C. Quérel, O. Grondin & C. Letellier
Semi-physical mean-value NOx model for diesel engine control
Control Engineering Practice, 40, 27-44, 2015. Online

- Abstract A semi-physical model has been developed to predict nitrogen oxide (NOx) emissions produced by diesel engines. This model is suitable for online NOx estimation and for model-based engine control. It is derived from a zero-dimensional thermodynamic model which was simplified by only retaining main phenomena contributing to NOx formation. The crank angle evolution of the burned gas temperature, which has a strong impact on NOx formation rate, is described by a semi-empirical model whose key variable is the maximum burned gas temperature. This variable presents a good correlation with the molar fraction of NOx at the end of combustion and can be expressed as a function of the intake burned gas ratio and the start of combustion. The maximum burned gas temperature sub-model is then coupled to an averaged NOx formation kinetic model (based on the Zeldovich mechanism) to form a mean-value model for NOx computation. This latter model was validated using data sets recorded in two diesel engines for steady-state operating conditions as well as for several driving cycles including parametric variations of the engine calibration.

F. Denis, S. Yossi, Senna, A.-L. Septans, A. Charron, E. Voog, O. Dupuis, G. Ganem, Y. Pointreau & C. Letellier
Improving survival in patients treated for a lung cancer using self-evaluated symptoms reported through a web application,
American Journal of Clinical Oncology, 40 (5), 464-469, 2017. Online

- Abstract
Objectives : We retrospectively compared survivals in patients with a lung cancer history and followed by the so-called sentinel Web-application that allows early detection of relapse and early palliative care initiation versus a conventional follow-up in our center.
Methods : The survival in 98 consecutive patients with lung cancer was assessed. The first part of them (the control arm) was retrospectively recruited between March 2011 and August 2012. The second half of them (the experimental arm) was prospectively recruited between August 2012 and December 2013 to weekly fill a form of 11 self-assessed symptoms, then processed by the "sentinel" Web-application. Data were sent to this sentinel application in real-time between planned visits. An email alert was sent to the oncologist when self-scored symptoms matched some predefined criteria. Follow-up visit and imaging were then organized after a phone call for confirming the suspect symptoms. In the control arm (49 patients), a common follow-up was applied (visit and imaging every 2 to 6 mo according to stage of tumor and kind of treatment).
Results : Median follow-up duration was 12.3 months in the experimental arm and 16.7 months in the control arm (p=0.27). Survival was significantly better in the sentinel arm than in the control arm (p=0.0014). Median survival was 16.7 months in the control arm and 22.4 months in the experimental arm. One-year survival was 86.6% in the experimental arm and 59.1% in the control arm.
Conclusions : Survival may be improved by early detection of relapse and early palliative care initiation by using sentinel-like Web-application.

C. Lainscsek, J. Weyhenmeyer, T. J. Sejnowski, C. Letellier
Discovering independent parameters in complex dynamical systems
Chaos, Solitons & Fractals, 76, 182-189, 2015. Online

- Abstract
The transformation of a nonlinear dynamical system into a standard form by using one of its variables and its successive derivatives can be used to identify the relationships that may exist between the parameters of the original system such as the subset of the parameter space over which the dynamics is left invariant. We show how the size of the attractor or the time scale (the pseudo-period) can be varied without affecting the underlying dynamics. This is demonstrated for the Rössler and the Lorenz systems. We also consider the case when two Rössler systems are unidirectionally coupled and when a Lorenz system is driven by a Rössler system. In both cases, the dynamics of the coupled system is affected.

M. Rosalie & C. Letellier
Systematic template extraction from chaotic attractors : II. Genus-one attractors with multiple unimodal folding mechanisms
Journal of Physics A, 48, 235101, 2015. Online

- Abstract
Asymmetric and symmetric chaotic attractors produced by the simplest jerk equivariant system are topologically characterized. In the case of this system with an inversion symmetry, it is shown that symmetric attractors bounded by genus-one tori are conveniently analyzed using a two-components Poincaré section. Resulting from a merging attractor crisis, these attractors can be easily described as being made of two folding mechanisms (here described as mixers), one for each of the two attractors co-existing before the crisis : symmetric attractors are thus described by a template made of two mixers. We thus developed a procedure for concatenating two mixers (here associated with unimodal maps) into a single one, allowing the description of a reduced template, that is, a template simplified under an isotopy. The so-obtained reduced template is associated with a description of symmetric attractors based on one-component Poincaré section as suggested by the corresponding genus-one bounding torus. It is shown that several reduced templates can be obtained depending on the choice of the retained one-component Poincaré section.

