Use Of Surrogate Data Research Articles

Stability of infraslow correlation structure in time-shifted intracranial EEG signals.

It is increasingly understood that the epilepsies are characterized by network pathology that can span multiple spatial and temporal scales. Recent work indicates that infraslow (<0.2Hz) envelope correlations may form a basis for distant spatial coupling in the brain. We speculated that infraslow correlation structure may be preserved even with some time lag between signals. To this end, we studied intracranial EEG (icEEG) data collected from 22 medically refractory epilepsy patients. For each patient, we selected hour-long background, awake icEEG epochs before and after antiseizure medication (ASM) taper. For each epoch, we selected 5,000 random electrode contact pairs and estimated magnitude-squared coherence (MSC) below 0.15Hz of band power time-series in the traditional EEG frequency bands. Using these same contact pairs, we shifted one signal of the pair by random durations in 15-s increments between 0 and 300s. We aggregated these data across all patients to determine how infraslow MSC varies with duration of lag. We further examined the effect of ASM taper on infraslow correlation structure. We also used surrogate data to empirically characterize MSC estimator and to set optimal parameters for estimation specifically for the study of infraslow activity. Our empirical analysis of the MSC estimator showed that hour-long segments with MSC computed using 3-min windows with 50% overlap was sufficient to capture infraslow envelope correlations while minimizing estimator bias and variance. The mean MSC decreased monotonically with increasing time lag until 105s of lag, then plateaued between 106 and 300s. Significantly nonzero infraslow envelope MSC was preserved in all frequency bands until about 1min of time lag, both pre- and post-ASM taper. We also saw a slight, but significant increase in infraslow MSC post-ASM taper, consistent with prior work. These results provide evidence for the feasibility of examining infraslow activity via its modulation of higher-frequency activity in the absence of DC-coupled recordings. The use of surrogate data also provides a general methodology for benchmarking measures used in network neuroscience studies. Finally, our study points to the clinical relevance of infraslow activity in assessing seizure risk.

AIS-based characterization of navigation conflicts along the US Atlantic Coast prior to development of wind energy

This study characterizes navigation conflicts in a region with a large traffic volume along the United States (US) Atlantic Coast, using an empirical approach that analyzes Automated Identification System (AIS) data for a full year (2010). The region includes areas proposed for wind energy development, and this characterization of vessel conflicts could be useful as a baseline to evaluating the effect of offshore wind areas on navigation conflicts and vessel collisions. There have been no collisions reported within the study area. This study analyzes the one year of AIS data to obtain vessel tracks and makes simultaneous pairwise comparisons to determine the number and rate of vessel encounters and near-misses (navigation conflicts). For vessel pairs in an encounter (3 nm distance; crossing, head-on, overtaking), a ‘blind vessel’ assumption was used to calculate the number of potential near misses and potential collisions. Graphical analysis of the frequency of vessels involved in potential near misses produced vessel response curves that provided the time of peak frequencies prior to the time of closest approach for each encounter type. These peak times were up to 600 s prior to the time of closest approach. The analyses of potential near misses and collision used the data during the period between the time of peak frequency and the time of closest approach to filter the data used in the calculation of the probability of potential collisions. The period included collsion avoidance maneuvering. Statistical analyses are made to estimate the point values and uncertainty of near miss rates and the probability of potential collisions for each type of encounter from which bounding estimates of the collision rates are made. These bounding collision rates are found to be comparable with estimates from previous studies. Causation probabilities were also estimated and compared with previous studies. The response curves may also have utility in the simulation of navigation conflicts. The use of surrogate data to evaluate the effect of wind energy areas is considered, though their usefulness depends on comparability of traffic density and the level and type of traffic control systems implemented.

Data-Based Testing for Nonlinearity in Dynamical Systems: The Use of Surrogate Data

The use of Fourier-based surrogates for data-based testing for nonlinearity within system identification is introduced. It is shown that the presented method handles multi-input multi-output systems as easily as single-input single-output systems. In addition, the approach can be readily applied as a tool for validating nonlinear models by residual analysis. Furthermore, an extensive empirical analysis shows that the proposed methodology appears to be the most reliable alternative for detecting nonlinearity in general dynamical systems.

