Non-invasive autonomic evaluation has used fast Fourier transform (FFT) to assign a range of low (LF) and high frequencies (HF) as markers of sympathetic and parasympathetic influences, respectively. However, FFT cannot be applied to brief transient phenomena, such as those observed on performing autonomic tests where the acute changes of cardiovascular signals (blood pressure and heart rate) that represent the first and most important stage of the autonomic performance towards a new state of equilibrium occur. Wavelet analysis has been proposed as a method to overcome and complement information taken exclusively in the frequency domain. With discrete wavelet transform (DWT), a time-frequency analysis can be done, allowing the visualization in time of the contribution of LF and HF to the observed changes of a particular signal. In this study, we evaluate with wavelets the acute changes in R-R intervals and systolic blood pressure that are observed in normal subjects during four classical autonomic tests: headup tilt (HUT), cold pressor test (CPT), deep breathing (DB) and Valsalva manoeuvre (VM). Continuous monitoring of ECG and blood presure was performed. Also LF, HF and LF/HF were calculated. Consistent with previous interpretations, data showed an increase of sympathetic activity in HUT, CPT and VM. On DB, results reflected an increase in parasympathetic activity and frequencies. In conclusion, when compared with FFT, wavelet analysis allows the evaluation of autonomic variability during short and non-stationary periods of time and may constitute a useful advance in the assessment of autonomic function in both physiological and pathological conditions.

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models such as multi-strain dynamics to describe the virus -host interaction in dengue fever, even the most recently developed parameter estimation techniques, such as maximum likelihood iterated filtering, reach their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and the deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors.

We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using Kullback-Leibler divergence we evaluate the best model out from four biparametric models standardly used in the context of financial data analysis. In our present data sets we conclude that the inverse Γ-distribution is a good model, particularly for the distribution tail of the largest volume-price fluctuations. Extracting the time-series of the corresponding parameter values we show that they evolve in time as stochastic variables themselves. For the particular case of the parameter controlling the volume-price distribution tail we are able to extract an Ornstein-Uhlenbeck equation which describes the fluctuations of the largest volume-prices observed in the data. Finally, we discuss how to bridge from the stochastic evolution of the distribution parameters to the stochastic evolution of the (non-stationary) observable and put our conclusions into perspective for other applications in geophysics and biology.