external electric fields were carried out under microgravity conditions using the PK-4 dc discharge setup. The focus was put on the comparative analysis of the formation of stringlike anisotropic structures due to reciprocal (hamiltonian) and nonreciprocal (non-hamiltonian) interactions between microparticles (induced by ac and dc fields, respectively). The experiments complemented by numerical simulations demonstrate that the responses of complex plasmas in these two regimes are drastically different. It is suggested that the observed difference is a manifestation of intrinsic thermodynamic openness of driven strongly coupled systems.

Using experiments and combining theory and computer simulations, we show that binary complex plasmas are particularly good model systems to study the kinetics of fluid-fluid demixing at the "atomistic" (individual particle) level. The essential parameters of interparticle interactions in complex plasmas, such as the interaction range(s) and degree of nonadditivity, can be varied significantly, which allows systematic investigations of different demixing regimes. The critical role of competition between long-range and short-range interactions at the initial stage of the spinodal decomposition is discussed.

According to Wolff's law bone remodels in response to the mechanical stresses it experiences so as to produce a minimal-weight structure that is adapted to its applied stresses. Here, we investigate the relations between bone volume and structure for the trabecular bone using 3D μCT images taken from different skeletal sites in vitro, namely from the distal radii (96 specimens), thoracic (73 specimens) and lumbar vertebrae (78 specimens). We determine the local structure of the trabecular network by calculating isotropic and anisotropic scaling indices (α, αz). These measures have been proven to be able to discriminate rod- from sheet-like structures and to quantify the alignment of structures with respect to a preferential direction as given by the direction of the external force. Comparing global structure measures derived from the scaling indices (mean, standard deviation) with the bone mass (BV/TV) we find that all correlations obey very accurately power laws with scaling exponents of 0.14, 0.12, 0.15 (

The standard diagnostic technique for assessing osteoporosis is dual X-ray absorptiometry (DXA) measuring bone mass parameters. In this study, a combination of DXA and trabecular structure parameters (acquired by computed tomography [CT]) most accurately predicted the biomechanical strength of the proximal femur and allowed for a better prediction than DXA alone. Introduction: An automated 3D segmentation algorithm was applied to determine specific structure parameters of the trabecular bone in CT images of the proximal femur. This was done to evaluate the ability of these parameters for predicting biomechanical femoral bone strength in comparison with bone mineral content (BMC) and bone mineral density (BMD) acquired by DXA as standard diagnostic technique. Methods: One hundred eighty-seven proximal femur specimens were harvested from formalin-fixed human cadavers. BMC and BMD were determined by DXA. Structure parameters of the trabecular bone (i.e., morphometry, fuzzy logic, Minkowski functionals, and the scaling index method [SIM]) were computed from CT images. Absolute femoral bone strength was assessed with a biomechanical sideimpact test measuring failure load (FL). Adjusted FL parameters for appraisal of relative bone strength were calculated by dividing FL by influencing variables such as body height, weight, or femoral head diameter. Results: The best single parameter predicting FL and adjusted FL parameters was apparent trabecular separation (morphometry) or DXA-derived BMC or BMD with correlations up to r=0.802. In combination with DXA, structure parameters (most notably the SIM and morphometry) added in linear regression models significant information in predicting FL and all adjusted FL parameters (up to Radj=0.872) and allowed for a significant better prediction than DXA alone. Conclusion: A combination of bone mass (DXA) and structure parameters of the trabecular bone (linear and nonlinear, global and local) most accurately predicted absolute and relative femoral bone strength. © The Author(s) 2009.

We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.

