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In this work, some new results to exploit the recurrence properties of quasiperiodic dynamical systems are presented by means of a two dimensional visualization technique, Recurrence Plots(RPs). Quasiperiodicity is the simplest form of dynamics exhibiting nontrivial recurrences, which are common in many nonlinear systems. The concept of recurrence was introduced to study the restricted three body problem and it is very useful for the characterization of nonlinear systems. I have analyzed in detail the recurrence patterns of systems with quasiperiodic dynamics both analytically and numerically. Based on a theoretical analysis, I have proposed a new procedure to distinguish quasiperiodic dynamics from chaos. This algorithm is particular useful in the analysis of short time series. Furthermore, this approach demonstrates to be efficient in recognizing regular and chaotic trajectories of dynamical systems with mixed phase space. Regarding the application to real situations, I have shown the capability and validity of this method by analyzing time series from fluid experiments.
As land-cover conversion continues to expand into ever more remote areas in the humid tropics, montane rainforests are increasingly threatened. In the south Ecuadorian Andes, they are not only subject to man-made disturbances but also to naturally occurring landslides. I was interested in the impact of this ecosystem dynamics on a key parameter of the hydrologic cycle, the soil saturated hydraulic conductivity (synonym: permeability; Ks from here on), because it is a sensitive indicator for soil disturbances. My general objective was to quantify the effects of the regional natural and human disturbances on the saturated hydraulic conductivity and to describe the resulting spatial-temporal patterns. The main hypotheses were: 1) disturbances cause an apparent displacement of the less permeable soil layer towards the surface, either due to a loss of the permeable surface soil after land-sliding, or as a consequence of the surface soil compaction under cattle pastures; 2) ‘recovery’ from disturbance, either because of landslide re-vegetation or because of secondary succession after pasture abandonment, involves an apparent displacement of the less permeable layer back towards the original depth an 3) disturbances cause a simplification of the Ks spatial structure, i.e. the spatially dependent random variation diminishes; the subsequent recovery entails the re-establishment of the original structure. In my first study, I developed a synthesis of recent geostatistical research regarding its applicability to soil hydraulic data, including exploratory data analysis and variogram estimation techniques; I subsequently evaluated the results in terms of spatial prediction uncertainty. Concerning the exploratory data analysis, my main results were: 1) Gaussian uni- and bivariate distributions of the log-transformed data; 2) the existence of significant local trends; 3) no need for robust estimation; 4) no anisotropic variation. I found partly considerable differences in covariance parameters resulting from different variogram estimation techniques, which, in the framework of spatial prediction, were mainly reflected in the spatial connectivity of the Ks-field. Ignoring the trend component and an arbitrary use of robust estimators, however, would have the most severe consequences in this respect. Regarding variogram modeling, I encouraged restricted maximum likelihood estimation because of its accuracy and independence on the selected lags needed for experimental variograms. The second study dealt with the Ks spatial-temporal pattern in the sequences of natural and man-made disturbances characteristic for the montane rainforest study area. To investigate the disturbance effects both on global means and the spatial structure of Ks, a combined design-and model-based sampling approach was used for field-measurements at soil depths of 12.5, 20, and 50 cm (n=30-150/depth) under landslides of different ages (2 and 8 years), under actively grazed pasture, fallows following pasture abandonment (2 to 25 years of age), and under natural forest. Concerning global means, our main findings were 1) global means of the soil permeability generally decrease with increasing soil depth; 2) no significant Ks differences can be observed among landslides and compared to the natural forest; 3) a distinct permeability decrease of two orders of magnitude occurs after forest conversion to pasture at shallow soil depths, and 4) the slow regeneration process after pasture abandonment requires at least one decade. Regarding the Ks spatial structure, we found that 1) disturbances affect the Ks spatial structure in the topsoil, and 2) the largest differences in spatial patterns are associated with the subsoil permeability. In summary, the regional landslide activity seems to affect soil hydrology to a marginal extend only, which is in contrast to the pronounced drop of Ks after forest conversion. We used this spatial-temporal information combined with local rain intensities to assess the partitioning of rainfall into vertical and lateral flowpaths under undisturbed, disturbed, and regenerating land-cover types in the third study. It turned out that 1) the montane rainforest is characterized by prevailing vertical flowpaths in the topsoil, which can switch to lateral directions below 20 cm depth for a small number of rain events, which may, however, transport a high portion of the annual runoff; 2) similar hydrological flowpaths occur under the landslides except for a somewhat higher probability of impermeable layer formation in the topsoil of a young landslide, and 3) pronounced differences in runoff components can be observed for the human disturbance sequence involving the development of near-surface impeding layers for 24, 44, and 8 % of rain events for pasture, a two-year-old fallow, and a ten-year-old fallow, respectively.
