Detecting changes in the fluctuations of a Gaussian process and an application to heartbeat time series

The aim of this paper is first the detection of multiple abrupt changes of the long-range dependence (respectively self-similarity, local fractality) parameters from a sample of a Gaussian stationary times series (respectively time series, continuous-time process having stationary increments). The estimator of the $m$ change instants (the number $m$ is supposed to be known) is proved to satisfied a limit theorem with an explicit convergence rate. Moreover, a central limit theorem is established for an estimator of each long-range dependence (respectively self-similarity, local fractality) parameter. Finally, a goodness-of-fit test is also built in each time domain without change and proved to asymptotically follow a Khi-square distribution. Such statistics are applied to heart rate data of marathon's runners and lead to interesting conclusions

Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process

In this paper, an estimator of $m$ instants ($m$ is known) of abrupt changes of the parameter of long-range dependence or self-similarity is proved to satisfy a limit theorem with an explicit convergence rate for a sample of a Gaussian process. In each estimated zone where the parameter is supposed not to change, a central limit theorem is established for the parameter's (of long-range dependence, self-similarity) estimator and a goodness-of-fit test is also built. {\it To cite this article: J.M. Bardet, I. Kammoun, C. R. Acad. Sci. Paris, Ser. I 340 (2007).

Asymptotic Properties of the Detrended Fluctuation Analysis of Long Range Dependence Processes

International audienceIn the past few years, a certain number of authors have proposed analysis methods of the time series built from a long range dependence noise. One of these methods is the Detrended Fluctuation Analysis (DFA), frequently used in the case of physiological data processing. The aim of this method is to highlight the long-range dependence of a time series with trend. In this study asymptotic properties of DFA of the fractional Gaussian noise are provided. Those results are also extended to a general class of stationary long-range dependent processes. As a consequence, the convergence of the semi-parametric estimator of the Hurst parameter is established. However, several simple exemples also show that this method is not at all robust in case of trend

Modélisation et détection de ruptures des signaux physiologiques issus de compétitions d'endurance

This work focuses on the modeling and the estimation of relevant parameters characterizing instantaneous heart rate (HR) signals. We choose to focus especially in an exponent that can be called "Fractal", which indicates the local regularity of the path and the dependency between data. The asymptotic properties of the DFA (Detrended Fluctuation Analysis) function and the deduced estimator of H are studied in the case of fractional Gaussian noise (FGN) and extended to a general class of stationary semi-parametric long-range dependent processes with or without trend. We show that this method is not at all robust. We propose the modeling of HR data with a generalization of FGN, called locally fractional Gaussian noise. Such stationary process is built from a parameter called of local fractality which is a kind of Hurst parameter (that may take values in IR) in restricted band frequency. The estimation of local fractality parameter and also the construction of goodness-of-fit test can be made with wavelet analysis. We also show the relevance of model and an evolution of the parameter during the race. Then, change detection in this parameter can be extremely meaningful. We propose a method detecting multiple abrupt changes of long memory parameter (respectively self-similarity, local fractality). From a wavelet analysis, an estimator of the change points is proved to satisfy a limit theorem. A central limit theorem is established for the estimator of each parameter and a goodness-of-fit test is also built in each zona where the parameter does not change. Finally, we show the same evolution of local fractality parameter relating to HR time series.Ce travail de thèse porte sur la modélisation et l'estimation de paramètres pertinents pour les signaux de fréquences cardiaques (FC) instantanées. Nous nous intéressons à un paramètre (appelé grossièrement "fractal"), qui témoigne de la régularité locale de la trajectoire et de la dépendance entre les données. Les propriétés asymptotiques de la fonction DFA (Detrended Fluctuation Analysis) et de l'estimateur de H sont étudiées pour le bruit gaussien fractionnaire (FGN) et plus généralement pour une classe semi-paramétrique de processus stationnaires à longue mémoire avec ou sans tendance. On montre que cette méthode n'est pas robuste. On propose la modélisation des séries de FC par une généralisation du FGN, appelée bruit gaussien localement fractionnaire. Un tel processus stationnaire est construit à partir du paramètre dit de fractalité locale (une sorte de paramètre de Hurst avec des valeurs dans IR) sur une bande de fréquences. L'estimation du paramètre est faite par une analyse par ondelettes, tout comme le test d'adéquation. On montre la pertinence du modèle et une évolution du paramètre pendant la course. Une détection des changements de ce paramètre pourrait être extrêmement appropriée. On propose alors une méthode de détection de multiples ruptures du paramètre de longue mémoire (respectivement d'autosimilarité, de fractalité locale). Un estimateur des points de changements est construit, il vérifie un théorème limite. Un théorème de la limite centrale est établi pour l'estimateur des paramètres et un test d'ajustement est mis en place dans chaque zone où le paramètre est inchangé. Enfin, on montre la même évolution du paramètre de fractalité locale sur les FC

A new stochastic process to model Heart Rate series during exhaustive run and an estimator of its fractality parameter

