Recurrence quantification of fractal structures

Four Methods to Distinguish between Fractal Dimensions in Time Series through Recurrence Quantification Analysis

Fractal properties in time series of human behavior and physiology are quite ubiquitous, and several methods to capture such properties have been proposed in the past decades. Fractal properties are marked by similarities in statistical characteristics over time and space, and it has been suggested that such properties can be well-captured through recurrence quantification analysis. However, no methods to capture fractal fluctuations by means of recurrence-based methods have been developed yet. The present paper takes this suggestion as a point of departure to propose and test several approaches to quantifying fractal fluctuations in synthetic and empirical time-series data using recurrence-based analysis. We show that such measures can be extracted based on recurrence plots, and contrast the different approaches in terms of their accuracy and range of applicability.

Empirical Evidence for Extended Cognitive Systems

We present an empirically supported theoretical and methodological framework for quantifying the system‐level properties of person‐plus‐tool interactions in order to answer the question: “Are person‐plus‐tool‐systems extended cognitive systems?” Nineteen participants provided perceptual judgments regarding their ability to pass through apertures of various widths while using visual information, blindfolded wielding a rod, or blindfolded wielding an Enactive Torch—a vibrotactile sensory‐substitution device for detecting distance. Monofractal, multifractal, and recurrence quantification analyses were conducted to assess features of person‐plus‐tool movement dynamics. Trials where people utilized the rod or Enactive Torch demonstrated stable “self‐similarity,” or indices of healthy and adaptive single systems, regardless of aperture width, trial order, features of the participants’ judgments, and participant characteristics. Enactive Torch trials exhibited a somewhat greater range of dynamic fluctuations than the rod trials, as well as less movement recurrence, suggesting that the Enactive Torch allowed for more exploratory movements. Findings provide support for the notion that person‐plus‐tool systems can be classified as extended cognitive systems and a framework for quantifying system‐level properties of these systems. Implications concerning future research on extended cognition are discussed.

Impact of Chronic Fetal Hypoxia and Inflammation on Cardiac Pacemaker Cell Development

Chronic fetal hypoxia and infection are examples of adverse conditions during complicated pregnancy, which impact cardiac myogenesis and increase the lifetime risk of heart disease. However, the effects that chronic hypoxic or inflammatory environments exert on cardiac pacemaker cells are poorly understood. Here, we review the current evidence and novel avenues of bench-to-bed research in this field of perinatal cardiogenesis as well as its translational significance for early detection of future risk for cardiovascular disease.

Phase Diagram-Based Sensing with Adaptive Waveform Design and Recurrent States Quantification for the Instantaneous Frequency Law Tracking

Monitoring highly dynamic environments is a difficult task when the changes within the systems require high speed monitoring systems. An active sensing system has to solve the problem of overlapped responses coming from different parts of the surveyed environment. Thus, the need of a new representation space which separates the overlapped responses, is mandatory. This paper describes two new concepts for high speed active sensing systems. On the emitter side, we propose a phase-space-based waveform design that presents a unique shape in the phase space, which can be easily converted into a real signal. We call it phase space lobe. The instantaneous frequency (IF) law of the emitted signal is found inside the time series. The main advantage of this new concept is its capability to generate several distinct signals, non-orthogonal in the time/frequency domain but orthogonal within the representation space, namely the phase diagram. On the receiver side, the IF law information is estimated in the phase diagram representation domain by quantifying the recurrent states of the system. This waveform design technique gives the possibility to develop the high speed sensing methods, adapted for monitoring complex dynamic phenomena In our paper, as an applicative context, we consider the problem of estimating the time of flight in an dynamic acoustic environment. In this context, we show through experimental trials that our approach provides three times more accurate estimation of time of flight than spectrogram based technique. This very good accuracy comes from the capability of our approach to generate separable IF law components as well as from the quantification in phase diagram, both of them being the key element of our approach for high speed sensing.

