The modelling of complex steel structures under static loading using rigid perfectly plastic material is presented within the framework of second-order cone programming (SOCP). The classic upper and lower bound principles of yield analysis, naturally written as optimization problems, are formulated as a pair of dual second-order cone programs which...
International audience
The prefix exchange distance of a permutation is the length of its shortest factorisation into transpositions that all contain 1. Using a probabilistic approach, we obtain expressions for the mean and the variance, and prove the asymptotic normality of the distribution of this distance for a random permutation verifying the Ewens sampling formula. ...
This work addresses the problem of analyzing multi-channel time series data by proposing an unsupervised fusion framework based on convolutional transform learning. Each channel is processed by a separate 1D convolutional transform; the output of all the channels are fused by a fully connected layer of transform learning. The training procedure tak...
The present manuscript presents a framework for automating the formulation and resolution of limit analysis problems in a very general manner. This framework relies on FEniCS domain-specific language and the representation of material strength criteria and their corresponding support function in the conic programming setting. Various choices of fin...
Several natural language models rely on an assumption modeling each word context as a bag of words. We study the combinatorial implications of such assumption for the corresponding word or sentences representations. In particular , we present theoretical results concerning the family of sequence graphs, for which realizations yield equivalent repre...
Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as polytopic) elements have received considerable attention in recent years. Due to the physical frame basis functions used typically and the quadrature challenges involved, the matrix-assembly step for these methods is often computatio...
The so-called l0 pseudonorm on Rd counts the number of nonzero components of a vector. We say that a sequence of norms on Rd is strictly increasingly graded (with respect to the l0 pseudonorm) if it is nondecreasing and that the sequence of norms of a vector x becomes stationary exactly at the index l0(x). In the same way, we define strictly decrea...
We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In particular, our analysis allows for curved element shapes, without the use of non-linear elemental maps. The feasi...
