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.

A novel approach for analysing cardiac rhythm data is presented in this paper. Heartbeats are decomposed into the five fundamental P, Q, R, S and T waves plus an error term to account for artifacts in the data which provides a meaningful, physical interpretation of the heart’s electric system. The morphology of each wave is concisely described using four parameters that allow all the different patterns in heartbeats to be characterized and thus differentiated This multi-purpose approach solves such questions as the extraction of interpretable features, the detection of the fiducial marks of the fundamental waves, or the generation of synthetic data and the denoising of signals. Yet the greatest benefit from this new discovery will be the automatic diagnosis of heart anomalies as well as other clinical uses with great advantages compared to the rigid, vulnerable and black box machine learning procedures, widely used in medical devices. The paper shows the enormous potential of the method in practice; specifically, the capability to discriminate subjects, characterize morphologies and detect the fiducial marks (reference points) are validated numerically using simulated and real data, thus proving that it outperforms its competitors.

A cell division cycle is a well-coordinated process in eukaryotes with cell cycle genes exhibiting a periodic expression over time. There is considerable interest among cell biologists to determine genes that are periodic in multiple organisms and whether such genes are also evolutionarily conserved in their relative order of time to peak expression. Interestingly, periodicity is not well-conserved evolutionarily. A conservative estimate of a number of periodic genes common to fission yeast (Schizosaccharomyces pombe) and budding yeast (Saccharomyces cerevisiae) (‘core set FB’) is 35, while those common to fission yeast and humans (Homo sapiens) (‘core set FH’) is 24. Using a novel statistical methodology, we discover that the relative order of peak expression is conserved in ∼80% of FB genes and in ∼40% of FH genes. We also discover that the order is evolutionarily conserved in six genes which are potentially the core set of signature cell cycle genes. These include ace2 (a transcription factor) and polo-kinase plo1, which are well-known hubs of early M-phase clusters, cdc18 a key component of pre-replication complexes, mik1 which is critical for the establishment and maintenance of DNA damage check point, and histones hhf1 and hta2.

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.

Mathematical models of cardiac electrical activity are one of the most important tools for elucidating information about heart diagnostics. In this paper, we present an efficient mathematical formulation for this modeling simple enough to be easily parameterized and rich enough to provide realistic signals. It relies on a five dipole representation of the cardiac electric source, each one associated with the well-known waves of the electrocardiogram signal. Beyond the physical basis of the model, the parameters are physiologically interpretable as they characterize the wave shape, similar to what a physician would look for in signals, thus making them very useful in diagnosis. The model accurately reproduces the electrocardiogram signals of any diseased or healthy heart. This new discovery represents a significant advance in electrocardiography research. It is especially useful for diagnosis, patient follow-up or decision-making on new therapies; is also a promising tool for well-performing, transparent and interpretable AI approaches.

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/.