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The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (7). There is a large variety of such symbolic sequences, ranging from texts written in natural languages,…

Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to…

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…

Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…

Let $\alpha$ be an arbritary ordinal, and $2<n<\omega$. In \cite{3} accepted for publication in Quaestiones Mathematicae, we studied using algebraic logic, interpolation, amalgamation using $\alpha$ many variables for topological logic with…

Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…

We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…

The matrix profile is an effective data mining tool that provides similarity join functionality for time series data. Users of the matrix profile can either join a time series with itself using intra-similarity join (i.e., self-join) or…

Many multivariate time series anomaly detection frameworks have been proposed and widely applied. However, most of these frameworks do not consider intrinsic relationships between variables in multivariate time series data, thus ignoring…

Time series are ubiquitous in numerous science and engineering domains, e.g., signal processing, bioinformatics, and astronomy. Previous work has verified the efficacy of symbolic time series representation in a variety of engineering…

We study what we call topological cylindric algebras and tense cylindric algebras defined for every ordinal $\alpha$. The former are cylindric algebras of dimension $\alpha$ expanded with $\sf S4$ modalities indexed by $\alpha$. The…

Time series analysis has become crucial in various fields, from engineering and finance to healthcare and social sciences. Due to their multidimensional nature, time series often need to be embedded into a fixed-dimensional feature space to…

Temporal networks are ubiquitous and evolve over time by the addition, deletion, and changing of links, nodes, and attributes. Although many relational datasets contain temporal information, the majority of existing techniques in relational…

Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…

Embeddings are a fundamental component of many modern machine learning and natural language processing models. Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior…

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has…

Temporal networks model a variety of important phenomena involving timed interactions between entities. Existing methods for machine learning on temporal networks generally exhibit at least one of two limitations. First, time is assumed to…

Time-series classification is one of the most frequently performed tasks in industrial data science, and one of the most widely used data representation in the industrial setting is tabular representation. In this work, we propose a novel…

Comparing time series is essential in various tasks such as clustering and classification. While elastic distance measures that allow warping provide a robust quantitative comparison, a qualitative comparison on top of them is missing.…