Attribute Exploration of Discrete Temporal Transitions

Discrete temporal transitions occur in a variety of domains, but this work is mainly motivated by applications in molecular biology: explaining and analyzing observed transcriptome and proteome time series by literature and database knowledge. The starting point of a formal concept analysis model is presented. The objects of a formal context are states of the interesting entities, and the attributes are the variable properties defining the current state (e.g. observed presence or absence of proteins). Temporal transitions assign a relation to the objects, defined by deterministic or non-deterministic transition rules between sets of pre- and postconditions. This relation can be generalized to its transitive closure, i.e. states are related if one results from the other by a transition sequence of arbitrary length. The focus of the work is the adaptation of the attribute exploration algorithm to such a relational context, so that questions concerning temporal dependencies can be asked during the exploration process and be answered from the computed stem base. Results are given for the abstract example of a game and a small gene regulatory network relevant to a biomedical question.Comment: Only the email address and reference have been replace

Attribute Exploration of Gene Regulatory Processes

This thesis aims at the logical analysis of discrete processes, in particular of such generated by gene regulatory networks. States, transitions and operators from temporal logics are expressed in the language of Formal Concept Analysis. By the attribute exploration algorithm, an expert or a computer program is enabled to validate a minimal and complete set of implications, e.g. by comparison of predictions derived from literature with observed data. Here, these rules represent temporal dependencies within gene regulatory networks including coexpression of genes, reachability of states, invariants or possible causal relationships. This new approach is embedded into the theory of universal coalgebras, particularly automata, Kripke structures and Labelled Transition Systems. A comparison with the temporal expressivity of Description Logics is made. The main theoretical results concern the integration of background knowledge into the successive exploration of the defined data structures (formal contexts). Applying the method a Boolean network from literature modelling sporulation of Bacillus subtilis is examined. Finally, we developed an asynchronous Boolean network for extracellular matrix formation and destruction in the context of rheumatoid arthritis.Comment: 111 pages, 9 figures, file size 2.1 MB, PhD thesis University of Jena, Germany, Faculty of Mathematics and Computer Science, 2011. Online available at http://www.db-thueringen.de/servlets/DocumentServlet?id=1960