E. Roulin, U. S. Freitas & C. Letellier
Working conditions for safe detection of nonlinearity and noise titration
Physical Review E, 83, 046225, 2011. online

- Abstract
Even if noise titration cannot be satisfactorily used to prove the presence of chaos, it can still be used to detect nonlinear component in dynamics. Nevertheless, since the technique have the use of nonlinear models for one-step-ahead predictions, it requires an acute choice of modeling parameters, i.e., the number of terms and the nonlinearity degree of the models. Based on illustrative examples, we propose conditions under which the method of noise titration can be reliably applied to characterize nonlinearity in the time series. It is thus possible to compare different time series and state which one is governed by the strongest nonlinearity. For instance, it is shown that, when there is a single nonlinear term in the equations describing the system, the variable on which it acts can be identified among the others.

Y. Ouahchi, C. Letellier, N. Bon-Mardion, J.-P. Marie, C. Tardif & E.Verin
Effects of chronic aspirations on breathing pattern and ventilatory drive in vagatomized rats
Respiratory Physiology & Neurobiology, 176, 98–102, 2011. On line

- Abstract
The aim of this study was to test the hypothesis that aspirations induced by unilateral vagotomy destabilise ventilatory pattern during swallowing. The study was carried out on 15 Wistar rats (2–3 months, 290–350 g) using whole-body plethysmography and video recordings, before and after unilateral vagotomy. The rats were given water ad libitum via a baby bottle fitted with a nipple. The experiment was continued until rest ventilation and swallowing periods were identified on the video recordings. Following the sectioning of the right vagus nerve, all the rats presented bronchial aspirations and unilateral vocal cord paralysis in the aperture position. After the vagotomy there were no changes at rest of the ventilatory variables compared to healthy controls. In healthy animals during swallowing, we observed a decrease in total ventilatory time (TbTOT), a decrease in inspiratory time (TI) (p < 0.001), a decrease in expiratory time (TE) (p < 0.001), no change in tidal volume (VT) and an increase in mean inspiratory time (VT/TI) (p < 0.001) compared to the rest period. Animals with chronic aspiration presented during swallowing an increase in TbTOT (p < 0.001), TI (p < 0.01), and TE (p < 0.001), no change in VT and a decrease of VT/TI (p < 0.001) and a modification of ventilatory pattern. In conclusion, our results confirmed that swallowing modifies ventilation in healthy animals and that chronic aspiration decreases ventilatory drive and modifies ventilatory pattern during swallowing.

G. G. Rodrigues, L. A. Aguirre, A. Cuvelier, J.-F. Muir & C. Letellier
Global models for patient–ventilator interactions in noninvasive ventilation with asynchronies
Computers in Biology and Medicine, 41 (5), 253-264, 2011. online

- Abstract
Noninvasive ventilation is a clinical procedure that enables patients with chronic respiratory failure to reduce the work of breathing and to improve blood oxygenation. In order to attain such goals, the ventilation support is expected to be phase synchronized with the patient spontaneous breathing. Unfortunately, asynchrony events are not rare. In order to provide more effective ventilation schemes, the patient–ventilator interactions should be better understood both during normal rhythm and asynchronism. This paper investigates this problem using data-driven modeling. Hence the estimation of input–output and autonomous models from pressure and airflow time series is discussed and illustrated. Issues concerning the nonlinearity of the interactions and modeling assumptions are dealt with. The results presented include models obtained from airflow and pressure measurements of a set of patients.

D. Amroun-Aliane, L. Pastur, & C. Letellier
Defects in spatiotemporal diagrams and their relations to phase coherence and lack of observability
Physical Review E, 83, 056212, 2011. Online

- Abstract
Spatiotemporal systems are commonly investigated in terms of spatiotemporal diagrams and, most often, the analysis is limited to the first instabilities. Due to the lack of a Takens-like theorem for spatiotemporal systems, the resulting dynamics is almost never interpreted using phase portraits reconstructed from one variable locally recorded. This work is an attempt to make an explicit link between reconstructed phase portraits and spatiotemporal diagrams. Defects distributions are interpreted in terms of a lack of phase coherence. The lack of a simple structure—as a torus characterized by a closed curve for PoincarŽe section when a quasiperiodic regime is identified—is tentatively interpreted in terms of observability. A first link is thus made between the defects distribution and the nature of the underlying dynamics.

L. A. Aguirre & C. Letellier
Investigating observability properties from data in nonlinear dynamics
Physical Review E, 83, 066209, 2011. Online

- Abstract
Investigation of observability properties of nonlinear dynamical systems aims at giving a hint on how much dynamical information can be retrieved from a system using a certain measuring function. Such an investigation usually requires knowledge of the system equations. This paper addresses the challenging problem of investigating observability properties of a system only from recorded data. From previous studies it is known that phase spaces reconstructed from poor observables are characterized by local sharp pleatings, local strong squeezing of trajectories, and global inhomogeneity. A statistic is then proposed to quantify such properties of poor observability. Such a statistic was computed for a number of bench models for which observability studies had been previously performed. It was found that the statistic proposed in this paper, estimated exclusively from data, correlates generally well with observability results obtained using the system equations. It is possible to arrive at the same order of observability among the state variables using the proposed statistic even in the presence of noise with a standard deviation as high as 10% of the data. The paper includes the application of the proposed statistic to sunspot time series.

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