Indoor radon, geogenic radon surrogates and geology – Investigations on their correlation

The indoor radon concentration was measured in most houses in a couple of municipalities in Austria. At the same time the activity concentration of radium in soil, the soil gas radon concentration, the permeability of the ground and the ambient dose equivalent rate were also measured and the geological situations (geological units) were recorded too. From the indoor radon concentration and different house and living parameters a radon potential (Austrian radon potential) was derived which should represent the radon concentration in a standard room. Another radon potential (Neznal radon potential) was calculated from the soil gas radon concentration and the permeability. The aim of the investigation was to correlate all the different variables and to test if the use of surrogate data (e.g. geological information, ambient dose equivalent rate, etc.) can be used to judge the radon risk for an area without performing numerous indoor measurements.

The Use of Surrogate Data in Demographic Population Viability Analysis: A Case Study of California Sea Lions.

Reliable data necessary to parameterize population models are seldom available for imperiled species. As an alternative, data from populations of the same species or from ecologically similar species have been used to construct models. In this study, we evaluated the use of demographic data collected at one California sea lion colony (Los Islotes) to predict the population dynamics of the same species from two other colonies (San Jorge and Granito) in the Gulf of California, Mexico, for which demographic data are lacking. To do so, we developed a stochastic demographic age-structured matrix model and conducted a population viability analysis for each colony. For the Los Islotes colony we used site-specific pup, juvenile, and adult survival probabilities, as well as birth rates for older females. For the other colonies, we used site-specific pup and juvenile survival probabilities, but used surrogate data from Los Islotes for adult survival probabilities and birth rates. We assessed these models by comparing simulated retrospective population trajectories to observed population trends based on count data. The projected population trajectories approximated the observed trends when surrogate data were used for one colony but failed to match for a second colony. Our results indicate that species-specific and even region-specific surrogate data may lead to erroneous conservation decisions. These results highlight the importance of using population-specific demographic data in assessing extinction risk. When vital rates are not available and immediate management actions must be taken, in particular for imperiled species, we recommend the use of surrogate data only when the populations appear to have similar population trends.

AM-PAC "6-Clicks" functional assessment scores predict acute care hospital discharge destination.

Physical therapists and occupational therapists practicing in acute care hospitals play a crucial role in discharge planning. A standardized assessment of patients' function could be useful for discharge recommendations. The study objective was to determine the accuracy of "6-Clicks" basic mobility and daily activity measures for predicting discharge from an acute care hospital to a home or institutional setting. The study was retrospective and observational. "6-Clicks" scores obtained at initial visits by physical therapists or occupational therapists and patients' discharge destinations were used to develop and validate receiver operating characteristic curves for predicting discharge destination. Positive predictive values (PPV), negative predictive values (NPV), and likelihood ratios were calculated. Areas under the receiver operating characteristic curves for basic mobility scores were 0.857 (95% confidence interval [CI]=0.852, 0.862) and 0.855 (95% CI=0.850, 0.860) in development and validation samples, respectively. Areas under the curves for daily activity scores were 0.846 (95% CI=0.841, 0.851) and 0.845 (95% CI=0.840, 0.850) in development and validation samples, respectively. Cutoff scores providing the best accuracy for determining discharge destination were 42.9 for basic mobility and 39.4 for daily activity. For basic mobility, the PPV was 0.748 and the NPV was 0.801 in both development and validation samples. For daily activity, the PPVs were 0.787 and 0.784 and the NPVs were 0.748 and 0.746 in development and validation samples, respectively. Limitations included lack of information on the rater reliability of "6-Clicks" instruments, use of surrogate data for some discharge designations, and use of a clinical database for research purposes. This study provides evidence of the accuracy of "6-Clicks" scores for predicting destination after discharge from an acute care hospital.

