Vaccination strategy on a geographic network

We considered a mathematical model describing the propagation of an epidemic on a geographical network. The initial growth rate of the disease is the maximal eigenvalue of the epidemic matrix formed by the susceptibles and the graph Laplacian representing the mobility. We use matrix perturbation theory to analyze the epidemic matrix and define a vaccination strategy, assuming the vaccination reduces the susceptibles. When the mobility is small compared to the local disease dynamics, it is best to vaccinate the vertex of least degree and not vaccinate neighboring vertices. Then the epidemic grows on the vertex corresponding to the largest eigenvalue. When the mobility is comparable to the local disease dynamics, the most efficient strategy is to vaccinate the whole network because the disease grows uniformly. However, if only a few vertices can be vaccinated then which ones do we choose? We answer this question, and show that it is most efficient to vaccinate along the eigenvector corresponding to the largest eigenvalue of the Laplacian. We illustrate these general results on a 7 vertex graph, a grid, and a realistic example of the french rail network

Identifying Elderly Patients at Risk of Falling using Time-Domain and Cyclostationarity Related Features

Falls are a prevalent and severe health problem in the elderly community, leading to unfortunate and devastating consequences. Some falls can be prevented through interventions, proper management, and extra care. Therefore, studying and identifying elderly people with risk of falls is essential to minimize the falling risk and to minimize the severity of injuries that can occur from these falls. Besides, identifying at-risk patients can profoundly affect public health in a positive way. In this paper, we use classification techniques to identify at-risk patients using pressure signals of the innersoles of 520 elderly people. These people reported whether they had experienced previous falls or not. Two different types of feature sets were used as inputs to the classification models and were compared: The first feature set includes time-domain, physiological, and cyclostationary features, whereas the second includes a subset of those features chosen by Relief-F as the most important features. Our study showed that the use of features from different walking conditions and using Relief-F as a feature selection method significantly improved the model prediction accuracy, i.e. by 5.24% from the best previously existing model. The results also point out that the mean and standard deviation of the stride time, gender, the degree of cyclostationarity were the most important features to include in classification models for the identification of elderly people at risk of falling

G-graphes et les graphes d’expansion

Applying algebraic and combinatorics techniques to solve graph problems leads to the birthof algebraic and combinatorial graph theory. This thesis deals mainly with a crossroads questbetween the two theories, that is, the problem of constructing infinite families of expandergraphs.From a combinatorial point of view, expander graphs are sparse graphs that have strongconnectivity properties. Expanders constructions have found extensive applications in bothpure and applied mathematics. Although expanders exist in great abundance, yet their explicitconstructions, which are very desirable for applications, are in general a hard task. Mostconstructions use deep algebraic and combinatorial approaches. Following the huge amountof research published in this direction, mainly through Cayley graphs and the Zig-Zagproduct, we choose to investigate this problem from a new perspective; namely by usingG-graphs theory and spectral hypergraph theory as well as some other techniques. G-graphsare like Cayley graphs defined from groups, but they correspond to an alternative construction.The reason that stands behind our choice is first a notable identifiable link between thesetwo classes of graphs that we prove. This relation is employed significantly to get many newresults. Another reason is the general form of G-graphs, that gives us the intuition that theymust have in many cases such as the relatively high connectivity property.The adopted methodology in this thesis leads to the identification of various approaches forconstructing an infinite family of expander graphs. The effectiveness of our techniques isillustrated by presenting new infinite expander families of Cayley and G-graphs on certaingroups. Also, since expanders stand in no single stem of graph theory, this brings us toinvestigate several closely related threads from a new angle. For instance, we obtain newresults concerning the computation of spectra of certain Cayley and G-graphs, and theconstruction of several new infinite classes of integral and Hamiltonian Cayley graphs.L’utilisation de l’algèbre pour résoudre des problèmes de graphes a conduit au développement de trois branches : théorie spectrale des graphes, géométrie et combinatoire des groupes et études des invariants de graphes. La notion de graphe d’expansions (invariant de graphes) est relativement récente, elle a été développée afin d’étudier la robustesse des réseaux de télécommunication. Il s’avère que la construction de familles infinies de graphes expanseurs est un problème difficile. Cette thèse traite principalement de la construction de nouvelles familles de tels graphes. Les graphes expanseurs possèdent des nombreuses applications en informatique, notamment dans la construction de certains algorithmes, en théorie de la complexité, sur les marches aléatoires (random walk), etc. En informatique théorique, ils sont utilisés pour construire des familles de codes correcteurs d’erreur. Comme nous l’avons déjà vu les familles d’expanseurs sont difficiles à construire. La plupart des constructions s'appuient sur des techniques algébriques complexes, principalement en utilisant des graphes de Cayley et des produit Zig-Zag. Dans cette thèse, nous présentons une nouvelle méthode de construction de familles infinies d’expanseurs en utilisant les G-graphes. Ceux-ci sont en quelque sorte une généralisation des graphes de Cayley. Plusieurs nouvelles familles infinies d’expanseurs sont construites, notamment la première famille d’expanseurs irréguliers

