Paired Time Series Research Articles

Unbiased Proxy Calibration

The linear calibration model is a powerful statistical tool that can be utilized to predict an unknown response variable, Y, through observations of a proxy or predictor variable, X. Since calibration involves estimation of regression model parameters on the basis of a limited amount of noisy data, an unbiased calibration slope estimation is of utmost importance. This can be achieved by means of state-of-the-art, data-driven statistical techniques. The present paper shows that weighted least-squares for both variables estimation (WLSXY) is able to deliver unbiased slope estimations under heteroscedasticity. In the case of homoscedasticity, besides WLSXY, ordinary least-squares (OLS) estimation with bias correction (OLSBC) also performs well. For achieving unbiasedness, it is further necessary to take the correct regression direction (i.e., of Y on X) into account. The present paper introduces a pairwise moving block bootstrap resampling approach for obtaining accurate estimation confidence intervals (CIs) under real-world climate conditions (i.e., non-Gaussian distributional shapes and autocorrelations in the noise components). A Monte Carlo simulation experiment confirms the feasibility and validity of this approach. The parameter estimates and bootstrap replications serve to predict the response with CIs. The methodological approach to unbiased calibration is illustrated for a paired time series dataset of sea-surface temperature and coral oxygen isotopic composition. Fortran software with implementation of OLSBC and WLSXY accompanies this paper.

Maintaining forest cover to enhance temperature buffering under future climate change

Forest canopies buffer macroclimatic temperature fluctuations. However, we do not know if and how the capacity of canopies to buffer understorey temperature will change with accelerating climate change. Here we map the difference (offset) between temperatures inside and outside forests in the recent past and project these into the future in boreal, temperate and tropical forests. Using linear mixed-effect models, we combined a global database of 714 paired time series of temperatures (mean, minimum and maximum) measured inside forests vs. in nearby open habitats with maps of macroclimate, topography and forest cover to hindcast past (1970–2000) and to project future (2060–2080) temperature differences between free-air temperatures and sub-canopy microclimates. For all tested future climate scenarios, we project that the difference between maximum temperatures inside and outside forests across the globe will increase (i.e. result in stronger cooling in forests), on average during 2060–2080, by 0.27 ± 0.16 °C (RCP2.6) and 0.60 ± 0.14 °C (RCP8.5) due to macroclimate changes. This suggests that extremely hot temperatures under forest canopies will, on average, warm less than outside forests as macroclimate warms. This knowledge is of utmost importance as it suggests that forest microclimates will warm at a slower rate than non-forested areas, assuming that forest cover is maintained. Species adapted to colder growing conditions may thus find shelter and survive longer than anticipated at a given forest site. This highlights the potential role of forests as a whole as microrefugia for biodiversity under future climate change.

Viral etiology and seasonal trends of pediatric acute febrile illness in southern Puerto Rico; a seven-year review.

BackgroundAcute febrile illness (AFI) is an important cause for seeking health care among children. Knowledge of the most common etiologic agents of AFI and its seasonality is limited in most tropical regions.Methodology/Principal findingsTo describe the viral etiology of AFI in pediatric patients (≤18 years) recruited through a sentinel enhanced dengue surveillance system (SEDSS) in Southern Puerto Rico, we analyzed data for patients enrolled from 2012 to May 2018. To identify seasonal patterns, we applied time-series analyses to monthly arboviral and respiratory infection case data. We calculated coherence and phase differences for paired time-series to quantify the association between each time series.A viral pathogen was found in 47% of the 14,738 patients. Influenza A virus was the most common pathogen detected (26%). The incidence of Zika and dengue virus etiologies increased with age. Arboviral infections peaked between June and September throughout the times-series. Respiratory infections have seasonal peaks occurring in the fall and winter months of each year, though patterns vary by individual respiratory pathogen.Conclusions/SignificanceDistinct seasonal patterns and differences in relative frequency by age groups seen in this study can guide clinical and laboratory assessment in pediatric patients with AFI in Puerto Rico.

