Wages and Utilities in a Closed Economy

The broad objective of this paper is to propose a mathematical model for the study of causes of wage inequality and relate it to choices of consumption, the technologies of production, and the composition of labor in an economy. The paper constructs a Simple Closed Model, or an SCM, for short, for closed economies, in which the consumption and the production parts are clearly separated and yet coupled. The model is established as a specialization of the Arrow-Debreu model and its equilibria correspond directly with those of the general Arrow-Debreu model. The formulation allows us to identify the combinatorial data which link parameters of the economic system with its equilibria, in particular, the impact of consumer preferences on wages. The SCM model also allows the formulation and explicit construction of the consumer choice game, where expressed utilities of various labor classes serve as strategies with total or relative wages as the pay-offs. We illustrate, through examples, the mathematical details of the consumer choice game. We show that consumer preferences, expressed through modified utility functions, do indeed percolate through the economy, and influence not only prices but also production and wages. Thus, consumer choice may serve as an effective tool for wage redistribution

Load Balancing in Multiprocessor Systems

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOffice of Naval Research / N00014-85-K-057

Clustering of protein structural fragments reveals modular building block approach of nature

Structures of peptide fragments drawn from a protein can potentially occupy a vast conformational continuum. We co-ordinatize this conformational space with the help of geometric invariants and demonstrate that the peptide conformations of the currently available protein structures are heavily biased in favor of a finite number of conformational types or structural building blocks. This is achieved by representing a peptides' backbone structure with geometric invariants and then clustering peptides based on closeness of the geometric invariants. This results in 12,903 clusters, of which 2207 are made up of peptides drawn from functionally and/or structurally related proteins. These are termed “functional” clusters and provide clues about potential functional sites. The rest of the clusters, including the largest few, are made up of peptides drawn from unrelated proteins and are termed “structural” clusters. The largest clusters are of regular secondary structures such as helices and beta strands as well as of beta hairpins. Several categories of helices and strands are discovered based on geometric differences. In addition to the known classes of loops, we discover several new classes, which will be useful in protein structure modeling. Our algorithm does not require assignment of secondary structure and, therefore, overcomes the limitations in loop classification due to ambiguity in secondary structure assignment at loop boundaries.© Elsevie