Observation of vibrating systems at different time instants

In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper by A. Szij\'art\'o and J. Heged\H{u}s in which the authors ask the question of determining the initial data by only knowing the position of the string at two distinct time instants. The choice of the observation instants is crucial and the estimations rely on the Fourier series expansion of the solutions and results of Diophantine approximation.Comment: 14 page

Biomedical Research, A Tool to Address the Health Issues that Affect African Populations.

Traditionally, biomedical research endeavors in low to middle resources countries have focused on communicable diseases. However, data collected over the past 20 years by the World Health Organization (WHO) show a significant increase in the number of people suffering from non-communicable diseases (e.g. heart disease, diabetes, cancer and pulmonary diseases). Within the coming years, WHO predicts significant decreases in communicable diseases while non-communicable diseases are expected to double in low and middle income countries in sub-Saharan Africa. The predicted increase in the non-communicable diseases population could be economically burdensome for the basic healthcare infrastructure of countries that lack resources to address this emerging disease burden. Biomedical research could stimulate development of healthcare and biomedical infrastructure. If this development is sustainable, it provides an opportunity to alleviate the burden of both communicable and non-communicable diseases through diagnosis, prevention and treatment. In this paper, we discuss how research using biomedical technology, especially genomics, has produced data that enhances the understanding and treatment of both communicable and non-communicable diseases in sub-Saharan Africa. We further discuss how scientific development can provide opportunities to pursue research areas responsive to the African populations. We limit our discussion to biomedical research in the areas of genomics due to its substantial impact on the scientific community in recent years however, we also recognize that targeted investments in other scientific disciplines could also foster further development in African countries

Screened exchange dynamical mean field theory and its relation to density functional theory: SrVO3 and SrTiO3

We present the first application of a recently proposed electronic-structure scheme to transition metal oxides: screened exchange dynamical mean-field theory includes non-local exchange beyond the local density approximation and dynamical correlations beyond standard dynamical mean-field theory. Our results for the spectral function of SrVO3 are in agreement with the available experimental data, including photoemission spectroscopy and thermodynamics. Finally, the 3d0 compound SrTiO3 serves as a test case to illustrate how the theory reduces to the band structure of standard electronic-structure techniques for weakly correlated compounds.Comment: 6 pages, 4 figure

Defining a robust biological prior from Pathway Analysis to drive Network Inference

Inferring genetic networks from gene expression data is one of the most challenging work in the post-genomic era, partly due to the vast space of possible networks and the relatively small amount of data available. In this field, Gaussian Graphical Model (GGM) provides a convenient framework for the discovery of biological networks. In this paper, we propose an original approach for inferring gene regulation networks using a robust biological prior on their structure in order to limit the set of candidate networks. Pathways, that represent biological knowledge on the regulatory networks, will be used as an informative prior knowledge to drive Network Inference. This approach is based on the selection of a relevant set of genes, called the "molecular signature", associated with a condition of interest (for instance, the genes involved in disease development). In this context, differential expression analysis is a well established strategy. However outcome signatures are often not consistent and show little overlap between studies. Thus, we will dedicate the first part of our work to the improvement of the standard process of biomarker identification to guarantee the robustness and reproducibility of the molecular signature. Our approach enables to compare the networks inferred between two conditions of interest (for instance case and control networks) and help along the biological interpretation of results. Thus it allows to identify differential regulations that occur in these conditions. We illustrate the proposed approach by applying our method to a study of breast cancer's response to treatment

Overlapping stochastic block models with application to the French political blogosphere

Complex systems in nature and in society are often represented as networks, describing the rich set of interactions between objects of interest. Many deterministic and probabilistic clustering methods have been developed to analyze such structures. Given a network, almost all of them partition the vertices into disjoint clusters, according to their connection profile. However, recent studies have shown that these techniques were too restrictive and that most of the existing networks contained overlapping clusters. To tackle this issue, we present in this paper the Overlapping Stochastic Block Model. Our approach allows the vertices to belong to multiple clusters, and, to some extent, generalizes the well-known Stochastic Block Model [Nowicki and Snijders (2001)]. We show that the model is generically identifiable within classes of equivalence and we propose an approximate inference procedure, based on global and local variational techniques. Using toy data sets as well as the French Political Blogosphere network and the transcriptional network of Saccharomyces cerevisiae, we compare our work with other approaches.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS382 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org