Using Surrogate Data for Nonlinear Identification: A Case Study

The use of surrogate data for nonlinear identification is illustrated using a case study. It is shown how the surrogate data approach can be used to detect nonlinear features in the experimental data, and how this approach can be used to determine whether a model is insufficient for describing the detected nonlinear predictability. In order to develop a nonlinear model, the structure of an identified continuous time linear model is used. The developed continuous time nonlinear models are then evaluated, and some deemed adequate for capturing the nonlinear predictability of the data.

The effect of habitat degradation on the long term survival of the Critically Endangered Madagascar spider tortoise (Pyxis arachnoides)

Pyxis arachnoides inhabits the dry, coastal forests of southwest Madagascar; a biologically unique ecoregion severely threatened by unsustainable small scale agricultural practices. Using remotely sensed data we established vegetation loss remains unabated within our study area at 1.2% year−1; consistent with ecoregion wide vegetation loss between 1990 and 2000. We monitored tortoise population density on four occasions over 8years and developed a stage class projection matrix to model the finite growth rate, matrix sensitivities and elasticities of the population. Monitoring revealed an actual mean population decline of 10.8% between 2003 and 2011. Our projection matrix model suggested the finite rate of growth to be λ=0.986, indicative of 1.4% year−1 decline for the duration of the existence of the population, with adult survival as the most sensitive parameter to overall survival of the population. Projection modeling suggests that the population would possibly become functionally non viable in approximately 170years. As our study was heavily reliant on the use of surrogate data, more information is needed on pre-adult survival and wild reproductive rates. Our study site currently represents a population of exceptional density, therefore, other less dense populations, subjected to the further stresses of poaching will likely become functionally non viable much sooner. This study highlights the utility of population projection matrices in determining the vulnerability of chelonians; a globally threatened taxon. In the case of the spider tortoise, well coordinated development programs and tighter protected area management are required to address the poverty induced drivers forcing this species closer to extinction.

Monitoring forest areas from continental to territorial levels using a sample of medium spatial resolution satellite imagery

A global systematic sampling scheme has been developed by the UN FAO and the EC TREES project to estimate rates of deforestation at global or continental levels at intervals of 5 to 10 years. This global scheme can be intensified to produce results at the national level. In this paper, using surrogate observations, we compare the deforestation estimates derived from these two levels of sampling intensities (one, the global, for the Brazilian Amazon the other, national, for French Guiana) to estimates derived from the official inventories. We also report the precisions that are achieved due to sampling errors and, in the case of French Guiana, compare such precision with the official inventory precision. We extract nine sample data sets from the official wall-to-wall deforestation map derived from satellite interpretations produced for the Brazilian Amazon for the year 2002 to 2003. This global sampling scheme estimate gives 2.81 million ha of deforestation (mean from nine simulated replicates) with a standard error of 0.10 million ha. This compares with the full population estimate from the wall-to-wall interpretations of 2.73 million ha deforested, which is within one standard error of our sampling test estimate. The relative difference between the mean estimate from sampling approach and the full population estimate is 3.1%, and the standard error represents 4.0% of the full population estimate. This global sampling is then intensified to a territorial level with a case study over French Guiana to estimate deforestation between the years 1990 and 2006. For the historical reference period, 1990, Landsat-5 Thematic Mapper data were used. A coverage of SPOT-HRV imagery at 20 m × 20 m resolution acquired at the Cayenne receiving station in French Guiana was used for year 2006. Our estimates from the intensified global sampling scheme over French Guiana are compared with those produced by the national authority to report on deforestation rates under the Kyoto protocol rules for its overseas department. The latter estimates come from a sample of nearly 17,000 plots analyzed from same spatial imagery acquired between year 1990 and year 2006. This sampling scheme is derived from the traditional forest inventory methods carried out by IFN (Inventaire Forestier National). Our intensified global sampling scheme leads to an estimate of 96,650 ha deforested between 1990 and 2006, which is within the 95% confidence interval of the IFN sampling scheme, which gives an estimate of 91,722 ha, representing a relative difference from the IFN of 5.4%. These results demonstrate that the intensification of the global sampling scheme can provide forest area change estimates close to those achieved by official forest inventories (<6%), with precisions of between 4% and 7%, although we only estimate errors from sampling, not from the use of surrogate data. Such methods could be used by developing countries to demonstrate that they are fulfilling requirements for reducing emissions from deforestation in the framework of an REDD (Reducing Emissions from Deforestation in Developing Countries) mechanism under discussion within the United Nations Framework Convention on Climate Change (UNFCCC). Monitoring systems at national levels in tropical countries can also benefit from pan-tropical and regional observations, to ensure consistency between different national monitoring systems.