On a relationship between Cayley graphs and G-graphs with some applications

International audienceLike Cayley graphs, G-graphs are graphs that are constructed from groups but they correspond to alternative constructions. The purpose of this article is to study the connection between these two types of graphs. Such a connection opens up a possible pathway between these two theories and thus investigating certain problems from one of these areas might be easier to tackle when dealt with them as problems in the other. First, we show the existence of a link that connects classes of these two types of graphs, and then we investigate the implications of this result on certain open problems in the theory of Cayley graphs. In particular, we show that computing the spectra of a certain infinite family of Cayley graphs can be easily realized via the use of G-graphs. In the process, general results concerning G-graphs and the spectra of a hypergraph are presented. Finally, we use a certain graph operation to present a new alternative tool for constructing integral graphs

Vaccination strategy on a geographic network

We considered a simple model describing the propagation of an epidemic on a geographical network. The initial rate of growth of the epidemic is the maximal eigenvalue of a matrix formed by the susceptibles and the graph Laplacian. Assuming the vaccination reduces the susceptibles, we define different vaccination strategies: uniform, local, or following a given vector. Using perturbation theory and the special form of the graph Laplacian, we show that it is most efficient to vaccinate along with the eigenvector corresponding to the largest eigenvalue of the Laplacian. This result is illustrated on a 7 vertex graph, a grid, and a realistic example of the french rail network. KeywordsSIR epidemic model, Graph, Matrix perturbation AMS indices 92D30, 05C50, 47A5

On constructing expander families of G-graphs

International audienc

Elder Tracking and Fall Detection System using Smart Tiles

International audienceFall detection for elderly and patient is a very important service that has the potential of increasing autonomy of elders while minimizing the risks of living alone. It has been an active research topic due to the fact that health care industry has a big demand for products and technology of fall detection systems. Owing to the recent rapid advancement in sensing and wireless communication technologies, fall detection systems have become possible. They allow detecting fall events for the elderly, monitoring them, and consequently providing necessary help whenever needed. This paper describes the ongoing work of detecting falls in independent living senior apartments using force sensors and 3-axis accelerometers concealed under intelligent tiles. The force sensors permit detecting elders' falls, locating, tracking and recognizing human activities (walking, standing, sitting, lying down, falling, and the transitions between them). However, the detection accuracy on real data contains false alarms coming from falling and lying postures. To solve this issue, we propose the fusion between the force sensor measurements and the accelerometer sensor decisions. As a consequence, the system accuracy is satisfactory and the results show that the proposed methods are efficient, and they can be easily used in a real elder tracking and fall detection syste

Towards a usable and an efficient elder fall detection system

International audienceIn-house monitoring of elders and automatic fall detection using intelligent sensors is a very desirable service that has the potential of increasing autonomy and independence while minimizing the risks of living alone. The efforts of building such systems have been spanning for decades, but there still is a lot of room for improvement. This paper proposes a novel approach to make a successful monitoring and assistive services for elderly. Moreover, we present our current progress of data collection, parameters extraction and parameters selection that are essential phases of our project. Our results on the data demonstrate that the proposed system methods are efficient and accurate and can be easily used in a real fall detection system

Automatic Fall Detection System using Sensing Floors

International audienceAutomatic fall detection is a major issue in taking care of the health of elderly people and has the potentialof increasing autonomy and independence while minimizing the risks of living alone. It has been an active researcharea due to the large demand of the healthcare association for fall detection goods. Fortunately, due to the recentfast progression in sensing technologies, fall detection system becomes prospective. It permits to monitor elders anddetect their falls, and consequently provides emergency support whenever needed. This paper describes the currentwork of detecting falls in independent living apartments using accelerometer concealed under tiles. We present theup-to-date advancement of data collection, feature extraction, feature selection, and signal changing detection, whichare essential phases of this work