Declined trend in herbaceous plant green-up dates on the Qinghai–Tibetan Plateau caused by spring warming slowdown

There has been much debate on the temporal change trend and existence of a turning point in spring green-up date (GUD) of plants on the Qinghai–Tibetan Plateau (QTP). Most previous studies on the QTP used remote sensing data, which have large uncertainties. In this study, using a large amount of long-term ground observation data at 27 phenological stations across the QTP (1694 GUD records), we showed that on the whole, QTP herbaceous plant GUD insignificantly advanced during 1982–2017. Although the direction of the GUD trend did not change from 1982 to 2017, the magnitude of the advancing trend greatly weakened after 1999. According to our estimated results from 28 paired GUD time series, the overall GUD trend shifted from −2.70 days/decade during 1982–1999 to −0.56 days/decade during 2000–2017. This finding contrasts with the conclusions of previous satellite-based studies, which either reported a continuous significant advancement of GUD or a turning point in the mid-to-late 1990s. Through partial correlation analysis and partial least squares regression, we found that winter and spring air temperatures were the primary climatic factors that influenced the temporal change in GUD, and both had negative effects on GUD. The decreased GUD trend was mainly attributable to the warming slowdown in spring. On average, the spring warming rate decreased by 52.43% after 1999, whereas the winter warming rate displayed no obvious change. This study also found that the GUD of forbs showed stronger sensitivity to air temperature change than that of sedges and grasses. This indicates that forbs are more competitive in adaptation to climate warming, which might shift plant community structure and affect ecosystem service function. Moreover, the declined advancement in GUD implies that the spring phenologically driven increase in carbon uptake may have also slowed in the past two decades.

Contrast Pattern Mining in Paired Multivariate Time Series of a Controlled Driving Behavior Experiment

The controlled experiment is an important scientific method for researchers seeking to determine the influence of the intervention, by interpreting the contrast patterns between the temporal observations from control and experimental groups (i.e., paired multivariate time series (PMTS)). Due to recent technological advances and the growing popularity of sensing technology such as in-vehicle sensors and activity trackers, time series data is experiencing explosive growth in both size and complexity. This is threatening to overwhelm the interpretation of control experiments, which conventionally rely on human analysts. Thus, it is imperative to develop automated methods that are expected to simultaneously characterize and detect the interpretable contrast patterns in PMTS generated by controlled experiments. However, a few challenges prohibit existing methods from directly addressing this problem: (1) handling the coupling of contrast identification and pattern characterization, (2) dynamically characterizing the patterns in PMTS, and (3) mining the contrast patterns in multiple PMTS with ubiquitous individual differences. Therefore, we propose a novel framework to mine interpretable contrast patterns based on the dynamic feature dependencies for PMTS through optimization. The proposed framework simultaneously characterizes the dynamic feature dependency networks for PMTS and detects the contrast patterns. Specifically, we characterize the generative process of PMTS as a probabilistic model defined by pairwise Markov random fields whose likelihoods are maximized using our group graphical lasso. The model is then generalized to handle multiple PMTS and solved by proposing a customized algorithm based on the expectation-maximization framework. Extensive experiments demonstrate the effectiveness, scalability, and interpretability of our approach.

Refining the processing of paired time series data to improve velocity estimation in snow flows

For effective avalanche risk mitigation, numerical models with a correct description of snow rheology are needed. Conventionally, velocity in snow flow experiments is inferred by cross-correlating the voltage signals of paired sensors. The intention of this paper is to reconsider this problem to enhance processing of these data, leading to more effective estimates of fluctuating velocity quantities. The algorithm consists of a wavelet decomposition, a denoising step and a weighting method for the reconstituted signal. The resulting velocity time series are both consistent and informative, providing confidence that one can analyse not only the mean velocity profiles, but also the velocity distribution. Our approach is illustrated using a typical chute experiment undertaken at Col du Lac Blanc in the French Alps. Not only has the mean velocity profile a more complex shape than the bilinear one postulated from the results of the standard cross-correlation processing, but the probability distribution functions of the velocity at different heights is much more continuous and dispersed, revealing interesting new patterns of greater dynamical relevance.