Information Flow and Application to Epileptogenic Focus Localization From Intracranial EEG

Transfer entropy ( TE) is a recently proposed measure of the information flow between coupled linear or nonlinear systems. In this study, we suggest improvements in the selection of parameters for the estimation of TE that significantly enhance its accuracy and robustness in identifying the direction and the level of information flow between observed data series generated by coupled complex systems. We show the application of the improved TE method to long (in the order of days; approximately a total of 600 h across all patients), continuous, intracranial electroencephalograms (EEG) recorded in two different medical centers from four patients with focal temporal lobe epilepsy (TLE) for localization of their foci. All patients underwent ablative surgery of their clinically assessed foci. Based on a surrogate statistical analysis of the TE results, it is shown that the identified potential focal sites through the suggested analysis were in agreement with the clinically assessed sites of the epileptogenic focus in all patients analyzed. It is noteworthy that the analysis was conducted on the available whole-duration multielectrode EEG, that is, without any subjective prior selection of EEG segments or electrodes for analysis. The above, in conjunction with the use of surrogate data, make the results of this analysis robust. These findings suggest a critical role TE may play in epilepsy research in general, and as a tool for robust localization of the epileptogenic focus/foci in patients with focal epilepsy in particular.

Data-Driven Significance Estimation for Precise Spike Correlation

The mechanisms underlying neuronal coding and, in particular, the role of temporal spike coordination are hotly debated. However, this debate is often confounded by an implicit discussion about the use of appropriate analysis methods. To avoid incorrect interpretation of data, the analysis of simultaneous spike trains for precise spike correlation needs to be properly adjusted to the features of the experimental spike trains. In particular, nonstationarity of the firing of individual neurons in time or across trials, a spike train structure deviating from Poisson, or a co-occurrence of such features in parallel spike trains are potent generators of false positives. Problems can be avoided by including these features in the null hypothesis of the significance test. In this context, the use of surrogate data becomes increasingly important, because the complexity of the data typically prevents analytical solutions. This review provides an overview of the potential obstacles in the correlation analysis of parallel spike data and possible routes to overcome them. The discussion is illustrated at every stage of the argument by referring to a specific analysis tool (the Unitary Events method). The conclusions, however, are of a general nature and hold for other analysis techniques. Thorough testing and calibration of analysis tools and the impact of potentially erroneous preprocessing stages are emphasized.

Surrogate data – a secure way to share corporate data

The privacy of chemical structure is of paramount importance for the industrial sector, in particular for the pharmaceutical industry. At the same time, companies handle large amounts of physico-chemical and biological data that could be shared in order to improve our molecular understanding of pharmacokinetic and toxicological properties, which could lead to improved predictivity and shorten the development time for drugs, in particular in the early phases of drug discovery. The current study provides some theoretical limits on the information required to produce reverse engineering of molecules from generated descriptors and demonstrates that the information content of molecules can be as low as less than one bit per atom. Thus theoretically just one descriptor can be used to completely disclose the molecular structure. Instead of sharing descriptors, we propose to share surrogate data. The sharing of surrogate data is nothing else but sharing of reliably predicted molecules. The use of surrogate data can provide the same information as the original set. We consider the practical application of this idea to predict lipophilicity of chemical compounds and we demonstrate that surrogate and real (original) data provides similar prediction ability. Thus, our proposed strategy makes it possible not only to share descriptors, but also complete collections of surrogate molecules without the danger of disclosing the underlying molecular structures.

