Early warning of the Indian Ocean Dipole using climate network analysis.

SignificanceThe Indian Ocean Dipole (IOD), an air-sea coupled phenomenon over the tropical Indian Ocean, has substantial impacts on the climate, ecosystems, and society. Due to the winter predictability barrier, however, a reliable prediction of the IOD has been limited to 3 or 4 mo in advance. Our work approaches this problem from a new data-driven perspective: the climate network analysis. Using this network-based method, an efficient early warning signal for the IOD event was revealed in boreal winter. Our approach can correctly predict the IOD events one calendar year in advance (from December of the previous year) with a hit rate of higher than 70%, which strongly outperforms current dynamic models.

Effects of dynamical and structural modifications on synchronization.

Synchronization is a phenomenon of the collective behavior of coupled oscillators and involves the detailed interplay of the intrinsic frequencies of the oscillators, the underlying topological features of their interaction network, and external perturbations. In this work we investigate, in the strong coupling regime, the response of a system to external perturbations of its natural frequencies and network modifications. Our investigation relies on two performance measures (one for phases and the other for frequencies) and a spectral perturbation analysis. Given strongly localized perturbations in time, corresponding to the dominant eigenmode of the weighted Laplacian matrix of the network, we present a sufficient condition for the maximization of the system's stability, along with analytical results for the effects of structural perturbations on the system's response. A number of simulations are conducted to illustrate the theory presented.

Transports in a rough ratchet induced by Lévy noises.

We study the transport of a particle subjected to a Lévy noise in a rough ratchet potential which is constructed by superimposing a fast oscillating trigonometric function on a common ratchet background. Due to the superposition of roughness, the transport process exhibits significantly different properties under the excitation of Lévy noises compared to smooth cases. The influence of the roughness on the directional motion is explored by calculating the mean velocities with respect to the Lévy stable index α and the spatial asymmetry parameter q of the ratchet. Variations in the splitting probability have been analyzed to illustrate how roughness affects the transport. In addition, we have examined the influences of roughness on the mean first passage time to know when it accelerates or slows down the first passage process. We find that the roughness can lead to a fast reduction of the absolute value of the mean velocity for small α, however the influence is small for large α. We have illustrated that the ladder-like roughness on the potential wall increases the possibility for particles to cross the gentle side of the ratchet, which results in an increase of the splitting probability to right for the right-skewed ratchet potential. Although the roughness increases the corresponding probability, it does not accelerate the mean first passage process to the right adjacent well. Our results show that the influences of roughness on the mean first passage time are sensitive to the combination of q and α. Hence, the proper q and α can speed up the passage process, otherwise it will slow down it.

Entropy-based complexity measures for gait data of patients with Parkinson's disease.

Shannon, Kullback-Leibler, and Klimontovich's renormalized entropies are applied as three different complexity measures on gait data of patients with Parkinson's disease (PD) and healthy control group. We show that the renormalized entropy of variability of total reaction force of gait is a very efficient tool to compare patients with respect to disease severity. Moreover, it is a good risk predictor such that the sensitivity, i.e., the percentage of patients with PD who are correctly identified as having PD, increases from 25% to 67% while the Hoehn-Yahr stage increases from 2.5 to 3.0 (this stage goes from 0 to 5 as the disease severity increases). The renormalized entropy method for stride time variability of gait is found to correctly identify patients with a sensitivity of 80%, while the Shannon entropy and the Kullback-Leibler relative entropy can do this with a sensitivity of only 26.7% and 13.3%, respectively.

Method for reconstructing nonlinear modes with adaptive structure from multidimensional data.

We present a detailed description of a new approach for the extraction of principal nonlinear dynamical modes (NDMs) from high-dimensional data. The method of NDMs allows the joint reconstruction of hidden scalar time series underlying the observational variability together with a transformation mapping these time series to the physical space. Special Bayesian prior restrictions on the solution properties provide an efficient recognition of spatial patterns evolving in time and characterized by clearly separated time scales. In particular, we focus on adaptive properties of the NDMs and demonstrate for model examples of different complexities that, depending on the data properties, the obtained NDMs may have either substantially nonlinear or linear structures. It is shown that even linear NDMs give us more information about the internal system dynamics than the traditional empirical orthogonal function decomposition. The performance of the method is demonstrated on two examples. First, this approach is successfully tested on a low-dimensional problem to decode a chaotic signal from nonlinearly entangled time series with noise. Then, it is applied to the analysis of 250-year preindustrial control run of the INMCM4.0 global climate model. There, a set of principal modes of different nonlinearities is found capturing the internal model variability on the time scales from annual to multidecadal.

Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition.

Currently, causes of the middle Pleistocene transition (MPT) - the onset of large-amplitude glacial variability with 100 kyr time scale instead of regular 41 kyr cycles before - are a challenging puzzle in Paleoclimatology. Here we show how a Bayesian data analysis based on machine learning approaches can help to reveal the main mechanisms underlying the Pleistocene variability, which most likely explain proxy records and can be used for testing existing theories. We construct a Bayesian data-driven model from benthic δ18O records (LR04 stack) accounting for the main factors which may potentially impact climate of the Pleistocene: internal climate dynamics, gradual trends, variations of insolation, and millennial variability. In contrast to some theories, we uncover that under long-term trends in climate, the strong glacial cycles have appeared due to internal nonlinear oscillations induced by millennial noise. We find that while the orbital Milankovitch forcing does not matter for the MPT onset, the obliquity oscillation phase-locks the climate cycles through the meridional gradient of insolation.

