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Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.

Olive (Olea europaea L.) is one of the first domesticated and cultivated tree species and has historical, social and economical relevance. However, its future as a strategic commodity in Mediterranean agriculture is threatened by diverse biotic (traditional and new/emerging pests and diseases) and abiotic (erosion, climate change) menaces. These problems could also be of relevance for new geographical areas where olive cultivation is not traditional but is increasingly spreading (i.e., South America, Australia, etc). One of the major constraints for olive cultivation is Verticillium wilt, a vascular disease caused by the soil-borne fungus Verticillium dahliae Kleb. In this review we describe how Verticillium wilt of olive (VWO) has become a major problem for olive cultivation during the last two decades. Similar to other vascular diseases, VWO is difficult to manage and single control measure are mostly ineffective. Therefore, an integrated disease management strategy that fits modern sustainable agriculture criteria must be implemented. Multidisciplinary research efforts and advances to understand this pathosystem and to develop appropriate control measures are summarized. The main conclusion is that a holistic approach is the best strategy to effectively control VWO, integrating biological, chemical, physical, and cultural approaches.

The evaluation of complexity in univariate signals has attracted considerable attention in recent years. This is often done using the framework of Multiscale Entropy, which entails two basic steps: coarse-graining to consider multiple temporal scales, and evaluation of irregularity for each of those scales with entropy estimators. Recent developments in the field have proposed modifications to this approach to facilitate the analysis of short-time series. However, the role of the downsampling in the classical coarse-graining process and its relationships with alternative filtering techniques has not been systematically explored yet. Here, we assess the impact of coarse-graining in multiscale entropy estimations based on both Sample Entropy and Dispersion Entropy. We compare the classical moving average approach with low-pass Butterworth filtering, both with and without downsampling, and empirical mode decomposition in Intrinsic Multiscale Entropy, in selected synthetic data and two real physiological datasets. The results show that when the sampling frequency is low or high, downsampling respectively decreases or increases the entropy values. Our results suggest that, when dealing with long signals and relatively low levels of noise, the refine composite method makes little difference in the quality of the entropy estimation at the expense of considerable additional computational cost. It is also found that downsampling within the coarse-graining procedure may not be required to quantify the complexity of signals, especially for short ones. Overall, we expect these results to contribute to the ongoing discussion about the development of stable, fast and robust-to-noise multiscale entropy techniques suited for either short or long recordings.

Due to the non-linearity of numerous physiological recordings, non-linear analysis of multi-channel signals has been extensively used in biomedical engineering and neuroscience. Multivariate multiscale sample entropy (MSE–mvMSE) is a popular non-linear metric to quantify the irregularity of multi-channel time series. However, mvMSE has two main drawbacks: (1) the entropy values obtained by the original algorithm of mvMSE are either undefined or unreliable for short signals (300 sample points); and (2) the computation of mvMSE for signals with a large number of channels requires the storage of a huge number of elements. To deal with these problems and improve the stability of mvMSE, we introduce multivariate multiscale dispersion entropy (MDE–mvMDE), as an extension of our recently developed MDE, to quantify the complexity of multivariate time series. We assess mvMDE, in comparison with the state-of-the-art and most widespread multivariate approaches, namely, mvMSE and multivariate multiscale fuzzy entropy (mvMFE), on multi-channel noise signals, bivariate autoregressive processes, and three biomedical datasets. The results show that mvMDE takes into account dependencies in patterns across both the time and spatial domains. The mvMDE, mvMSE, and mvMFE methods are consistent in that they lead to similar conclusions about the underlying physiological conditions. However, the proposed mvMDE discriminates various physiological states of the biomedical recordings better than mvMSE and mvMFE. In addition, for both the short and long time series, the mvMDE-based results are noticeably more stable than the mvMSE- and mvMFE-based ones. For short multivariate time series, mvMDE, unlike mvMSE, does not result in undefined values. Furthermore, mvMDE is faster than mvMFE and mvMSE and also needs to store a considerably smaller number of elements. Due to its ability to detect different kinds of dynamics of multivariate signals, mvMDE has great potential to analyse various signals.

