Low Autocorrelation Research Articles

Online Removal of Muscle Artifact from Electroencephalogram Signals Based on Canonical Correlation Analysis

The electroencephalogram (EEG) is often contaminated by electromyography (EMG). In this paper, a novel and robust technique is presented to eliminate EMG artifacts from EEG signals in real-time. First, the canonical correlation analysis (CCA) method is applied on the simulated EEG data contaminated by EMG and electrooculography (EOG) artifacts for separating EMG artifacts from EEG signals. The components responsible for EMG artifacts are distinguished from those responsible for brain activity based on the relative low autocorrelation. We demonstrate that the CCA method is more suitable to reconstruct the EMG-free EEG data than independent component analysis (ICA) methods. In addition, by applying CCA to analyze a number of EEG data contaminated by EMG artifacts, a correlation threshold is determined using an unbiased procedure. Hence, CCA can be used to remove EMG artifacts automatically. Finally, an example is given to verify that, after EMG artifacts were removed successfully from the EEG data contaminated by EMG and EOG simultaneously, not only the underlying brain activity signals but the EOG artifacts are preserved with little distortion.

Application of the PnET-BGC – An integrated biogeochemical model – To assess the surface water ANC recovery in the Adirondack region of New York under three multi-pollutant proposals

We applied an integrated biogeochemical model PnET-BGC to predict the response of acid neutralizing capacity (ANC) in lakes – a measure of the ability of water to neutralize inputs of strong acid – from 2001 to 2050 in the Adirondack region of New York, USA under three multi-pollutant proposal scenarios. Through model predictions, we assessed the impacts of these proposals on ecosystem recovery for research and policy initiatives. Our analysis indicated that the predicted recovery rates of surface water ANC obtained from the PnET-BGC model show low spatial autocorrelation. Predicted recovery rates are also closely related with the percentage of watershed areas of coniferous vegetation and deciduous vegetation, elevation and lake area, which turn out not to be significantly different from each other over the entire period of future scenarios (2001–2050). We applied a Geographic Weighted Regression model (GWR) to study the spatial patterns of predicted lake ANC in the Adirondacks through 2050 due to its high spatial autocorrelation. These results showed that lake depth and square of elevation can explain 40% of variation in the predicted ANC, which is 26% more variation than explained by the non-spatial Ordinary Least-Squares Regression (OLS). Our calculations also suggest that even under the Carper Bill, the most aggressive air pollutant control scenario considered, not all Adirondack lakes will recover (i.e., ANC > 50 μeq/L) from elevated acidic deposition by 2050. The research provides a basis for more informed emission controls and land use/land cover (LULC) policy-making in the north-eastern USA and elsewhere.

Low autocorrelation binary sequences: Number theory-based analysis for minimum energy level, Barker codes

Low autocorrelation binary sequences (LABS) are very important for communication applications. And it is a notoriously difficult computational problem to find binary sequences with low aperiodic autocorrelations. The problem can also be stated in terms of finding binary sequences with minimum energy levels or maximum merit factor defined by M.J.E. Golay, F=N22E, N and E being the sequence length and energy respectively. Conjectured asymptotic value of F is 12.32 for very long sequences. In this paper, a theorem has been proved to show that there are finite number of possible energy levels, spaced at an equal interval of 4, for the binary sequence of a particular length. Two more theorems are proved to derive the theoretical minimum energy level of a binary sequence of even and odd length of N to be N2 and N−12 respectively, making the merit factor equal to N and N2N−1 respectively. The derived theoretical minimum energy level successfully explains the case of N=13, for which the merit factor (F=14.083) is higher than the conjectured value. Sequence of lengths 4, 5, 7, 11, 13 are also found to be following the theoretical minimum energy level. These sequences are exactly the Barker sequences which are widely used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties. Further analysis shows physical reasoning in support of the conjecture that Barker sequences exists only when N⩽13 (this has been proven for all odd N).

