The tropical double description method

We develop a tropical analogue of the classical double description method allowing one to compute an internal representation (in terms of vertices) of a polyhedron defined externally (by inequalities). The heart of the tropical algorithm is a characterization of the extreme points of a polyhedron in terms of a system of constraints which define it. We show that checking the extremality of a point reduces to checking whether there is only one minimal strongly connected component in an hypergraph. The latter problem can be solved in almost linear time, which allows us to eliminate quickly redundant generators. We report extensive tests (including benchmarks from an application to static analysis) showing that the method outperforms experimentally the previous ones by orders of magnitude. The present tools also lead to worst case bounds which improve the ones provided by previous methods.Comment: 12 pages, prepared for the Proceedings of the Symposium on Theoretical Aspects of Computer Science, 2010, Nancy, Franc

Tropical polar cones, hypergraph transversals, and mean payoff games

We discuss the tropical analogues of several basic questions of convex duality. In particular, the polar of a tropical polyhedral cone represents the set of linear inequalities that its elements satisfy. We characterize the extreme rays of the polar in terms of certain minimal set covers which may be thought of as weighted generalizations of minimal transversals in hypergraphs. We also give a tropical analogue of Farkas lemma, which allows one to check whether a linear inequality is implied by a finite family of linear inequalities. Here, the certificate is a strategy of a mean payoff game. We discuss examples, showing that the number of extreme rays of the polar of the tropical cyclic polyhedral cone is polynomially bounded, and that there is no unique minimal system of inequalities defining a given tropical polyhedral cone.Comment: 27 pages, 6 figures, revised versio

Design and Experimentation of a Large Scale Distributed Stochastic Control Algorithm Applied to Energy Management Problems

The Stochastic Dynamic Programming method often used to solve some stochastic optimization problems is only usable in low dimension, being plagued by the curse of dimensionality. In this article, we explain how to postpone this limit by using High Performance Computing: parallel and distributed algorithms design, optimized implementations and usage of large scale distributed architectures (PC clusters and Blue Gene/P)

Exposição e intoxicação por naftaleno e paradiclorobenzeno, avaliação da gravidade em uma série de casos

Trabalho de Conclusão de Curso - Universidade Federal de Santa Catarina. Curso de Medicina. Departamento de Saúde Pública

CANU-ReID: A Conditional Adversarial Network for Unsupervised person Re-IDentification

Unsupervised person re-ID is the task of identifying people on a target data set for which the ID labels are unavailable during training. In this paper, we propose to unify two trends in unsupervised person re-ID: clustering & fine-tuning and adversarial learning. On one side, clustering groups training images into pseudo-ID labels, and uses them to fine-tune the feature extractor. On the other side, adversarial learning is used, inspired by domain adaptation, to match distributions from different domains. Since target data is distributed across different camera viewpoints, we propose to model each camera as an independent domain, and aim to learn domain-independent features. Straightforward adversarial learning yields negative transfer, we thus introduce a conditioning vector to mitigate this undesirable effect. In our framework, the centroid of the cluster to which the visual sample belongs is used as conditioning vector of our conditional adversarial network, where the vector is permutation invariant (clusters ordering does not matter) and its size is independent of the number of clusters. To our knowledge, we are the first to propose the use of conditional adversarial networks for unsupervised person re-ID. We evaluate the proposed architecture on top of two state-of-the-art clustering-based unsupervised person re-identification (re-ID) methods on four different experimental settings with three different data sets and set the new state-of-the-art performance on all four of them. Our code and model will be made publicly available at https://team.inria.fr/perception/canu-reid/