Research into binary network analysis of brain function faces a methodological challenge in selecting an appropriate threshold to binarise edge weights. For EEG phase-based functional connectivity, we test the hypothesis that such binarisation should take into account the complex hierarchical structure found in functional connectivity. We explore the density range suitable for such structure and provide a comparison of state-of-the-art binarisation techniques, the recently proposed Cluster-Span Threshold (CST), minimum spanning trees, efficiency-cost optimisation and union of shortest path graphs, with arbitrary proportional thresholds and weighted networks. We test these techniques on weighted complex hierarchy models by contrasting model realisations with small parametric differences. We also test the robustness of these techniques to random and targeted topological attacks. We find that the CST performs consistenty well in state-of-the-art modelling of EEG network topology, robustness to topological network attacks, and in three real datasets, agreeing with our hypothesis of hierarchical complexity. This provides interesting new evidence into the relevance of considering a large number of edges in EEG functional connectivity research to provide informational density in the topology.

Background and aims The olive root endophyte Pseudomonas fluorescens PICF7 is an effective biocontrol agent of Verticillium wilt of olive (VWO). Colonization of olive roots either by strain PICF7 or by Verticillium dahliae triggers differential systemic transcriptomic responses, many of them related with defense-related genes. The aims were to develop an olive split-root system for assessing VWO development and biocontrol effectiveness of strain PICF7 in plants with a divided root architecture, and for evaluating systemic defense responses during this tripartite interaction when strain PICF7 and V. dahliae are spatially separated. Methods An olive split-root system was generated and disease development, biocontrol effectiveness and systemic genetic responses in these plants upon strain PICF7 and V. dahliae colonization were compared to those reported and observed in olive plants grown under standard conditions (single pots). Specific defense-related genes, previously identified during PICF7- and/ or V. dahliae-olive root interactions were selected and their expression patterns assessed in above-ground tissues by real-time qPCR analyses. Results Symptoms of VWO developed similarly both in split-root and single-root plants. However, even though PICF7 triggered systemic defense responses in aerial tissues prior to the infection by V. dahliae, effective biocontrol was not observed under these experimental conditions. While most of studied genes showed similar expression patterns along time in both systems (i.e. split root and single pot), some of them (e.g. the caffeoyl-O-methyltransferase coding gene) varied depending on whether strain PICF7 and V. dahliae were spatially separated or shared the same compartment. Conclusions A successful split-root system was generated to investigate genetic events taking place during the tripartite interaction olive-V. dahliae-P. fluorescens PICF7. VWO biocontrol by strain PICF7 must rely on mechanisms other than induction of systemic resistance responses. The expression pattern of specific defense-related olive genes depended on whether or not the biocontrol agent and the pathogen share the same root/soil region.

Modularity is a well-established concept for assessing community structures in various single and multi-layer networks, including those in biological and social domains. Brain networks are known to exhibit community structure at a variety of scales—local, meso, and global scale. However, modularity, while useful in describing mesoscale brain organization, is limited as a metric to a global scale describing the overall strength of community structure. This approach, while valuable, overlooks important variations in community structure at node level. To address this limitation, we extended modularity to individual nodes. This novel measure of nodal modularity ( nQ ) captures both mesoscale and local-scale changes in modularity. We hypothesized that nQ would illuminate granular changes in the brain due to diseases such as Alzheimer’s disease (AD), which are known to disrupt the brain’s modular structure. We explored nQ in multiplex networks of a visual short-term memory binding task in fMRI and DTI data in the early stages of AD. While limited by sample size, changes in nQ for individual regions of interest (ROIs) in our fMRI networks were predominantly observed in visual, limbic, and paralimbic systems in the brain, aligning with known AD trajectories and linked to amyloid- β and tau deposition. Furthermore, observed changes in white-matter microstructure in our DTI networks in parietal and frontal regions may compliment studies of white-matter integrity in poor memory binders. Additionally, nQ clearly differentiated MCI from MCI converters indicating that nQ may be sensitive to this key turning point of AD. Our findings demonstrate the utility of nQ as a measure of localized group structure, providing novel insights into task and disease-related variability at the node level. Given the widespread application of modularity as a global measure, nQ represents a significant advancement, providing a granular measure of network organization applicable to a wide range of disciplines.

