Analysis of properties of Ising and Kuramoto models that are preserved in networks constructed by visualization algorithms.

Recently it has been shown that building networks from time series allows to study complex systems to characterize them when they go through a phase transition. This give us the opportunity to study this systems from a entire new point of view. In the present work we have used the natural and horizontal visualization algorithms to built networks of two popular models, which present phase transitions: the Ising model and the Kuramoto model. By measuring some topological quantities as the average degree, or the clustering coefficient, it was found that the networks retain the capability of detecting the phase transition of the system. From our results it is possible to establish that both visibility algorithms are capable of detecting the critical control parameter, as in every quantity analyzed (the average degree, the average path and the clustering coefficient) there is a minimum or a maximum value. In the case of the natural visualization algorithm, the average path results are much more noisy than in the other quantities in the study. Specially for the Kuramoto Model, which in this case does not allow a detection of the critical point at plain sight as for the other quantities. The horizontal visualization algorithm has proven to be more explicit in every quantity, as every one of them show a clear change of behavior before and after the critical point of the transition.

The Role of the Autonomic Nervous System on Cardiac Rhythm during the Evolution of Diabetes Mellitus Using Heart Rate Variability as a Biomarker.

Heart rate variability (HRV) is highly influenced by the Autonomic Nervous System (ANS). Several illnesses have been associated with changes in the ANS, thus altering the pattern of HRV. However, the variability of the heart rhythm is originated within the Sinus Atrial Node (SAN) which has its own variability. Still, although both oscillators produce HRV, the influence of the SAN on HRV has not yet been exhaustively studied. On the other hand, the complications of diabetes mellitus (DM), for instance, nephropathy, retinopathy, and neuropathy, increase cardiovascular morbidity and mortality. Traditionally, these complications are diagnosed only when the patient is already suffering from the negative symptoms these complications implicate. Consequently, it is of paramount importance to develop new techniques for early diagnosis prior to any deterioration on healthy patients. HRV has been proved to be a valuable, noninvasive clinical evidence for evaluating diseases and even for describing aging and behavior. In this study, several ECGs were recorded and their RR and PP intervals were analyzed to detect the interpotential interval (ii) of the SAN. Additionally, HRV reduction was quantified to identify alterations in the nervous system within the nodal tissue via measuring the SD1/SD2 ratio in a Poincaré plot. With 15 years of DM development, the data showed an age-dependent increase in HRV due to the axon retraction of ANS neurons from its effectors. In addition, these alterations modify the heart rhythm-producing fatal arrhythmias. Therefore, it is possible to avoid the consequences of DM identifying alterations in SAN previous to its symptomatic appearance. This could be used as an early diagnosis indicator.

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.