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Random sampling of bandlimited signals on graphs
No full textInternational audienceWe study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than O(k log(k)) measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques. [Code available at http://grsamplingbox.gforge.inria.fr/
The role of user requirements in data repository design
No full textInternational audienceRequirements engineering plays a crucial role in the development process of an information system as it aims at providing a complete and accurate requirement specification. In the life cycle of a Data Repository (DR) such as a database or a data warehouse, the requirements are mainly used to define the conceptual model once they have been identified from the informal specification. In this paper, we study the interest of requirements in the other phases of the DR life cycle. As the data integration problem, handled in the Extract, Transform, Load (ETL) phase, comes from the heterogeneity of requirements, we introduce a requirement integration framework based on ontologies and a generic model to unify the used vocabularies and requirement languages. Then we propose an approach to check the consistency of the requirements, w.r.t. the integrity constraints defined on the logical schema using the formal B method. We also show that requirements help define appropriate access structures such as indexes and materialized views to optimize SQL queries of a DR. Our approach is based on transformation rules that identify important queries that will be executed on a DR directly from the requirements. The experiments conducted on the Star Schema Benchmark (SSB) confirm the interest of this approach for the selection of different optimization structures. Finally, we present the OntoReqTool that implements the previous functionality on top of the OntoDB/OntoQL platform
Optimal Design of the Adaptive Normalized Matched Filter Detector
No full textInternational audienceThis article addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well-acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive radar detection. In this paper, we consider regularized estimation methods which force by construction the eigenvalues of the scatter estimates to be greater than a positive regularization parameter ρ. This makes them more suitable for high dimensional problems with a limited number of secondary data samples than traditional sample covariance estimates. While an increase of ρ seems to improve the conditioning of the estimate, it might however cause it to significantly deviate from the true covariance matrix. The setting of the optimal regularization parameter is a difficult question for which no convincing answers have thus far been provided. This constitutes the major motivation behind our work. More specifically, we consider the design of the ANMF detector for two kinds of regularized estimators, namely the regularized sample covariance matrix (RSCM), appropriate when the clutter follows a Gaussian distribution and the regularized Tyler estimator (RTE) for non-Gaussian spherically invariant distributed clutters. The rationale behind this choice is that the RTE is efficient in mitigating the degradation caused by the presence of impulsive noises while inducing little loss when the noise is Gaussian. Based on recent random matrix theory results studying the asymptotic fluctuations of the statistics of the ANMF detector when the number of samples and their dimension grow together to infinity, we propose a design for the regularization parameter that maximizes the detection probability under constant false alarm rates. Simulation results which support the efficiency of the proposed method are provided in order to illustrate the gain of the proposed optimal design over conventional settings of the regularization parameter. Index Terms—Regularized Tyler's estimator, Adaptive Normalized Mached Filter, robust detection, Random Matrix Theory, Optimal design
Définir le fini : deux formalisations d'espaces de dimension finie
No full textNational audienceLes espaces de dimension finie permettent de décrire mathématiquement certaines méthodes numériques comme la méthode des éléments finis. Leur formalisation est nécessaire pour certifier que ces méthodes sont correctes et plus précisément qu'elles sont convergentes. Dans cet article, nous présentons deux méthodes pour formaliser les espaces de dimension finie en Coq, dans un cadre de topologie générale. Les deux approches utilisent des mécanismes différents et ne présentent pas les mêmes avantages et inconvénients. La première repose sur l'extension, à l'aide de structures canoniques, de la hiérarchie algébrique de la bibliothèque Coquelicot. Elle permet aisément de montrer que les espaces R n sont de dimension finie et plus généralement que le produit cartésien d'espaces de dimension finie est de dimension finie. La seconde repose sur l'utilisation de sous-espaces en tant que prédicats sur l'espace total. Elle permet d'extraire des propriétés topologiques sur des sous-espaces de dimension finie d'un espace de dimension infinie, comme la fermeture des sous-espaces de dimension finie des espaces de Hilbert. Nous proposons par ailleurs une étude comparative de ces deux approches
A fast integral equation based method for solving electromagnetic inverse scattering problems with inhomogeneous background