Controlling Verticillium wilt of olive (VWO), caused by the fungus Verticillium dahliae , is a challenge in all olive-growing regions worldwide. Although a wide variety of strategies against this disease have been evaluated, they are not useful for achieving optimal control. Biological control has been postulated as one of the most promising alternatives to prevent VWO. Thus, the goal of this study was to evaluate the effects of 19 natural products and microbial strains, including amino acids, microorganisms, organic amendments, biofertilizers based on copper and potassium, and essential thyme oils, under field conditions. The compounds were selected from 49 treatments that were previously evaluated against V. dahliae under laboratory or field conditions to confirm or validate their effectiveness against VWO. To this end, two experimental fields of the olive cv. Picual were established in orchards with moderate V. dahliae inoculum densities in the soil as representative of the main olive growing areas across southern Spain. The treatments were applied by spraying or irrigation in spring and autumn, and the disease severity was monitored over three experimental years. Our results confirmed the effectiveness of Fusarium oxysporum FO12, the organic amendment olive waste compost CAL03 and grape marc compost CGR03, and the CAL03 + FO12 mixture as the most effective treatments against VWO in the field. This work provides useful information about the use of environmentally friendly products against VWO.

We performed a comparative study to select the efficient mother wavelet (MWT) basis functions that optimally represent the signal characteristics of the electrical activity of the human brain during a working memory (WM) task recorded through electro-encephalography (EEG). Nineteen EEG electrodes were placed on the scalp following the 10–20 system. These electrodes were then grouped into five recording regions corresponding to the scalp area of the cerebral cortex. Sixty-second WM task data were recorded from ten control subjects. Forty-five MWT basis functions from orthogonal families were investigated. These functions included Daubechies (db1–db20), Symlets (sym1–sym20), and Coiflets (coif1–coif5). Using ANOVA, we determined the MWT basis functions with the most significant differences in the ability of the five scalp regions to maximize their cross-correlation with the EEG signals. The best results were obtained using “sym9” across the five scalp regions. Therefore, the most compatible MWT with the EEG signals should be selected to achieve wavelet denoising, decomposition, reconstruction, and sub-band feature extraction. This study provides a reference of the selection of efficient MWT basis functions.

Olive trees are the most cultivated evergreen trees in the Mediterranean Basin, where they have deep historical and socioeconomic roots. The fungus Verticillium dahliae develops inside the vascular bundles of the host, and there are no effective applicable treatments, making it difficult to control the disease. In this sense, the use of integrated disease management, specifically the use of resistant cultivars, is the most effective means to alleviate the serious damage that these diseases are causing and reduce the expansion of this pathogen. In 2008, the University of Cordoba started a project under the UCO Olive Breeding Program whose main objective has been to develop new olive cultivars with high resistance to Verticillium wilt. Since 2008, more than 18,000 genotypes from 154 progenies have been evaluated. Only 19.9% have shown some resistance to the disease in controlled conditions and only 28 have been preselected due to their resistance in field condition and remarkable agronomic characteristics. The results of this study represent an important advancement in the generation of resistant olive genotypes that will become commercial cultivars currently demanded by the olive growing sector. Our breeding program has proven successful, allowing the selection of several new genotypes with high resistance to the disease and agronomical performance. It also highlights the need for long-term field evaluations for the evaluation of resistance and characterization of olive genotypes.