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See detailDescribing the complexity of systems: multivariable "set complexity" and the information basis of systems biology.
Galas, David J.; Sakhanenko, Nikita A.; Skupin, Alexander UL et al

in Journal of computational biology : a journal of computational molecular cell biology (2014), 21(2), 118-40

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity," we use an information theory approach to formulate general measures of systems ... [more ▼]

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity," we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multivariable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multivariable dependency, "differential interaction information." This quantity for two variables reduces to the pairwise "set complexity" previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the "differential interaction information" are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for the study of complexity. The properties of "differential interaction information" also suggest new approaches to data analysis. Given a data set of system measurements, differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multivariable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system. [less ▲]

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See detailDiscovering pair-wise genetic interactions: an information theory-based approach.
Ignac, Tomasz UL; Skupin, Alexander UL; Sakhanenko, Nikita A. et al

in PloS one (2014), 9(3), 92310

Phenotypic variation, including that which underlies health and disease in humans, results in part from multiple interactions among both genetic variation and environmental factors. While diseases or ... [more ▼]

Phenotypic variation, including that which underlies health and disease in humans, results in part from multiple interactions among both genetic variation and environmental factors. While diseases or phenotypes caused by single gene variants can be identified by established association methods and family-based approaches, complex phenotypic traits resulting from multi-gene interactions remain very difficult to characterize. Here we describe a new method based on information theory, and demonstrate how it improves on previous approaches to identifying genetic interactions, including both synthetic and modifier kinds of interactions. We apply our measure, called interaction distance, to previously analyzed data sets of yeast sporulation efficiency, lipid related mouse data and several human disease models to characterize the method. We show how the interaction distance can reveal novel gene interaction candidates in experimental and simulated data sets, and outperforms other measures in several circumstances. The method also allows us to optimize case/control sample composition for clinical studies. [less ▲]

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See detailNew methods for finding associations in large data sets: Generalizing the maximal information coefficient (MIC)
Ignac, Tomasz UL; Sakhanenko, N. A.; Skupin, Alexander UL et al

in Proceedings of the Ninth International Workshop on Computational Systems Biology (2012)

We propose here a natural, but substantive, extension of the MIC. Defined for two variables, MIC has a distinct advance for detecting potentially complex dependencies. Our extension provides a similar ... [more ▼]

We propose here a natural, but substantive, extension of the MIC. Defined for two variables, MIC has a distinct advance for detecting potentially complex dependencies. Our extension provides a similar means for dependencies among three variables. This itself is an important step for practical applications. We show that by merging two concepts, the interaction information, which is a generalization of the mutual information to three variables, and the normalized information distance, which measures informational sharing between two variables, we can extend the fundamental idea of MIC. Our results also exhibit some attractive properties that should be useful for practical applications in data analysis. Finally, the conceptual and mathematical framework presented here can be used to generalize the idea of MIC to the multi-variable case. [less ▲]

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See detailComplexity of Networks II: The Set Complexity of Edge-Colored Graphs
Ignac, Tomasz UL; Sakhanenko, N. A.; Galas, David J. UL

in Complexity (2012), 17(5), 23-36

We previously introduced the concept of “set-complexity”, based on a context-dependent measure of information, and used this concept to describe the complexity of gene interaction networks. In the ... [more ▼]

We previously introduced the concept of “set-complexity”, based on a context-dependent measure of information, and used this concept to describe the complexity of gene interaction networks. In the previous paper in this series we analyzed the set-complexity of binary graphs. Here we extend this analysis to graphs with multi-colored edges that more closely match biological structures like the gene interaction networks. All highly complex graphs by this measure exhibit a modular structure. A principal result of this work is that for the most complex graphs of a given size the number of edge colors is equal to the number of “modules” of the graph. Complete multipartite graphs (CMGs) are defined and analyzed, and the relation between complexity and structure of these graphs is examined in detail. We establish that the mutual information between any two nodes in a CMG can be fully expressed in terms of entropy, and present an explicit expression for the set complexity of CMGs (Theorem 3). An algorithm for generating highly complex graphs from CMGs is described. We establish several theorems relating these concepts and connecting complex graphs with a variety of practical network properties. In exploring the relation between symmetry and complexity we use the idea of a similarity matrix and its spectrum for highly complex graphs. [less ▲]

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See detailRelations between the set-complexity and the structure of graphs and their sub-graphs
Ignac, Tomasz UL; Sakhanenko, Nikita; Galas, David J. UL

in EURASIP Journal on Bioinformatics & Systems Biology (2012), 13

We describe some new conceptual tools for the rigorous, mathematical description of the “set-complexity” of graphs. This set-complexity has been shown previously to be a useful measure for analyzing some ... [more ▼]

We describe some new conceptual tools for the rigorous, mathematical description of the “set-complexity” of graphs. This set-complexity has been shown previously to be a useful measure for analyzing some biological networks, and in discussing biological information in a quantitative fashion. The advances described here allow us to define some significant relationships between the set-complexity measure and the structure of graphs, and of their component sub-graphs. We show here that modular graph structures tend to maximize the set-complexity of graphs. We point out the relationship between modularity and redundancy, and discuss the significance of set-complexity in this regard. We specifically discuss the relationship between complexity and entropy in the case of complete-bipartite graphs, and present a new method for constructing highly complex, binary graphs. These results can be extended to the case of ternary graphs, and to other multi-edge graphs, which are fundamentally more relevant to biological structures and systems. Finally, our results lead us to an approach for extracting high complexity modular graphs from large, noisy graphs with low information content. We illustrate this approach with two examples. [less ▲]

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See detailRELATION BETWEEN THE SET-COMPLEXITY OF A GRAPH AND ITS STRUCTURE
Ignac, Tomasz UL; Galas, David J. UL; Sakhanenko, Nikita

in Proceedings of the 8th International Workshop on Computational Systems Biology (2011)

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See detailTree-Based computation in probalistic models
Ignac, Tomasz UL

Doctoral thesis (2010)

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See detailFunctions on Probabilistic Graphical Models
Ignac, Tomasz UL; Sorger, Ulrich UL

in Proceedings of the International Multiconference on Computer Science and Information Technology IMCSIT 2009 (2009)

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See detailProbabilistic Packet Relaying in Wireless Mobile Ad Hoc Network
Seredynski, Marcin UL; Ignac, Tomasz UL; Bouvry, Pascal UL

in Parallel Processing and Applied Mathematics (Proc. Parallel Processing and Applied Mathematics (PPAM 2009)), Springer LNCS (2009)

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