A flexible and qualitatively stable model for cell cycle dynamics including DNA damage effects.

This paper includes a conceptual framework for cell cycle modeling into which the experimenter can map observed data and evaluate mechanisms of cell cycle control. The basic model exhibits qualitative stability, meaning that regardless of magnitudes of system parameters its instances are guaranteed to be stable in the sense that all feasible trajectories converge to a certain trajectory. Qualitative stability can also be described by the signs of real parts of eigenvalues of the system matrix.

Quality control in combinatorial chemistry: determination of the quantity, purity, and quantitative purity of compounds in combinatorial libraries.

The quality of combinatorial libraries determines the success of biological screening in drug discovery programs. In this paper, we evaluate and compare various methods for measuring identity, purity, and quantity (yield) of combinatorial libraries. Determination of quantitative purity reveals the true library quality and often indicates potential quality problems before full-scale library production.

Partitioned and Hadamard Product Matrix Inequalities.

This note is partly expositor). Inequalities relating inversion with, respectively, extraction of principal submatriees and the Hadamard product in the two possible orders are developed in a simple and unified way for positive definite matrices. These inequalities are known, hut we also characterize the cases of equality and strict inequality.

Eigenset Generalizations of the Eigenvalue Concept.

For an complex matrix some generalizations of the eigenvalue-eigenvector equation are investigated. These take the form where is a suhset of C about which various assumptions are made. For example, it is shown that there exists a finite set ⊂ , the sum of whose elements is not 0, such that , if and only if is an eigenvalue of in the usual sense.