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We study a multimarginal optimal transportation problem in one dimension. For a symmetric, repulsive cost function, we show that, given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is uni ...
A standard question arising in optimal transport theory is whether the Monge problem and the Kantorovich relaxation have the same infimum; the positive answer means that we can pass to the relaxed problem without loss of information. In the classical case ...
We present a new algorithm for computational caustic design. Our algorithm solves for the shape of a transparent object such that the refracted light paints a desired caustic image on a receiver screen. We introduce an optimal transport formulation to esta ...
The recent literature discusses the use of the relaxed Second Order Cone Programming (SOCP) for formulating Optimal Power Flow problems (OPF) for radial power grids. However, if the shunt parameters of the lines that compose the power grid are considered, ...
A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place of the Cauchy po ...
Artists and architects often need to handle multiple constraints during design of physical constructions. We define a performative constraint as any constraint on design that is tied to the performance of the model--either during fabrication, construction, ...
The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For s ...
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree, and the nervous or cardiovascular systems. Given a flow (traffic path) that transports ...
This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces, W2(Rd). This question arises naturally from the problem of separating amplitude and phase variation i ...
Entre traces et résilience, la zone traitée est marquée par l'empreinte d'événements climatiques liés aux précipitations. Aux différentes échelles, du bâtiment au quartier, de nouveaux niveaux de référence sont traités de manière visible. Ils sont directem ...