Insights into succession processes using temporally repeated habitat models: results from a long‐term study in a post‐mining landscape

AbstractQuestions: The early phases of primary succession are governed by chance events and dispersal‐related processes in an environment that is largely free of competition. Thus, the predictability of vegetation patterns using environmental site factors can be expected to be low and spatial autocorrelation to be high. We asked whether the match between vegetation and environment becomes better in the course of succession, and whether vegetation types shift their realized niche with time.Location: Lignite mining region in Central Germany, the post‐mining landscape “Goitzsche” (Saxony‐Anhalt).Methods: Vegetation types were mapped in a 10‐m grid (total area 4.8 ha), starting in 1995, at 3‐year intervals until 2007. We used a temporal comparison of habitat models. We applied: GLS regression to partition the variation in coverage of vegetation types into environmental (soil pH) and spatial components; logistic regression to model the presence/absence of vegetation types along a soil acidity gradient; and autologistic regression allowing for soil acidity and neighbourhood effects.Results: For most vegetation types, the proportion of variation explained by space was high but declined during succession. The outcome of autologistic models suggests that soil acidity often plays a minor role compared to neighbourhood effects in the earlier phase of succession than 12 years later. For four vegetation types, the pH range in which the type was expected to be dominant clearly became smaller with time. These trends support the view that the role of processes related to chance and dispersal decrease with time, while those related to environmental filtering mediated by biotic interactions increase.Conclusions: We conclude that temporal comparisons of spatially explicit habitat models provide insights into changing biotic community processes and their effects on habitat specificity of species or their communities. Thus, this approach may be particularly important for analysis of ecological systems that are not in equilibrium with their environmental drivers.

Finding low autocorrelation binary sequences with memetic algorithms

This paper deals with the construction of binary sequences with low autocorrelation, a very hard problem with many practical applications. The paper analyzes several metaheuristic approaches to tackle this kind of sequences. More specifically, the paper provides an analysis of different local search strategies, used as stand-alone techniques and embedded within memetic algorithms. One of our proposals, namely a memetic algorithm endowed with a Tabu Search local searcher, performs at the state-of-the-art, as it consistently finds optimal sequences in considerably less time than previous approaches reported in the literature. Moreover, this algorithm is also able to provide new best-known solutions for large instances of the problem. In addition, a variant of this algorithm that explores only a promising subset of the whole search space (known as skew-symmetric sequences) is also analyzed. Experimental results show that this new algorithm provides new best-known solutions for very large instances of the problem.

Impacts of thinning on structure, growth and risk of crown fire in a Pinus sylvestris L. plantation in northern Spain

We studied the combined effects of thinning on stand structure, growth, and fire risk for a Scots pine thinning trial in northern Spain 4 years following treatment. The thinning treatments were: no thinning, heavy thinning (32–46% of basal area removed) and very heavy thinning (51–57% of basal area removed). Thinning was achieved via a combination of systematic and selective methods by removing every seventh row of trees and then by cutting suppressed and subdominant trees in the remaining rows (i.e., thinning from below). Four years after thinning, mean values and probability density distributions of stand structural indices showed that the heavier the thinning, the stronger the tendency towards random tree spatial positions. Height and diameter differentiation were initially low for these plantations and decreased after the 4-year period in both control and thinned plots. Mark variograms indicated low spatial autocorrelation in tree diameters at short distances. Diameter increment was significantly correlated with the inter-tree competition indices, and also with the mean directional stand structural index. Two mixed models were proposed for estimating diameter increment using a spatial index based on basal area of larger trees (BALMOD) in one model versus spatial competition index by Bella in the other model. As well, a model to estimate canopy bulk density (CBD) was developed, as this variable is important for fire risk assessment. Both heavy and very heavy thinning resulted in a decrease of crown fire risk over no thinning, because of the reduction in CBD. However, thinning had no effect on the height to crown base and thus on the flame length for torching. Overall, although thinning did not increase size differentiation between trees in the short term, the increase in diameter increment following thinning and the reduction of crown fire risks support the use of thinning. Also, thinning is a necessary first step towards converting Scots pine plantations to more natural mixed broadleaved woodlands. In particular, the very heavy thinning treatment could be considered a first step towards conversion of overstocked stands.

