A multivariate approach for processing magnetization effects in triggered event-related functional magnetic resonance imaging time series

Triggered event-related functional magnetic resonance imaging requires sparse intervals of temporally resolved functional data acquisitions, whose initiation corresponds to the occurrence of an event, typically an epileptic spike in the electroencephalographic trace. However, conventional fMRI time series are greatly affected by non-steady-state magnetization effects, which obscure initial blood oxygen level-dependent (BOLD) signals. Here, conventional echo-planar imaging and a post-processing solution based on principal component analysis were employed to remove the dominant eigenimages of the time series, to filter out the global signal changes induced by magnetization decay and to recover BOLD signals starting with the first functional volume. This approach was compared with a physical solution using radiofrequency preparation, which nullifies magnetization effects. As an application of the method, the detectability of the initial transient BOLD response in the auditory cortex, which is elicited by the onset of acoustic scanner noise, was used to demonstrate that post-processing-based removal of magnetization effects allows to detect brain activity patterns identical with those obtained using the radiofrequency preparation. Using the auditory responses as an ideal experimental model of triggered brain activity, our results suggest that reducing the initial magnetization effects by removing a few principal components from fMRI data may be potentially useful in the analysis of triggered event-related echo-planar time series. The implications of this study are discussed with special caution to remaining technical limitations and the additional neurophysiological issues of the triggered acquisition.

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Underestimation of Standard Errors in Multi-Site Time Series Studies

Multi-site time series studies of air pollution and mortality and morbidity have figured prominently in the literature as comprehensive approaches for estimating acute effects of air pollution on health. Hierarchical models are generally used to combine site-specific information and estimate pooled air pollution effects taking into account both within-site statistical uncertainty, and across-site heterogeneity. Within a site, characteristics of time series data of air pollution and health (small pollution effects, missing data, highly correlated predictors, non linear confounding etc.) make modelling all sources of uncertainty challenging. One potential consequence is underestimation of the statistical variance of the site-specific effects to be combined. In this paper we investigate the impact of variance underestimation on the pooled relative rate estimate. We focus on two-stage normal-normal hierarchical models and on under- estimation of the statistical variance at the first stage. By mathematical considerations and simulation studies, we found that variance underestimation does not affect the pooled estimate substantially. However, some sensitivity of the pooled estimate to variance underestimation is observed when the number of sites is small and underestimation is severe. These simulation results are applicable to any two-stage normal-normal hierarchical model for combining information of site-specific results, and they can be easily extended to more general hierarchical formulations. We also examined the impact of variance underestimation on the national average relative rate estimate from the National Morbidity Mortality Air Pollution Study and we found that variance underestimation as much as 40% has little effect on the national average.

A Method for Visualizing Multivariate Time Series Data

Visualization and exploratory analysis is an important part of any data analysis and is made more challenging when the data are voluminous and high-dimensional. One such example is environmental monitoring data, which are often collected over time and at multiple locations, resulting in a geographically indexed multivariate time series. Financial data, although not necessarily containing a geographic component, present another source of high-volume multivariate time series data. We present the mvtsplot function which provides a method for visualizing multivariate time series data. We outline the basic design concepts and provide some examples of its usage by applying it to a database of ambient air pollution measurements in the United States and to a hypothetical portfolio of stocks.

ESTIMATING TEMPORAL ASSOCIATIONS IN ELECTROCORTICOGRAPHIC (ECoG) TIME SERIES WITH FIRST ORDER PRUNING

Granger causality (GC) is a statistical technique used to estimate temporal associations in multivariate time series. Many applications and extensions of GC have been proposed since its formulation by Granger in 1969. Here we control for potentially mediating or confounding associations between time series in the context of event-related electrocorticographic (ECoG) time series. A pruning approach to remove spurious connections and simultaneously reduce the required number of estimations to fit the effective connectivity graph is proposed. Additionally, we consider the potential of adjusted GC applied to independent components as a method to explore temporal relationships between underlying source signals. Both approaches overcome limitations encountered when estimating many parameters in multivariate time-series data, an increasingly common predicament in today's brain mapping studies.

