Differentiating acute from chronic insomnia with machine learning from actigraphy time series data.

Acute and chronic insomnia have different causes and may require different treatments. They are investigated with multi-night nocturnal actigraphy data from two sleep studies. Two different wrist-worn actigraphy devices were used to measure physical activities. This required data pre-processing and transformations to smooth the differences between devices. Statistical, power spectrum, fractal and entropy analyses were used to derive features from the actigraphy data. Sleep parameters were also extracted from the signals. The features were then submitted to four machine learning algorithms. The best performing model was able to distinguish acute from chronic insomnia with an accuracy of 81%. The algorithms were then used to evaluate the acute and chronic groups compared to healthy sleepers. The differences between acute insomnia and healthy sleep were more prominent than between chronic insomnia and healthy sleep. This may be associated with the adaptation of the physiology to prolonged periods of disturbed sleep for individuals with chronic insomnia. The new model is a powerful addition to our suite of machine learning models aiming to pre-screen insomnia at home with wearable devices.

Scale invariance in a nonvibrating magnetic granular system.

A nonvibrating magnetic granular system is studied by using a time series approach. The system consists of steel balls confined inside a circular wall that surrounds a glass plate. Kinetic energy is provided to the particles by the application of an external vertical time-dependent magnetic field of different amplitudes. We carried out a characterization of the system dynamics through the measurement of the correlations present in the time series of positions, in the x-direction, of each particle. In particular, by performing Fourier spectral analysis, we find that the time series are fractal and scale invariant, in such a way that the corresponding Fourier power spectra follow a power law [Formula: see text], with [Formula: see text]. More specifically, we find that the values of [Formula: see text], and therefore the strength of the correlations, increase as the magnetic field also increases. In this way, the present system constitutes an experimental model to generate correlated random walks. Additionally, we show how the introduction of a constant magnetic field breaks down this scale invariance property in the positions of each particle. Finally, we confirm the above results by applying detrended fluctuation analysis.

Crossover in nonstandard random-matrix spectral fluctuations without unfolding.

Recently, singular value decomposition (SVD) was applied to standard Gaussian ensembles of random-matrix theory to determine the scale invariance in spectral fluctuations without performing any unfolding procedure. Here, SVD is applied directly to the ß-Hermite ensemble and to a sparse matrix ensemble, decomposing the corresponding spectra in trend and fluctuation modes. In correspondence with known results, we obtain that fluctuation modes exhibit a crossover between soft and rigid behavior. In this way, possible artifacts introduced applying unfolding techniques are avoided. By using the trend modes, we perform data-adaptive unfolding, and we calculate traditional spectral fluctuation measures. Additionally, ensemble-averaged and individual-spectrum averaged statistics are calculated consistently within the same basis of normal modes.

Determination of scale invariance in random-matrix spectral fluctuations without unfolding.

We apply the singular value decomposition (SVD) method, based on normal-mode analysis, to decompose the spectra of finite random matrices of standard Gaussian ensembles in trend and fluctuation modes. We use the fact that the fluctuation modes are scale invariant and follow a power law, to characterize the transition between the extreme regular and chaotic cases. Thereby, we quantify the quantum chaos in systems described by random matrix theory in a direct way, without performing any previous unfolding procedure, and therefore, avoiding possible artifacts.

Random-matrix spectra as a time series.

Spectra of ordered eigenvalues of finite random matrices are interpreted as a time series. Data-adaptive techniques from signal analysis are applied to decompose the spectrum in clearly differentiated trend and fluctuation modes, avoiding possible artifacts introduced by standard unfolding techniques. The fluctuation modes are scale invariant and follow different power laws for Poisson and Gaussian ensembles, which already during the unfolding allows one to distinguish the two cases.

Criticality and long-range correlations in time series in classical and quantum systems.

We present arguments which indicate that a transitional state in between two different regimes implies the occurrence of 1/f time series and that this property is generic in both classical and quantum systems. Our study focuses on two particular examples: the one-dimensional module-1 logistic map and nuclear excitation spectra obtained with a schematic shell-model Hamiltonian. We suggest that a transitional point is characterized by the long-range correlations implied by 1/f time series. We apply a Fourier spectral analysis and the detrended fluctuation analysis method to study the fluctuations to each system.