Convergent Mapping Research Articles

Detecting causality from time series in a machine learning framework.

Detecting causality from observational data is a challenging problem. Here, we propose a machine learning based causality approach, Reservoir Computing Causality (RCC), in order to systematically identify causal relationships between variables. We demonstrate that RCC is able to identify the causal direction, coupling delay, and causal chain relations from time series. Compared to a well-known phase space reconstruction based causality method, Extended Convergent Cross Mapping, RCC does not require the estimation of the embedding dimension and delay time. Moreover, RCC has three additional advantages: (i) robustness to noisy time series; (ii) computational efficiency; and (iii) seamless causal inference from high-dimensional data. We also illustrate the power of RCC in identifying remote causal interactions of high-dimensional systems and demonstrate its usability on a real-world example using atmospheric circulation data. Our results suggest that RCC can accurately detect causal relationships in complex systems.

Detecting the causal interaction between Siberian High and Winter Surface Air Temperature over Northeast Asia

Past Results indicate that there is a significant negative correlation between the Siberian High (SH) and winter surface air temperature (SAT) over Eurasian continent and East Asia. However, correlation does not mean causation, especially in nonlinear dynamic systems. Here, we apply a recently developed method, Convergent Cross Mapping (CCM), to detect the causal connection between SH and winter SAT over Northeast Asia. It suggests the winter SAT variability in Northeast Asia and SH shows two-way causation, SH ↔ winter SAT. Meanwhile, the influence of SH characteristic variables on wintertime SAT is in order of area, longitude of east edge, intensity and latitude of south edge of SH, respectively. What's more, the impact of wintertime SAT on SH characteristic variables is in order of area, intensity, longitude of east edge, and latitude of south edge of SH. Besides, we apply the CCM to analyze the causality between the Northern Hemisphere Annular Mode (NAM) and the intensity of SH. It indicates that the NAM forces the intensity of SH, but not vise versa. Hence, we suggest that the NAM can influence winter SAT through the SH. The mechanism of the causality is presented preliminarily. These causal relationships and feedback effects in dynamic systems have opened up the possibility to improve the seasonal prediction of winter SAT over Northeast Asia by using the external factors of the SH.

DISCOVERING CAUSALITIES FROM CARDIOTOCOGRAPHY SIGNALS USING IMPROVED CONVERGENT CROSS MAPPING WITH GAUSSIAN PROCESSES.

Convergent cross mapping (CCM) is designed for causal discovery in coupled time series, where Granger causality may not be applicable because of a separability assumption. However, CCM is not robust to observation noise which limits its applicability on signals that are known to be noisy. Moreover, the parameters for state space reconstruction need to be selected using grid search methods. In this paper, we propose a novel improved version of CCM using Gaussian processes for discovery of causality from noisy time series. Specifically, we adopt the concept of CCM and carry out the key steps using Gaussian processes within a non-parametric Bayesian probabilistic framework in a principled manner. The proposed approach is first validated on simulated data, and then used for understanding the interaction between fetal heart rate and uterine activity in the last two hours before delivery and of interest in obstetrics. Our results indicate that uterine activity affects the fetal heart rate, which agrees with recent clinical studies.

Density and temperature of cosmic-web filaments on scales of tens of megaparsecs

We studied physical properties of matter in 24 544 filaments ranging from 30 to 100 Mpc in length, identified in the Sloan Digital Sky Survey. We stacked the Comptonizationymap produced by the Planck Collaboration around the filaments, excluding the resolved galaxy groups and clusters above a mass of ∼3 × 1013 M⊙. We detected the thermal Sunyaev-Zel’dovich signal for the first time at a significance of 4.4σin filamentary structures on such a large scale. We also stacked thePlanckcosmic microwave background lensing convergence map in the same manner and detected the lensing signal at a significance of 8.1σ. To estimate physical properties of the matter, we considered an isothermal cylindrical filament model with a density distribution following aβ-model (β= 2/3). Assuming that the gas distribution follows the dark matter distribution, we estimate that the central gas and matter overdensityδand gas temperatureTeareδ= 19.0−12.1+27.3andTe= 1.4−0.4+0.4× 106K, which results in a measured baryon fraction of 0.080−0.051+0.116× Ωb.

The Gravitational Lensing Signatures of BOSS Voids in the Cosmic Microwave Background

Abstract We report a detection of the gravitational lensing effect of cosmic voids from the Baryon Oscillation Spectroscopic Data Release 12 seen in the Planck 2018 cosmic microwave background (CMB) lensing convergence map. To make this detection, we introduce new optimal techniques for void stacking and filtering of the CMB maps, such as binning voids by a combination of their observed galaxy density and size to separate those with distinctive lensing signatures. We calibrate theoretical expectations for the void lensing signal using mock catalogs generated in a suite of 108 full-sky lensing simulations from Takahashi et al. Relative to these templates, we measure the lensing amplitude parameter in the data to be A L = 1.10 ± 0.21 using a matched-filter stacking technique and confirm it using an alternative Wiener-filtering method. We demonstrate that the result is robust against thermal Sunyaev–Zel’dovich contamination and other sources of systematics. We use the lensing measurements to test the relationship between the matter and galaxy distributions within voids and show that the assumption of linear bias with a value consistent with galaxy clustering results is discrepant with observation at ∼3σ; we explain why such a result is consistent with simulations and previous results, and is expected as a consequence of void selection effects. We forecast the potential for void CMB lensing measurements in future data from the Advanced ACT, Simons Observatory, and CMB-S4 experiments, showing that, for the same number of voids, the achievable precision improves by a factor of more than 2 compared to Planck.

Modeling interaction as a complex system

ABSTRACT Researchers in Human-Computer Interaction typically rely on experiments to assess the causal effects of experimental conditions on variables of interest. Although this classic approach can be very useful, it offers little help in tackling questions of causality in the kind of data that are increasingly common in HCI – capturing user behavior ‘in the wild.’ To analyze such data, model-based regressions such as cross-lagged panel models or vector autoregressions can be used, but these require parametric assumptions about the structural form of effects among the variables. To overcome some of the limitations associated with experiments and model-based regressions, we adopt and extend ‘empirical dynamic modelling’ methods from ecology that lend themselves to conceptualizing multiple users’ behavior as complex nonlinear dynamical systems. Extending a method known as ‘convergent cross mapping’ or CCM, we show how to make causal inferences that do not rely on experimental manipulations or model-based regressions and, by virtue of being non-parametric, can accommodate data emanating from complex nonlinear dynamical systems. By using this approach for multiple users, which we call ‘multiple convergent cross mapping’ or MCCM, researchers can achieve a better understanding of the interactions between users and technology – by distinguishing causality from correlation – in real-world settings.

Small temperature variations are a key regulator of reproductive growth and assimilate storage in oil palm (Elaeis guineensis)

Oil palm is an important crop for global vegetable oil production, and is widely grown in the humid tropical regions of Southeast Asia. Projected future climate change may well threaten palm oil production. However, oil palm plantations currently produce large amounts of unutilised biological waste. Oil palm stems – which comprise two-thirds of the waste - are especially relevant because they can contain high levels of non-structural carbohydrates (NSC) that can serve as feedstock for biorefineries. The NSC in stem are also considered a potent buffer to source-sink imbalances. In the present study, we monitored stem NSC levels and female reproductive growth. We then applied convergent cross mapping (CCM) to assess the causal relationship between the time-series. Mutual causal relationships between female reproductive growth and the stem NSC were detected, with the exception of a relationship between female reproductive organ growth and starch levels. The NSC levels were also influenced by long-term cumulative temperature, with the relationship showing a seven-month time lag. The dynamic between NSC levels and long-term cumulative rainfall showed a shorter time lag. The lower temperatures and higher cumulative rainfall observed from October to December identify this as a period with maximum stem NSC stocks.

Temporal variations of ambient air pollutants and meteorological influences on their concentrations in Tehran during 2012\u20132017

We investigated temporal variations of ambient air pollutants and the influences of meteorological parameters on their concentrations using a robust method; convergent cross mapping; in Tehran (2012–2017). Tehran citizens were consistently exposed to annual PM2.5, PM10 and NO2 approximately 3.0–4.5, 3.5–4.5 and 1.5–2.5 times higher than the World Health Organization air quality guideline levels during the period. Except for O3, all air pollutants demonstrated the lowest and highest concentrations in summertime and wintertime, respectively. The highest O3 concentrations were found on weekend (weekend effect), whereas other ambient air pollutants had statistically significant (P < 0.05) daily variations in which higher concentrations were observed on weekdays compared to weekend (holiday effect). Hourly O3 concentration reached its peak at 3.00 p.m., though other air pollutants displayed two peaks; morning and late night. Approximately 45% to 65% of AQI values were in the subcategory of unhealthy for sensitive groups and PM2.5 was the responsible air pollutant in Tehran. Amongst meteorological factors, temperature was the key influencing factor for PM2.5 and PM10 concentrations, while nebulosity and solar radiation exerted major influences on ambient SO2 and O3 concentrations. Additionally, there is a moderate coupling between wind speed and NO2 and CO concentrations.