Construction of multivariate surrogate sets from nonlinear data using the wavelet transform

The use of surrogate data has become a crucial first step in the study of nonlinearity in time series data. A widely used technique to construct surrogate data is to randomize the phases of the data in the Fourier domain. In this paper, an alternative technique based on the resampling of wavelet coefficients is discussed. This approach exploits between scale correlations that exist within nonlinear data but which are either absent or weak in stochastic data. It proceeds by transforming the data into the wavelet domain and permuting the wavelet coefficients. Experimental and numerical time series data are used to demonstrate that the performance of the wavelet resampling technique is comparable to phase randomization in terms of the preservation of linear properties, removal of nonlinear structure and computational demands. However, the wavelet technique may have specific and distinct advantages in the application to complex data sets, such as numerical analysis of turbulence and experimental brain imaging data, where wavelets give a more parsimonious representation of spatio-temporal patterns than Fourier modes. It is shown that different techniques of resampling the data in the wavelet domain may optimize the construction of surrogate data according to the properties of the experimental time series and computational constraints.

A quantitative study of gamma-band activity in human intracranial recordings triggered by visual stimuli.

This paper studies gamma-band responses from two implanted epileptic patients during a simple visual discrimination task. Our main aim was to ascertain, in a reliable manner, whether evoked (stimulus-locked) and induced (triggered by, but not locked to, stimuli) responses are present in intracranial recordings. For this purpose, we introduce new methods adapted to detect the presence of gamma responses at this level of recording, intermediary between EEG-scalp and unicellular responses. The analysis relies on a trial-by-trial time-frequency analysis and on the use of surrogate data for statistical testing. We report that visual stimulation reliably elicits evoked and induced responses in human intracranial recordings. Induced intracranial gamma activity is significantly present in short oscillatory bursts (a few cycles) following visual stimulation. These responses are highly variable from trial to trial, beginning after 200 ms and lasting up to 500 ms. In contrast, intracranial-evoked gamma responses concentrate around 100 ms latencies corresponding to evoked responses observed on the scalp. We discuss our results in relation to scalp gamma response in a similar protocol [Tallon-Baudry et al. (1996) J. Neurosci., 16, 4240-4249] and draw some conclusions for bridging the gap between gamma oscillations observed on the scalp surface and their possible cortical sources.

Entropies of short binary sequences in heart period dynamics.

Dynamic aspects of R-R intervals have often been analyzed by means of linear and nonlinear measures. The goal of this study was to analyze binary sequences, in which only the dynamic information is retained, by means of two different aspects of regularity. R-R interval sequences derived from 24-h electrocardiogram (ECG) recordings of 118 healthy subjects were converted to symbolic binary sequences that coded the beat-to-beat increase or decrease in the R-R interval. Shannon entropy was used to quantify the occurrence of short binary patterns (length N = 5) in binary sequences derived from 10-min intervals. The regularity of the short binary patterns was analyzed on the basis of approximate entropy (ApEn). ApEn had a linear dependence on mean R-R interval length, with increasing irregularity occurring at longer R-R interval length. Shannon entropy of the same sequences showed that the increase in irregularity is accompanied by a decrease in occurrence of some patterns. Taken together, these data indicate that irregular binary patterns are more probable when the mean R-R interval increases. The use of surrogate data confirmed a nonlinear component in the binary sequence. Analysis of two consecutive 24-h ECG recordings for each subject demonstrated good intraindividual reproducibility of the results. In conclusion, quantification of binary sequences derived from ECG recordings reveals properties that cannot be found using the full information of R-R interval sequences.

