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- ItemPath integral solutions for n-dimensional stochastic differential equations under α-stable Lévy excitation(College Park, Md : [Verlag nicht ermittelbar], 2023) Zan, Wanrong; Xu, Yong; Kurths, JürgenIn this paper, the path integral solutions for a general n-dimensional stochastic differential equations (SDEs) with α-stable Lévy noise are derived and verified. Firstly, the governing equations for the solutions of n-dimensional SDEs under the excitation of α-stable Lévy noise are obtained through the characteristic function of stochastic processes. Then, the short-time transition probability density function of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski (CKS) equation and the characteristic function, and its correctness is demonstrated by proving that it satisfies the governing equation of the solution of the SDE, which is also called the Fokker-Planck-Kolmogorov equation. Besides, illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method, and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.
- ItemEarly Warning of the Pacific Decadal Oscillation Phase Transition Using Complex Network Analysis(Hoboken, NJ : Wiley, 2021) Lu, Zhenghui; Yuan, Naiming; Yang, Qing; Ma, Zhuguo; Kurths, JürgenObtaining an efficient prediction of the Pacific Decadal Oscillation (PDO) phase transition is a worldwide challenge. Here, we employed the climate network analysis to uncover early warning signals prior to a PDO phase transition. This way an examination of cooperative behavior in the PDO region revealed an enhanced signal that propagated from the western Pacific to the northwest coast of North America. The detection of this signal corresponds very well to the time when the upper ocean heat content in the off-equatorial northwestern tropical Pacific reaches a threshold, in which case a PDO phase transition may be expected with the arising of the next El Ni urn:x-wiley:00948276:media:grl61986:grl61986-math-0001o/La Niurn:x-wiley:00948276:media:grl61986:grl61986-math-0002 a event. The objectively detected early warning signal successfully forewarned all the six PDO phase transitions from the 1890–2000, and also underpinned the possible PDO phase transition around 2015, which may be triggered by the strong El Niurn:x-wiley:00948276:media:grl61986:grl61986-math-0003o event in 2015–2016.
- ItemBasin stability and limit cycles in a conceptual model for climate tipping cascades([London] : IOP, 2020) Wunderling, Nico; Gelbrecht, Maximilian; Winkelmann, Ricarda; Kurths, Jürgen; Donges, Jonathan F.Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and their interactions in a conceptual and easily extendable framework: the Greenland Ice Sheets (GIS) and West Antarctic Ice Sheets, the Atlantic meridional overturning circulation (AMOC), the El–Niño Southern Oscillation and the Amazon rainforest. In this nonlinear and multistable system, we perform a basin stability analysis to detect its stable states and their associated Earth system resilience. By combining these two methodologies with a large-scale Monte Carlo approach, we are able to propagate the many uncertainties associated with the critical temperature thresholds and the interaction strengths of the tipping elements. Using this approach, we perform a system-wide and comprehensive robustness analysis with more than 3.5 billion ensemble members. Further, we investigate dynamic regimes where some of the states lose stability and oscillations appear using a newly developed basin bifurcation analysis methodology. Our results reveal that the state of four or five tipped elements has the largest basin volume for large levels of global warming beyond 4 °C above pre-industrial climate conditions, representing a highly undesired state where a majority of the tipping elements reside in the transitioned regime. For lower levels of warming, states including disintegrated ice sheets on west Antarctica and Greenland have higher basin volume than other state configurations. Therefore in our model, we find that the large ice sheets are of particular importance for Earth system resilience. We also detect the emergence of limit cycles for 0.6% of all ensemble members at rare parameter combinations. Such limit cycle oscillations mainly occur between the GIS and AMOC (86%), due to their negative feedback coupling. These limit cycles point to possibly dangerous internal modes of variability in the climate system that could have played a role in paleoclimatic dynamics such as those unfolding during the Pleistocene ice age cycles.
- ItemPhotomodulation of lymphatic delivery of liposomes to the brain bypassing the blood-brain barrier: new perspectives for glioma therapy(Berlin : de Gruyter, 2021) Semyachkina-Glushkovskaya, Oxana; Fedosov, Ivan; Shirokov, Alexander; Vodovozova, Elena; Alekseeva, Anna; Khorovodov, Alexandr; Blokhina, Inna; Terskov, Andrey; Mamedova, Aysel; Klimova, Maria; Dubrovsky, Alexander; Ageev, Vasily; Agranovich, Ilana; Vinnik, Valeria; Tsven, Anna; Sokolovski, Sergey; Rafailov, Edik; Penzel, Thomas; Kurths, JürgenThe blood-brain barrier (BBB) has a significant contribution to the protection of the central nervous system (CNS). However, it also limits the brain drug delivery and thereby complicates the treatment of CNS diseases. The development of safe methods for an effective delivery of medications and nanocarriers to the brain can be a revolutionary step in the overcoming this limitation. Here, we report the unique properties of the lymphatic system to deliver tracers and liposomes to the brain meninges, brain tissues, and glioma in rats. Using a quantum-dot-based 1267 nm laser (for photosensitizer-free generation of singlet oxygen), we clearly demonstrate photostimulation of lymphatic delivery of liposomes to glioma as well as lymphatic clearance of liposomes from the brain. These pilot findings open promising perspectives for photomodulation of lymphatic delivery of drugs and nanocarriers to the brain pathology bypassing the BBB. The lymphatic “smart” delivery of liposomes with antitumor drugs in the new brain tumor branches might be a breakthrough strategy for the therapy of gliomas.
