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Symbolic relative entropy, an efficient nonlinear complexity parameter measuring probabilistic divergences of symbolic sequences, is proposed in our nonlinear dynamics analysis of heart rates considering equal states. Equalities are not…
The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…
Complex, oscillatory data arises from a large variety of biological, physical, and social systems. However, the inherent oscillation and ubiquitous noise pose great challenges to current methodology such as linear and nonlinear time series…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…
Cities are inherently dynamic. Interesting patterns of behavior typically manifest at several key areas of a city over multiple temporal resolutions. Studying these patterns can greatly help a variety of experts ranging from city planners…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
Symbolic music representation is a fundamental challenge in computational musicology. While grid-based representations effectively preserve pitch-time spatial correspondence, their inherent data sparsity leads to low encoding efficiency.…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We provide a pipeline for calculating, managing and visualising correlations and other pairwise association scores for numerical and categorical data. We present a uniform interface for calculating a plethora of pairwise scores and propose…
Convolutional neural networks (CNN) have demonstrated their ability to segment 2D cardiac ultrasound images. However, despite recent successes according to which the intra-observer variability on end-diastole and end-systole images has been…
Frequently, transient changes in physiological signals, such as ECG morphology, precede or follow a rate change. Current methods for visualizing morphology allow only the tracking of preselected changes, severely limiting analytical…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
Dimensionless learning is a data-driven framework for discovering dimensionless numbers and scaling laws from experimental measurements. This tutorial introduces the method, explaining how it transforms experimental data into compact…
We present a novel descriptor for crowd behavior analysis and anomaly detection. The goal is to measure by appropriate patterns the speed of formation and disintegration of groups in the crowd. This descriptor is inspired by the concept of…
A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several…
In this paper we propose numerical measures for evaluating the aesthetic interest of simple patterns. The patterns consist of elements (symbols, pixels, etc.) in regular square arrays. The measures depend on two characteristics of the…
Symbolic music analysis tasks are often performed by models originally developed for Natural Language Processing, such as Transformers. Such models require the input data to be represented as sequences, which is achieved through a process…
Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects…
Dynamic networks, a.k.a. graph streams, consist of a set of vertices and a collection of timestamped interaction events (i.e., temporal edges) between vertices. Temporal motifs are defined as classes of (small) isomorphic induced subgraphs…