Motivated by applications in physical and biological sciences, we developed a Frequency Modulated Möbius (FMM) model to describe rhythmic patterns in oscillatory systems. Unlike standard symmetric sinusoidal models, FMM is a flexible parametric model that allows deformations to sinusoidal shape to accommodate commonly seen asymmetries in applications. FMM model parameters are easy to estimate and the model is easy to interpret complex rhythmic data. We illustrate FMM model in three disparate applications, namely, circadian clock gene expression, corticoptropin levels in depressed patients and the temporal light intensity patterns of distant stars. In each case, FMM model is demonstrated to be flexible, scientifically plausible and easy to interpret. Analysis of synthetic data derived from patterns of real data, suggest that FMM model fits the data very well both visually as well as in terms of the goodness of fit measure total mean squared error. An R language based software for implementing FMM model is available.

The electrocardiogram (ECG) is the most important non-invasive method for elucidating information about heart and cardiovascular disease diagnosis. Typically, the ECG system manufacturing companies provide ECG images, but store the numerical data in a proprietary format that is not interpretable and is not therefore useful for automatic diagnosis. There have been many efforts to digitize paper-based ECGs. The main limitations of previous works in ECG digitization are that they require manual selection of the regions of interest, only partly provide signal digitization, and offer limited accuracy. We have developed the ECGMiner, an open-source software to digitize ECG images. It is precise, fast, and simple to use. This software digitizes ECGs in four steps: 1) recognizing the image composition; 2) removing the gridline; 3) extracting the signals; 4) post-processing and storing the data. We have evaluated the ECGMiner digitization capabilities using the Pearson Correlation Coefficient (PCC) and the Root Mean Square Error (RMSE) measures, and we consider ECG from two large, public, and widely used databases, LUDB and PTB-XL. The actual and digitized values of signals in both databases have been compared. The software's ability to correctly identify the location of characteristic waves has also been validated. Specifically, the PCC values are between 0.971 and 0.995, and the RMSE values are between 0.011 and 0.031 mV. The ECGMiner software presented in this paper is open access, easy to install, easy to use, and capable of precisely recovering the paper-based/digital ECG signal data, regardless of the input format and signal complexity. ECGMiner outperforms existing digitization algorithms in terms of PCC and RMSE values.

Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct physiological meaning, they are not useful in practice as a result of the parameter adjustment complexity and the presence of noise. In this paper, a novel decomposition approach in AM-FM components, competing with Fourier and other decompositions is presented. Several interesting theoretical properties are derived including the ordinary differential equations describing the signal. Furthermore, the usefulness in real practice is demonstrated to analyse signals associated to neuron synapses and by addressing other questions in neuroscience.

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/.

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.