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Subject of this work is the investigation of generic synchronization phenomena in interacting complex systems. These phenomena are observed, among all, in coupled deterministic chaotic systems. At very weak interactions between individual systems a transition to a weakly coherent behavior of the systems can take place. In coupled continuous time chaotic systems this transition manifests itself with the effect of phase synchronization, in coupled chaotic discrete time systems with the effect of non-vanishing macroscopic mean field. Transition to coherence in a chain of locally coupled oscillators described with phase equations is investigated with respect to the symmetries in the system. It is shown that the reversibility of the system caused by these symmetries results to non-trivial topological properties of trajectories so that the system constructed to be dissipative reveals in a whole parameter range quasi-Hamiltonian features, i.e. the phase volume is conserved on average and Lyapunov exponents come in symmetric pairs. Transition to coherence in an ensemble of globally coupled chaotic maps is described with the loss of stability of the disordered state. The method is to break the self-consistensy of the macroscopic field and to characterize the ensemble in analogy to an amplifier circuit with feedback with a complex linear transfer function. This theory is then generalized for several cases of theoretic interest.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
Geochemical homogeneity in shale is often assumed when tracing subsurface fluids and characterizing sedimentary basins. This study presents measurements of the bulk gas composition, stable isotopes, and noble gas volume fraction and isotopes for shale gas samples collected from gas wells in the Wufeng-Longmaxi Shale, the southern Sichuan Basin, China. The dryness [C-1 /(C-2 + C-3)] ranging from 166.3 to 251.2, combined with delta C-13(1) and delta DC1 that vary from -28.8 to -27.3 parts per thousand and - 153 to -145 parts per thousand, respectively, point to a late mature thermogenic origin of hydrocarbon gas. He-3/He-4 ratios of gas samples are around 0.01 times the air value suggesting dominantly crust-derived He. Ne-21/Ne-22 and Ar-40/Ar-36 ratios of many gas samples are higher than the corresponding air values indicating the mixing of crustal and atmospheric noble gases. Multiple dichotomous patterns are observed in noble gas signatures of forelimb and backlimb samples, and depression and crest samples. Ne-20/Ne-22 ratios of some crest samples are higher than that of depression samples in the backlimb, pointing to the presence of diffusion-driven fractionation that is likely caused by the long-distance migration from depression to crest. Elemental ratios of air-derived noble gas isotopes - Ne-22/Ar-36, Kr-84/Ar-36, and Xe-132/Ar-36 are compared to the recharge water values, suggesting the interactions of oil, gas, and water phases in the shale over geologic time. Forelimb samples generally display older ages than backlimb samples, indicating a larger flux of external radiogenic He-4 due to the higher density of deep faults in the forelimb area caused by the basementinvolved deformation. The basement-involved deformation also causes pore collapse especially in the forelimb leading to a lower porosity that results in a more pristine noble gas signature in the forelimb due to the reduced impact of younger recharge water.
A recent advancement in the field of neuromodulation is to adapt stimulation parameters according to prespecified biomarkers tracked in real-time. These markers comprise short and transient signal features, such as bursts of elevated band power. To capture these features, instantaneous measures of phase and/or amplitude are employed, which inform stimulation adjustment with high temporal specificity. For adaptive neuromodulation it is therefore necessary to precisely estimate a signal's phase and amplitude with minimum delay and in a causal way, i.e. without depending on future parts of the signal. Here we demonstrate a method that utilizes oscillation theory to estimate phase and amplitude in real-time and compare it to a recently proposed causal modification of the Hilbert transform. By simulating real-time processing of human LFP data, we show that our approach almost perfectly tracks offline phase and amplitude with minimum delay and is computationally highly efficient.
The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.