Chained structure of directed graphs with applications to social and transportation networks.

The need to determine the structure of a graph arises in many applications. This paper studies directed graphs and defines the notions of -chained and -chained directed graphs. These notions reveal structural properties of directed graphs that shed light on how the nodes of the graph are connected.

Accuracy optimization of combined multiparameter measuring systems with application to polarized light microscopy.

We study the accuracy of combined multiparameter measuring systems (CMPMSs) that determine several unknown quantities from measurements of a single variable at different preprogrammed conditions determined by control parameters. To reduce inaccuracies of determined quantities, we propose a mathematical method for selection of control parameters that are optimal for all possible values of determined quantities. Using the submultiplicativity of the spectral and Frobenius matrix norms, we construct the upper bound of the error function and determine the set of control parameters by minimizing this bound.

The relationship between protein sequences and their gene ontology functions.

Background: One main research challenge in the post-genomic era is to understand the relationship between protein sequences and their biological functions. In recent years, several automated annotation systems have been developed for the functional assignment of uncharacterized proteins. The underlying assumption of these systems is that similar sequences imply similar biological functions.