Data-driven estimates of the number of clusters in multivariate time series

An important problem in unsupervised data clustering is how to determine the number of clusters. Here we investigate how this can be achieved in an automated way by using interrelation matrices of multivariate time series. Two nonparametric and purely data driven algorithms are expounded and compared. The first exploits the eigenvalue spectra of surrogate data, while the second employs the eigenvector components of the interrelation matrix. Compared to the first algorithm, the second approach is computationally faster and not limited to linear interrelation measures.

Detecting offsets in GPS time series: first results from the Detection of Offsets in GPS Experiment

The accuracy of Global Positioning System (GPS) time series is degraded by the presence of offsets. To assess the effectiveness of methods that detect and remove these offsets, we designed and managed the Detection of Offsets in GPS Experiment. We simulated time series that mimicked realistic GPS data consisting of a velocity component, offsets, white and flicker noises (1/f spectrum noises) composed in an additive model. The data set was made available to the GPS analysis community without revealing the offsets, and several groups conducted blind tests with a range of detection approaches. The results show that, at present, manual methods (where offsets are hand picked) almost always give better results than automated or semi‒automated methods (two automated methods give quite similar velocity bias as the best manual solutions). For instance, the fifth percentile range (5% to 95%) in velocity bias for automated approaches is equal to 4.2 mm/year (most commonly ±0.4 mm/yr from the truth), whereas it is equal to 1.8 mm/yr for the manual solutions (most commonly 0.2 mm/yr from the truth). The magnitude of offsets detectable by manual solutions is smaller than for automated solutions, with the smallest detectable offset for the best manual and automatic solutions equal to 5 mm and 8 mm, respectively. Assuming the simulated time series noise levels are representative of real GPS time series, robust geophysical interpretation of individual site velocities lower than 0.2–0.4 mm/yr is therefore certainly not robust, although a limit of nearer 1 mm/yr would be a more conservative choice. Further work to improve offset detection in GPS coordinates time series is required before we can routinely interpret sub‒mm/yr velocities for single GPS stations.

Stable-Isotope Time Series and Precipitation Origin from Firn-Core and Snow Samples, Altai Glaciers, Siberia

In the summers of 2001 and 2002, glacio-climatological research was performed at 4110-4120 m a.s.l. on the Belukha snow/firn plateau, Siberian Altai. Hundreds of samples from snow pits and a 21 m snow/firn core were collected to establish the annual/seasonal/monthly depth-accumulation scale, based on stable-isotope records, stratigraphic analyses and meteorological and synoptic data. The fluctuations of water stable-isotope records show well-preserved seasonal variations. The delta(18)O and delta D relationships in precipitation, snow pits and the snow/firn core have the same slope to the covariance as that of the global meteoric water line. The origins of precipitation nourishing the Belukha plateau were determined based on clustering analysis of delta(18)O and d-excess records and examination of synoptic atmospheric patterns. Calibration and validation of the developed clusters occurred at event and monthly timescales with about 15% uncertainty. Two distinct moisture sources were shown: oceanic sources with d-excess < 12 parts per thousand, and the Aral-Caspian closed drainage basin sources with d-excess > 12 parts per thousand. Two-thirds of the annual accumulation was from oceanic precipitation, of which more than half had isotopic ratios corresponding to moisture evaporated over the Atlantic Ocean. Precipitation from the Arctic/Pacific Ocean had the lowest deuterium excess, contributing one-tenth to annual accumulation.

Chow–Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series

Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20–30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g., in the context of therapeutical brain stimulation. In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct graphical models (so called Chow–Liu (CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient (CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature. Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones. Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.

