Time-Series Analysis Using Third-Order Recurrence Plots

Higher-order recurrence plots may enable us to reveal more structure than what is possible with traditional recurrence plots (RPs). While RPs attempt to detect recurrence relations by pair-wise comparison of time-delayed embeddings, given a time series, higher-order RPs may detect recurrences by comparing multiple time-delayed embeddings simultaneously. In this work, we limit ourselves to third-order recurrence plots (TORPs) for time series analysis, as they can still be graphed straightforwardly, and propose future directions

Noninvasive Assessment of Spatio-Temporal Recurrence in Atrial Fibrillation

Propagation of Atrial Activity during atrial fibrillation (AF) is a complex phenomenon characterized by a certain degree of recurrence (periodic repetition). In this study, we investigated the possibility to detect recurrence noninvasively from body surface potential map recordings in patients affected by persistent AF, and localize this recurrence both in time and space. Results showed that clusters of recurrence can be identified from body surface recordings in these patients. Moreover, the number of clusters detected and their location on the top-right of the back of the torso were significantly associated with AF recurrence 4 to 6 weeks after electrical cardioversion. This suggests that noninvasive quantification of recurrence in persistent AF patients is possible, and may contribute to improve patient stratification

Unexpected diversity in socially synchronized rhythms of shorebirds

The behavioural rhythms of organisms are thought to be under strong selection, influenced by the rhythmicity of the environment. Such behavioural rhythms are well studied in isolated individuals under laboratory conditions, but free-living individuals have to temporally synchronize their activities with those of others, including potential mates, competitors, prey and predators. Individuals can temporally segregate their daily activities (for example, prey avoiding predators, subordinates avoiding dominants) or synchronize their activities (for example, group foraging, communal defence, pairs reproducing or caring for offspring). The behavioural rhythms that emerge from such social synchronization and the underlying evolutionary and ecological drivers that shape them remain poorly understood. Here we investigate these rhythms in the context of biparental care, a particularly sensitive phase of social synchronization where pair members potentially compromise their individual rhythms. Using data from 729 nests of 91 populations of 32 biparentally incubating shorebird species, where parents synchronize to achieve continuous coverage of developing eggs, we report remarkable within-and between-species diversity in incubation rhythms. Between species, the median length of one parent's incubation bout varied from 1-19 h, whereas period length-the time in which a parent's probability to incubate cycles once between its highest and lowest value-varied from 6-43 h. The length of incubation bouts was unrelated to variables reflecting energetic demands, but species relying on crypsis (the ability to avoid detection by other animals) had longer incubation bouts than those that are readily visible or who actively protect their nest against predators. Rhythms entrainable to the 24-h light-dark cycle were less prevalent at high latitudes and absent in 18 species. Our results indicate that even under similar environmental conditions and despite 24-h environmental cues, social synchronization can generate far more diverse behavioural rhythms than expected from studies of individuals in captivity. The risk of predation, not the risk of starvation, may be a key factor underlying the diversity in these rhythms.</p

Unexpected diversity in socially synchronized rhythms of shorebirds

The behavioural rhythms of organisms are thought to be under strong selection, influenced by the rhythmicity of the environment1, 2, 3, 4. Such behavioural rhythms are well studied in isolated individuals under laboratory conditions1, 5, but free-living individuals have to temporally synchronize their activities with those of others, including potential mates, competitors, prey and predators6, 7, 8, 9, 10. Individuals can temporally segregate their daily activities (for example, prey avoiding predators, subordinates avoiding dominants) or synchronize their activities (for example, group foraging, communal defence, pairs reproducing or caring for offspring)6, 7, 8, 9, 11. The behavioural rhythms that emerge from such social synchronization and the underlying evolutionary and ecological drivers that shape them remain poorly understood5, 6, 7, 9. Here we investigate these rhythms in the context of biparental care, a particularly sensitive phase of social synchronization12 where pair members potentially compromise their individual rhythms. Using data from 729 nests of 91 populations of 32 biparentally incubating shorebird species, where parents synchronize to achieve continuous coverage of developing eggs, we report remarkable within- and between-species diversity in incubation rhythms. Between species, the median length of one parent’s incubation bout varied from 1–19 h, whereas period length—the time in which a parent’s probability to incubate cycles once between its highest and lowest value—varied from 6–43 h. The length of incubation bouts was unrelated to variables reflecting energetic demands, but species relying on crypsis (the ability to avoid detection by other animals) had longer incubation bouts than those that are readily visible or who actively protect their nest against predators. Rhythms entrainable to the 24-h light–dark cycle were less prevalent at high latitudes and absent in 18 species. Our results indicate that even under similar environmental conditions and despite 24-h environmental cues, social synchronization can generate far more diverse behavioural rhythms than expected from studies of individuals in captivity5, 6, 7, 9. The risk of predation, not the risk of starvation, may be a key factor underlying the diversity in these rhythms

Data driven design of an orthogonal wavelet with vanishing moments

We present a framework to design an orthogonal wavelet with compact support and vanishing moments, tuned to a given application. This is achieved by optimizing a criterion, such that a prototype signal, which is characteristic for the application, becomes sparse in the wavelet domain. This approach is beneficial for compression and detection purposes. A parameterization is developed for which orthogonality and compact support are built in, and in terms of which we can express the vanishing moment conditions conveniently. The ap- proach is developed for critically sampled wavelet transforms as well as for the stationary wavelet transform. Several examples illustrate the methods