Entrainment degree of globally coupled Winfree oscillators under external forcing.

We consider globally connected coupled Winfree oscillators under the influence of an external periodic forcing. Such systems exhibit many qualitatively different regimes of collective dynamics. Our aim is to understand this collective dynamics and, in particular, the system's capability of entrainment to the external forcing. To quantify the entrainment of the system, we introduce the entrainment degree, that is, the proportion of oscillators that synchronize to the forcing, as the main focus of this paper. Through a series of numerical simulations, we study the entrainment degree for different inter-oscillator coupling strengths, external forcing strengths, and distributions of natural frequencies of the Winfree oscillators, and we compare the results for the different cases. In the case of identical oscillators, we give a precise description of the parameter regions where oscillators are entrained. Finally, we use a mean-field method, based on the Ott-Antonsen ansatz, to obtain a low-dimensional description of the collective dynamics and to compute an approximation of the entrainment degree. The mean-field results turn out to be strikingly similar to the results obtained through numerical simulations of the full system dynamics.

Investigation of metabolites for estimating blood deposition time.

Trace deposition timing reflects a novel concept in forensic molecular biology involving the use of rhythmic biomarkers for estimating the time within a 24-h day/night cycle a human biological sample was left at the crime scene, which in principle allows verifying a sample donor's alibi. Previously, we introduced two circadian hormones for trace deposition timing and recently demonstrated that messenger RNA (mRNA) biomarkers significantly improve time prediction accuracy. Here, we investigate the suitability of metabolites measured using a targeted metabolomics approach, for trace deposition timing. Analysis of 171 plasma metabolites collected around the clock at 2-h intervals for 36 h from 12 male participants under controlled laboratory conditions identified 56 metabolites showing statistically significant oscillations, with peak times falling into three day/night time categories: morning/noon, afternoon/evening and night/early morning. Time prediction modelling identified 10 independently contributing metabolite biomarkers, which together achieved prediction accuracies expressed as AUC of 0.81, 0.86 and 0.90 for these three time categories respectively. Combining metabolites with previously established hormone and mRNA biomarkers in time prediction modelling resulted in an improved prediction accuracy reaching AUCs of 0.85, 0.89 and 0.96 respectively. The additional impact of metabolite biomarkers, however, was rather minor as the previously established model with melatonin, cortisol and three mRNA biomarkers achieved AUC values of 0.88, 0.88 and 0.95 for the same three time categories respectively. Nevertheless, the selected metabolites could become practically useful in scenarios where RNA marker information is unavailable such as due to RNA degradation. This is the first metabolomics study investigating circulating metabolites for trace deposition timing, and more work is needed to fully establish their usefulness for this forensic purpose.