Joel Mendoza-Temis

Heart Rate and Systolic Blood Pressure Variability in the Time Domain in Patients with Recent and Long-Standing Diabetes Mellitus

Diabetes Mellitus (DM) affects the cardiovascular response of patients. To study this effect, interbeat intervals (IBI) and beat-to-beat systolic blood pressure (SBP) variability of patients during supine, standing and controlled breathing tests were analyzed in the time domain. Simultaneous noninvasive measurements of IBI and SBP for 30 recently diagnosed and 15 long-standing DM patients were compared with the results for 30 rigorously screened healthy subjects (control). A statistically significant distinction between control and diabetic subjects was provided by the standard deviation and the higher moments of the distributions (skewness, and kurtosis) with respect to the median. To compare IBI and SBP for different populations, we define a parameter, α, that combines the variability of the heart rate and the blood pressure, as the ratio of the radius of the moments for IBI and the same radius for SBP. As diabetes evolves, α decreases, standard deviation of the IBI detrended signal diminishes (heart rate signal becomes more “rigid”), skewness with respect to the median approaches zero (signal fluctuations gain symmetry), and kurtosis increases (fluctuations concentrate around the median). Diabetes produces not only a rigid heart rate, but also increases symmetry and has leptokurtic distributions. SBP time series exhibit the most variable behavior for recently diagnosed DM with platykurtic distributions. Under controlled breathing, SBP has symmetric distributions for DM patients, while control subjects have non-zero skewness. This may be due to a progressive decrease of parasympathetic and sympathetic activity to the heart and blood vessels as diabetes evolves.

The anatomy of the simplest Duflo–Zuker mass formula

Abstract The simplest version of the Duflo–Zuker mass model (due entirely to the late Jean Duflo) is described by following step by step the published computer code. The model contains six macroscopic monopole terms leading asymptotically to a Liquid Drop form, three microscopic terms supposed to mock configuration mixing (multipole) corrections to the monopole shell effects, and one term in charge of detecting deformed nuclei and calculating their masses. A careful analysis of the model suggests a program of future developments that includes a complementary approach to masses based on an independently determined monopole Hamiltonian, a better description of deformations and specific suggestions for the treatment of three body forces.

THE ART OF PREDICTING NUCLEAR MASSES

A review of recent advances in the theoretical analysis of nuclear mass models and their predictive power is presented. After introducing two tests which probe the ability of nuclear mass models to extrapolate, three models are analyzed in detail: the liquid drop model (LDM), the liquid drop model plus empirical shell corrections (LDMM) and the Duflo–Zuker mass formula (DZ). The DZ model is exhibited as the most predictive model. The Garvey–Kelson mass relations are also discussed. It is shown that their fulfillment probes the consistency of the most commonly used mass formulae, and that they can be used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses, offering a simple and reproducible procedure for short range mass predictions.

Enhancement of early warning properties in the Kuramoto model and in an atrial fibrillation model due to an external perturbation of the system

When a complex dynamical system is externally disturbed, the statistical moments of signals associated to it can be affected in ways that depend on the nature and amplitude of the perturbation. In systems that exhibit phase transitions, the statistical moments can be used as Early Warnings (EW) of the transition. A natural question is thus to wonder what effect external disturbances have on the EWs of system. In this work we study the impact of external noise added to the system on the EWs, with particular focus on understanding the importance of the amplitude and complexity of the noise. We do this by analyzing the EWs of two computational models related to biology: the Kuramoto model, which is a paradigm of synchronization for biological systems, and a cellular automaton model of cardiac dynamics which has been used as a model for atrial fibrillation. For each model we first characterize the EWs. Then, we introduce external noise of varying intensity and nature to observe what effect this has on the EWs. In both cases we find that the introduction of noise amplified the EWs, with more complex noise having a greater effect. This both offers a way to improve the chance of detection of EWs in real systems and suggests that natural variability in the real world does not have a detrimental effect on EWs, but the opposite.

Microscopic mass estimations

The quest to build a mass formula which has in it the most relevant microscopic contributions is analyzed. Inspired by the successful Duflo–Zuker mass description, the challenges to describe the shell closures in a more transparent but equally powerful formalism are discussed.

Early warning studies in an atrial model to prevent fibrillation

A cellular automata model is used to simulate an atrial tissue. We were able to obtain and study signals of the heart that resemble the electrocardiograms for different topological cases. Considering that the heart is a dynamic system in a critical state, we used new techniques known as early warnings, based in the statistical behavior of the signals. We found that it is possible to determine how healthy is an atrial tissue and how far it is from suffering an atrial fibrillation (AF) episode. Another analysis related with the memory of the system (Lag-1 and power spectrum analysis) was performed and we obtained that the atrial tissue goes through a phase transition from a healthy state to a deteriorated one. This can help us to understand the dynamics of the AF and possibly apply this to prevent them with non-invasive methods and with a high degree of confidence.

Robust Calculation of Nuclear Masses by means of Image Reconstruction

We use a new approach based on image reconstruction techniques to improve model‐based predictions of nuclear masses. A partial view image pattern is built by taking the differences between experimentally measured masses and the predictions given by different theoretical models which describe the smooth macroscopic behavior. We show that it is possible to significantly improve predictions in regions not too far from measured nuclear masses.