Multiscale synchrony behaviors of paired financial time series by 3D multi-continuum percolation

Multiscale synchrony behaviors and nonlinear dynamics of paired financial time series are investigated, in an attempt to study the cross correlation relationships between two stock markets. A random stock price model is developed by a new system called three-dimensional (3D) multi-continuum percolation system, which is utilized to imitate the formation mechanism of price dynamics and explain the nonlinear behaviors found in financial time series. We assume that the price fluctuations are caused by the spread of investment information. The cluster of 3D multi-continuum percolation represents the cluster of investors who share the same investment attitude. In this paper, we focus on the paired return series, the paired volatility series, and the paired intrinsic mode functions which are decomposed by empirical mode decomposition. A new cross recurrence quantification analysis is put forward, combining with multiscale cross-sample entropy, to investigate the multiscale synchrony of these paired series from the proposed model. The corresponding research is also carried out for two China stock markets as comparison.

Tracer experiment and model evidence for macrofaunal shaping of microbial nitrogen functions along rocky shores

Abstract. Seawater microbes as well as those associated with macrobiota are increasingly recognized as a key feature affecting nutrient cycling. Tidepools are ideal natural mesocosms to test macrofauna and microbe interactions, and we quantified rates of microbial nitrogen processing using tracer enrichment of ammonium (15NNH4) or nitrate (15NNO3) when tidepools were isolated from the ocean during low intertidal periods. Experiments were conducted during both day and night as well as in control tidepools and those from which mussels had been removed, allowing us to determine the role of both mussels and daylight in microbial nitrogen processing. We paired time series observations of 15N enrichment in NH4+, NO2− and NO3− with a differential equation model to quantify multiple, simultaneous nitrogen transformations. Mussel presence and daylight increased remineralization and photosynthetic nitrogen uptake. When we compared ammonium gain or loss that was attributed to any tidepool microbes vs. photosynthetic uptake, microbes accounted for 32 % of this ammonium flux on average. Microbial transformations averaged 61 % of total nitrate use; thus, microbial activity was almost 3 times that of photosynthetic nitrate uptake. Because it accounted for processes that diluted our tracer, our differential equation model assigned higher rates of nitrogen processing compared to prior source–product models. Our in situ experiments showed that animals alone elevate microbial nitrogen transformations by 2 orders of magnitude, suggesting that coastal macrobiota are key players in complex microbial nitrogen transformations.

The Connected Scatterplot for Presenting Paired Time Series.

The connected scatterplot visualizes two related time series in a scatterplot and connects the points with a line in temporal sequence. News media are increasingly using this technique to present data under the intuition that it is understandable and engaging. To explore these intuitions, we (1) describe how paired time series relationships appear in a connected scatterplot, (2) qualitatively evaluate how well people understand trends depicted in this format, (3) quantitatively measure the types and frequency of misinter pretations, and (4) empirically evaluate whether viewers will preferentially view graphs in this format over the more traditional format. The results suggest that low-complexity connected scatterplots can be understood with little explanation, and that viewers are biased towards inspecting connected scatterplots over the more traditional format. We also describe misinterpretations of connected scatterplots and propose further research into mitigating these mistakes for viewers unfamiliar with the technique.

