Searcharxiv⌕ Search

arXiv subjects

Pierre R. Bertrand

Publications and source records attributed to Pierre R. Bertrand.

6 recordsLinked to original sources
arXiv2025

Automatic determination of the different control mechanisms in upright position by a wavelet method

A recent model to analyze the Center of Pressure trajectories is based on the fractional Brownian motion. By doing so, one note that standing still is describe by different mechanisms following the frequency. Previous studies exhibit the existence of a control mechanism which stabilize the upright position at a large enough time scales (from 0.3 s to 1.2 s depending on the method and on the authors) or equivalently at low frequencies. The different mechanisms are separated by a critical time scale or equivalently a critical frequency. This critical frequency is fundamental to understand the control mechanism of upright position : only physiological phenomenon at frequencies larger than this critical frequency could contribute to the task of maintaining equilibrium. A new statistical method is introduced based onto the recent progress in signal processing : the wavelets analysis. The algorithm is entirely automatic. Seventeen healthy young subjects were studied under quiet-standing conditions, the mean value of critical frequency is 1.8 Hz corresponding to a mean critical time scale 0.68 s. The algorithm is entirely automatic.

physics.med-ph↗
arXiv2011

Fast change point analysis on the Hurst index of piecewise fractional Brownian motion

In this presentation, we introduce a new method for change point analysis on the Hurst index for a piecewise fractional Brownian motion. We first set the model and the statistical problem. The proposed method is a transposition of the FDpV (Filtered Derivative with p-value) method introduced for the detection of change points on the mean in Bertrand et al. (2011) to the case of changes on the Hurst index. The underlying statistics of the FDpV technology is a new statistic estimator for Hurst index, so-called Increment Bernoulli Statistic (IBS). Both FDpV and IBS are methods with linear time and memory complexity, with respect to the size of the series. Thus the resulting method for change point analysis on Hurst index reaches also a linear complexity.

math.ST↗
arXiv2011

Off-line detection of multiple change points with the Filtered Derivative with p-Value method

This paper deals with off-line detection of change points for time series of independent observations, when the number of change points is unknown. We propose a sequential analysis like method with linear time and memory complexity. Our method is based at first step, on Filtered Derivative method which detects the right change points but also false ones. We improve Filtered Derivative method by adding a second step in which we compute the p-values associated to each potential change points. Then we eliminate as false alarms the points which have p-value smaller than a given critical level. Next, our method is compared with the Penalized Least Square Criterion procedure on simulated data sets. Eventually, we apply Filtered Derivative with p-Value method to segmentation of heartbeat time series, and detection of change points in the average daily volume of financial time series.

math.ST↗
arXiv2009

A process very similar to multifractional Brownian motion

In Ayache and Taqqu (2005), the multifractional Brownian (mBm) motion is obtained by replacing the constant parameter $H$ of the fractional Brownian motion (fBm) by a smooth enough functional parameter $H(.)$ depending on the time $t$. Here, we consider the process $Z$ obtained by replacing in the wavelet expansion of the fBm the index $H$ by a function $H(.)$ depending on the dyadic point $k/2^j$. This process was introduced in Benassi et al (2000) to model fBm with piece-wise constant Hurst index and continuous paths. In this work, we investigate the case where the functional parameter satisfies an uniform Hölder condition of order $β>\sup_{t\in \rit} H(t)$ and ones shows that, in this case, the process $Z$ is very similar to the mBm in the following senses: i) the difference between $Z$ and a mBm satisfies an uniform Hölder condition of order $d>\sup_{t\in \R} H(t)$; ii) as a by product, one deduces that at each point $t\in \R$ the pointwise Hölder exponent of $Z$ is $H(t)$ and that $Z$ is tangent to a fBm with Hurst parameter $H(t)$.

stat.ME↗
arXiv2009

Detection of Change--Points in the Spectral Density. With Applications to ECG Data

We propose a new method for estimating the change-points of heart rate in the orthosympathetic and parasympathetic bands, based on the wavelet transform in the complex domain and the study of the change-points in the moments of the modulus of these wavelet transforms. We observe change-points in the distribution for both bands.

stat.ME↗