The null space problem I. complexity
SIAM Journal on Algebraic and Discrete Methods
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The null space problem II. Algorithms
SIAM Journal on Algebraic and Discrete Methods
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
A Generalized Framework for Network Component Analysis
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Structural Identifiability in Low-Rank Matrix Factorization
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
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The study of gene regulatory networks is a significant problem in systems biology. Of particular interest is the problem of determining the unknown or hidden higher level regulatory signals by using gene expression data from DNA microarray experiments. Several studies in this area have demonstrated the critical aspect of the network structure in tackling the network modelling problem. Structural analysis of systems has proved useful in a number of contexts, viz., observability, controllability, fault diagnosis, sparse matrix computations etc. In this contribution, we formally define structural properties that are relevant to Gene Regulatory Networks. We explore the structural implications of certain quantitative methods and explain completely the connections between the identifiability conditions and structural criteria of observability and distinguishability. We illustrate these concepts in case studies using representative biologically motivated network examples. The present work bridges the quantitative modelling methods with those based on the structural analysis.