Environmental diversity: on the best-possible use of surrogate data for assessing the relative biodiversity of sets of areas

The conservation goal of representation of biodiversity (in the broad sense of all species) in protected areas requires best-possible use of available surrogate information. One standard approach is based on ‘indicator’ groups of taxa. A minimum set of areas having at least one representation of each indicator species is taken to be representative of other organisms. This same minimum-set approach is adapted to other ‘attributes’ of biodiversity, for example, derived environmental clusters. A weakness of these approaches is that useful information is lost; for example, for environmental clusters, there is no distinction made either among or within clusters. A more powerful surrogate approach can use some expression of environmental and/or biotic pattern so that variation among areas is seen as part of a continuum rather than partitioned into arbitrary clusters/attributes. The challenge in using pattern effectively is to adopt a robust model for the relationship between pattern and the underlying units of biodiversity, i.e. species. An environmental space (a continuum or ordination pattern), combined with the standard ecological continuum model relating species to environmental space, has advantages over other patterns based on hierarchy or distance matrices. Because an environmental space can be estimated either directly (observed environmental data) or indirectly (data on indicator groups), the corresponding surrogate-measure of biodiversity, ‘environmental diversity’ (ED) makes best-possible use of either kind of data. We conclude that the arbitrariness of the ‘attribute’ approach can be replaced by a robust surrogate ‘pattern’ approach that is flexible and avoids unwarranted assumptions.

Fast wavelet transformation of EEG

Wavelet transforms offer certain advantages over Fourier transform techniques for the analysis of EEG. Recent work has demonstrated the applicability of wavelets for both spike and seizure detection, but the computational demands have been excessive. We compare the quality of feature extraction of continuous wavelet transforms using standard numerical techniques, with more rapid algorithms utilizing both polynomial splines and multiresolution frameworks. We further contrast the difference between filtering with and without the use of surrogate data to model background noise, demonstrate the preservation of feature extraction with critical versus redundant sampling, and perform the analyses with wavelets of different shape. Comparison is made with windowed Fourier transforms, similarity filtered, at different data window lengths. We here report a dramatic reduction in computational time required to perform this analysis, without compromising the accuracy of feature extraction. It now appears technically feasible to filter and decompose EEG using wavelet transforms in real time with ordinary microprocessors.

Chaos and physiology: deterministic chaos in excitable cell assemblies.

In this review we examined the emerging science of deterministic chaos (nonlinear systems theory) and its application to selected physiological systems. Although many of the popular images of fractals represent fascination and beauty that by analogy corresponds to nature as we see it, the question remains as to its ultimate meaning for physiological processes. It was our intent to help clarify this somewhat popular, somewhat obscure area of nonlinear dynamics in the context of an ever-changing procedural base. We examined not only the basic concepts of chaos, but also its applications ranging from observations in single cells to the complexity of the EEG. We have not suggested that nonlinear dynamics will answer all of our questions; however, we did attempt to illustrate ways in which this approach may help us to answer new questions and to rearticulate old ones. Chaos is revolutionary in that the overall approach requires us to adopt a different frame of reference which, at times, may move us away from previous concerns and methods of data analysis. In sections I-IV, we summarized the nonlinear dynamics approach and described its application to physiology and neural systems. First, we presented a general overview of the application of nonlinear dynamical techniques to neural systems. We discussed the manner in which even apparently simple deterministic systems can behave in an unpredictable manner. Second, we described the principles of nonlinear dynamical systems including the derived analytical techniques. We now see a variety of procedures for delineating whether frenetic chaotic behavior results from a nonlinear dynamical system with a few degrees of freedom, or whether it is caused by an infinite number of variables, i.e., noise. Third, we approached the applications of nonlinear procedures to the cardiovascular systems and to the neurosciences. In terms of time series, we described initial studies which applied the now "traditional" measures of dimensionality (e.g., based on the algorithm by Grassberger and Procaccia) and information change (e.g., Lyapunov exponents). Examples include our own work and that of Pritchard et al., demonstrating that the dynamics of neural mass activity reflect psychopathological states. Today, however, the trend has expanded to include the use of surrogate data and statistical null hypotheses testing to examine whether a given time series can be considered different from that of white or colored noise (cf. Ref. 262). One of the most important potential applications is that of quantifying changes in nonlinear dynamics to predict future states of the system.(ABSTRACT TRUNCATED AT 400 WORDS)