Necessary and Sufficient Conditions on Partial Orders for Modeling Concurrent Computations

Partial orders are used extensively for modeling and analyzing concurrent computations. In this paper, we define two properties of partially ordered sets: width-extensibility and interleaving-consistency, and show that a partial order can be a valid state based model: (1) of some synchronous concurrent computation iff it is width-extensible, and (2) of some asynchronous concurrent computation iff it is width-extensible and interleaving-consistent. We also show a duality between the event based and state based models of concurrent computations, and give algorithms to convert models between the two domains. When applied to the problem of checkpointing, our theory leads to a better understanding of some existing results and algorithms in the field. It also leads to efficient detection algorithms for predicates whose evaluation requires knowledge of states from all the processes in the system

Agenesis of distal segment of right vertebral artery: a case report.

A case is being reported in which the basilar artery was formed only by the left vertebral artery. This was detected incidentally in a female on a non contrast magnetic resonance angiogram. The right vertebral artery arose as a direct branch of the right subclavian artery but terminated blindly at the level of second cervical vertebra. The left vertebral artery which contributed to the formation of basilar artery continued as left posterior cerebral artery while right posterior cerebral artery was seen as a continuation of right posterior communicating artery. The knowledge of variations of the vertebrobasilar arterial complex is important to Clinicians, Radiologists and Surgeons operating on the great vessels and its branches, particularly vascular surgeons dealing with vertebral artery in order to prevent a vascular catastrophe