Abstract B2-38: Learning the dynamic response to Ras-ERK signaling with paired reporters

Abstract To characterize key cell signaling pathways in cancer, we employ a modular strategy to examine how signals propagate between two members in a pathway, using paired time series measurements in live cells. The two pathway members chosen bracket a sub-network for which we measure input and output signals. In this study, we characterize models for the response of FRA1 (Fos related antigen 1) to ERK (extracelluar regulated kinase) activity. Mathematical response models are constrained by the paired signal data to produce a predictive module for the ERK-to-FRA1 sub-network, complementing existing modeling efforts as a building block for complete models. Background: Many mutations in cancer impair cellular information processing by hyperactivating signaling pathways associated with proliferation and migration. However, targeted inhibitors for hyperactivated elements have not yielded consistent responses, and acquired resistance hinders their use in therapy. Cell signaling can be a complex dynamic process [1], the detailed understanding of which will support development of new research directions and clinical therapies. The Ras-ERK signaling pathway regulates cell proliferation and migration, and is often mutated in cancer. ERK activity (the nominal pathway output) regulates major drivers of cell decision making, such as the transcription factor FRA1 which is involved in migration and invasion [2]. FRA1 is observed being regulated by ERK at three levels: (1) transcription via ERK-dependent phosphorylation of transcription factors; (2) translation via promotion of mTORC1 (mammalian target of rapamycin complex 1), and (3) stability via ERK-dependent phosphorylation of a c-terminal destabilization motif. The interplay of multiple regulation points in this feed-forward manner may lead to complex responses, including behavior as a ‘persistence detector’ for ERK activity, where only long term activity produces strong responses because short pulses fail to stabilize the protein. Experimental method: To make paired measurements, we generate a cell line expressing both a fluorescent reporter for ERK activity, and a fluorescent FRA1 fusion protein on the genomic locus. Cells are treated with varied levels of extracellular ligands and therapeutic drugs to elicit varied ERK responses, and time series images taken for up to 72 hours. Segmentation and particle tracking yield individual cell time courses over the length of the experiment. Modeling: Models of the FRA1 response to ERK activity are considered at several levels of abstraction to evaluate the complexity of the response against a mechanistic model. The most parsimonious model, that which satisfies data with the least complexity, can then predict FRA1 levels based on ERK activity, with minimal bias from overfitting. Fitting individual cell time courses produces the distribution of cell responses over populations. Conclusions: The characterized response models demonstrate the predictive capacity for FRA1 from ERK activity, revealing that the responsiveness to ERK varies from cell to cell. Over the cell populations observed, the models capture the distribution of the response. These models augment the existing body of work describing the ERK activity resulting from receptor stimulation, and may be further combined with future modular models toward a predictive global model.

CHRONOS: a time-varying method for microRNA-mediated subpathway enrichment analysis.

In the era of network medicine and the rapid growth of paired time series mRNA/microRNA expression experiments, there is an urgent need for pathway enrichment analysis methods able to capture the time- and condition-specific 'active parts' of the biological circuitry as well as the microRNA impact. Current methods ignore the multiple dynamical 'themes'-in the form of enriched biologically relevant microRNA-mediated subpathways-that determine the functionality of signaling networks across time. To address these challenges, we developed time-vaRying enriCHment integrOmics Subpathway aNalysis tOol (CHRONOS) by integrating time series mRNA/microRNA expression data with KEGG pathway maps and microRNA-target interactions. Specifically, microRNA-mediated subpathway topologies are extracted and evaluated based on the temporal transition and the fold change activity of the linked genes/microRNAs. Further, we provide measures that capture the structural and functional features of subpathways in relation to the complete organism pathway atlas. Our application to synthetic and real data shows that CHRONOS outperforms current subpathway-based methods into unraveling the inherent dynamic properties of pathways. CHRONOS is freely available at http://biosignal.med.upatras.gr/chronos/ tassos.bezerianos@nus.edu.sg Supplementary data are available at Bioinformatics online.