The dynamical onset of lane formation is studied in experiments with binary complex plasmas under microgravity conditions. Small microparticles are driven and penetrate into a cloud of big particles, revealing a strong tendency towards lane formation. The observed time-resolved lane formation process is in good agreement with computer simulations of a binary Yukawa model with Langevin dynamics. The laning is quantified in terms of the anisotropic scaling index, leading to a universal order parameter for driven systems., Comment: 4 pages, 3 figures, movies available at http://www.mpe.mpg.de/pke/lane-formation/

The method of surrogates is widely used in the field of nonlinear data analysis for testing for weak nonlinearities. The two most commonly used algorithms for generating surrogates are the amplitude adjusted Fourier transform (AAFT) and the iterated amplitude adjusted Fourier transfom (IAAFT) algorithm. Both the AAFT and IAAFT algorithm conserve the amplitude distribution in real space and reproduce the power spectrum (PS) of the original data set very accurately. The basic assumption in both algorithms is that higher-order correlations can be wiped out using a Fourier phase randomization procedure. In both cases, however, the randomness of the Fourier phases is only imposed before the (first) Fourier back tranformation. Until now, it has not been studied how the subsequent remapping and iteration steps may affect the randomness of the phases. Using the Lorenz system as an example, we show that both algorithms may create surrogate realizations containing Fourier phase correlations. We present two new iterative surrogate data generating methods being able to control the randomization of Fourier phases at every iteration step. The resulting surrogate realizations which are truly linear by construction display all properties needed for surrogate data., Comment: To appear in: "Topics on Chaotic Systems: Selected Papers from Chaos 2008 International Conference", World Scientific

PK‐3 Plus is the second generation laboratory for investigations of complex plasmas under microgravity conditions on the International Space Station. Compared to its pre‐cursor PKE‐Nefedov, operational 2001–2005, it has an advanced hardware and software. Improved diagnostics and especially a much better homogeneity of the complex plasma allow more detailed investigations, helping to understand the fundamentals of complex plasmas. Typical investigations are performed to observe the structure of homogeneous and isotropic complex plasmas and instabilities occurring at high particle densities. In addition, the new setup allows the tuning of the interaction potential between the microparticles by using external ac electric fields. Thus, we are able to initiate electrorheological phenomena in complex plasma fluids in the PK‐3 Plus laboratory, and observe the phase transition from a normal fluid to a string fluid state at the individual particle level for the first time. Such new possibilities open up new directions of research under microgravity conditions.

Ziele: Die trabekulare Knochenstruktur von Calcanei alterer Kadaver wurde mit hochauflosendem MRT bei 1,5T und 3T dargestellt. Zur getrennten Analyse von Signal-zu-Rausch-Verhaltnis (SNR) und Suszeptibilitats-Artefakten wurden Bilddatensatze mit abnehmendem SNR simuliert. Mittels histomorphometrischer und nichtlinearer Strukturparameter wurde untersucht, welchen Informationsgehalt die Bilddaten in Bezug auf die Osteoporosediagnostik besitzen. Methode: Sagittale Gradienten Echo Sequenzen wurden von 43 Calcaneus-Praparaten alterer Kadaver (80±10 Jahre, Manner:Frauen=21:22) akquiriert (Auflosung 156×156×500µm). In diesen Bilddaten wurde das Rauschen verstarkt, so dass funf neue Datensatze mit abnehmendem SNR, jeweils gleich bei 1,5T und 3T, entstanden. Dabei wurde das SNR als Quotient der Standardabweichung des trabekularen Knochens zu Standardabweichung des Hintergrundes berechnet. Histomorphometrische Parameter (HM) und Skalierungs-Indices (mp(alpha)) wurden in korrespondierenden Bereichen aller Bilddaten bestimmt. Als Goldstandard dienten identische Parameter aus hochauflosenden µCT Datensatzen (26µm isotrop), sowie die biomechanische Versagenslast der Knochenproben. Ergebnis: Das SNR der ursprunglichen Bilddaten betrug 7,3 bei 3T und 3,5 bei 1,5T. In den simulierten Datensatzen nahm es bis auf 1 ab. Fur SNR >1,6 konnten die µCT-basierten Strukturparameter des trabekularen Knochens mit identischem Fehler (fRMS) vorhergesagt werden. Dieser war signifikant groser bei 3.0T als bei 1.5T trotz gleichen SNR (z.B. Knochenfraktion bei SNR=1,6: fRMS[3,0T]=15%; fRMS[1,5T]=21%, p

