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- ItemTiming cellular decision making under noise via cell-cell communication(San Francisco, CA : Public Library of Science (PLoS), 2009) Koseska, A.; Zaikin, A.; Kurths, J.; García-Ojalvo, J.Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words, the summation performed by the cell population would average out the noise and reduce its detrimental impact.
- ItemDigital IIR filters design using differential evolution algorithm with a controllable probabilistic population size(San Francisco, CA : Public Library of Science (PLoS), 2012) Zhu, W.; Fang, J.-A.; Tang, Y.; Zhang, W.; Du, W.Design of a digital infinite-impulse-response (IIR) filter is the process of synthesizing and implementing a recursive filter network so that a set of prescribed excitations results a set of desired responses. However, the error surface of IIR filters is usually non-linear and multi-modal. In order to find the global minimum indeed, an improved differential evolution (DE) is proposed for digital IIR filter design in this paper. The suggested algorithm is a kind of DE variants with a controllable probabilistic (CPDE) population size. It considers the convergence speed and the computational cost simultaneously by nonperiodic partial increasing or declining individuals according to fitness diversities. In addition, we discuss as well some important aspects for IIR filter design, such as the cost function value, the influence of (noise) perturbations, the convergence rate and successful percentage, the parameter measurement, etc. As to the simulation result, it shows that the presented algorithm is viable and comparable. Compared with six existing State-of-the-Art algorithms-based digital IIR filter design methods obtained by numerical experiments, CPDE is relatively more promising and competitive.
- ItemNoise-Aided Logic in an Electronic Analog of Synthetic Genetic Networks(San Francisco, CA : Public Library of Science (PLoS), 2013) Hellen, E.H.; Dana, S.K.; Kurths, J.; Kehler, E.; Sinha, S.We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.
- ItemLévy noise improves the electrical activity in a neuron under electromagnetic radiation(San Francisco, CA : Public Library of Science (PLoS), 2017) Wu, J.; Xu, Y.; Ma, J.As the fluctuations of the internal bioelectricity of nervous system is various and complex, the external electromagnetic radiation induced by magnet flux on membrane can be described by the non-Gaussian type distribution of Levy noise. Thus, the electrical activities in an improved Hindmarsh-Rose model excited by the external electromagnetic radiation of Levy noise are investigated and some interesting modes of the electrical activities are exhibited. The external electromagnetic radiation of Levy noise leads to the mode transition of the electrical activities and spatial phase, such as from the rest state to the firing state, from the spiking state to the spiking state with more spikes, and from the spiking state to the bursting state. Then the time points of the firing state versus Levy noise intensity are depicted. The increasing of Levy noise intensity heightens the neuron firing. Also the stationary probability distribution functions of the membrane potential of the neuron induced by the external electromagnetic radiation of Levy noise with different intensity, stability index and skewness papremeters are analyzed. Moreover, through the positive largest Lyapunov exponent, the parameter regions of chaotic electrical mode of the neuron induced by the external electromagnetic radiation of Levy noise distribution are detected.
- ItemBayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition([London] : Macmillan Publishers Limited, part of Springer Nature, 2019) Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Kurths, Juergen; Feigin, AlexanderCurrently, 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.
- ItemReconstruction of Complex Network based on the Noise via QR Decomposition and Compressed Sensing(London : Nature Publishing Group, 2017) Li, L.; Xu, D.; Peng, H.; Kurths, J.; Yang, Y.It is generally known that the states of network nodes are stable and have strong correlations in a linear network system. We find that without the control input, the method of compressed sensing can not succeed in reconstructing complex networks in which the states of nodes are generated through the linear network system. However, noise can drive the dynamics between nodes to break the stability of the system state. Therefore, a new method integrating QR decomposition and compressed sensing is proposed to solve the reconstruction problem of complex networks under the assistance of the input noise. The state matrix of the system is decomposed by QR decomposition. We construct the measurement matrix with the aid of Gaussian noise so that the sparse input matrix can be reconstructed by compressed sensing. We also discover that noise can build a bridge between the dynamics and the topological structure. Experiments are presented to show that the proposed method is more accurate and more efficient to reconstruct four model networks and six real networks by the comparisons between the proposed method and only compressed sensing. In addition, the proposed method can reconstruct not only the sparse complex networks, but also the dense complex networks.
- ItemMetastability for discontinuous dynamical systems under Lévy noise: Case study on Amazonian Vegetation(London : Nature Publishing Group, 2017) Serdukova, L.; Zheng, Y.; Duan, J.; Kurths, J.For the tipping elements in the Earth's climate system, the most important issue to address is how stable is the desirable state against random perturbations. Extreme biotic and climatic events pose severe hazards to tropical rainforests. Their local effects are extremely stochastic and difficult to measure. Moreover, the direction and intensity of the response of forest trees to such perturbations are unknown, especially given the lack of efficient dynamical vegetation models to evaluate forest tree cover changes over time. In this study, we consider randomness in the mathematical modelling of forest trees by incorporating uncertainty through a stochastic differential equation. According to field-based evidence, the interactions between fires and droughts are a more direct mechanism that may describe sudden forest degradation in the south-eastern Amazon. In modeling the Amazonian vegetation system, we include symmetric α-stable Lévy perturbations. We report results of stability analysis of the metastable fertile forest state. We conclude that even a very slight threat to the forest state stability represents Ĺevy noise with large jumps of low intensity, that can be interpreted as a fire occurring in a non-drought year. During years of severe drought, high-intensity fires significantly accelerate the transition between a forest and savanna state.
- ItemInfluence of Anthropogenic Climate Change on Planetary Wave Resonance and Extreme Weather Events(London : Nature Publishing Group, 2017) Mann, M.E.; Rahmstorf, S.; Kornhuber, K.; Steinman, B.A.; Miller, S.K.; Coumou, D.Persistent episodes of extreme weather in the Northern Hemisphere summer have been shown to be associated with the presence of high-amplitude quasi-stationary atmospheric Rossby waves within a particular wavelength range (zonal wavenumber 6-8). The underlying mechanistic relationship involves the phenomenon of quasi-resonant amplification (QRA) of synoptic-scale waves with that wavenumber range becoming trapped within an effective mid-latitude atmospheric waveguide. Recent work suggests an increase in recent decades in the occurrence of QRA-favorable conditions and associated extreme weather, possibly linked to amplified Arctic warming and thus a climate change influence. Here, we isolate a specific fingerprint in the zonal mean surface temperature profile that is associated with QRA-favorable conditions. State-of-the-art ("CMIP5") historical climate model simulations subject to anthropogenic forcing display an increase in the projection of this fingerprint that is mirrored in multiple observational surface temperature datasets. Both the models and observations suggest this signal has only recently emerged from the background noise of natural variability.
- ItemThe Switch in a Genetic Toggle System with Lévy Noise(London : Nature Publishing Group, 2016) Xu, Y.; Li, Y.; Zhang, H.; Li, X.; Kurths, J.
- ItemAveraged recurrence quantification analysis: Method omitting the recurrence threshold choice(Berlin ; Heidelberg : Springer, 2022) Pánis, Radim; Adámek, Karel; Marwan, NorbertRecurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work, we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in the tested data set with different and even very small signal-to-noise ratios of lengths 10 2, 10 3, 10 4, and 10 5. To make the calculations possible, a new effective algorithm was developed for streamlining of the numerical operations on graphics processing unit (GPU).