No full texton-line, May 2018International audienceA family of difference integral equations, consisting of difference Lippmann-Schwinger integral equation (D-LSIE)and difference new integral equation (D-NIE), is proposed to solve the electromagnetic inverse scattering problems(ISPs) with inhomogeneous background medium bounded in a finite domain. Without resorting to Green’s function forinhomogeneous background medium, in the frame of the difference integral equation methods, the Green’s functionwith homogeneous medium is utilized such that not only fast algorithms (referring to those used in forwardscattering problems, like CG-FFT, FMM) can be adopted but also the burdensome calculation for the numericalGreen’s function for the inhomogeneous background medium is avoided. Especially, to tackle the ISPs with strongnon-linearity, those with large contrast and/or large dimensions, a Low-Pass Filter-Matching (LPFM) regularizationis introduced, which aims to stably match the information from the background medium to the unknown scatterer.Together with the D-NIE model, the proposed inversion method can efficiently tackle the ISPs with strong non-linearitywhile a bounded inhomogeneous medium being present. Against both synthetic and experimental data, several representativenumerical tests illustrate the efficacy of the proposed inversion method
Energy Efficiency in Cache Enabled Small Cell Networks With Adaptive User Clustering
No full textInternational audienceUsing a network of cache enabled small cells, traffic during peak hours can be reduced by proactively fetching the content that is most likely to be requested. In this paper, we aim to explore the impact of proactive caching on an important metric for future generation networks, namely, energy efficiency (EE). We argue that, exploiting the spatial repartitions of users in addition to the correlation in their content popularity profiles, can result in considerable improvement of the achievable EE. In this paper, the optimization of EE is decoupled into two related subproblems. The first one addresses the issue of content popularity modeling. While most existing works assume similar popularity profiles for all users, we consider an alternative framework in which, users are clustered according to their popularity profiles. In order to showcase the utility of the proposed clustering, we use a statistical model selection criterion, namely, Akaike information criterion. Using stochastic geometry, we derive a closed-form expression of the achievable EE and we find the optimal active small cell density vector that maximizes it. The second subproblem investigates the impact of exploiting the spatial repartitions of users. After considering a snapshot of the network, we formulate a combinatorial problem that optimizes content placement in order to minimize the transmission power. Numerical results show that the clustering scheme considerably improves the cache hit probability and consequently the EE, compared with an unclustered approach. Simulations also show that the small base station allocation algorithm improves the energy efficiency and hit probability
Asymptotically optimal pilot allocation over Markovian fading channels.
No full textInternational audienceWe investigate a pilot allocation problem in wireless networks over Markovian fading channels. In wireless systems, the channel state information (CSI) is collected at the base station, in particular, this paper considers a pilot-aided channel estimation method (TDD mode). Typically, there are less available pilots than users, hence at each slot the scheduler needs to decide an allocation of pilots to users with the goal of maximizing the long-term average throughput. There is an inherent tradeoff in how the limited pilots are used: assign a pilot to a user with up-to-date CSI and good channel condition for exploitation, or assign a pilot to a user with outdated CSI for exploration. As we show, the arising pilot allocation problem is a restless bandit problem and thus its optimal solution is out of reach. In this paper, we propose an approximation based on the Lagrangian relaxation method, which provides a low-complexity Whittle index policy. We prove this policy to be asymptotically optimal in the many users regime (when the number of users in the system and the available pilots for channel sensing grow large). We evaluate the performance of Whittle's index policy in various scenarios and illustrate its remarkably good performance for small number of users, where it is not guaranteed to be optimal
A compact optimization model for the tail assignment problem
No full textInternational audienceThis paper investigates a new model for the so-called Tail Assignment Problem, which consists in assigning a well-identified airplane to each flight leg of a given flight schedule, in order to minimize total cost (cost of operating the flights and possible maintenance costs) while complying with a number of operational constraints. The mathematical programming formulation proposed is compact (i.e., involves a number of 0−1 decision variables and constraints polynomial in the problem size parameters) and is shown to be of significantly reduced dimension as compared with previously known compact models. Computational experiments on series of realistic problem instances (obtained by random sampling from real-world data set) are reported. It is shown that with the proposed model, current state-of-the art MIP solvers can efficiently solve to exact optimality large instances representing 30-day flight schedules with typically up to 40 airplanes and 1500 flight legs connecting as many as 21 airports. The model also includes the main existing types of maintenance constraints, and extensive computational experiments are reported on problem instances of size typical of practical applications
Tree-sequent calculi and decision procedures for intuitionistic modal logics
No full textInternational audienceIn this article we define label-free sequent calculi for the intuitionistic modal logics obtained from the combinations of the axioms T, B, 4 and 5. These calculi are based on a multi-contextual sequent structure, called Tree-sequent, which allows us to define such calculi for such intuitionistic modal logics. From the calculi defined for the IK, IT, IB4 and ITB logics, we also provide new decision procedures and alternative syntactic proofs of decidability