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New models and algorithms for RNA pseudoknot order assignment

Zok Tomasz, Badura Jan, Swat Sylwester, Figurski Kacper, Popenda Mariusz, Antczak Maciej

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 2

315--324

The pseudoknot is a specific motif of the RNA structure that highly influences the overall shape and stability of a molecule. It occurs when nucleotides of two disjoint single-stranded fragments of the same chain, separated by a helical fragment, interact with each other and form base pairs. Pseudoknots are characterized by great topological diversity, and their systematic description is still a challenge. In our previous work, we have introduced the pseudoknot order: a new coefficient representing the topological complexity of the pseudoknotted RNA structure. It is defined as the minimum number of base pair set decompositions, aimed to obtain the unknotted RNA structure. We have suggested how it can be useful in the interpretation and understanding of a hierarchy of RNA folding. However, it is not trivial to unambiguously identify pseudoknots and determine their orders in an RNA structure. Therefore, since the introduction of this coefficient, we have worked on the method to reliably assign pseudoknot orders in correspondence to the mechanisms that control the biological process leading to their formation in the molecule. Here, we introduce a novel graph coloring-based model for the problem of pseudoknot order assignment. We show a specialized heuristic operating on the proposed model and an alternative integer programming algorithm. The performance of both approaches is compared with that of state-of-the-art algorithms which so far have been most efficient in solving the problem in question. We summarize the results of computational experiments that evaluate our new methods in terms of classification quality on a representative data set originating from the non-redundant RNA 3D structure repository.

Approaches to Conflict Dynamics Based on Rough Sets

Ramanna S., Peters J.F., Skowron A.

Fundamenta Informaticae

2007

Vol. 75, nr 1-4

453-468

Conflict analysis and conflict resolution play an important role in negotiation during contract-management situations in many organizations. The issue here is how to model a combination of complex situations among agents where there are disagreements leading to a conflict situation, and there is a need for an acceptable set of agreements. Conflict situations also result due to different sets of view points about issues under negotiation. The solution to this problem stems from pioneering work on this subject by Zdzisaw Pawlak, which provides a basis for a complex conflict model encapsulating a decision system with complex decisions. Several approaches to the analysis of conflicts situations are presented in this paper, namely, conflict graphs, approximation spaces and risk patterns. An illustrative example of a requirements scope negotiation for an automated lighting system is presented. The contribution of this paper is a rough set-based requirements scope determination model and assessment mechanisms using a complex conflict model.