Description:
The present paper deals with uncertain linear inequality systems viewed as nonempty closed coefficient sets in the (n+ 1) -dimensional Euclidean space. The perturbation size of these uncertainty sets is measured by the (extended) Hausdorff distance. We focus on calmness constants—and their associated neighborhoods—for the feasible set mapping at a given point of its graph. To this aim, the paper introduces an appropriate indexation function which allows us to provide our aimed calmness constants through their counterparts in the setting of linear inequality systems with a fixed index set, where a wide background exists in the literature.
Description:
Understanding the way how genes interact is one of the fundamental questions in systems biology. The modeling of gene regulations currently assumes that genes interact either instantaneously or with a certain amount of time delay. In this paper, we propose an information theory based novel two-phase gene regulatory network (GRN) inference algorithm using the Bayesian network formalism that can model both instantaneous and single-step time-delayed interactions between genes simultaneously. We show the effectiveness of our approach by applying it to the analysis of synthetic data as well as the Saccharomyces cerevisiae gene expression data.
Description:
Understanding gene interactions is a fundamental question in systems biology. Currently, modeling of gene regulations assumes that genes interact either instantaneously or with time delay. In this paper, we introduce a framework based on the Bayesian Network (BN) formalism that can represent both instantaneous and time-delayed interactions between genes simultaneously. Also, a novel scoring metric having firm mathematical underpinnings is then proposed that, unlike other recent methods, can score both interactions concurrently and takes into account the biological fact that multiple regulators may regulate a gene jointly, rather than in an isolated pair-wise manner. Further, a gene regulatory network inference method employing evolutionary search that makes use of the framework and the scoring metric is also presented. Experiments carried out using synthetic data as well as the well known Saccharomyces cerevisiae gene expression data show the effectiveness of our approach.