MODELING MULTIPLE REGIMES IN FINANCIAL VOLATILITY WITH A FLEXIBLE COEFFICIENT GARCH(1,1) MODEL

In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes is determined by a simple sequence of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the novel stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis and low first-order autocorrelation of the squared observations and exhibit the so-called Taylor effect, even with Gaussian errors. Estimation of the parameters is addressed, and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite-sample properties of the sequence of tests. Empirical examples are also considered.

Reparameterized and Marginalized Posterior and Predictive Sampling for Complex Bayesian Geostatistical Models

This article proposes a four-pronged approach to efficient Bayesian estimation and prediction for complex Bayesian hierarchical Gaussian models for spatial and spatiotemporal data. The method involves reparameterizing the covariance structure of the model, reformulating the means structure, marginalizing the joint posterior distribution, and applying a simplex-based slice sampling algorithm. The approach permits fusion of point-source data and areal data measured at different resolutions and accommodates nonspatial correlation and variance heterogeneity as well as spatial and/or temporal correlation. The method produces Markov chain Monte Carlo samplers with low autocorrelation in the output, so that fewer iterations are needed for Bayesian inference than would be the case with other sampling algorithms. Supplemental materials are available online.

SIDELOBES REDUCTION USING SIMPLE TWO AND TRI-STAGES NON LINEAR FREQUENCY MODULATION (NLFM)

The Linear Frequency Modulation (LFM) waveform is the most commonly and extensively used signal in practical radar system. However a compressed LFM signal at the receiver will produce the flrst sidelobe at a level of i13dB to the peak of the main lobe. A weighting function is needed to apply in order to reduce the sidelobes. However, the penalty of mismatch loss is clearly evident. It may reduce output SNR, typically by 1 to 2dB. Every single dB of additional SNR can have great efiects in reducing false alarm rates in target detection applications. In an efiort to achieve low autocorrelation sidelobe level without applying weighting function, Non-Linear Frequency Modulation (NLFM) signal has been investigated. This paper describes the sidelobe reduction techniques using simple two-stage FM waveform, modifled two-stage FM waveform and tri-stage FM waveform. Simulation results of the proposed NLFM signal are presented. Sidelobe reduction of more than i19dB can be achieved by this design without any weighting technique applied.

The Effect of Out-Wintering Pad Design on the Synchrony of Dairy Cow Behavior

The study investigated differences in behavior synchrony of dairy cows during the winter confinement period when managed in 1 of 3 out-wintering pad (OWP) systems, or indoors in free-stall housing. There were 2 replicates of each treatment, and observations were carried out on 3 recording occasions in January and February 2006. On each recording occasion, behavior was recorded every 30min between 0600 and 0130h the following day (n = 40). The outcomes for measurement were eligible cows lying (ECL), cow comfort index (CCI), and proportion of animals feeding (AF). Autocorrelation as an indicator of synchrony was calculated using the Durban-Watson statistic and compared across treatments. A centered moving average was calculated, used to obtain the residual, and compared between treatments. Low autocorrelations were recorded in free stalls (39.6±0.1%), indicating lower temporal behavioral synchrony than in the 3 OWP designs. Overall, the greatest proportion of ECL, CCI, and AF occurred in free stalls (60%). However, high proportions (>90%) of ECL were recorded on OWP in the early morning, whereas the range of ECL in free stalls (22 to 87%) was lower. The low overall proportions for ECL (44, 52, and 54%) and CCI (48, 55, and 58%) in the OWP were caused by the cows standing without feeding during daylight hours. Nevertheless, these cows performed more synchronized lying at night, and their behavior was more highly autocorrelated (65.9±0.1, 73.3±0.1, and 52.3±0.1%) than cows in free stalls. Synchrony of behavior is part of the normal behavior repertoire of herd-living animals such as dairy cattle, and OWP may promote a more natural circadian behavior pattern than do free-stall systems. It is important that indices such as CCI and ECL are utilized at appropriate times of the day, when cows are expected to lie; that is, during the evening time. Estimated acceptable levels of these indices may be dependent on the confinement system employed.

