Control of dynamics via identical time-lagged stochastic inputs.

We investigate the impact of a stochastic forcing, comprised of a sum of time-lagged copies of a single source of noise, on the system dynamics. This type of stochastic forcing could be made artificially, or it could be the result of shared upstream inputs to a system through different channel lengths. By means of a rigorous mathematical framework, we show that such a system is, in fact, equivalent to the classical case of a stochastically-driven dynamical system with time-delayed intrinsic dynamics but without a time lag in the input noise. We also observe a resonancelike effect between the intrinsic period of the oscillation and the time lag of the stochastic forcing, which may be used to determine the intrinsic period of oscillations or the inherent time delay in dynamical systems with oscillatory behavior or delays. As another useful application of imposing time-lagged stochastic forcing, we show that the dynamics of a system can be controlled by changing the time lag of this stochastic forcing, in a fashion similar to the classical case of Pyragas control via delayed feedback. To confirm these results experimentally, we set up a laser diode system with such stochastic inputs, which effectively behaves as a Langevin system. As in the theory, a peak emerged in the autocorrelation function of the output signal that could be tuned by the lag of the stochastic input. Our findings, thus, indicate a new approach for controlling useful instabilities in dynamical systems.

Hybrid feature engineering of medical data via variational autoencoders with triplet loss: a COVID-19 prognosis study.

Medical machine learning frameworks have received much attention in recent years. The recent COVID-19 pandemic was also accompanied by a surge in proposed machine learning algorithms for tasks such as diagnosis and mortality prognosis. Machine learning frameworks can be helpful medical assistants by extracting data patterns that are otherwise hard to detect by humans. Efficient feature engineering and dimensionality reduction are major challenges in most medical machine learning frameworks. Autoencoders are novel unsupervised tools that can perform data-driven dimensionality reduction with minimum prior assumptions. This study, in a novel approach, investigated the predictive power of latent representations obtained from a hybrid autoencoder (HAE) framework combining variational autoencoder (VAE) characteristics with mean squared error (MSE) and triplet loss for forecasting COVID-19 patients with high mortality risk in a retrospective framework. Electronic laboratory and clinical data of 1474 patients were used in the study. Logistic regression with elastic net regularization (EN) and random forest (RF) models were used as final classifiers. Moreover, we also investigated the contribution of utilized features towards latent representations via mutual information analysis. HAE Latent representations model achieved decent performance with an area under ROC curve of 0.921 (±0.027) and 0.910 (±0.036) with EN and RF predictors, respectively, over the hold-out data in comparison with the raw (AUC EN: 0.913 (±0.022); RF: 0.903 (±0.020)) models. The study aims to provide an interpretable feature engineering framework for the medical environment with the potential to integrate imaging data for efficient feature engineering in rapid triage and other clinical predictive models.

Synchronization of oscillators through time-shifted common inputs.

Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between otherwise common inputs are unavoidable. Since common inputs can be a source of correlation between the elements of multi-unit dynamical systems, regardless of whether these elements are directly connected with one another or not, it is of importance to understand their impact on synchronization. As a canonical model that is representative for a variety of different dynamical systems, we study limit-cycle oscillators that are driven by stochastic time-shifted common inputs. We show that if the oscillators are coupled, time shifts in stochastic common inputs do not simply shift the distribution of the phase differences, but rather the distribution actually changes as a result. The best synchronization is therefore achieved at a precise intermediate value of the time shift, which is due to a resonance-like effect with the most probable phase difference that is determined by the deterministic dynamics.

Stabilizing synchrony by inhomogeneity.

We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity-mismatch in the intrinsic firing rate of the neurons-can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.