Traveling Companions Add Complexity and Hinder Performance in the Spatial Behavior of Rats

We sought to uncover the impact of the social environment on the spatial behavior of rats. Food-deprived rats were trained in a spatial task of collecting food items from 16 equispaced objects. Following training, they were tested, first alone and then with a similarly-trained cage-mate. It was found that the presence of another rat substantially altered the rats' spatial behavior. Lone rats collected the food items faster while traveling a shorter distance, reflecting a higher efficiency of task completion. When accompanied by a partner, however, the rats traveled together, visiting the same set of objects in each trip with one of them leading. Whether alone or with a partner, rats continued to revisit the same objects; however, more such revisits occurred with a partner. We argue that revisiting objects is not necessarily an error, since returning to past places is an important aspect of rats' natural behavior. Revisiting an object following food depletion implies that searching for food was not the main driving force in the rats' spatial behavior. Specifically, despite food deprivation, rats were more attentive to one another than to the food. This could be adaptive, since foraging and feeding in groups is a way of poison avoidance in wild rats. Finally, the addition of a social component added complexity to the environment since the rats organized their spatial behavior in reference to one another in addition to their organization in the physical surrounding. Consequently, when tested with a partner, spatial behavior was less structured, less predictable and more chaotic.

Dancers entrain more effectively than non-dancers to another actor's movements

For many everyday sensorimotor tasks, trained dancers have been found to exhibit distinct and sometimes superior (more stable or robust) patterns of behavior compared to non-dancers. Past research has demonstrated that experts in fields requiring specialized physical training and behavioral control exhibit superior interpersonal coordination capabilities for expertise-related tasks. To date, however, no published studies have compared dancers' abilities to coordinate their movements with the movements of another individual-i.e., during a so-called visual-motor interpersonal coordination task. The current study was designed to investigate whether trained dancers would be better able to coordinate with a partner performing short sequences of dance-like movements than non-dancers. Movement time series were recorded for individual dancers and non-dancers asked to synchronize with a confederate during three different movement sequences characterized by distinct dance styles (i.e., dance team routine, contemporary ballet, mixed style) without hearing any auditory signals or music. A diverse range of linear and non-linear analyses (i.e., cross-correlation, cross-recurrence quantification analysis, and cross-wavelet analysis) provided converging measures of coordination across multiple time scales. While overall levels of interpersonal coordination were influenced by differences in movement sequence for both groups, dancers consistently displayed higher levels of coordination with the confederate at both short and long time scales. These findings demonstrate that the visual-motor coordination capabilities of trained dancers allow them to better synchronize with other individuals performing dance-like movements than non-dancers. Further investigation of similar tasks may help to increase the understanding of visual-motor entrainment in general, as well as provide insight into the effects of focused training on visual-motor and interpersonal coordination.

Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.

Characteristics of atrial fibrillation cycle length predict restoration of sinus rhythm by catheter ablation

BACKGROUND

Successful termination of atrial fibrillation (AF) during catheter ablation (CA) is associated with arrhythmia-free follow-up. Preablation factors such as mean atrial fibrillation cycle length (AFCL) predict the likelihood of AF termination during ablation but recurring patterns and AFCL stability have not been evaluated.

OBJECTIVE

To investigate novel predictors of acute and postoperative ablation outcomes from intracardiac electrograms: (1) recurring AFCL patterns and (2) localization index (LI) of the instantaneous fibrillatory rate distribution.

METHODS

Sixty-two patients with AF (32 paroxysmal AF; 45 men; age 57 ± 10 years) referred for CA were enrolled. One-minute electrogram was recorded from coronary sinus (CS; 5 bipoles) and right atrial appendage (HRA; 2 bipoles). Atrial activations were detected automatically to derive the AFCL and instantaneous fibrillatory rate (inverse of AFCL) time series. Recurring AFCL patterns were quantified by using recurrence plot indices (RPIs): percentage determinism, entropy of determinism, and maximum diagonal length. AFCL stability was determined by using the LI. The CA outcome predictivity of individual indices was assessed.

RESULTS

Patients with terminated atrial fibrillation (T-AF) had higher RPI (P < .05 in CS7-8) and LI than did those with nonterminated atrial fibrillation (P < .005 in CS3-4; P < .05 in CS5-6, CS7-8, and HRA). Patients free of arrhythmia after 3-month follow-up had higher RPI and LI (all P < .05 in CS7-8). All indices except percentage determinism predicted T-AF in CS7-8 (area under the curve [AUC] ≥ 0.71; odds ratio [OR] ≥ 4.50; P < .05). The median AFCL and LI predicted T-AF in HRAD (AUC ≥ 0.75; OR ≥ 7.76; P < .05). The RPI and LI predicted 3-month follow-up in CS7-8 (AUC ≥ 0.68; OR ≥ 4.17; P < .05).

CONCLUSIONS

AFCL recurrence and stability indices could be used in selecting patients more likely to benefit from CA.