Transformation of ENSO‐related rainwater to dripwater δ18O variability by vadose water mixing

AbstractSpeleothem oxygen isotopes (δ18O) are often used to reconstruct past rainfall δ18O variability, and thereby hydroclimate changes, in many regions of the world. However, poor constraints on the karst hydrological processes that transform rainfall signals into cave dripwater add significant uncertainty to interpretations of speleothem‐based reconstructions. Here we present several 6.5 year, biweekly dripwater δ18O time series from northern Borneo and compare them to local rainfall δ18O variability. We demonstrate that vadose water mixing is the primary rainfall‐to‐dripwater transformation process at our site, where dripwater δ18O reflects amount‐weighted rainfall δ18O integrated over the previous 3–10 months. We document large interannual dripwater δ18O variability related to the El Niño–Southern Oscillation (ENSO), with amplitudes inversely correlated to dripwater residence times. According to a simple stalagmite forward model, asymmetrical ENSO extremes produce significant offsets in stalagmite δ18O time series given different dripwater residence times. Our study highlights the utility of generating multiyear, paired time series of rainfall and dripwater δ18O to aid interpretations of stalagmite δ18O reconstructions.

Thoracic surface temperature rhythms as circadian biomarkers for cancer chronotherapy

The disruption of the temperature circadian rhythm has been associated with cancer progression, while its amplification resulted in cancer inhibition in experimental tumor models. The current study investigated the relevance of skin surface temperature rhythms as biomarkers of the Circadian Timing System (CTS) in order to optimize chronotherapy timing in individual cancer patients. Baseline skin surface temperature at four sites and wrist accelerations were measured every minute for 4 days in 16 patients with metastatic gastro-intestinal cancer before chronotherapy administration. Temperature and rest-activity were recorded, respectively, with wireless skin surface temperature patches (Respironics, Phillips) and an actigraph (Ambulatory Monitoring). Both variables were further monitored in 10 of these patients during and after a 4-day course of a fixed chronotherapy protocol. Collected at baseline, during and after therapy longitudinal data sets were processed using Fast Fourier Transform Cosinor and Linear Discriminant Analyses methods. A circadian rhythm was statistically validated with a period of 24 h (p < 0.05) for 49/61 temperature time series (80.3%), and 15/16 rest-activity patterns (93.7%) at baseline. However, individual circadian amplitudes varied from 0.04 °C to 2.86 °C for skin surface temperature (median, 0.72 °C), and from 16.6 to 146.1 acc/min for rest-activity (median, 88.9 acc/min). Thirty-nine pairs of baseline temperature and rest-activity time series (75%) were correlated (r > |0.7|; p < 0.05). Individual circadian acrophases at baseline were scattered from 15:18 to 6:05 for skin surface temperature, and from 12:19 to 15:18 for rest-activity, with respective median values of 01:10 (25–75% quartiles, 22:35–3:07) and 14:12 (13:14–14:31). The circadian patterns in skin surface temperature and rest-activity persisted or were amplified during and after fixed chronotherapy delivery for 5/10 patients. In contrast, transient or sustained disruption of these biomarkers was found for the five other patients, as indicated by the lack of any statistically significant dominant period in the circadian range. No consistent correlation (r < |0.7|, p ≥ 0.05) was found between paired rest-activity and temperature time series during fixed chronotherapy delivery. In conclusion, large inter-patient differences in circadian amplitudes and acrophases of skin surface temperature were demonstrated for the first time in cancer patients, despite rather similar rest-activity acrophases. The patient-dependent coupling between both CTS biomarkers, and its possible alteration on a fixed chronotherapy protocol, support the concept of personalized cancer chronotherapy.

Do cormorant colonies affect local fish communities in the Baltic Sea?

The effects that cormorants have on fish communities have been debated, yet few studies have used the necessary controls and replications to make valid and general assessments. Using both a paired design and time series analysis, we studied associations between colony size of the great cormorant ( Phalacrocorax carbo sinesis ) in the Baltic Sea and local fish community composition. Overall, colony size showed few associations with local fish communities. Most evident was a negative association between colony size and perch ( Perca fluviatilis ) abundances in some areas. But for other species, results were nonsignificant or variable among areas. The Baltic Sea cormorant population has increased over the last decades, and our results suggest that management actions to reduce local cormorant colonies may have a positive effect on local perch abundance. Otherwise, our results predict colony reductions to either have variable or weak effects on adjacent local fish communities.