Rapidly switched random links enhance spatiotemporal regularity.

We investigate the spatiotemporal properties of a lattice of chaotic maps whose coupling connections are rewired to random sites with probability p . Keeping p constant, we change the random links at different frequencies in order to discern the effect (if any) of the time dependence of the links. We observe two different regimes in this network: (i) when the network is rewired slowly, namely, when the random connections are quite static, the dynamics of the network is spatiotemporally chaotic and (ii) when these random links are switched around fast, namely, the network is rewired frequently, one obtains a spatiotemporal fixed point over a large range of coupling strengths. We provide evidence of a sharp transition from a globally attracting spatiotemporal fixed point to spatiotemporal chaos as the rewiring frequency is decreased. Thus, in addition to geometrical properties such as the fraction of random links in the network, dynamical information on the time dependence of these links is crucial in determining the spatiotemporal properties of complex dynamical networks.

Application of optical coherence tomography for in vivo monitoring of the meningeal lymphatic vessels during opening of blood-brain barrier: mechanisms of brain clearing.

The meningeal lymphatic vessels were discovered 2 years ago as the drainage system involved in the mechanisms underlying the clearance of waste products from the brain. The blood-brain barrier (BBB) is a gatekeeper that strongly controls the movement of different molecules from the blood into the brain. We know the scenarios during the opening of the BBB, but there is extremely limited information on how the brain clears the substances that cross the BBB. Here, using the model of sound-induced opening of the BBB, we clearly show how the brain clears dextran after it crosses the BBB via the meningeal lymphatic vessels. We first demonstrate successful application of optical coherence tomography (OCT) for imaging of the lymphatic vessels in the meninges after opening of the BBB, which might be a new useful strategy for noninvasive analysis of lymphatic drainage in daily clinical practice. Also, we give information about the depth and size of the meningeal lymphatic vessels in mice. These new fundamental data with the applied focus on the OCT shed light on the mechanisms of brain clearance and the role of lymphatic drainage in these processes that could serve as an informative platform for a development of therapy and diagnostics of diseases associated with injuries of the BBB such as stroke, brain trauma, glioma, depression, or Alzheimer disease.

Principal nonlinear dynamical modes of climate variability.

We suggest a new nonlinear expansion of space-distributed observational time series. The expansion allows constructing principal nonlinear manifolds holding essential part of observed variability. It yields low-dimensional hidden time series interpreted as internal modes driving observed multivariate dynamics as well as their mapping to a geographic grid. Bayesian optimality is used for selecting relevant structure of nonlinear transformation, including both the number of principal modes and degree of nonlinearity. Furthermore, the optimal characteristic time scale of the reconstructed modes is also found. The technique is applied to monthly sea surface temperature (SST) time series having a duration of 33 years and covering the globe. Three dominant nonlinear modes were extracted from the time series: the first efficiently separates the annual cycle, the second is responsible for ENSO variability, and combinations of the second and the third modes explain substantial parts of Pacific and Atlantic dynamics. A relation of the obtained modes to decadal natural climate variability including current hiatus in global warming is exhibited and discussed.

Synchronization in time-varying networks.

We study the stability of the synchronized state in time-varying complex networks using the concept of basin stability, which is a nonlocal and nonlinear measure of stability that can be easily applied to high-dimensional systems [P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Phys. 9, 89 (2013)]. The time-varying character is included by stochastically rewiring each link with the average frequency f. We find that the time taken to reach synchronization is lowered and the stability range of the synchronized state increases considerably in dynamic networks. Further we uncover that small-world networks are much more sensitive to link changes than random ones, with the time-varying character of the network having a significant effect at much lower rewiring frequencies. At very high rewiring frequencies, random networks perform better than small-world networks and the synchronized state is stable over a much wider window of coupling strengths. Lastly we show that the stability range of the synchronized state may be quite different for small and large perturbations, and so the linear stability analysis and the basin stability criterion provide complementary indicators of stability.

Cardio-respiratory coordination increases during sleep apnea.

Cardiovascular diseases are the main source of morbidity and mortality in the United States with costs of more than $170 billion. Repetitive respiratory disorders during sleep are assumed to be a major cause of these diseases. Therefore, the understanding of the cardio-respiratory regulation during these events is of high public interest. One of the governing mechanisms is the mutual influence of the cardiac and respiratory oscillations on their respective onsets, the cardio-respiratory coordination (CRC). We analyze this mechanism based on nocturnal measurements of 27 males suffering from obstructive sleep apnea syndrome. Here we find, by using an advanced analysis technique, the cardiogram, not only that the occurrence of CRC is significantly more frequent during respiratory sleep disturbances than in normal respiration (p-value<10(-51)) but also more frequent after these events (p-value<10(-15)). Especially, the latter finding contradicts the common assumption that spontaneous CRC can only be observed in epochs of relaxed conditions, while our newly discovered epochs of CRC after disturbances are characterized by high autonomic stress. Our findings on the connection between CRC and the appearance of sleep-disordered events require a substantial extension of the current understanding of obstructive sleep apneas and hypopneas.

Optimal length transportation hypothesis to model proteasome product size distribution.

This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.