Uniform approach to linear and nonlinear interrelation patterns in multivariate time series

Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.

Time courses and quantitative analysis of atrial fibrillation episode number and duration after circular plus linear left atrial lesions: trigger elimination or substrate modification: early or delayed cure?

OBJECTIVES We sought to analyze the time course of atrial fibrillation (AF) episodes before and after circular plus linear left atrial ablation and the percentage of patients with complete freedom from AF after ablation by using serial seven-day electrocardiograms (ECGs). BACKGROUND The curative treatment of AF targets the pathophysiological corner stones of AF (i.e., the initiating triggers and/or the perpetuation of AF). The pathophysiological complexity of both may not result in an "all-or-nothing" response but may modify number and duration of AF episodes. METHODS In patients with highly symptomatic AF, circular plus linear ablation lesions were placed around the left and right pulmonary veins, between the two circles, and from the left circle to the mitral annulus using the electroanatomic mapping system. Repetitive continuous 7-day ECGs administered before and after catheter ablation were used for rhythm follow-up. RESULTS In 100 patients with paroxysmal (n = 80) and persistent (n = 20) AF, relative duration of time spent in AF significantly decreased over time (35 +/- 37% before ablation, 26 +/- 41% directly after ablation, and 10 +/- 22% after 12 months). Freedom from AF stepwise increased in patients with paroxysmal AF and after 12 months measured at 88% or 74% depending on whether 24-h ECG or 7-day ECG was used. Complete pulmonary vein isolation was demonstrated in <20% of the circular lesions. CONCLUSIONS The results obtained in patients with AF treated with circular plus linear left atrial lesions strongly indicate that substrate modification is the main underlying pathophysiologic mechanism and that it results in a delayed cure instead of an immediate cure.

Plant regeneration directs changes in grassland composition after extreme drought: a 13-year study in southern Switzerland

1. The cover of plant species was recorded annually from 1988 to 2000 in nine spatially replicated plots in a species-rich, semi-natural meadow at Negrentino (southern Alps). This period showed large climatic variation and included the centennial maximum and minimum frequency of days with ≥ 10 mm of rain. 2. Changes in species composition were compared between three 4-year intervals characterized by increasingly dry weather (1988–91), a preceding extreme drought (1992–95), and increasingly wet weather (1997–2000). Redundancy analysis and anova with repeated spatial replicates were used to find trends in vegetation data across time. 3. Recruitment capacity, the potential for fast clonal growth and seasonal expansion rate were determined for abundant taxa and tested in general linear models (GLM) as predictors for rates of change in relative cover of species across the climatically defined 4-year intervals. 4. Relative cover of the major growth forms present, graminoids and forbs, changed more in the period following extreme drought than at other times. Recruitment capacity was the only predictor of species’ rates of change. 5. Following perturbation, re-colonization was the primary driver of vegetation dynamics. The dominant grasses, which lacked high recruitment from seed, therefore decreased in relative abundance. This effect persisted until the end of the study and may represent a lasting response to an extreme climatic event.