A space-time analysis of reported shigellosis and salmonellosis cases in Texas from 2000 to 2004

Background. The purpose of this study was to describe the risk factors and demographics of persons with salmonellosis and shigellosis and to investigate both seasonal and spatial variations in the occurrence of these infections in Texas from 2000 to 2004, utilizing time series analyses and the geographic information system digital mapping methods. ^ Methods. Spatial Analysis: MapInfo software was used to map the distribution of age-adjusted rates of reported shigellosis and salmonellosis in Texas from 2000–2004 by zip codes. Census data on above or below poverty level, household income, highest level of educational attainment, race, ethnicity, and urban/rural community status was obtained from the 2000 Decennial Census for each zip code. The zip codes with the upper 10% and lower 10% were compared using t-tests and logistic regression to determine whether there were any potential risk factors. ^ Temporal analysis. Seasonal patterns in the prevalence of infections in Texas from 2000 to 2003 were determined by performing time-series analysis on the numbers of cases of salmonellosis and shigellosis. A linear regression was also performed to assess for trends in the incidence of each disease, along with auto-correlation and multi-component cosinor analysis. ^ Results. Spatial analysis: Analysis by general linear model showed a significant association between infection rates and age, with young children aged less than 5 and those aged 5–9 years having increased risk of infection for both disease conditions. The data demonstrated that those populations with high percentages of people who attained a higher than high school education were less likely to be represented in zip codes with high rates of shigellosis. However, for salmonellosis, logistic regression models indicated that when compared to populations with high percentages of non-high school graduates, having a high school diploma or equivalent increased the odds of having a high rate of infection. ^ Temporal analysis. For shigellosis, multi-component cosinor analyses were used to determine the approximated cosine curve which represented a statistically significant representation of the time series data for all age groups by sex. The shigellosis results show 2 peaks, with a major peak occurring in June and a secondary peak appearing around October. Salmonellosis results showed a single peak and trough in all age groups with the peak occurring in August and the trough occurring in February. ^ Conclusion. The results from this study can be used by public health agencies to determine the timing of public health awareness programs and interventions in order to prevent salmonellosis and shigellosis from occurring. Because young children depend on adults for their meals, it is important to increase the awareness of day-care workers and new parents about modes of transmission and hygienic methods of food preparation and storage. ^

Robust trends of landscape dynamics in the Arctic Lena Delta with temporally dense Landsat time-series stacks, with links to GeoTIFFs

Arctic permafrost landscapes are among the most vulnerable and dynamic landscapes globally, but due to their extent and remoteness most of the landscape changes remain unnoticed. In order to detect disturbances in these areas we developed an automated processing chain for the calculation and analysis of robust trends of key land surface indicators based on the full record of available Landsat TM, ETM +, and OLI data. The methodology was applied to the ~ 29,000 km**2 Lena Delta in Northeast Siberia, where robust trend parameters (slope, confidence intervals of the slope, and intercept) were calculated for Tasseled Cap Greenness, Wetness and Brightness, NDVI, and NDWI, and NDMI based on 204 Landsat scenes for the observation period between 1999 and 2014. The resulting datasets revealed regional greening trends within the Lena Delta with several localized hot-spots of change, particularly in the vicinity of the main river channels. With a 30-m spatial resolution various permafrost-thaw related processes and disturbances, such as thermokarst lake expansion and drainage, fluvial erosion, and coastal changes were detected within the Lena Delta region, many of which have not been noticed or described before. Such hotspots of permafrost change exhibit significantly different trend parameters compared to non-disturbed areas. The processed dataset, which is made freely available through the data archive PANGAEA, will be a useful resource for further process specific analysis by researchers and land managers. With the high level of automation and the use of the freely available Landsat archive data, the workflow is scalable and transferrable to other regions, which should enable the comparison of land surface changes in different permafrost affected regions and help to understand and quantify permafrost landscape dynamics.

The C37 alkenone record of sea water of time series station DYNAPROC

The concentrations of suspended particulate pigments, C37-C38 alkenones, total organic carbon and nitrogen in the Ligurian Sea (northwestern Mediterranean) have been studied at 5 and 30 m depth during well defined thermocline conditions. An accurate description of the short term changes of these compounds has been achieved by means of four 36-h sampling cycles each encompassing consecutive filtration periods of 4 h. During sampling the thermocline changes were followed closely by simultaneous measurements of water column temperature, salinity and other physical parameters. The analysis of the collected samples indicates that the Haptophyte pigments and alkenones are essentially synthesized at the levels of highest primary production and therefore the C37 alkenone record reflects the seawater temperature at this depth level. The study also shows that part of these alkenones are distributed throughout the water column in association to the suspended particles. This process results in C37 alkenone distributions that, due to their high resistance to chemical and microbial degradation, record the temperature of the highest primary productivity layers even at shallow (e.g., 5 m depth) or deep (e.g., 1100 m depth) waters.

