Gene duplication and hierarchical modularity in intracellular interaction networks

Networks of interactions evolve in many different domains. They tend to have topological characteristics in common, possibly due to common factors in the way the networks grow and develop. It has been recently suggested that one such common characteristic is the presence of a hierarchically modular organization. In this paper, we describe a new algorithm for the detection and quantification of hierarchical modularity, and demonstrate that the yeast protein-protein interaction network does have a hierarchically modular organization. We further show that such organization is evident in artificial networks produced by computational evolution using a gene duplication operator, but not in those developing via preferential attachment of new nodes to highly connected existing nodes. (C) 2004 Elsevier Ireland Ltd. All rights reserved.

The Hierarchical Structure of the Firm: A Geometric Perspective

This paper incorporates hierarchical structure into the neoclassical theory of the firm. Firms are hierarchical in two respects: the organization of workers in production and the wage structure. The firm’s hierarchy is represented as the sector of a circle, where the radius represents the hierarchy’s height, the width of the sector represents the breadth of the hierarchy at a given height, and the angle of the sector represents span of control for any given supervisor. A perfectly competitive firm then chooses height and width, as well as capital inputs, in order to maximize profit. We analyze the short run and long run impact of changes in scale economies, input substitutability and input and output prices on the firm’s hierarchical structure. We find that the firm unambiguously becomes more hierarchical as the specialization of its workers increases or as its output price increases relative to input prices. The effect of changes in scale economies is contingent on the output price. The model also brings forth an analysis of wage inequality within the firm, which is found to be independent of technological considerations, and only depends on the firm’s wage schedule.