We report the experimental discovery of "electrorheological (ER) complex plasmas," where the control of the interparticle interaction by an externally applied electric field is due to distortion of the Debye spheres that surround microparticles (dust) in a plasma. We show that interactions in ER plasmas under weak ac fields are mathematically equivalent to those in conventional ER fluids. Microgravity experiments, as well as molecular dynamics simulations, show a phase transition from an isotropic to an anisotropic (string) plasma state as the electric field is increased.

Methods derived from nonlinear time series analyses are applied to three-dimensional point distributions as they are typical in the analysis of the cosmic large scale structure. Using the technique of constrained randomisation we generate for a given data set surrogate data sets which have the same linear properties (power spectrum) as well as the same density amplitude distribution but different morphological features. It is shown that the original data set can be discriminated from the surrogates by analysing the local scaling properties of the point sets as measured by weighted scaling indices.

Growing international competition is forcing salmon farmers to incorporate innovative techniques into the production process. The use of triploid, all-female breeding populations offers multiple advantages over diploid populations. Currently, an exact, simple, and non- hazardous method for the quantification of diploid- and triploid salmon erythrocytes does not exist. We present a method that combines a standard microscopic bright field technique (contrast staining with GIEMSA) with multi-parameter image analysis and termed it quantitative morphologic microscopy (QMM). We used flow cytometry (FC) as the reference method to determine the DNA content of di- and triplod erythrocytes from immature rainbow trout (Oncorhynchus mykiss). Additionally, we applied quantitative fluorescence microscopy (QFM), using the DNA stains 4',6-diamidino-2-phenylindole (DAPI), propidium iodide (PI), and acridine orange (AO). Our data show that QMM possess comparable or even superior discriminating capacities than FC or QFM. The developed method opens a perspective for the classification of microscopic objects with many possible applications., La creciente competencia internacional ha forzado a la industria del salmón a la incorporación de técnicas innovadoras. El cultivo de hembras triploides tiene múltiples ventajas sobre poblaciones diploides. En la actualidad, no existe un método simple, exacto y de bajo riesgo para la cuantificación de tasas de triploidización. En este trabajo presentamos un método que combina microscopía de campo claro convencional (con marcación GIEMSA) con el análisis multiparamétrico de imágenes, denominándolo como microscopía morfológica cuantitativa (QMM). Se utilizó citometría de flujo (FC) como un método de referencia para determinar el contenido de ADN en eritrocitos diploides y triploides extraídos de truchas arco iris inmaduras (Oncorhynchus mykiss). Además, se aplicó microscopía de fluorescencia cuantitativa (QFM), usando los marcadores de ADN: 4,6-diamidina-2-fenilindol (DAPI), Yoduro de Propidio (PI), y Naranja de Acridina (AO). Nuestros datos muestran que QMM posee una capacidad discriminante comparable o incluso superior a FC o QFM. El método desarrollado ofrece una nueva perspectiva para clasificar objetos microscópicos, con muchas posibles aplicaciones.

Complex plasma being the 'plasma state of soft matter' is especially suitable for investigations of non-equilibrium phase transitions. Non-equilibrium phase transitions can manifest in dissipative structures or self-organization. Two specific examples are lane formation and phase separation. Using the permanent microgravity laboratory PK-3 Plus, operating onboard the International Space Station, we performed unique experiments with binary mixtures of complex plasmas that showed both lane formation and phase separation. These observations have been augmented by comprehensive numerical and theoretical studies. In this paper we present an overview of our most important results. In addition we put our results in context with research of complex plasmas, binary systems and non-equilibrium phase transitions. Necessary and promising future complex plasma experiments on phase separation and lane formation are briefly discussed.