E. Bianco-Martinez, M. S. Baptista & C. Letellier
Symbolic computations of nonlinear observability
Physical Review E, 91, 062912, 2015 Online

- Abstract
Observability is a very useful concept for determining whether the dynamics of complicated systems can be correctly reconstructed from a single (univariate or multivariate) time series. When the governing equations of dynamical systems are high-dimensional and/or rational, analytical computations of observability coefficients produce large polynomial functions with a number of terms that become exponentially large with the dimension and the nature of the system. In order to overcome this difficulty, we introduce here a symbolic observability coefficient based on a symbolic computation of the determinant of the observability matrix. The computation of such coefficients is straightforward and can be easily analytically carried out, as demonstrated in this paper for a five-dimensional rational system.

V. Messager & C. Letellier
A genesis of special relativity
International Journal of Modern Physics D, 24 (10), 1530024, 2015. Online

- Abstract
The genesis of special relativity is intimately related to the development of the theory of light propagation. When optical phenomena were described, there are typically two kinds of theories : (i) One based on light rays and light particles and (ii) one considering the light as waves. When diffraction and refraction were experimentally discovered, light propagation became more often described in terms of waves. Nevertheless, when attempts were made to explain how light was propagated, it was nearly always in terms of a corpuscular theory combined with an ether, a subtle medium supporting the waves. Consequently, most of the theories from Newton’s to those developed in the 19th century were dual and required the existence of an ether. We therefore used the ether as our Ariadne thread for explaining how the principle of relativity became generalized to the so-called Maxwell equations around the 1900’s. Our aim is more to describe how the successive ideas were developed and interconnected than framing the context in which these ideas arose.

E. Fresnel, E. Yacoub, U. Freitas, A. Kerfourn, V. Messager, E. Mallet, J.-F. Muir & C. Letellier
An easy-to-use technique to characterize cardiodynamics from first-return maps on ΔRR-intervals
Chaos, 25 (8), 083111, 2015. Online

- Abstract
Heart rate variability analysis using 24 h Holter monitoring is frequently performed to assess the cardiovascular status of a patient. The present retrospective study is based on the beat-to-beat interval variations or ΔRR, which offer a better view of the underlying structures governing the cardiodynamics than the common RR-intervals. By investigating data for three groups of adults (with normal sinus rhythm, congestive heart failure, and atrial fibrillation, respectively), we showed that the first-return maps built on ΔRR can be classified according to three structures : (i) a moderate central disk, (ii) a reduced central disk with well-defined segments, and (iii) a large triangular shape. These three very different structures can be distinguished by computing a Shannon entropy based on a symbolic dynamics and an asymmetry coefficient, here introduced to quantify the balance between accelerations and decelerations in the cardiac rhythm. The probability P111111 of successive heart beats without large beat-to-beat fluctuations allows to assess the regularity of the cardiodynamics. A characteristic time scale, corresponding to the partition inducing the largest Shannon entropy, was also introduced to quantify the ability of the heart to modulate its rhythm : it was significantly different for the three structures of first-return maps. A blind validation was performed to validate the technique.

S. Mangiarotti & C. Letellier
Topological analysis for designing a suspension of the Hénon map
Physics Letters A, 379, 3069-3074, 2015. Online

- Abstract
A suspension of a map consists in the flow for which the Poincaré section is that map. Designing a suspension of a given map remains a non trivial task in general. The case of suspending the Hénon map is here considered. Depending on the parameter values, the Hénon map is orientation preserving or reversing ; it is here shown that while a tridimensional suspension can be obtained in the former case, a four-dimensional flow is required to suspend the latter. A topological characterization of the three-dimensional suspension proposed by Starrett and Nicholas for the orientation preserving area is performed. A template is proposed for the four-dimensional case, for which the governing equations remain to be obtained.

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