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In ordinal symbolic dynamics, transcripts describe the algebraic relationship between ordinal patterns. Using the concept of transcript, we exploit the mathematical structure of the group of permutations to derive properties and relations…
Multi-track music generation has garnered significant research interest due to its precise mixing and remixing capabilities. However, existing models often overlook essential attributes such as rhythmic stability and synchronization,…
A systematic procedure to synthesize interval observers for nonlinear discrete-time systems is proposed. The feedback gains and other matrices are found from the solutions to semidefinite feasibility programs. Two cases are considered: (1)…
Periodically occurring accumulations of events or measured values are present in many time-dependent datasets and can be of interest for analyses. The frequency of such periodic behavior is often not known in advance, making it difficult to…
A novel continuous-time framework is proposed for modeling neuromorphic image sensors in the form of an initial canonical representation with analytical tractability. Exact simulation algorithms are developed in parallel with closed-form…
Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific,…
We propose Local Dirac Synchronization which uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Quantifying numerical data involves addressing two key challenges: first, determining whether the data can be naturally quantified, and second, identifying the numerical intervals or ranges of values that correspond to specific value…
We propose a model for finding one-dimensional structure in a given measure. Our approach is based on minimizing an objective functional which combines the average-distance functional to measure the quality of the approximation and…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…
We introduce a segmentation algorithm to probe temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local values of heart rates follow a power-law…
Quantifying the level of atomic disorder within materials is critical to understanding how evolving local structural environments dictate performance and durability. Here, we leverage graph neural networks to define a physically…
This paper proposes a novel framework to alleviate the model drift problem in visual tracking, which is based on paced updates and trajectory selection. Given a base tracker, an ensemble of trackers is generated, in which each tracker's…
Rhythm is a fundamental aspect of human behaviour, present from infancy and deeply embedded in cultural practices. Rhythm anticipation is a spontaneous cognitive process that typically occurs before the onset of actual beats. While most…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
We introduce a novel statistical framework for analyzing the GPS data of a single individual. Our approach models daily GPS observations as noisy measurements of an underlying random trajectory, enabling the definition of meaningful…
In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image…
Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual…