Yolanda Larriba

Accurately estimating peak width and wave duration (WD) is a significant challenge across various scientific disciplines. Traditional methods, such as Full Width at Half Maximum (FWHM), often encounter difficulties with overlapping peaks, asymmetric patterns, noisy data, and, especially, multi-channel data where these challenges multiply. This paper introduces a novel approach for estimating peak width and WDs in curve-fitting applications, leveraging the oscillatory nature of signals through Frequency Modulated Möbius (FMM) decomposition. We derive a parametric expression for FWHM and propose a novel WD measure. Beyond being both mathematically and physiologically sound, this method offers several advantages, including a straightforward parametric formulation, robust estimation, and flexibility to handle single and overlapping peaks, as well as peaks recorded across multiple channels. While potential applications extend across disciplines, we demonstrate this method's effectiveness in addressing critical challenges in electrocardiogram (ECG) signal and spectroscopic analysis. In ECG analysis, the WD measure effectively estimates ECG segments that capture critical aspects of cardiac electrical activity. In spectroscopy, we evaluate the new FWHM estimator, a key parameter for determining spectral resolution and material properties. Extensive testing confirms the suitability and robustness of the new measures, outperforming standard techniques in both applications.

The Frequency Modulated Möbius (FMM) approach is a contemporary and versatile tool for analyzing oscillatory signals. Within the functional data analysis framework, the FMM model offers an accurate alternative for comprehending multidimensional synchronized oscillatory signals, which are common in various fields including biology and medicine. This approach decomposes the signals into scaled Möbius waves formulated in terms of four parameters, interpreted as measures of location and shape variation. Among these parameters, two are specific to individual signals, while the remaining two are global and describe the interconnections between signals. In this paper we extend the utility of the FMM by developing inferential procedures based on likelihood estimations for nonlinear models. These procedures cover the core parameters, the signals themselves, and their derivatives. We explore various techniques, including the Gauss–Seidel approach and profile likelihood, for obtaining estimators and their asymptotic properties. Our methodology undergoes rigorous validation, drawing on a combination of theoretical insights and numerical experiments. Furthermore, as our research is primarily motivated by the analysis of biomedical oscillatory signals, we apply this methodology to address two pertinent real-world problems involving electrocardiogram and pattern-reversal visual evoked potential data. These applications illustrate the practical efficacy of the new paradigm.

The Pattern Electroretinogram (PERG) is an essential tool in ophthalmic electrophysiology, providing an objective assessment of the central retinal function. It quantifies the activity of cells in the macula and the ganglion cells of the retina, assisting in the differentiation of macular and optic nerve conditions. In this study, we present the IOBA-PERG dataset, an extensive collection of 1354 transient PERG responses accessible on the PhysioNet repository. These recordings were conducted at the Institute of Applied Ophthalmobiology (IOBA) at University of Valladolid, over an extended period spanning nearly two decades, from 2003 to 2022. The dataset includes 336 records, ensuring at least one PERG signal per eye. The dataset thoughtfully includes demographic and clinical data, comprising information such as age, gender, visual acuity measurements, and expert diagnoses. This comprehensive dataset fills a gap in ocular electrophysiological repositories, enhancing ophthalmology research. Researchers can explore a broad range of eye-related conditions and diseases, leading to enhanced diagnostic accuracy, innovative treatment strategies, methodological advancements, and a deeper understanding of ocular electrophysiology.

The circadian system drives near-24-h oscillations in behaviors and biological processes. The underlying core molecular clock regulates the expression of other genes, and it has been shown that the expression of more than 50 percent of genes in mammals displays 24-h rhythmic patterns, with the specific genes that cycle varying from one tissue to another. Determining rhythmic gene expression patterns in human tissues sampled as single timepoints has several challenges, including the reconstruction of temporal order of highly noisy data. Previous methodologies have attempted to address these challenges in one or a small number of tissues for which rhythmic gene evolutionary conservation is assumed to be preserved. Here we introduce CIRCUST, a novel CIRCular-robUST methodology for analyzing molecular rhythms, that relies on circular statistics, is robust against noise, and requires fewer assumptions than existing methodologies. Next, we validated the method against four controlled experiments in which sampling times were known, and finally, CIRCUST was applied to 34 tissues from the Genotype-Tissue Expression (GTEx) dataset with the aim towards building a comprehensive daily rhythm gene expression atlas in humans. The validation and application shown here indicate that CIRCUST provides a flexible framework to formulate and solve the issues related to the analysis of molecular rhythms in human tissues. CIRCUST methodology is publicly available at https://github.com/yolandalago/CIRCUST/.

A bstract: The circadian system drives near-24-h oscillations in behaviors and biological processes. The underlying core molecular clock regulates the expression of other genes, and it has been shown that the expression of more than 50 percent of genes in mammals displays 24-h rhythmic patterns, with the specific genes that cycle varying from one tissue to another. Determining rhythmic gene expression patterns in human tissues sampled as single timepoints has several challenges, including the reconstruction of temporal order of highly noisy data. Previous methodologies have attempted to address these challenges in one or a small number of tissues for which clock gene evolutionary conservation is assumed to be preserved. Here we introduce CIRCUST, a novel CIRCular-robUST methodology for analyzing molecular rhythms, that relies on circular statistics, is robust against noise, and requires fewer assumptions than existing methodologies. Next, we validated the method against two controlled experiments in which sampling times were known, and finally, CIRCUST was applied to 34 tissues from the Genotype-Tissue Expression (GTEx) dataset with the aim towards building a comprehensive daily rhythm gene expression atlas in humans. The validation and application shown here indicate that CIRCUST provides a flexible framework to formulate and solve the issues related to the analysis of molecular rhythms in human tissues. CIRCUST methodology is publicly available at https://github.com/yolandalago/CIRCUST/ .