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Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior
Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes.
Extreme Rainfall of the South American Monsoon System: A Dataset Comparison Using Complex Networks
(2015)
In this study, the authors compare six different rainfall datasets for South America with a focus on their representation of extreme rainfall during the monsoon season (December February): the gauge-calibrated TRMM 3B42 V7 satellite product; the near-real-time TRMM 3B42 V7 RT, the GPCP 1 degrees daily (1DD) V1.2 satellite gauge combination product, the Interim ECMWF Re-Analysis (ERA-Interim) product; output of a high-spatial-resolution run of the ECHAM6 global circulation model; and output of the regional climate model Eta. For the latter three, this study can be understood as a model evaluation. In addition to statistical values of local rainfall distributions, the authors focus on the spatial characteristics of extreme rainfall covariability. Since traditional approaches based on principal component analysis are not applicable in the context of extreme events, they apply and further develop methods based on complex network theory. This way, the authors uncover substantial differences in extreme rainfall patterns between the different datasets: (i) The three model-derived datasets yield very different results than the satellite gauge combinations regarding the main climatological propagation pathways of extreme events as well as the main convergence zones of the monsoon system. (ii) Large discrepancies are found for the development of mesoscale convective systems in southeastern South America. (iii) Both TRMM datasets and ECHAM6 indicate a linkage of extreme rainfall events between the central Amazon basin and the eastern slopes of the central Andes, but this pattern is not reproduced by the remaining datasets. The authors' study suggests that none of the three model-derived datasets adequately captures extreme rainfall patterns in South America.
The South American Andes are frequently exposed to intense rainfall events with varying moisture sources and precipitation-forming processes. In this study, we assess the spatiotemporal characteristics and geographical origins of rainfall over the South American continent. Using high-spatiotemporal resolution satellite data (TRMM 3B42 V7), we define four different types of rainfall events based on their (1) high magnitude, (2) long temporal extent, (3) large spatial extent, and (4) high magnitude, long temporal and large spatial extent combined. In a first step, we analyze the spatiotemporal characteristics of these events over the entire South American continent and integrate their impact for the main Andean hydrologic catchments. Our results indicate that events of type 1 make the overall highest contributions to total seasonal rainfall (up to 50%). However, each consecutive episode of the infrequent events of type 4 still accounts for up to 20% of total seasonal rainfall in the subtropical Argentinean plains. In a second step, we employ complex network theory to unravel possibly non-linear and long-ranged climatic linkages for these four event types on the high-elevation Altiplano-Puna Plateau as well as in the main river catchments along the foothills of the Andes. Our results suggest that one to two particularly large squall lines per season, originating from northern Brazil, indirectly trigger large, long-lasting thunderstorms on the Altiplano Plateau. In general, we observe that extreme rainfall in the catchments north of approximately 20 degrees S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of 20 degrees S and the Puna Plateau originates from southeastern South America.
Climatic observables are often correlated across long spatial distances, and extreme events, such as heatwaves or floods, are typically assumed to be related to such teleconnections(1,2). Revealing atmospheric teleconnection patterns and understanding their underlying mechanisms is of great importance for weather forecasting in general and extreme-event prediction in particular(3,4), especially considering that the characteristics of extreme events have been suggested to change under ongoing anthropogenic climate change(5-8). Here we reveal the global coupling pattern of extreme-rainfall events by applying complex-network methodology to high-resolution satellite data and introducing a technique that corrects for multiple-comparison bias in functional networks. We find that the distance distribution of significant connections (P < 0.005) around the globe decays according to a power law up to distances of about 2,500 kilometres. For longer distances, the probability of significant connections is much higher than expected from the scaling of the power law. We attribute the shorter, power-law-distributed connections to regional weather systems. The longer, super-power-law-distributed connections form a global rainfall teleconnection pattern that is probably controlled by upper-level Rossby waves. We show that extreme-rainfall events in the monsoon systems of south-central Asia, east Asia and Africa are significantly synchronized. Moreover, we uncover concise links between south-central Asia and the European and North American extratropics, as well as the Southern Hemisphere extratropics. Analysis of the atmospheric conditions that lead to these teleconnections confirms Rossby waves as the physical mechanism underlying these global teleconnection patterns and emphasizes their crucial role in dynamical tropical-extratropical couplings. Our results provide insights into the function of Rossby waves in creating stable, global-scale dependencies of extreme-rainfall events, and into the potential predictability of associated natural hazards.
We give evidence of frequency entrainment of dominant peaks in the chaotic spectra of two coupled chaotic nonautonomous oscillators. At variance with the autonomous case, the phenomenon is here characterized by the vanishing of a previously positive Lyapunov exponent in the spectrum, which takes place for a broad range of the coupling strength parameter. Such a state is studied also for the case of chaotic oscillators with ill-defined phases due to the absence of a unique center of rotation. Different phase synchronization indicators are used to circumvent this difficulty
During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.
Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question.
We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage.
Despite many previous Studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent alpha 1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves' disease patients (32 females and 4 males; age 30 +/- 1 years, means +/- SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P < 0.001) in alpha 1 (hyperthyroid 1.28 +/- 0.04 versus control 0.91 +/- 0.02), long-term scaling exponent alpha 2 (1.05 +/- 0.02 versus 0.90 +/- 0.01), overall scaling exponent alpha (1.11 +/- 0.02 versus 0.89 +/- 0.01), low frequency power in normalized units (LF%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P < 0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients.
We introduce a modified dynamical optimization coupling scheme to enhance the synchronizability in the scale- free networks as well as to keep uniform and converging intensities during the transition to synchronization. Further, the size of networks that can be synchronizable exceeds by several orders of magnitude the size of unweighted networks.
Higher resilience to climatic disturbances in tropical vegetation exposed to more variable rainfall
(2019)
With ongoing global warming, the amount and frequency of precipitation in the tropics is projected to change substantially. While it has been shown that tropical forests and savannahs are sustained within the same intermediate mean annual precipitation range, the mechanisms that lead to the resilience of these ecosystems are still not fully understood. In particular, the long-term impact of rainfall variability on resilience is as yet unclear. Here we present observational evidence that both tropical forest and savannah exposed to a higher rainfall variability-in particular on interannual scales-during their long-term past are overall more resilient against climatic disturbances. Based on precipitation and tree cover data in the Brazilian Amazon basin, we constructed potential landscapes that enable us to systematically measure the resilience of the different ecosystems. Additionally, we infer that shifts from forest to savannah due to decreasing precipitation in the future are more likely to occur in regions with a precursory lower rainfall variability. Long-term rainfall variability thus needs to be taken into account in resilience analyses and projections of vegetation response to climate change.
Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months.
Droughts in tropical South America have an imminent and severe impact on the Amazon rainforest and affect the livelihoods of millions of people. Extremely dry conditions in Amazonia have been previously linked to sea surface temperature (SST) anomalies in the adjacent tropical oceans. Although the sources and impacts of such droughts have been widely studied, establishing reliable multi-year lead statistical forecasts of their occurrence is still an ongoing challenge. Here, we further investigate the relationship between SST and rainfall anomalies using a complex network approach. We identify four ocean regions which exhibit the strongest overall SST correlations with central Amazon rainfall, including two particularly prominent regions in the northern and southern tropical Atlantic. Based on the time-dependent correlation between SST anomalies in these two regions alone, we establish a new early-warning method for droughts in the central Amazon basin and demonstrate its robustness in hindcasting past major drought events with lead-times up to 18 months.
Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators
(2006)
We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models
The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution
(2011)
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B. P.), (ii) Early Pleistocene (2.25-1.6 Ma B. P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B. P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
Complex networks in climate dynamics : comparing linear and nonlinear network construction methods
(2009)
Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.
The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated.
We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system.
Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches - recurrence plots and recurrence networks -, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.
We study Hamiltonian chaos generated by the dynamics of passive tracers moving in a two-dimensional fluid flow and describe the complex structure formed in a chaotic layer that separates a vortex region from the shear flow. The stable and unstable manifolds of unstable periodic orbits are computed. It is shown that their intersections in the Poincare map as an invariant set of homoclinic points constitute the backbone of the chaotic layer. Special attention is paid to the finite time properties of the chaotic layer. In particular, finite time Lyapunov exponents are computed and a scaling law of the variance of their distribution is derived. Additionally, the box counting dimension as an effective dimension to characterize the fractal properties of the layer is estimated for different duration times of simulation. Its behavior in the asymptotic time limit is discussed. By computing the Lyapunov exponents and by applying methods of symbolic dynamics, the formation of the layer as a function of the external forcing strength, which in turn represents the perturbation of the originally integrable system, is characterized. In particular, it is shown that the capture of KAM tori by the layer has a remarkable influence on the averaged Lyapunov exponents. (C) 2004 Elsevier Ltd. All rights reserved
Experimental evidences point Out the participation of nonsynaptic mechanisms (e.g., fluctuations in extracellular tons) in epileptiform bursting and spreading depression (SD). During these abnormal oscillatory patterns, it is observed an increase of extracellular potassium concentration [K+](o) and a decrease of extracellular calcium concentration [Ca2+](o) which raises the neuronal excitability. However, whether the high [K+](o) triggers and propagates these abnormal neuronal activities or plays a secondary role into this process is unclear. To better understand the influence of extracellular potassium dynamics in these oscillatory patterns, the experimental conditions of high [K+](o) and zero [Ca2+](o) were replicated in an extended Golomb model where we added important regulatory mechanisms of ion concentration as Na+-K+ pump, ion diffusion and glial buffering. Within these Conditions, simulations of the cell model exhibit seizure-like discharges (ictal bursting). The SD was elicited by the interruption of the Na+- K+ pump activity, mimicking the effect of cellular hypoxia (an experimental protocol to elicit SD, the hypoxia-induced SD). We used the bifurcation theory and the fast-slow method to analyze the interference of K+ dynamics in the cellular excitability. This analysis indicates that the system loses its stability at a high [K+](o), transiting to an elevated state of neuronal excitability. Effects of high [K+](o), are observed in different stages of ictal bursting and SD. In the initial stage, the increase of [K+](o) creates favorable conditions to trigger both oscillatory patterns. During the neuronal activity, a continuous growth of [K+](o) by outward K+ flow depresses K+ Currents in a positive feedback way. At the last stage, due to the depression of K+ currents, the Na+-K+ pump is the main mechanism in the end of neuronal activity. Thus, this work suggests that [K+](o) dynamics may play a fundamental role in these abnormal oscillatory patterns.