Causal network construction based on convergent cross mapping (CCM) for alarm system root cause tracing of nonlinear industrial process

In terms of an alarm system, the propagation of a fault is identified as the main reason for low efficiency and the leading cause of dramatic industrial accidents. Thus, tracing the root causes of faulty conditions that lead to alarm floods is necessary. For root cause tracing, a widely accepted method is to characterize the process by causality at first and then trace the root causes. This work focuses on the former part. The conventional techniques to deal with causal analysis of industrial processes have difficulty in handling the nonlinearity of variables, obtaining accurate probability density and time lag, etc. In this work, a novel causal network construction method based on convergent cross mapping (CCM) that accurately describe process causality was proposed to deal with the above problems. First, the original monitoring variables were determined by a maximum Lyapunov method to determine whether they were chaotic time series, which aims to judge whether the application conditions of CCM can be satisfied. Then, some characteristic variables are selected from original variables through data preprocessing and descending dimension methods, which are defined as nodes that constitute the causal network. Second, the CCM-based methods are used to identify the causal direction and indirect causal relationship between variables, so as to construct the structure of the causal network. Since the CCM based on deterministic systems theory, it can handle nonlinearity and does not rely on the sample distribution. Finally, the weight of the edges in the graph is calculated to obtain the causal network which describes the process causality and serves as the basis for subsequent root causes tracing of alarms. The effectiveness of the proposed method is illustrated via a real industrial case study.

Network structure detection using convergent cross mapping on multivariate time series

Network structure detection using convergent cross mapping on multivariate time series

Visual Analytics of Causal Relationship Between Fish Catches Data in Adjacent Sea Areas Using Convergent Cross Mapping

Visual Analytics of Causal Relationship Between Fish Catches Data in Adjacent Sea Areas Using Convergent Cross Mapping

Going deep with Minkowski functionals of convergence maps

Aims. Stage IV lensing surveys promise to make an unprecedented amount of excellent data available. This will represent a huge leap in terms of quantity and quality and will open the way for the use of novel tools that surpass the standard second-order statistics for probing the high-order properties of the convergence field. Motivated by these considerations, some of us have started a long-term project aiming at using Minkowski functionals (MFs) as complementary and supplementary probes to increase the lensing figure of merit (FoM). Methods. As a second step on this path, we discuss the use of MFs for a survey consisting of a wide total area Atot that is imaged at a limiting magnitude magW and contains a subset of area Adeep, where observations are pushed to a deeper limiting magnitude magD. We present an updated procedure to match the theoretically predicted MFs to the measured MFs, and take the effect of map reconstruction from noisy shear data into account. We validate this renewed method against simulated datasets with different source redshift distributions and total number density, setting these quantities in accordance with the depth of the survey. We can then rely on a Fisher matrix analysis to forecast the improvement in the FoM that is due to the joint use of shear tomography and MFs under different assumptions on (Atot, Adeep, and magD), and the prior on the MFs nuisance parameters. Results. We find that MFs can provide valuable help in increasing the FoM of the lensing survey when the nuisance parameters are known with non-negligible precision. The possibility of compensating for the loss of FoM through a cut in the multipole range that is probed by shear tomography is even more interesting. This makes the results more robust against uncertainties in the modeling of nonlinearities. This makes MFs a promising tool for increasing the FoM and also protects the constraints on the cosmological parameters mainly from theoretical systematic effects.

Systemic risk, economic policy uncertainty and firm bankruptcies: Evidence from multivariate causal inference

The paper investigates causal relationships between systemic risk, economic policy uncertainty and firm bankruptcies, conditional on global volatility proxied by the VIX index, in a sample of 15 advanced and major emerging market economies during January 2008-June 2018. We test for Granger causality in time and frequency domains as well as dissect multivariate causal linkages in the dynamic complex system framework by applying a novel technique – convergent cross mapping (Sugihara et al., 2012). Based on strictly coincident results from all the three approaches, we find that systemic risk causes firm exit in Spain, while in the UK and the Netherlands bankruptcies are triggered by economic policy uncertainty. In South Korea and the USA, the VIX index causes the firm shutdown. For the rest of the countries, the causality inference provides less robust evidence. We argue that the magnitude of deleveraging by banks with respect to the private nonfinancial sector, proxied by the volatility of credit-to-GDP gaps, shapes the presence or absence of causal impact by systemic risk, economic policy uncertainty or the VIX index on bankruptcies.

