Union Formation and Bargaining Rules in the Labor Market

This paper analyzes union formation in a model of bargaining between a firm and several unions. We address two questions: first, the optimal configuration of unions (their number and size) and, second, the impact of the bargaining pattern (simultaneous or sequential). For workers, grouping into several unions works as a price discrimination device which, at the same time, decreases their market power. The analysis shows that optimal union configuration depends on the rules that regulate the bargaining process (monopoly union, Nash bargaining or right to manage).

Increase in the density of resting microglia precedes neuritic plaque formation and microglial activation in a transgenic model of Alzheimer's disease

The formation of cerebral senile plaques composed of amyloid beta peptide (A beta) is a fundamental feature of Alzheimer's disease (AD). Glial cells and more specifically microglia become reactive in the presence of A beta. In a triple transgenic model of AD (3 x Tg-AD), we found a significant increase in activated microglia at 12 (by 111%) and 18 (by 88%) months of age when compared with non-transgenic (non-Tg) controls. This microglial activation correlated with A beta plaque formation, and the activation in microglia was closely associated with A beta plaques and smaller A beta deposits. We also found a significant increase in the area density of resting microglia in 3 x Tg-AD animals both at plaque-free stage (at 9 months by 105%) and after the development of A plaques (at 12 months by 54% and at 18 months by 131%). Our results show for the first time that the increase in the density of resting microglia precedes both plaque formation and activation of microglia by extracellular A beta accumulation. We suggest that AD pathology triggers a complex microglial reaction: at the initial stages of the disease the number of resting microglia increases, as if in preparation for the ensuing activation in an attempt to fight the extracellular A beta load that is characteristic of the terminal stages of the disease. Cell Death and Disease (2010) 1, e1; doi:10.1038/cddis.2009.2; published online 14 January 2010

Pata contractions and coupled type fixed points

A new coupled fixed point theorem related to the Pata contraction for mappings having the mixed monotone property in partially ordered complete metric spaces is established. It is shown that the coupled fixed point can be unique under some extra suitable conditions involving mid point lower or upper bound properties. Also the corresponding convergence rate is estimated when the iterates of our function converge to its coupled fixed point.