In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results.
We employ a spectral decomposition method to analyze synchronization of a non-identical oscillator network. We study the case that a small parameter mismatch of oscillators is characterized by one parameter and phase synchronization is observed. We derive a linearized equation for each eigenmode of the coupling matrix. The parameter mismatch is reflected on inhomogeneous term in the linearized equation. We find that the oscillation of each mode is essentially characterized only by the eigenvalue of the coupling matrix with a suitable normalization. We refer to this property as spectral universality, because it is observed irrespective of network topology. Numerical results in various network topologies show good agreement with those based on linearized equation. This universality is also observed in a system driven by additive independent Gaussian noise.
Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this article, a nonlinear method for dimensionality reduction, Isomap, is applied to the sea surface temperature and thermocline data in the tropical Pacific Ocean, where the El Nino-Southern Oscillation (ENSO) phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. The knowledge of the minimum number of dimensions is expected to improve the development of low dimensional models for understanding and predicting ENSO
We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of the system is first studied in the presence of both forces separately without noise. In the presence of only one of the forces, no resonance behaviour is observed, however, hysteresis happens there. Then the influence of the high-frequency force in the presence of a low-frequency, i.e. biharmonic forcing, is studied. Vibrational resonance is found to occur when the amplitude of the high-frequency force is varied. The resonance curve resembles a stochastic resonance-like curve. It is maximum at the value of g at which the orbit lies in one well during one half of the drive cycle of the low-frequency force and in the other for the remaining half cycle. Vibrational resonance is characterized using the response amplitude and mean residence time. We show the occurrence of stochastic resonance behaviour in the overdamped system by replacing the high-frequency force by Gaussian noise. Similarities and differences between both types of resonance are presented. (c) 2006 Elsevier B.V. All rights reserved.
Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Nino-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.
Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an ‘uncertainty-aware’ framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.
Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record.
We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age-depth and proxy-depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India.
Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation.
We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations.
We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems.
We describe effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method which may lead to artifacts. We develop a modified method that overcomes these effects and apply it to study parkinsonian tremor. Our results indicate that there is synchronization between two different hands and provide information about the time delay separating their dynamics. These findings suggest that this method may be useful for detecting and quantifying weak synchronization between two non-stationary signals.
Spatiotemporal dynamics of the Calvin cycle multistationarity and symmetry breaking instabilities
(2011)
The possibility of controlling the Calvin cycle has paramount implications for increasing the production of biomass. Multistationarity, as a dynamical feature of systems, is the first obvious candidate whose control could find biotechnological applications. Here we set out to resolve the debate on the multistationarity of the Calvin cycle. Unlike the existing simulation-based studies, our approach is based on a sound mathematical framework, chemical reaction network theory and algebraic geometry, which results in provable results for the investigated model of the Calvin cycle in which we embed a hierarchy of realistic kinetic laws. Our theoretical findings demonstrate that there is a possibility for multistationarity resulting from two sources, homogeneous and inhomogeneous instabilities, which partially settle the debate on multistability of the Calvin cycle. In addition, our tractable analytical treatment of the bifurcation parameters can be employed in the design of validation experiments.
Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
Similar power laws for foreshock and aftershock sequences in a spring block model for earthquakes
(1999)
Seismic quiescence as an indicator for large earthquakes in a system of self-organized criticality
(2000)
Competitive random sequential adsorption of point and fixed-sized particles: analytical results
(2001)
Objectives: Scoring sleep visually based on polysomnography is an important but time-consuming element of sleep medicine. Where-as computer software assists human experts in the assignment of sleep stages to polysomnogram epochs, their performance is usually insufficient. This study evaluates the possibility to fully automatize sleep staging considering the reliability of the sleep stages available from human expert sleep scorers. Methods: We obtain features from EEG, ECG and respiratory signals of polysomnograms from ten healthy subjects. Using the sleep stages provided by three human experts, we evaluate the performance of linear discriminant analysis on the entire polysomnogram and:only on epochs where the three experts agree in their-sleep stage scoring. Results: We show that in polysomnogram intervals, to which all three scorers assign the same sleep stage, our algorithm achieves 90% accuracy. This high rate of agreement with the human experts is accomplished with only a small set of three frequency features from the EEG. We increase-the performance to 93% by including ECG and respiration features. In contrast, on intervals of ambiguous sleep stage, the sleep stage classification obtained from our algorithm, agrees with the human consensus scorer in approximately 61%. Conclusions: These findings suggest that machine classification is highly consistent with human sleep staging and that error in the algorithm's assignments is rather a problem of lack of well-defined criteria for human experts to judge certain polysomnogram epochs than an insufficiency of computational procedures