International audienceIn order to interpret and explain the physiological signal behaviors, it can be interesting to find some constants among the fluctuations of these data during all the effort or during different stages of the race (which can be detected using a change points detection method). Several recent papers have proposed the long-range dependence (Hurst) parameter as such a constant. However, their results induce two main problems. Firstly, DFA method is usually applied for estimating this parameter. Clearly, such a method does not provide the most efficient estimator and moreover it is not at all robust even in the case of smooth trends. Secondly, this method often gives estimated Hurst parameters larger than $1$, which is the larger possible value for long memory stationary processes. In this article we propose solutions for both these problems and we define a new model allowing such estimated parameters

Investigation of Antimicrobial Activity and Statistical Optimization of Bacillus subtilis SPB1 Biosurfactant Production in Solid-State Fermentation

During the last years, several applications of biosurfactants with medical purposes have been reported. Biosurfactants are considered relevant molecules for applications in combating many diseases. However, their use is currently extremely limited due to their high cost in relation to that of chemical surfactants. Use of inexpensive substrates can drastically decrease its production cost. Here, twelve solid substrates were screened for the production of Bacillus subtilis SPB1 biosurfactant and the maximum yield was found with millet. A Plackett-Burman design was then used to evaluate the effects of five variables (temperature, moisture, initial pH, inoculum age, and inoculum size). Statistical analyses showed that temperature, inoculum age, and moisture content had significantly positive effect on SPB1 biosurfactant production. Their values were further optimized using a central composite design and a response surface methodology. The optimal conditions of temperature, inoculum age, and moisture content obtained under the conditions of study were 37°C, 14 h, and 88%, respectively. The evaluation of the antimicrobial activity of this compound was carried out against 11 bacteria and 8 fungi. The results demonstrated that this biosurfactant exhibited an important antimicrobial activity against microorganisms with multidrug-resistant profiles. Its activity was very effective against Staphylococcus aureus, Staphylococcus xylosus, Enterococcus faecalis, Klebsiella pneumonia, and so forth

158 Prothetic abcess complicating Infective endocarditis

The cardiac abscess formation is appraised to 20–30% during the infectious endocarditis (IE). It is more frequent during prosthesis endocarditis and it can reach 60%. The prognosis is generally reserved. Objective To determine echocardiographic, bacteriological and evolutive features of prothetic IE complicated of abscess.Retrospective study including 51 patients having certain or probable IE according to Duke criterias between 2002 and 2005. At 9 patients (17,64%) the endocarditis was complicated of prothetic abscess. It was about 6 men and 3 women with a middle age of 39 ± years. IE was la ate IE in 5 cases. Clinical and biological infectious syndrome was constant. Isolated germs were staphylococcus aureus in 2 cases, GRAM négatif Bacillus in 2 cases. Culture negative endocarditis were noted in 5 cases. Brucellosis serology was positive at one patient. Prothetic abcess was diagnosed by transthoracic echocardiography (TTE) at 2 patients and by transesophagal echocardiography (TEE) at all patients.The abcess was localized on the aortic prosthesis at 5 patients, mitral prothesis at 3 patients and mitroaortic prothesis at one patient. TEE identified annular abcess at 2 patients and a myocardial abcess at 1 patient. Secondary septic localizations were noted at 6 patients: 4 cerebral abscesses, 2 splenic localization, a renal localization and an articular localization. High degree atrioventricular blocks were observed at 3 patients. The recourse to the surgery was frequent (7 patient/9 patient). It was an emergent sugery at 2 patients because of a heart failure. For the others, the indication for surgery was medical failure treatment at a mean delay of 19 days. The evolution was fatal at 5 patients. and the evolution was favorable at the others.Prothetic endocarditis complicated of abscess are serious requiring frequently a prothetic replacement, a very high risked surgery. TEE must be systematic at all patients carrier of prosthesis if they have infectious syndrome in order to carry the early diagnosis of IE and to avoid abcess formation

Beneficial Effects of Extra Virgin Olive Oil Rich in Phenolic Compounds on Cardiovascular Health

The Mediterranean diet (Med-diet) includes a high consumption of cereals, fruits, legumes and vegetables, a moderate fish intake and a low consumption of red meat. Olive oil is a basic component of the Med-diet due to its numerous health benefits. In the last decade, many epidemiological studies have confirmed the protective role of extra virgin olive oil (EVOO) against several chronic illnesses including cardiovascular diseases. EVOO is mainly composed of triacylglycerols, with oleic acid as the dominating esterified fatty acid, and other minor compounds. Among them, phenolic compounds, such as hydroxytyrosol and its derivatives (oleuropein and tyrosol), are the principal components responsible for the cardioprotective effects. They are endowed with wide biological activities, including strong antioxidant properties, allowing the prevention of cardiovascular risk factors, such as atherosclerosis, plasma lipid disorders, endothelial dysfunction, hypertension, obesity and type 2 diabetes. The aim of the present chapter was to elucidate the beneficial effect of EVOO, as part of the Mediterranean-style diets, on cardiovascular risk factors and to discuss the underlying mechanisms by which polyphenols exert their effects