Standardised Radon Index (SRI): a normalisation of radon data-sets in terms of standard normal variables

Abstract. During the second half of 2002, from late June to mid December, the University of Northampton Radon Research Group operated two continuous hourly-sampling radon detectors 2.25 km apart in the English East Midlands. This period included the Dudley earthquake (ML = 5, 22 September 2002) and also a smaller earthquake in the English Channel (ML = 3, 26 August 2002). Rolling/sliding windowed cross-correlation of the paired radon time-series revealed periods of simultaneous similar radon anomalies which occurred at the time of these earthquakes but at no other times during the overall radon monitoring period. Standardising the radon data in terms of probability of magnitude, analogous to the Standardised Precipitation Indices (SPIs) used in drought modelling, which effectively equalises different non-linear responses, reveals that the dissimilar relative magnitudes of the anomalies are in fact closely equiprobabilistic. Such methods could help in identifying anomalous signals in radon – and other – time-series and in evaluating their statistical significance in terms of earthquake precursory behaviour.

Analysis of time series data on agroecosystem vegetation using predictive clustering trees

We present an approach to modelling interdependent types of vegetation that support different functions in a managed ecosystem. For optimal management, plants that provide economic output (e.g., crops) and those that support ecological functions (e.g., wild plants or ‘weeds’) should coexist in an agroecosystem. To make progress with understanding how such plant communities interact over time, we analyse paired time series data about the cover of crop and weed vegetation in oilseed rape fields. The percentage crop and weed cover were measured every 7–14 days at 128 sites in the UK, covering a wide range of localities and management regimes. To analyze the data, we first cluster the time course profiles of crop cover (using the k-medoids clustering algorithm and the dynamic time warping distance between time series). The clustering revealed five typical clusters of crop cover profiles that differed in terms of rate of increase, lag phase and maximum value, but were largely independent of the type of crop (winter/spring oil seed rape) and the weed management regime. Cluster membership for each crop cover profile was used as an additional independent variable (attribute) in the predictive modelling analysis that followed. We then constructed predictive clustering trees (a generalized form of decision trees) that predict the weed cover profile (time series) from independent (input) variables that include the crop cover cluster, other crops descriptors and environmental variables. The crop cover cluster was more informative in predicting the weed cover profile than any other input variable, including the type of crop and the crop transgenic status (conventional or genetically modified / herbicide tolerant). The approach was successful in identifying the interdependencies between the two types of vegetation. We envisage that it will have plentiful further practical use in relating and interpreting ecological or environmental time series.

Modulus and direction of the neural current vector identify distinct functional connectivity modes between human MT+ areas

Reconstruction of neural current sources from magnetoencephalography (MEG) data provides two independent estimates of the instantaneous current modulus and its direction. Here, we explore how different information on the modulus and direction affects the inter-hemisphere connectivity of the human medial temporal complex (hMT+). Connectivity was quantified by mutual information values of paired time series of current moduli or directions, with the joint probability distribution estimated with an optimized Gaussian kernel. These time series were obtained from tomographic analysis of single-trial MEG responses to a visual motion stimulus. With a high-contrast stimulus, connectivity measures based on the modulus were relatively strong in the prestimulus period, continuing until 100 ms after stimulus onset. The strongest modulus connectivity was produced with a long lag (19 ms) of the right hMT+ after the left hMT+. On the other hand, connectivity measures based on direction were relatively strong after 100 ms, with a short delay of less than 6 ms. These results suggest that nonspecific and probably indirect communication between the homologous areas is turned, by the stimulus arrival, into more precise and direct communication through the corpus callosum. The orientation of the estimated current vector for the strong connectivity can be explained by the curvature of the active cortical sheet. The temporal patterns of modulus and directional connectivity were different at low contrast, but similar to those at high contrast. We conclude that the modulus and direction indicate distinct functional connectivity modes.

