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This article discusses aeroacoustic imaging methods based on correlation measurements in the frequency domain. Standard methods in this field assume that the estimated correlation matrix is superimposed with additive white noise. In this…
For the Research Topic Data Assimilation and Control: Theory and Applications in Life Sciences we first review the formulation of statistical data assimilation (SDA) and discuss algorithms for exploring variational approximations to the…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have…
For almost a century, since Bernal\'s attempts at a molecular theory of liquid structure(Bernal [1]), correlation functions have been the bridge to compare theoretical calculations with experimental measurements in the study of disordered…
Due to the multiple imperfections during the signal acquisition, Electrocardiogram (ECG) datasets are typically contaminated with numerous types of noise, like salt and pepper and baseline drift. These datasets may contain different…
Eigenvalues are defined for any element of an algebra of observables and do not require a representation in terms of wave functions or density matrices. A systematic algebraic derivation based on moments is presented here for the harmonic…
We evaluated the impact of changing the observation scale over the entropy measures for text descriptions. MIDI coded Music, computer code and two human natural languages were studied at the scale of characters, words, and at the…
Audio embeddings enable large scale comparisons of the similarity of audio files for applications such as search and recommendation. Due to the subjectivity of audio similarity, it can be desirable to design systems that answer not only…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
We develop a framework to uncover and analyze dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive data sets to eliminate erroneous data segments,…
The electrovacuum around a rotating massive body with electric charge density is described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). A small uncharged test particle orbiting…
Music relies heavily on repetition to build structure and meaning. Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure. The Transformer (Vaswani…
We consider the origin of noise and distortions in power spectral estimates of randomly sampled data, specifically velocity data measured with a burst-mode laser Doppler anemometer. The analysis guides us to new ways of reducing noise and…
Based on a review of anecdotal beliefs, we explored patterns of track-sequencing within professional music albums. We found that songs with high levels of valence, energy and loudness are more likely to be positioned at the beginning of…
We explore the chaotic dynamics and complexity of a neuro-system with respect to variable synaptic weights in both noise free and noisy conditions. The chaotic dynamics of the system is investigated by bifurcation analysis and 0-1 test. A…
We extract the frequency content of a noisy signal by use of Discrete Fourier Transform. Our analysis overcomes the limitations imposed by incommensurate lattices. After computing the deterministic component, we show the relevance of the…
Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Biomedical signal processing extract meaningful information from physiological signals like electrocardiograms (ECGs), electroencephalograms (EEGs), and electromyograms (EMGs) to diagnose, monitor, and treat medical conditions and diseases…