Temperature and pressure variability in mid-latitude low atmosphere and stratosphere-ionosphere coupling

This study presents the continuation of our previous analysis of variations of atmospheric and space weather parameters above Iberian Peninsula along two years near the 24th solar cycle maximum. In the previous paper (Morozova et al., 2017) we mainly discussed the first mode of principal component analysis of tropospheric and lower stratospheric temperature and pressure fields, which was shown to be correlated with lower stratospheric ozone and anti-correlated with cosmic ray flux. Now we extend the investigation to the second mode, which suggests a coupling between the stratosphere and the ionosphere.This second mode, located in the low and middle stratosphere (and explaining ~7% of temperature and ~3% of geopotential height variations), showed to be statistically significantly correlated with variations of the middle stratosphere ozone content and anti-correlated with variations of ionospheric total electron content. Similar co-variability of these stratospheric and ionospheric parameters was also obtained with the wavelet cross-coherence analysis.To investigate the role of atmospheric circulation dynamics and the causal nature of the found correlations, we applied the convergent cross mapping (CCM) analysis to our series. Strong evidence for the stratosphere-ionosphere coupling were obtained for the winter 2012–2013 that is characterized by the easterly QBO phase (quasi-biennial oscillations of the direction of the stratospheric zonal winds) and a strong SSW (sudden stratospheric warming event). Further analysis (for the three-year time interval 2012–2015) hint that SSWs events play main role in emphasizing the stratosphere-ionosphere coupling.

Nonlinear time series analysis unravels underlying mechanisms of interspecific synchrony among foliage‐feeding forest Lepidoptera species

AbstractInterspecific synchrony, that is, synchrony in population dynamics among sympatric populations of different species can arise via several possible mechanisms, including common environmental effects, direct interactions between species, and shared trophic interactions, so that distinguishing the relative importance of these causes can be challenging. In this study, to overcome this difficulty, we combine traditional correlation analysis with a novel framework of nonlinear time series analysis, empirical dynamic modeling (EDM). The EDM is an analytical framework to identify causal relationships and measure changing interaction strength from time series. We apply this approach to time series of sympatric foliage‐feeding forest Lepidoptera species in the Slovak Republic and yearly mean temperature, precipitation and North Atlantic Oscillation Index. These Lepidoptera species include both free‐feeding and leaf‐roller larval life histories: the former are hypothesized to be more strongly affected by similar exogenous environments, while the latter are isolated from such pressures. Correlation analysis showed that interspecific synchrony is generally strongest between species within same feeding guild. In addition, the convergent cross mapping analysis detected causal effects of meteorological factors on most of the free‐feeding species while such effects were not observed in the leaf‐rolling species. However, there were fewer causal relationships among species. The multivariate S‐map analysis showed that meteorological factors tend to affect similar free‐feeding species that are synchronous with each other. These results indicate that shared meteorological factors are key drivers of interspecific synchrony among members of the free‐feeding guild, but do not play the same role in synchronizing species within the leaf‐roller guild.

Brain–heart interactions considering complex physiological data: processing schemes for time-variant, frequency-dependent, topographical and statistical examination of directed interactions by convergent cross mapping

Background: A multitude of complex methods is available to quantify interactions in highly complex physiological systems. Brain–heart interactions play an important role in identifying couplings between the central nervous system and the autonomic nervous system during defined physiological states or specific diseases. The crucial point of those interaction analyses is adequate pre-processing taking into account nonlinearity of data, intuitive graphical representation and suitable statistical evaluation of the achieved results. Objective: The aim of this study is to provide generalized processing schemes for such investigations taking into account pre-processing, graphical representation and statistical analysis. Approach: Two defined data sets were used to develop these processing schemes. Brain–heart interactions in children with temporal lobe epilepsy during the pre-ictal, ictal and post-ictal periods as well as in patients with paranoid schizophrenia and healthy control subjects during the resting state period were investigated by nonlinear convergent cross mapping (CCM). Surrogate data, bootstrapping and linear mixed-effects model approaches were utilized for statistical analyses. Main results: CCM was able to reveal specific and statistically significant time- and frequency-dependent patterns of brain–heart interactions for children with temporal lobe epilepsy and provide a statistically significant pattern of topographic- and frequency-dependent brain–heart interactions for schizophrenic patients, as well as to show the differences from healthy control subjects. Suitable statistical models were found to quantify group differences. Significance: Generalized processing schemes and crucial points of pre-processing, adapted interaction analysis and performed statistical analysis are provided. The general concept of analyses is transferable also to other methods of interactions analysis and data representing even more complex physiological systems.

Detecting Causality using Deep Gaussian Processes.

Convergent cross mapping (CCM) is a state space reconstruction (SSR)-based method designed for causal discovery in coupled time series, where Granger causality may not be applicable due to a separability assumption. However, CCM requires a large number of observations and is not robust to observation noise which limits its applicability. Moreover, in CCM and its variants, the SSR step is mostly implemented with delay embedding where the parameters for reconstruction usually need to be selected using grid search-based methods. In this paper, we propose a Bayesian version of CCM using deep Gaussian processes (DGPs), which are naturally connected with deep neural networks. In particular, we adopt the framework of SSR-based causal discovery and carry out the key steps using DGPs within a non-parametric Bayesian probabilistic framework in a principled manner. The proposed approach is first validated on simulated data and then tested on data used in obstetrics for monitoring the well-being of fetuses, i.e., fetal heart rate (FHR) and uterine activity (UA) signals in the last two hours before delivery. Our results indicate that UA affects the FHR, which agrees with recent clinical studies.

An Assessment of Contamination in the Thermal-SZ Map Using Cross-correlations

Abstract We search for potential galactic and extragalactic dust contamination in thermal Sunyaev–Zeldovich maps derived from the Planck data. To test for contamination, we apply a variety of galactic dust and cosmic infrared background (CIB) models to the data as part of the y map reconstruction process. We evaluate the level of contamination by cross-correlating these y maps with mass tracers based on weak lensing data. The lensing data we use are the convergence map, κ, from the Red Sequence Cluster Lensing survey, and the cosmic microwave background (CMB) lensing potential map, ϕ, from the Planck Collaboration. We make a CIB-subtracted y map and measure the cross-correlation between it and the lensing data. By comparing it with CIB-contaminated cross-correlation, we find that the cross-correlation between κ and y is only slightly contaminated by CIB signal, at the level of 6.8 ± 3.5%, which implies that previous detections of κ × y are robust to CIB contamination. However, we find that ϕ × y is more significantly contaminated, by 16.7 ± 3.5%, because the CMB lensing potential probes higher redshift sources that overlap more with the CIB sources. We find that Galactic dust does not significantly contaminate either cross-correlation signal.

The analysis of influential factors for urban water supply system considering causality with time-series data

Recently, the research on critical infrastructures have been extended its boundary and some previous research analysed interdependency between infrastructures tried to suggest operation and management policy of the infrastructure. This highlighted the importance of systemic approach such as System Dynamics. But there still exist the limit to select the modelling component in terms of causality. In this study, convergent cross mapping was applied to time series variables in Songpa-gu and Gangdong-gu in Seoul, South Korea. Selected variables include operating variable of water supply system, floating population and meteorological variables and 330 observations were collected. The result shows that daily average temperature and floating population that are equivalent to mobile population influences to the daily water supply, and vice versa. Other weather factors such as average precipitation and wind speed showed little causality with the daily water supply. The influential factors of water supply system can be investigated with convergent cross mapping and the result can be utilized for the pre-process of other methodology such as LSTM in short-term water demand prediction. It is expected to collect more available data to improve this study further.

Effects of baryons on weak lensing peak statistics

Upcoming weak-lensing surveys have the potential to become leading cosmological probes provided all systematic effects are under control. Recently, the ejection of gas due to feedback energy from active galactic nuclei (AGN) has been identified as major source of uncertainty, challenging the success of future weak-lensing probes in terms of cosmology. In this paper we investigate the effects of baryons on the number of weak-lensing peaks in the convergence field. Our analysis is based on full-sky convergence maps constructed via light-cones from N-body simulations, and we rely on the baryonic correction model of [1] to model the baryonic effects on the density field. As a result we find that the baryonic effects strongly depend on the Gaussian smoothing applied to the convergence map. For a DES-like survey setup, a smoothing of θk≳8 arcmin is sufficient to keep the baryon signal below the expected statistical error. Smaller smoothing scales lead to a significant suppression of high peaks with \U0001d4ae/\U0001d4a9> 2, while lower peaks are not affected. The situation is more severe for a Euclid-like setup, where a smoothing of θk≳16 arcmin is required to keep the baryonic suppression signal below the statistical error. Smaller smoothing scales require a full modelling of baryonic effects since both low and high peaks are strongly affected by baryonic feedback.