Spectral-decomposition techniques for the identification of radon anomalies temporally associated with earthquakes occurring in the UK in 2002 and 2008

Abstract. During the second half of 2002, the University of Northampton Radon Research Group operated two continuous hourly-sampling radon detectors 2.25 km apart in the English East Midlands. This period included the Dudley earthquake (ML=5, 22 September 2002). Also, at various periods during 2008 the Group has operated other pairs of continuous hourly-sampling radon detectors similar distances apart in the same region. One such period included the Market Rasen earthquake (ML=5.2, 27 February 2008). Windowed cross-correlation of the paired time-series was used to identify simultaneous short-duration anomalies. In the 2002 data, only two periods of significant cross-correlation were observed, each corresponding temporally to a UK earthquake, one to the Dudley earthquake and the other to a smaller earthquake in the English Channel (ML=3, 26 August 2002). In the 2008 data, cross-correlation initially revealed little evidence of simultaneous short-duration anomalies but cross-correlation of data de-noised and de-trended using Empirical Mode Decomposition (EMD) revealed clear simultaneous short-duration anomalies which correspond temporally to the Market Rasen earthquake.

Analysis of EEG Structural Synchrony in Adolescents with Schizophrenic Disorders

Schizophrenia falls into the small category of diseases that impair the total psychic activity rather than particular brain systems and functions. It is not surprising that researchers have long been interested in the integrative activity of the human brain in schizophrenia. They have reported considerable data on histological and physiological changes in the human brain, providing evidence for disturbance of interrelationships and functional association between different parts of the brain at different stages of schizophrenia [1‐3]. The most conspicuous data have been obtained for the brain electrical activity [4‐10]. Based on these data, a hypothesis of disintegration of cortical functions (the disconnection hypothesis) has been advanced [11] to explain the schizophrenic disorders [11‐13]. In EEG studies, spectral and correlation analyses are a common method for investigating the integrative activity of the human brain, yielding evidence for the impairment of local and distant synchronies of neuronal networks in schizophrenia [4, 5, 7, 8, 14]. However, a number of limitations typical of spectral methods, specifically, of the coherence function [7, 15‐17], have motivated the development of new techniques to examine the interdependences of EEG paired time series data in schizophrenia, including nonlinear interdependence [9], mutual information transmission measure [18], and phase locking [10], which reflect nonlinear and, in the last case, also in-phase components of the interdependence of cortical electrical processes. The results of the above studies are also in line with Friston’s hypothesis of disintegration of neuronal networks in schizophrenia [11].

Extracting signals of predation and competition from paired plankton time series

Although competition and predation among plankton in seasonal aquatic systems must be ubiquitous, it remains a challenge to actually identify these interactions and to evaluate their relative strengths. Based on paired time series for zooplankton and phytoplankton in three lakes: Mjosa (12 years), Farris (2 years) and Lake Washington (29 years), we construct phase portraits and quantitatively analyse their trajectories in an attempt to characterize interaction types and strengths. Because we can infer the type of interactions each pair partake in a priori (e.g., a phytoplankton/zooplankton pair is a prey/predator pair), we hypothesize that it is possible to distinguish trajectories resulting from a pair that compete from those of a pair constituting a prey/predator pair. We found that competition and predation can be distinguished based on the time series of the interacting species' biomass. Break points in population trajectories (i.e., population collapse) and the counter clockwise rotation of the trajectory in the phase portrait give the strongest signals of predation and the signals correspond to what we expect from classical predation theory. For competition we can only give plausible biological interpretations of identified signals, since signals from grazing, seasonality and competition are confounded.