Short-term treatment with atorvastatin significantly reduces the incidence of major adverse cardiovascular events after vascular surgery.

In this work we prove a shape theorem for a growing set of Simple Random Walks (SRWs) on Z d , known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, it becomes active too. At time 0 all particles are sleeping, except for that placed at the origin. We prove that the set of the original positions of all the active particles, rescaled by the elapsed time, converges to some compact convex set. In some specific cases we are able to identify (at least partially) this set.

We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1 − p. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for Z d and regular trees.

Sepsis is a major cause of mortality and morbidity in intensive care units. Organ dysfunction is triggered by inflammatory insults and tissue hypoperfusion. The brain plays a pivotal role in sepsis, acting as both a mediator of the immune response and a target for the pathologic process. The measurement of brain dysfunction is difficult because there are no specific biomarkers of neuronal injury, and bedside evaluation of cognitive performance is difficult in an intensive care unit. Although sepsis-associated encephalopathy was described decades ago, it has only recently been subjected to scientific scrutiny and is not yet completely understood. The pathophysiology of sepsis-associated encephalopathy involves direct cellular damage to the brain, mitochondrial and endothelial dysfunction and disturbances in neurotransmission. This review describes the most recent findings in the pathophysiology, diagnosis, and management of sepsis-associated encephalopathy and focuses on its many presentations.

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