Studying the functional connectivity of the primary motor cortex with the binarized cross recurrence plot: The influence of Parkinson’s disease

Two new recurrence plot methods (the binary recurrence plot and binary cross recurrence plot) were introduced here to study the long-term dynamic of the primary motor cortex and its interaction with the primary somatosensory cortex, the anterior motor thalamus of the basal ganglia motor loop and the precuneous nucleus of the default mode network. These recurrence plot methods: 1. identify short-term transient interactions; 2. identify long-lasting delayed interactions that are common in complex systems; 3. work with non-stationary blood oxygen level dependent (BOLD) data; 4. may study the relationship of centers with non-linear functional interactions; 5 may compare different experimental groups performing different tasks. These methods were applied to BOLD time-series obtained in 20 control subjects and 20 Parkinson´s patients during the execution of motor activity and body posture tasks (task-block design). The binary recurrence plot showed the task-block BOLD response normally observed in the primary motor cortex with functional magnetic resonance imaging methods, but also shorter and longer BOLD-fluctuations than the task-block and which provided information about the long-term dynamic of this center. The binary cross recurrence plot showed short-lasting and long-lasting functional interactions between the primary motor cortex and the primary somatosensory cortex, anterior motor thalamus and precuneous nucleus, interactions which changed with the resting and motor tasks. Most of the interactions found in healthy controls were disrupted in Parkinson’s patients, and may be at the basis of some of the motor disorders and side-effects of dopaminergic drugs commonly observed in these patients.

Correlation between friction coefficient and friction vibration in running-in process based on cross recurrence plots

Friction coefficient is difficult to measure in real application, whether it can be replaced by friction coefficient for dynamic analysis is an urgent issue to be solved. To study the correlation between the two signals, the friction tests were carried out under dry friction, starved and flooded lubrications, respectively. Cross recurrence plot (CRP) and its measures (recurrence rate, determinism, average diagonal line length and entropy) were used to explore the correlation. The results show that the more obvious the diagonal structures in CRPs, the stronger the correlation between the two signals, and average diagonal length is more sensitive to the degree of correlation. Irrespective of lubrication conditions, friction coefficient and vibration measured in a friction system have similar recursive characteristics. Thus, friction coefficient or vibration can be selected according to the convenience of measurement to monitor the running-in process.

A Strategy for the Use of the Cross Recurrence Quantification Analysis

In this work, our goal is to analyze the use of the Cross Recurrence Plot (CRP) and its quantification (CRQA) as tools to detect the possible existence of a relationship between two systems. To do that, we define three tests that are a bivariate extension of those proposed by Aparicio et al. (Aparicio, T., E. Pozo, and D. Saura. 2008. “Detecting Determinism Using Recurrence Quantification Analysis: Three Test Procedures.” Journal of Economic Behavior & Organization 65: 768–787, Aparicio, T., E. F. Pozo, and D. Saura. 2011. “Detecting Determinism Using Recurrence Quantification Analysis: A Solution to the Problem of Embedding.” Studies in Nonlinear Dynamics and Econometrics 15: 1–10) within the context of the Recurrence Quantification Analysis. These tests, based on the diagonal lines of the CRP, are applied to a large number of simulated pairs of series. The results obtained are not always satisfactory, with problems being detected specifically when the series have a high degree of laminarity. We study the identified problems and we implement a strategy that we consider adequate for the use of these tools. Finally, as an example, we apply this strategy to several economic series.

Recurrence Based Similarity Identification of Climate Data

Climate change has become a challenging and emerging research problem in many research related areas. One of the key parameters in analyzing climate change is to analyze temperature variations in different regions. The temperature variation in a region is periodic within the interval. Temperature variations, though periodic in nature, may vary from one region to another and such variations are mainly dependent on the location and altitude of the region and also on other factors like the nearness of sea and vegetation. In this paper, we analyze such periodic variations using recurrence plot (RP), cross recurrence plot (CRP), recurrence rate (RR), and correlation of probability of recurrence (CPR) methods to find similarities of periodic variations between and within climatic regions and to identify their connectivity trend. First, we test the correctness of our method by applying it on voice and heart rate data and then experimentation is performed on synthetic climate data of nine regions in the United States and eight regions in China. Finally, the accuracy of our approach is validated on both real and synthetic datasets and demonstrated using ANOVA, Kruskal–Wallis, and z-statistics significance tests.