Ordinal patterns are a time-series data analysis tool used as preliminary step to construct the permutation entropy, which itself allows same characterization of dynamics chaotic or regular more theoretical constructs such Lyapunov exponent. However, ordinal store strictly information than entropy exponents. We present results working with Duffing oscillator showing that reflect changes in dyna...

Several observations suggest that overlearned ordinal categories (e.g., letters, numbers, weekdays, months) are processed differently than non-ordinal categories in the brain. In synesthesia, for example, anomalous perceptual experiences are most often triggered by members of ordinal categories (Rich et al., 2005; Eagleman, 2009). In semantic dementia (SD), the processing of ordinal stimuli app...

In some statistical process monitoring applications, quality of a process or product is described by more than one ordinal factors called ordinal multivariate process. To show the relationship between these factors, an ordinal contingency table is used and modeled with ordinal log-linear model. In this paper, a new control charts based on ordinal-normal statistic is developed to monitor the ord...

Epileptic seizures are associated with high behavioral stereotypy of the patients. In the EEG of epilepsy patients characteristic signal patterns can be found during and between seizures. Here we use ordinal patterns to analyze EEGs of epilepsy patients and quantify the degree of signal determinism. Besides relative signal redundancy and the fraction of forbidden patterns we introduce the fract...

Brain connectivity networks have been widely used for diagnosis of brain-related diseases, e.g., Alzheimer’s disease (AD), mild cognitive impairment (MCI), and attention deficit hyperactivity disorder (ADHD). Although several network descriptors have been designed for representing brain connectivity networks, most of them not only ignore the important weight information of edges, but also canno...

SUMMARY Existing linkage-analysis methods address binary or quantitative traits. However, many complex diseases and human conditions, particularly behavioral disorders, are rated on ordinal scales. Herein, we introduce, LOT, a tool that performs linkage analysis of ordinal traits for pedigree data. It implements a latent-variable proportional-odds logistic model that relates inheritance pattern...

In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. We generally discuss this phenomenon by considering the distribution of ordinal patterns, which describe the up and down in the orbits of a Borel measurable map on a subset of the real numbers. In particular, we give a natural ordinal description of...

Zunino et al. analyzed the problem of discrimination of developed and emergent markets by the use of ordinal patterns methods: number of forbidden patterns and ordinal pattern probability distribution as a basis for entropy and statistical measure of complexity. In this paper we apply the same methodology for the analysis of Polish stock market (index WIG). The results indicate that Polish mark...

Permutation entropy, introduced by Bandt and Pompe, is a conceptually simple and well-interpretable measure of time series complexity. In this paper, we propose efficient methods for computing it and related ordinal-patterns-based characteristics. The methods are based on precomputing values of successive ordinal patterns of order d, considering the fact that they are “overlapped” in d points, ...

We consider the problem of monitoring for existence serial dependence in real-valued and continuously distributed processes. These can exist when a process goes out-of-control. Besides, as many control charts are designed under assumption independent identically observations, validity this needs to be checked. In literature, majority studies handled by using specific case autoregressive moving-...