Multi-lag tone–entropy in neonatal stress

Heart rate variability (HRV) has been analysed using linear and nonlinear methods. In the framework of a controlled neonatal stress model, we applied tone–entropy (T–E) analysis at multiple lags to understand the influence of external stressors on healthy term neonates. Forty term neonates were included in the study. HRV was analysed using multi-lag T–E at two resting and two stress phases (heel stimulation and a heel stick blood drawing phase). Higher mean entropy values and lower mean tone values when stressed showed a reduction in randomness with increased sympathetic and reduced parasympathetic activity. A ROC analysis was used to estimate the diagnostic performances of tone and entropy and combining both features. Comparing the resting and simulation phase separately, the performance of tone outperformed entropy, but combining the two in a quadratic linear regression model, neonates in resting as compared to stress phases could be distinguished with high accuracy. This raises the possibility that when applied across short time segments, multi-lag T–E becomes an additional tool for more objective assessment of neonatal stress.

Group multiple lags consensus of fractional-order nonlinear leader-following multi-agent systems via adaptive control

In this paper, group multiple lags consensus of fractional-order leader-following multi-agent systems with nonlinear dynamics are investigated, in which two kinds of lag consensus are considered. One is said to be outergroup lag consensus, which means that different group leaders reach lag consensus. The other one is called innergroup lag consensus, that is to say, the followers will reach lag consensus with their own group leader. Based on Mittag–Leffler stability for fractional-order systems, algebraic graph theory, a class of novel control protocols is designed and the corresponding sufficient conditions are derived to guarantee the achievement of group multiple lags consensus. Furthermore, considering parametric uncertainties, an adaptive control technology is employed to solve the group multiple lags consensus for fractional order multi-agent systems, and the corresponding adaptive control protocols and sufficient conditions are proposed. Finally, numerical simulations are given to demonstrate the effectiveness of the obtained results.

Empirical Models of Spatial Inter‐Dependence

This article discusses the role of ‘spatial interdependence’ between units of analysis by using a symmetric weighting matrix for the units of observation whose elements reflect the relative connectivity between unit i and unit j. It starts by addressing spatial interdependence in political science. There are two workhorse regression models in empirical spatial analysis: spatial lag and spatial error models. The article then addresses OLS estimation and specification testing under the null hypothesis of no spatial dependence. It turns to the topic of assessing spatial lag models, and a discussion of spatial error models. Moreover, it reports the calculation of spatial multipliers. Furthermore, it presents several newer applications of spatial techniques in empirical political science research: SAR models with multiple lags, SAR models for binary dependent variables, and spatio-temporal autoregressive (STAR) models for panel data.