Multifractional processes with random exponent

Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet series. We will use this type of representation to study their Hölder regularity and their self-similarity

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 H\"older condition of order \beta>\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 H\"older 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 H\"older exponent of $Z$ is $H(t)$ and that $Z$ is tangent to a fBm with Hurst parameter $H(t)$.Comment: 18 page

Asymptotic normality for a modified quadratic variation of the Hermite process

We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be independent and identically distributed up to asymptotically negligible remainders. We prove that this modified quadratic variation satisfies a Central Limit Theorem and we derive its rate of convergence under the Wasserstein distance via Stein-Malliavin calculus. As a consequence, we construct, for the first time in the literature related to Hermite processes, a strongly consistent and asymptotically normal estimator for the Hurst parameter

Radiotherapy planning for glioblastoma based on a tumor growth model: Improving target volume delineation

Glioblastoma are known to infiltrate the brain parenchyma instead of forming a solid tumor mass with a defined boundary. Only the part of the tumor with high tumor cell density can be localized through imaging directly. In contrast, brain tissue infiltrated by tumor cells at low density appears normal on current imaging modalities. In clinical practice, a uniform margin is applied to account for microscopic spread of disease. The current treatment planning procedure can potentially be improved by accounting for the anisotropy of tumor growth: Anatomical barriers such as the falx cerebri represent boundaries for migrating tumor cells. In addition, tumor cells primarily spread in white matter and infiltrate gray matter at lower rate. We investigate the use of a phenomenological tumor growth model for treatment planning. The model is based on the Fisher-Kolmogorov equation, which formalizes these growth characteristics and estimates the spatial distribution of tumor cells in normal appearing regions of the brain. The target volume for radiotherapy planning can be defined as an isoline of the simulated tumor cell density. A retrospective study involving 10 glioblastoma patients has been performed. To illustrate the main findings of the study, a detailed case study is presented for a glioblastoma located close to the falx. In this situation, the falx represents a boundary for migrating tumor cells, whereas the corpus callosum provides a route for the tumor to spread to the contralateral hemisphere. We further discuss the sensitivity of the model with respect to the input parameters. Correct segmentation of the brain appears to be the most crucial model input. We conclude that the tumor growth model provides a method to account for anisotropic growth patterns of glioblastoma, and may therefore provide a tool to make target delineation more objective and automated

Information-Theoretic Active Learning for Content-Based Image Retrieval

We propose Information-Theoretic Active Learning (ITAL), a novel batch-mode active learning method for binary classification, and apply it for acquiring meaningful user feedback in the context of content-based image retrieval. Instead of combining different heuristics such as uncertainty, diversity, or density, our method is based on maximizing the mutual information between the predicted relevance of the images and the expected user feedback regarding the selected batch. We propose suitable approximations to this computationally demanding problem and also integrate an explicit model of user behavior that accounts for possible incorrect labels and unnameable instances. Furthermore, our approach does not only take the structure of the data but also the expected model output change caused by the user feedback into account. In contrast to other methods, ITAL turns out to be highly flexible and provides state-of-the-art performance across various datasets, such as MIRFLICKR and ImageNet.Comment: GCPR 2018 paper (14 pages text + 2 pages references + 6 pages appendix

Hydrographic network extraction and watersheds delimitation software of the South Oran (North Wester Algeria)

The development of space technology has allowed a better understanding and effective use of water resources through the use of Digital Terrain Models (DTM) Mapping the river system from DTM has two objectives, namely identifying first topography  descriptors like hills, ridges and valleys of watersheds and second hydrological parameters to map areas of runoff recovery for a more efficient development and also a better representation of the actual land occupation. Our work is part of a methodological approach to satellite imagery processing and mapping of topographic and hydrographic parameters of watersheds. Thus, from DTM one was able to extract the full river system of the region. The results show a remarkable evolution of human activities and  especially in areas of high water recovery capacity.Keywords: remote sensing, DTM, network hydrology, geographic, steppe, west of  Algeria

Magnetic properties and phase diagrams of a bilayer spin-3/2 Ising model

The magnetic properties and phase diagrams of a bilayer spin-3/2 Ising model is studied, under the effect of crystal field, using the mean field (MF) theory and the Monte Carlo (MC) simulations. The ground state phase diagrams in the (Js1 / J, ∆s1 / J) and (Js2 / J, ∆s1 / J) planes are determined analytically. On the other hand, the magnetization and critical temperature is studied. The results found by the two methods are in good agreement with the ground state phase diagram. It was found that the critical temperature calculated by Monte Carlo simulations is less than that one obtained by the mean field method, for both positive and negative crystal field acting on each layer of the film.The magnetic properties and phase diagrams of a bilayer spin-3/2 Ising model is studied, under the effect of crystal field, using the mean field (MF) theory and the Monte Carlo (MC) simulations. The ground state phase diagrams in the (Js1 / J, ∆s1 / J) and (Js2 / J, ∆s1 / J) planes are determined analytically. On the other hand, the magnetization and critical temperature is studied. The results found by the two methods are in good agreement with the ground state phase diagram. It was found that the critical temperature calculated by Monte Carlo simulations is less than that one obtained by the mean field method, for both positive and negative crystal field acting on each layer of the film

Axial stereovision: modeling and calibration of the optical system, 3D reconstruction of natural objects

In passive binocular stereovision, we generally discern two approaches : the lateral stereovision and the axial stereovision . We present here a study relating more particularly to axial stereovision . The axial systems have been studied by numerous research teams because of their relative geometrical plainness which makes them interesting for industrial applications, by simplifying the matching phase . Among the optical systems previously studied, and able to be axial, we find - a camera with a zoom, - a camera moving along its optical axis . In this paper we first present the geometrical model of an axial stereovision system . Then, we describe a robust calibration method of such a system . This method takes into account the fact that the optical systems described above are not strictly axial because there always remain mechanical problems that do not allow a perfect motion of the optical center along the optical axis . Finally, we present a matching algorithm allowing to match characteristic points present in the images and making thus possible the reconstruction ofnon polyhedral objects .En stéréovision binoculaire passive, on distingue généralement deux approches: la stéréovision latérale et la stéréovision axiale. Nous présentons ici une étude portant plus particulièrement sur la stéréovision axiale. Les systèmes axiaux ont été étudiés par de nombreuses équipes de recherche, en raison de leur relative simplicité géométrique qui les rend intéressants pour des applications industrielles, en simplifiant la phase de mise en correspondance. Parmi les systèmes optiques étudiés antérieurement et pouvant être axiaux, nous trouvons: - une caméra munie d'un zoom, - une caméra se déplaçant le long de son axe optique. Dans cet article, nous présentons tout d'abord le modèle géométrique d'un système de stéréovision axiale. Puis nous décrivons une méthode robuste de calibrage d'un tel système de stéréovision. Cette méthode prend en compte le fait que les systèmes optiques décrits ci-dessus ne sont pas strictement des systèmes axiaux: en effet, il subsiste toujours des problèmes mécaniques ne permettant pas un mouvement parfait du centre optique le long de l'axe optique. En conclusion, nous présentons un algorithme d'appariement permettant de mettre en correspondance des points caractéristiques présents dans les images et rendant ainsi possible la reconstruction d'objets non polyédrique