An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Toxicidade aguda do nitrito em larvas do peixe-rei marinho Odontesthes argentinensis (Teleostei, Atherinopsidae) Acute toxicity of nitrite on larvae of the marine pejerrey Odontesthes argentinensis (Teleostei, Atherinopsidae)

Este trabalho visou a determinar o efeito tóxico do nitrito sobre larvas do peixe-rei marinho Odontesthes argentinensis através de testes agudos com 96h de duração. As larvas utilizadas neste experimento foram cultivadas no Laboratório de Maricultura da FURG (Rio Grande - RS). Foi utilizada água do mar filtrada na salinidade 35‰, na temperatura de 23&deg;C, com fotoperíodo de 14 horas de luz e aeração constante. Diariamente, as larvas mortas foram retiradas e, em seguida, 100% do meio experimental foi renovado. Não foi fornecido alimento durante a exposição ao nitrito. As larvas foram expostas a cinco concentrações de nitrito: 50, 150, 250, 350 e 450mg L-1 N-NO2-, mais um controle onde o nitrito não foi adicionado. A CL50-96h (concentração letal para 50% dos organismos após 96 horas) e seu intervalo de confiança (95%) foram de 199,3 (142,0-279,6)mg L-1 N-NO2-. Os resultados deste trabalho sugerem que, assim como outras espécies de peixes marinhos, o O. argentinensis é uma espécie tolerante a altas concentrações de nitrito e é pouco provável que este último seja um problema para o cultivo intensivo desta espécie.<br>This work evaluated the toxicity of nitrite on larvae of the marine pejerrey Odontesthes argentinensis through acute exposure during 96h. Larvae used in this experiment were cultivated in the Laboratory of Mariculture of the University of Rio Grande. During the tests temperature was 23&deg;C, salinity 35‰, and 14 hours of light were provided. Every day dead larvae were removed and the experimental media were completely renewed. Larvae were deprived of food during the test. Concentrations for the acute tests were 50, 150, 250, 350 and 450mg L-1 N-NO2-, plus a control with no nitrite added. Lethal concentration for 50% of the organisms (LC50-96h), and its confidence interval, was 199.3 (142.0-279.6)mg L-1 N-NO2-. The results of the acute tests suggest that, as other species of marine fish larvae, O. argentinensis is tolerant to high concentrations of nitrite, and it is unlikely that it would be a problem for the intensive culture of this species