Spatial variability of seabird distribution associated with environmental factors: a case study of marine Important Bird Areas in the Azores

Abstract Amorim, P., Figueiredo, M., Machete, M., Morato, T., Martins, A., and Serrão Santos, R. 2009. Spatial variability of seabird distribution associated with environmental factors: a case study of marine Important Bird Areas in the Azores. – ICES Journal of Marine Science, 66: 29–40. The spatial structure and distribution at sea of Cory's shearwaters (Calonectris diomedea borealis), common terns (Sterna hirundo), and roseate terns (Sterna dougallii) were analysed in the Azores for various environmental factors: sea surface temperature, chlorophyll a concentration, distance to fronts, wind, distance to island shore or tern colonies, distance to seamounts, seabed slope, and depth. Data on seabird sightings were collected by observers on board fishing vessels, 2002–2006. Generalized linear modelling (GLM) explained 43 and 11% of the abundance variability for terns (both species pooled) and Cory's shearwaters, respectively. Variability in seabird abundance was mainly explained by month, wind, distance to shore and/or tern colonies, and distance to seamounts. Variogram modelling indicated that species distribution presented a small-scale spatial structure (i.e. low autocorrelation). Cory's shearwater predictive distribution maps showed widespread distribution patterns of abundance, despite occurring at a greater intensity around the islands and around some seamounts, which are areas of fishery interest. Conversely, terns were essentially concentrated near the shore. The establishment of marine important bird areas should be encouraged close to seabird colonies and around some seamount areas.

A New Approach for the Study of the Coast Indentation Index

Abstract The indentation index, which is the ratio between the real length of a coast and its Euclidean length, is a parameter applied to characterize rock coasts and to study their evolution. Rather than subjectively selecting two or more sectors of a rock coast, the method proposed in this paper considers analyzing the indentation index on the same coastline previously split into several adjacent tracts with equal Euclidean length. By digitizing the coastline in a GIS environment, it becomes possible to test several Euclidean length values on the same coastline, obtaining a different spatial variability of the indentation index with each trial. The best length values that maximize the spatial variability of the indentation index are those that determine an indentation index pattern characterized by high variance and low spatial autocorrelation. The spatial distribution of the indentation index can eventually be analyzed considering known littoral forces acting on the studied coast. When more than one Eu...

The effect of spatial autocorrelation and class proportion on the accuracy measures from different sampling designs

Four binary thematic maps with combinations of two spatial autocorrelation levels and two different class proportions are simulated to study their effect on the precision of accuracy measures from different sampling designs. A series of eleven sample sizes (from a minimum of 25 to a maximum of 1296) are simulated using three popular sampling designs, including simple random sampling (SRS), systematic sampling (SYS), and stratified random sampling (StrRS) on the four simulated maps. The conventional error matrix and related accuracy measures are calculated for each simulation, and the precision of different estimates of accuracy measures is compared among the three sampling designs. The selection of a particular sampling design and sample size depends on the spatial autocorrelation level, the class proportion difference, and the accuracy indices that a given application requires. In general, the class proportion difference has a greater impact on the performance of different sampling methods than the spatial autocorrelation level does on a map. For estimating the accuracy of individual classes, stratified sampling achieves better precision than SRS and SYS with smaller sample sizes, especially for estimating the small class. For estimating the overall accuracy, different sampling designs achieve very similar levels of precision with fewer samples. To achieve a better estimate of the kappa coefficient, stratified random sampling is recommended for use on a map with a high class proportion difference, while random sampling is preferred for a map with low spatial autocorrelation and a low class proportion difference.

Does a Gibbs sampler approach to spatial Poisson regression models outperform a single site MH sampler?

A Gibbs sampler for a Poisson regression model including spatial effects is presented and evaluated. The approach is based on that a Poisson regression model can be transformed into an approximate normal linear model by data augmentation using the introduction of two sequences of latent variables. It is shown how this methodology can be extended to spatial Poisson regression models and details of the resulting Gibbs sampler are given. In particular, the influence of model parameterisation and different update strategies on the mixing of the MCMC chains is discussed. The developed Gibbs samplers are analysed in two simulation studies and applied to model the expected number of claims for policyholders of a German car insurance company. The mixing of the Gibbs samplers depends crucially on the model parameterisation and the update schemes. The best mixing is achieved when collapsed algorithms are used, reasonable low autocorrelations for the spatial effects are obtained in this case. For the regression effects however, autocorrelations are rather high, especially for data with very low heterogeneity. For comparison a single component Metropolis–Hastings algorithms is applied which displays very good mixing for all components. Although the Metropolis–Hastings sampler requires a higher computational effort, it outperforms the Gibbs samplers which would have to be run considerably longer in order to obtain the same precision of the parameters.