- ItemPhotodynamic Opening of the Blood–Brain Barrier and the Meningeal Lymphatic System: The New Niche in Immunotherapy for Brain Tumors(Basel : MDPI, 2022) Semyachkina-Glushkovskaya, Oxana; Terskov, Andrey; Khorovodov, Alexander; Telnova, Valeria; Blokhina, Inna; Saranceva, Elena; Kurths, JürgenPhotodynamic therapy (PDT) is a promising add-on therapy to the current standard of care for patients with glioblastoma (GBM). The traditional explanation of the anti-cancer PDT effects involves the PDT-induced generation of a singlet oxygen in the GBM cells, which causes tumor cell death and microvasculature collapse. Recently, new vascular mechanisms of PDT associated with opening of the blood–brain barrier (OBBB) and the activation of functions of the meningeal lymphatic vessels have been discovered. In this review, we highlight the emerging trends and future promises of immunotherapy for brain tumors and discuss PDT-OBBB as a new niche and an important informative platform for the development of innovative pharmacological strategies for the modulation of brain tumor immunity and the improvement of immunotherapy for GBM.
- ItemCommunicating sentiment and outlook reverses inaction against collective risks(Washington, DC : National Acad. of Sciences, 2020) Wang, Zhen; Jusup, Marko; Guo, Hao; Shi, Lei; Geček, Sunčana; Anand, Madhur; Perc, Matjaž; Bauch, Chris T.; Kurths, Jürgen; Boccaletti, Stefano; Schellnhuber, Hans JoachimCollective risks permeate society, triggering social dilemmas in which working toward a common goal is impeded by selfish interests. One such dilemma is mitigating runaway climate change. To study the social aspects of climate-change mitigation, we organized an experimental game and asked volunteer groups of three different sizes to invest toward a common mitigation goal. If investments reached a preset target, volunteers would avoid all consequences and convert their remaining capital into monetary payouts. In the opposite case, however, volunteers would lose all their capital with 50% probability. The dilemma was, therefore, whether to invest one's own capital or wait for others to step in. We find that communicating sentiment and outlook helps to resolve the dilemma by a fundamental shift in investment patterns. Groups in which communication is allowed invest persistently and hardly ever give up, even when their current investment deficits are substantial. The improved investment patterns are robust to group size, although larger groups are harder to coordinate, as evidenced by their overall lower success frequencies. A clustering algorithm reveals three behavioral types and shows that communication reduces the abundance of the free-riding type. Climate-change mitigation, however, is achieved mainly by cooperator and altruist types stepping up and increasing contributions as the failure looms. Meanwhile, contributions from free riders remain flat throughout the game. This reveals that the mechanisms behind avoiding collective risks depend on an interaction between behavioral type, communication, and timing.
- ItemEpidemics with mutating infectivity on small-world networks([London] : Macmillan Publishers Limited, part of Springer Nature, 2020) Rüdiger, Sten; Plietzsch, Anton; Sagués, Francesc; Sokolov, Igor M.; Kurths, JürgenEpidemics and evolution of many pathogens occur on similar timescales so that their dynamics are often entangled. Here, in a first step to study this problem theoretically, we analyze mutating pathogens spreading on simple SIR networks with grid-like connectivity. We have in mind the spatial aspect of epidemics, which often advance on transport links between hosts or groups of hosts such as cities or countries. We focus on the case of mutations that enhance an agent’s infection rate. We uncover that the small-world property, i.e., the presence of long-range connections, makes the network very vulnerable, supporting frequent supercritical mutations and bringing the network from disease extinction to full blown epidemic. For very large numbers of long-range links, however, the effect reverses and we find a reduced chance for large outbreaks. We study two cases, one with discrete number of mutational steps and one with a continuous genetic variable, and we analyze various scaling regimes. For the continuous case we derive a Fokker-Planck-like equation for the probability density and solve it for small numbers of shortcuts using the WKB approximation. Our analysis supports the claims that a potentiating mutation in the transmissibility might occur during an epidemic wave and not necessarily before its initiation. © 2020, The Author(s).
- ItemPredicting the data structure prior to extreme events from passive observables using echo state network(Lausanne : Frontiers Media, 2022) Banerjee, Abhirup; Mishra, Arindam; Dana, Syamal K.; Hens, Chittaranjan; Kapitaniak, Tomasz; Kurths, Jürgen; Marwan, NorbertExtreme events are defined as events that largely deviate from the nominal state of the system as observed in a time series. Due to the rarity and uncertainty of their occurrence, predicting extreme events has been challenging. In real life, some variables (passive variables) often encode significant information about the occurrence of extreme events manifested in another variable (active variable). For example, observables such as temperature, pressure, etc., act as passive variables in case of extreme precipitation events. These passive variables do not show any large excursion from the nominal condition yet carry the fingerprint of the extreme events. In this study, we propose a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable that leads to an extreme event using information from the passive variable. An appropriate threshold height of events is a prerequisite for detecting extreme events and improving the skill of their prediction. We demonstrate that the magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series affect the prediction skill. Quantitatively, we confirm this using a metric describing the mean phase difference between the input time signals, which decreases when the magnitude of the extreme event is relatively higher, thereby increasing the predictability skill.
- ItemNeural partial differential equations for chaotic systems([London] : IOP, 2021) Gelbrecht, Maximilian; Boers, Niklas; Kurths, JürgenWhen predicting complex systems one typically relies on differential equation which can often be incomplete, missing unknown influences or higher order effects. By augmenting the equations with artificial neural networks we can compensate these deficiencies. We show that this can be used to predict paradigmatic, high-dimensional chaotic partial differential equations even when only short and incomplete datasets are available. The forecast horizon for these high dimensional systems is about an order of magnitude larger than the length of the training data.
- ItemMonte Carlo basin bifurcation analysis([London] : IOP, 2020) Gelbrecht, Maximilian; Kurths, Jürgen; Hellmann, FrankMany high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds-Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart-Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.