20 results
Search Results
Now showing 1 - 10 of 20
- 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.
- 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.
- 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.
- ItemDynamical network size estimation from local observations([London] : IOP, 2020) Tang, Xiuchuan; Huo, Wei; Yuan, Ye; Li, Xiuting; Shi, Ling; Kurths, JürgenHere we present a method to estimate the total number of nodes of a network using locally observed response dynamics. The algorithm has the following advantages: (a) it is data-driven. Therefore it does not require any prior knowledge about the model; (b) it does not need to collect measurements from multiple stimulus; and (c) it is distributed as it uses local information only, without any prior information about the global network. Even if only a single node is measured, the exact network size can be correctly estimated using a single trajectory. The proposed algorithm has been applied to both linear and nonlinear networks in simulation, illustrating the applicability to real-world physical networks. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
- ItemHow to Optimize the Supply and Allocation of Medical Emergency Resources During Public Health Emergencies(Lausanne : Frontiers Media, 2020) Wang, Chunyu; Deng, Yue; Yuan, Ziheng; Zhang, Chijun; Zhang, Fan; Cai, Qing; Gao, Chao; Kurths, JürgenThe solutions to the supply and allocation of medical emergency resources during public health emergencies greatly affect the efficiency of epidemic prevention and control. Currently, the main problem in computational epidemiology is how the allocation scheme should be adjusted in accordance with epidemic trends to satisfy the needs of population coverage, epidemic propagation prevention, and the social allocation balance. More specifically, the metropolitan demand for medical emergency resources varies depending on different local epidemic situations. It is therefore difficult to satisfy all objectives at the same time in real applications. In this paper, a data-driven multi-objective optimization method, called as GA-PSO, is proposed to address such problem. It adopts the one-way crossover and mutation operations to modify the particle updating framework in order to escape the local optimum. Taking the megacity Shenzhen in China as an example, experiments show that GA-PSO effectively balances different objectives and generates a feasible allocation strategy. Such a strategy does not only support the decision-making process of the Shenzhen center in terms of disease control and prevention, but it also enables us to control the potential propagation of COVID-19 and other epidemics. © Copyright © 2020 Wang, Deng, Yuan, Zhang, Zhang, Cai, Gao and Kurths.
- ItemReconstructing complex system dynamics from time series: a method comparison([London] : IOP, 2020) Hassanibesheli, Forough; Boers, Niklas; Kurths, JürgenModeling complex systems with large numbers of degrees of freedom has become a grand challenge over the past decades. In many situations, only a few variables are actually observed in terms of measured time series, while the majority of variables - which potentially interact with the observed ones - remain hidden. A typical approach is then to focus on the comparably few observed, macroscopic variables, assuming that they determine the key dynamics of the system, while the remaining ones are represented by noise. This naturally leads to an approximate, inverse modeling of such systems in terms of stochastic differential equations (SDEs), with great potential for applications from biology to finance and Earth system dynamics. A well-known approach to retrieve such SDEs from small sets of observed time series is to reconstruct the drift and diffusion terms of a Langevin equation from the data-derived Kramers-Moyal (KM) coefficients. For systems where interactions between the observed and the unobserved variables are crucial, the Mori-Zwanzig formalism (MZ) allows to derive generalized Langevin equations that contain non-Markovian terms representing these interactions. In a similar spirit, the empirical model reduction (EMR) approach has more recently been introduced. In this work we attempt to reconstruct the dynamical equations of motion of both synthetical and real-world processes, by comparing these three approaches in terms of their capability to reconstruct the dynamics and statistics of the underlying systems. Through rigorous investigation of several synthetical and real-world systems, we confirm that the performance of the three methods strongly depends on the intrinsic dynamics of the system at hand. For instance, statistical properties of systems exhibiting weak history-dependence but strong state-dependence of the noise forcing, can be approximated better by the KM method than by the MZ and EMR approaches. In such situations, the KM method is of a considerable advantage since it can directly approximate the state-dependent noise. However, limitations of the KM approximation arise in cases where non-Markovian effects are crucial in the dynamics of the system. In these situations, our numerical results indicate that methods that take into account interactions between observed and unobserved variables in terms of non-Markovian closure terms (i.e., the MZ and EMR approaches), perform comparatively better. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft
- ItemComplex systems approaches for Earth system data analysis(Bristol : IOP Publ., 2021) Boers, Niklas; Kurths, Jürgen; Marwan, NorbertComplex systems can, to a first approximation, be characterized by the fact that their dynamics emerging at the macroscopic level cannot be easily explained from the microscopic dynamics of the individual constituents of the system. This property of complex systems can be identified in virtually all natural systems surrounding us, but also in many social, economic, and technological systems. The defining characteristics of complex systems imply that their dynamics can often only be captured from the analysis of simulated or observed data. Here, we summarize recent advances in nonlinear data analysis of both simulated and real-world complex systems, with a focus on recurrence analysis for the investigation of individual or small sets of time series, and complex networks for the analysis of possibly very large, spatiotemporal datasets. We review and explain the recent success of these two key concepts of complexity science with an emphasis on applications for the analysis of geoscientific and in particular (palaeo-) climate data. In particular, we present several prominent examples where challenging problems in Earth system and climate science have been successfully addressed using recurrence analysis and complex networks. We outline several open questions for future lines of research in the direction of data-based complex system analysis, again with a focus on applications in the Earth sciences, and suggest possible combinations with suitable machine learning approaches. Beyond Earth system analysis, these methods have proven valuable also in many other scientific disciplines, such as neuroscience, physiology, epidemics, or engineering.
- ItemParticle dynamics and transport enhancement in a confined channel with position-dependent diffusivity([London] : IOP, 2020) Li, Yongge; Mei, Ruoxing; Xu, Yong; Kurths, Jürgen; Duan, Jinqiao; Metzler, RalfThis work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D 0), as well as a low (D m) and a high (D d) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D m will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d, a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D m, a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two- or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed. © 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.