SPATIAL AND TEMPORAL DYNAMICS IN A SEXUAL SELECTION MOSAIC

Selective regimes and phenotypic optima could either change smoothly and in a clinal fashion or be spatially organized in a more unpredictable mosaic pattern over the geographic landscape. When natural or sexual selection is driven by intra- or interspecific biotic interactions, fine-grained spatial variation in selective regimes could result in selection mosaics rather than clinal variation in selection. We investigated temporal variation and spatial organization in sexual selection on male body size along an ecological coastal-inland gradient of a polymorphic damselfly Ischnura elegans. Body size increased in a clinal fashion along this gradient: animals were smaller in size at the coast, but became larger in the inland areas. In contrast, the sexual selection regimes on male body size showed evidence of more fine-grained spatial organization with no evidence for a clinal pattern and low spatial autocorrelations between populations. These spatially fine-grained sexual selection regimes varied in sign and magnitude and were driven by a combination of the densities of heritable female color morphs and local female body sizes. We suggest that the spatial organization of the selective regimes can be interpreted as a sexual selection mosaic that is influenced by highly localized density- and frequency-dependent social interactions.

Characteristics of radial growth and stable isotopes in a single oak tree to be used in climate studies

In this study we have analyzed the variability of tree-ring widths and stable isotopes ( δ 13C and δ 18O) of a single sessile oak tree ( Quercus petraea (Matt.) Liebl.) since these parameters are critical in reconstructing the environment, particularly climatic conditions. Tree rings were separated into early- and latewood (EW t ; LW t ), tree ring (TR t ), and transfer tree ring (TTR t, the latter being the latewood plus the earlywood of the subsequent year. Mean sensitivity, simple correlation, partial correlation and autocorrelation analyses were applied to describe data and relationships. Although this research focused on a single tree, the results compared well with average site data. Widths and δ 18O values showed generally low autocorrelation for all tree-ring components, whereas δ 13C revealed highly significant autocorrelations for most tree-ring components. Mean sensitivity of the standardized values turned out to be high for δ 18O, marginally lower for width and the lowest for δ 13C. Correlation analyses have proven that the relationships within the tree-ring widths or within the isotope parameters are much stronger than across widths and isotope parameters. The study demonstrates the unique potential of all measured tree-ring data to be used as climate proxies.

Two applications of relative difference sets: Difference triangles and negaperiodic autocorrelation functions

The well-known difference sets have various connections with sequences and their correlation properties. It is the purpose of this note to give two more applications of the (not so well known) relative difference sets: we use them to construct difference triangles (based on an idea of A. Ling) and we show that a certain nonexistence result for semiregular relative difference sets implies the nonexistence of negaperiodic autocorrelation sequences (answering a question of Parker [Even length binary sequence families with low negaperiodic autocorrelation, in: Applied Algebra, Algebraic Algorithms and Error-correcting Codes, Melbourne, 2001, Lecture Notes in Computer Science, vol. 2227, Springer, Berlin, 2001, pp. 200–209.]).

