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Horizontal holonomy and foliated manifolds
No full textInternational audienceWe introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving analogues of Ambrose-Singer's and Ozeki's theorems. We then give necessary and sufficient conditions in terms of the horizontal holonomy groups for existence of solutions of two problems on foliated manifolds: determining when a foliation can be either (a) totally geodesic or (b) endowed with a principal bundle structure.The subbundle plays the role of an orthogonal complement to the leaves of the foliation in case (a) and of a principal connection in case (b)
Computing version spaces in the qualitative approach to multicriteria decision aid
No full textInternational audienceWe consider a lattice-based model in multiattribute decision making , where preferences are represented by global utility functions that evaluate alternatives in a lattice structure (which can account for situations of indifference as well as of incomparability). Essentially, this evaluation is obtained by first encoding each of the attributes (nominal, qualitative, numeric, etc.) of each alternative into a distributive lattice, and then aggregating such values by lattice functions. We formulate version spaces within this model (global preferences consistent with empirical data) as solutions of an interpolation problem and present their complete descriptions accordingly. Moreover, we consider the computational complexity of this interpolation problem, and show that up to 3 attributes it is solvable in polynomial time, whereas it is NP complete over more than 3 attributes. Our results are then illustrated with a concrete example , namely, a recommender system for employees based on their psychological records throughout a year
A Random Block-Coordinate Douglas-Rachford Splitting Method with Low Computational Complexity for Binary Logistic Regression
No full textInternational audienceIn this paper, we propose a new optimization algorithm for sparse logistic regression based on a stochastic version of the Douglas-Rachford splitting method. Our algorithm sweeps the training set by randomly selecting a mini-batch of data at each iteration, and it allows us to update the variables in a block coordinate manner. Our approach leverages the proximity operator of the logistic loss, which is expressed with the generalized Lambert W function. Experiments carried out on standard datasets demonstrate the efficiency of our approach w.r.t. stochastic gradient-like methods
Effect of quantified irreducibility on the computability of subshift entropy
No full text28 pages, 1 table, 5 figures.International audienceWe study the difficulty of computing topological entropy of subshifts subjected to mixing restrictions. This problem is well-studied for multidimensional subshifts of finite type: there exists a threshold in the irreducibility rate where the difficulty jumps from computable to uncomputable, but its location is an open problem. In this paper, we establish the location of this threshold for a more general class, subshifts with decidable languages, in any dimension
Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -sets
No full textInternational audienceIn the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in , we generalize the definition of the Poincaré-Steklov operator to -set boundaries, , and give its spectral properties to compare to the spectra of the interior domain and also of a truncated domain, considered as an approximation of the exterior case. The well-posedness of the Robin boundary value problems for the truncated and exterior domains is given in the general framework of -sets. The results are obtained thanks to a generalization of the continuity and compactness properties of the trace and extension operators in Sobolev, Lebesgue and Besov spaces, in particular, by a generalization of the classical Rellich-Kondrachov Theorem of compact embeddings for and -sets
A Globally Exponentially Stable Speed Observer for a Class of Mechanical Systems: Experimental and Simulation Comparison with High-Gain and Sliding Mode Designs
No full textInternational audienceIt is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust (exponentially stable) solution with a Luenberger-like observer. This result should be contrasted with the very complicated observers based on immersion and invariance reported in the literature. A second contribution of the paper is to compare , via realistic simulations and highly detailed experiments, the performance of the proposed observer with well-known high-gain and sliding mode observers. In particular, to show that—due to their high sensitivity to noise, that is unavoidable in mechanical systems applications—the performance of the two latter designs is well below par
Algorithmic-level Approximate Computing Applied to Energy Efficient HEVC Decoding
No full textInternational audienceThis paper presents a novel method for applying approximate computing at the level of a complete application. The method decomposes the application into processing blocks which types define the classes of approximate computing techniques they may tolerate. By applying these approximation techniques to the most computationally intensive blocks, drastic energy reduction can be obtained at a limited cost in terms of Quality of Service. The algorithmic-level approximate computing method is applied to a software HEVC video decoder. The method is shown to offer multiple trade-offs between the quality of the decoded video and the energy required for the decoding process. The algorithmic-level approximate computing method offers new possibilities in terms of application energy budgeting. Energy reductions of up to 40% are demonstrated for a limited degradation of the application Quality of Service
Small-scale kinematics of two-phase flows: identifying relaxation processes in separated- and disperse-phase flow models
No full textInternational audienceWith the objective of modeling both separate and disperse two-phase flows, we use in this paper a methodology for deriving two-fluid models that do not assume any flow topology. This methodology is based on a variational principle and on entropy dissipation requirement. Some of the models that are such derived and studied are already known in the contexts of the description of separate-or disperse-phase flows. However, we here propose an arrangement of these models into a hierarchy based on their links through relaxation parameters. Moreover, the models are shown to be compatible with the description of a monodisperse bubbly flow and, within this frame, the relaxation parameters can be identified. This identification is finally verified and discussed through comparisons with experimental measures of sound dispersion and with dispersion relations of a reference model for bubbly media
Verifying the Correctness and Amortized Complexity of a Union-Find Implementation in Separation Logic with Time Credits
No full textInternational audienceUnion-Find is a famous example of a simple data structure whose amortized asymptotic time complexity analysis is nontrivial. We present a Coq formalization of this analysis, following Alstrup et al.'s recent proof (2014). Moreover, we implement Union-Find as an OCaml library and formally endow it with a modular specification that offers a full functional correctness guarantee as well as an amortized complexity bound. In order to reason in Coq about imperative OCaml code, we use the CFML tool, which implements Separation Logic for a subset of OCaml, and which we extend with time credits. Although it was known in principle that amortized analysis can be explained in terms of time credits and that time credits can be viewed as resources in Separation Logic, we believe our work is the first practical demonstration of this approach. Finally, in order to explain the meta-theoretical foundations of our approach, we define a Separation Logic with time credits for an untyped call-by-value lambda-calculus, and formally verify its soundness