Abstract. We translate the concept of succession rule and the ECO method into matrix notation, introducing the concept of a production matrix. This allows us to combine our method with other enumeration techniques using matrices, such as the method of Riordan matrices. Finally we treat the case of rational production matrices, i.e. those leading to rational generating functions.

Low-dose hydrocortisone seems to reduce MACR and serum C-reactive protein but not procalcitonin in patients with severe sepsis. Further studies are needed to confirm these results and to understand the underlying molecular mechanisms.

No abstract

Critical illness and particularly sepsis are associated with a significant redox imbalance resulting from an increased production of oxidant species and a decrease in endogenous antioxidant defences. In critical patients sources of oxidative stress include the mitochondrial respiratory electron transport chain, xanthine oxidase activation, the respiratory burst associated with neutrophil activation, and arachidonic acid metabolism. Several endogenous antioxidants have been identified including enzymes, like superoxide dismutases and glutathione peroxidase, vitamins and other molecules such as uric acid and bilirubin. Recent studies pointed out the correlations between oxidative stress, systemic inflammatory response and apoptosis. Prospective randomized clinical trials regarding antioxidant therapy in critical illness provide increasing evidence in support of selenium, glutamine and omega-3 fatty acids. In particular selenium seems to improve clinical outcome in terms of infections and organ failure, glutamine has been associated with a significant reduction in infectious complications and omega-3 fatty acids could be particularly efficacious in sepsis. Melatonin is a promising molecule that deserves the attention of future research, as well as vitamin C. Further studied should also try to establish the more beneficial combination of antioxidants, as well as the doses, and the timing of administration. When such problems will be resolved hopefully results about antioxidant therapy in critical illness will be more univocal and promising.

The aging world population will increase the incidence and mortality of severe sepsis. The aim of the present article is to review the pathophysiological differences in sepsis and its clinical impact on the elderly. The impact of immunosenescence on innate and acquired immunity is associated with relative immunologic depression that may favor the spreading of inflammation. Elderly patients also have enhanced apoptotic pathways that may contribute to the incidence of mortality due to sepsis. The inflammation-coagulation network is activated by age, explaining the success of some specific therapies. The initial clinical picture of sepsis in the elderly may be ambiguous but the specific pathopysiological changes of aging increase the risk of a sudden deterioration to severe sepsis with the development of a serious cardiovascular dysfunction. The reduced stress tolerance characteristic of aged tissues explains the high incidence of multi-organ failure in such patients. The specific pathophysiological and clinical picture of sepsis underlies the increased mortality in such patients and prompts research on therapeutic strategies with particular benefits to elderly septic patients.