A Multiresolution Analysis-Assisted Reinforcement Learning Approach to Run-by-Run Control

In recent years, the run-by run (RbR) control mechanism has emerged as a useful tool for keeping complex semiconductor manufacturing processes on target during repeated short production runs. Many types of RbR controllers exist in the literature of which the exponentially weighted moving average (EWMA) controller is widely used in the industry. However, EWMA controllers are known to have several limitations. For example, in the presence of multiscale disturbances and lack of accurate process models, the performance of EWMA controller deteriorates and often fails to control the process. Also, the control of complex manufacturing processes requires sensing of multiple parameters that may be spatially distributed. New control strategies that can successfully use spatially distributed sensor data are required. This paper presents a new multiresolution analysis (wavelet) assisted reinforcement learning (RL)-based control strategy that can effectively deal with both multiscale disturbances in processes and the lack of process models. The novel idea of a wavelet-aided RL-based controller represents a paradigm shift in the control of large-scale stochastic dynamic systems of which the control problem is a subset. Henceforth, we refer our new control strategy as a WRL-RbR controller. The WRL-RbR controller is tested on a multiple-input-multiple-output chemical mechanical planarization process of wafer fabrication for which the process model is available. Results show that the RL controller outperforms EWMA-based controllers for low autocorrelation. The new controller also performs quite well for strongly autocorrelated processes for which the EWMA controllers are known to fail. Convergence analysis of the new breed of the WRL-RbR controller is presented. Further enhancement of the controller to deal with model-free processes and for inputs coming from spatially distributed environments are also discussed. Note to Practitioners-This work was motivated by the need to develop an intelligent and efficient RbR process controller, especially for the control of processes with short production runs as in the case of the semiconductor manufacturing industry. A novel controller that is presented here is capable of generating optimal control actions in the presence of multiple time-frequency disturbances, and allows the use of realistic (often complex) process models without sacrificing robustness and speed of execution. Performance measures, such as reduction of variability in process output and control recipe, minimization of initial bias, and ability to control processes with high autocorrelations are shown to be superior in comparison to the commercially available exponentially weighted moving average controllers. The WRL-RbR controller is very generic, and can be easily extended to processes with drifts and sudden shifts in the mean and variance. The viability of extending the controller to distributed input parameter sensing environments, including those for which process models are not available, is also discussed

Spatial correlograms of soil cover as an indicator of landscape heterogeneity

Abstract Soil cover, which is one of the most informative and integrative landscape factors, can be used for the analysis of landscape patterns. We studied the spatial autocorrelation (Moran's I ) of raster format soil maps (1:10,000; 10 m pixel size) in 35 study areas representing all landscape regions in Estonia. The carbonate concentration of soils, volumetric soil moisture (%) and the depth of the groundwater table were taken into consideration in compiling a scale of contrast of 17 soil groups. We introduce a simple characteristic based on spatial correlograms: a half-value distance lag, h I = 0.5 —a distance where Moran's I drops below 0.5. Spatial autocorrelation decreased very rapidly in the case of heights with a very heterogeneous landscape composition, showing low values of h I = 0.5 ( h I = 0.5 I did decrease slowly with increasing lag, being >200 m in all forest and bog areas with complex topographical conditions due to the variety of glacial landforms and peatlands. All of the eight FRAGSTATS landscape metrics studied demonstrated significant correlations with h I = 0.5 , whereas five of them – Contrast Weighted Edge Density (CWED); Percentage of Like Adjacencies (PLADJ), Edge Density (ED), Patch Density (PD) and Mean Patch Area Distribution (AREA_MN) – had Spearman Rank Order Correlation values higher than 0.8. Landscapes with high ED, PD, and CWED values have a low autocorrelation: PD, ED, and CWED correlated negatively with h I = 0.5 . PD, ED, and CWED decreased and PLADJ increased with the power-law relationship with increasing h I = 0.5 . Spatial autocorrelation is lower in landscapes with complex structure and high contrast. The positive relationship with PLADJ indicates the same. Thus, spatial correlograms of potential landscape structure based on soil cover analysis can be used for the characterization of human-influenced landscape (land use) structure.

Designing substitution boxes for secure ciphers

In cryptography, a Substitution box (S-box) constitutes a cornerstone component of symmetric key algorithms. In block ciphers, they are typically used to obscure the relationship between the plaintext and the ciphertext. It is well-known that the more linear and the less auto-correlated the S-box is, the more resilient the cryptosystem that uses them. However, engineering a regular S-box that has the highest non-linearity and lowest auto-correlation properties is an NP-complete problem. In this paper, we exploit evolutionary computation to engineer regular S-boxes that present high non-linearity and low auto-correlation properties.