Atmospheric and seawater carbon dioxide at time series station DYFAMED

A time series of fCO2, SST, and fluorescence data was collected between 1995 and 1997 by a CARIOCA buoy moored at the DyFAMed station (Dynamique des Flux Atmospheriques en Mediterranée) located in the northwestern Mediterranean Sea. On seasonal timescales, the spring phytoplankton bloom decreases the surface water fCO2 to approximately 290 µatm, followed by summer heating and a strong increase in fCO2 to a maximum of approximately 510 µatm. While the DELTA fCO2 shows strong variations on seasonal timescales, the annual average air-sea disequilibrium is only 2 µatm. Temperature-normalized fCO2 shows a continued decrease in dissolved CO2 throughout the summer and fall at a rate of approximately 0.6 µatm/d. The calculated annual air-sea CO2 transfer rate is -0.10 to -0.15 moles CO2 m-2 y-1, with these low values reflecting the relatively weak wind speed regime and small annual air-sea fCO2 disequilibrium. Extrapolating this rate over the whole Mediterranean Sea would lead to a flux of approximately -3 * 10**12 to -4.5 * 10**12 grams C/y, in good agreement with other estimates. An analysis of the effects of sampling frequency on annual air-sea CO2 flux estimates showed that monthly sampling is adequate to resolve the annual CO2 flux to within approximately ±10 - 18% at this site. Annual flux estimates made using temperature-derived fCO2 based on the measured fCO2-SST correlations are in agreement with measurement-based calculations to within ± 7-10% (depending on the gas transfer parameterization used), and suggest that annual CO2 flux estimates may be reasonably well predicted in this region from satellite or model-derived SST and wind speed information.

Collection of data on soil carbon (particulate and dissolved) in the Jena Experiment (Main Experiment, time series since 2002)

This data set contains three time series of measurements of soil carbon (particular and dissolved) from the main experiment plots of a large grassland biodiversity experiment (the Jena Experiment; see further details below). In the main experiment, 82 grassland plots of 20 x 20 m were established from a pool of 60 species belonging to four functional groups (grasses, legumes, tall and small herbs). In May 2002, varying numbers of plant species from this species pool were sown into the plots to create a gradient of plant species richness (1, 2, 4, 8, 16 and 60 species) and functional richness (1, 2, 3, 4 functional groups). Plots were maintained by bi-annual weeding and mowing. 1. Particulate soil carbon: Stratified soil sampling was performed every two years since before sowing in April 2002 and was repeated in April 2004, 2006 and 2008 to a depth of 30 cm segmented to a depth resolution of 5 cm giving six depth subsamples per core. Total carbon concentration was analyzed on ball-milled subsamples by an elemental analyzer at 1150°C. Inorganic carbon concentration was measured by elemental analysis at 1150°C after removal of organic carbon for 16 h at 450°C in a muffle furnace. Organic carbon concentration was calculated as the difference between both measurements of total and inorganic carbon. 2. Particulate soil carbon (high intensity sampling): In one block of the Jena Experiment soil samples were taken to a depth of 1 m (segmented to a depth resolution of 5 cm giving 20 depth subsamples per core) with three replicates per block ever 5 years starting before sowing in April 2002. Samples were processed as for the more frequent sampling. 3. Dissolved organic carbon: Suction plates installed on the field site in 10, 20, 30 and 60 cm depth were used to sample soil pore water. Cumulative soil solution was sampled biweekly and analyzed for dissolved organic carbon concentration by a high TOC elemental analyzer. Annual mean values of DOC are provided.