On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

Studies of macropodidae in Queensland. 8. Age estimation in the red kangaroo (Megaleia rufa (Desmarest))

Methods of estimating the age of pouch young of the grey kangaroo (Macropus giganteus Shaw), the eastern wallaroo ( Osphranter robustus (Gould) ) and the red-necked wallaby (Wallabia rufogrisea (Desmarest)) from length of tail and hind feet, and regressions relating age to an index of progression of the molar teeth (Kirkpatrick 1964) for adults of these species and the red kangaroo (Megaleia rufa (Desmarest)), have been published (Kirkpatrick 1965)

Cortisol influence on testicular testosterone secretion in domestic cat: An in vitro study Ação do cortisol sobre a secreção de testosterona em testículos de gato doméstico: um estudo in vitro

The aim of the present experiment was to investigate the effect of corticosteroids (exogen) on in vitro testosterone secretion after stress by transportation (40 minutes). Feline testes (Felis silvestris catus) were incubated in the following media: TCM 199; TCM 199 + hCG 10_7M; TCM 199 + hydrocortisone 10_7M, or TCM 199 + hCG + hydrocortisone. The animals (n=21) were allocated into three groups: (S) that arrived at 3 h prior to surgery, (A) that remained in the laboratory for 36 h before being submitted to surgical procedure, and (C) that were also allowed to remain for 36 hours in the laboratory before the surgical procedure, but whose testes had been incubated with hydrocortisone prior to incubation in the referred media. The results showed that group S secreted higher levels of testosterone, regardless of the culture media. It is noteworthy that the suppressing action of hydrocortisone sodium succinate led to a reduction in the testosterone concentration, despite the presence of hCG.<br>O objetivo deste trabalho foi investigar o efeito da hidrocortisona sobre a secreção de testosterona após cultivo in vitro dos testículos, em distintas situações de estresse (transporte) de gatos domésticos (Felis silvestris catus). Testículos foram incubados nos seguintes meios de cultura: TCM 199; TCM 199 + hCG 10_7M; TCM 199 + hydrocortisona 10_7M e TCM 199 + hCG + hidrocortisona. Os animais (n=21) foram alocados em 3 sub-grupos: (S) animal admitido 3 horas antes da orquiectomia, (A) animais orquiectomizados após 36 horas de permanência no biotério e (C) animais que permaneceram por 36 horas no biotério antes da cirurgia e que tiveram seus testículos pré-incubados em hidrocortisona. Os resultados demonstraram que o grupo S secretou maiores valores de testosterona em todas as condições estudadas. É válido mencionar que a supressão promovida pela hidrocortisona também promoveu redução na concentração de testosterona no meio TCM 199, a despeito da presença de hCG