We compute the local spectrum of the magnetic field near a metallic microstructure at finite temperature. Our main focus is on deviations from a plane-layered geometry for which we review the main properties. Arbitrary geometries are handled with the help of numerical calculations based on surface integral equations. The magnetic noise shows a significant polarization anisotropy above flat wires with finite lateral width, in stark contrast to an infinitely wide wire. Within the limits of a two-dimensional setting, our results provide accurate estimates for loss and dephasing rates in so-called `atom chip traps' based on metallic wires. A simple approximation based on the incoherent summation of local current elements gives qualitative agreement with the numerics, but fails to describe current correlations among neighboring objects.
The mammalian brain is, with its numerous neural elements and structured complex connectivity, one of the most complex systems in nature. Recently, large-scale corticocortical connectivities, both structural and functional, have received a great deal of research attention, especially using the approach of complex networks. Here, we try to shed some light on the relationship between structural and functional connectivities by studying synchronization dynamics in a realistic anatomical network of cat cortical connectivity. We model the cortical areas by a subnetwork of interacting excitable neurons (multilevel model) and by a neural mass model (population model). With weak couplings, the multilevel model displays biologically plausible dynamics and the synchronization patterns reveal a hierarchical cluster organization in the network structure. We can identify a group of brain areas involved in multifunctional tasks by comparing the dynamical clusters to the topological communities of the network. With strong couplings of multilevel model and by using neural mass model, the dynamics are characterized by well-defined oscillations. The synchronization patterns are mainly determined by the node intensity (total input strengths of a node); the detailed network topology is of secondary importance. The biologically improved multilevel model exhibits similar dynamical patterns in the two regimes. Thus, the study of synchronization in a multilevel complex network model of cortex can provide insights into the relationship between network topology and functional organization of complex brain networks.
[1] Observations of hydrological response often exhibit considerable scatter that is difficult to interpret. In this paper, we examine runoff production of 53 sprinkling experiments on the water-repellent soils in the southern Alps of Switzerland; simulated plot scale tracer transport in the macroporous soils at the Weiherbach site, Germany; and runoff generation data from the 2.3-km(2) Tannhausen catchment, Germany, that has cracking soils. The response at the three sites is highly dependent on the initial soil moisture state as a result of the threshold dynamics of the systems. A simple statistical model of threshold behavior is proposed to help interpret the scatter in the observations. Specifically, the model portrays how the inherent macrostate uncertainty of initial soil moisture translates into the scatter of the observed system response. The statistical model is then used to explore the asymptotic pattern of predictability when increasing the number of observations, which is normally not possible in a field study. Although the physical and chemical mechanisms of the processes at the three sites are different, the predictability patterns are remarkably similar. Predictability is smallest when the system state is close to the threshold and increases as the system state moves away from it. There is inherent uncertainty in the response data that is not measurement error but is related to the observability of the initial conditions.
Rolle der GTPase ARFRP1 für die Golgi-Funktion und die Differenzierung epithelialer Zellen des Darms
(2007)
CAMPHOR: A GOOD MODEL FOR ILLUSTRATING NMR TECHNIQUES. The use of Nuclear Magnetic Resonance spectroscopy to establish the three-dimensional structures of molecules is an important component of modern Chemistry courses. The combination of techniques that can be used for this purpose is conveniently illustrated by their application to the camphor molecule. This paper presents applications of several techniques used in NMR spectral interpretation in an increasing order of complexity. The result of individual experiments is illustrated in order to familiarize the user with the way connectivity through bonds and through space is established from 1D/2D-NMR spectra and molecular stereochemistry is determined from different NMR experiments