Ramoni O. Lasisi

K-partite RNA secondary structures.

RNA secondary structure prediction is a fundamental problem in structural bioinformatics. The prediction problem is difficult because RNA secondary structures may contain pseudoknots formed by crossing base pairs. We introduce k-partite secondary structures as a simple classification of RNA secondary structures with pseudoknots. An RNA secondary structure is k-partite if it is the union of k pseudoknot-free sub-structures. Most known RNA secondary structures are either bipartite or tripartite. We show that there exists a constant number k such that any secondary structure can be modified into a k-partite secondary structure with approximately the same free energy. This offers a partial explanation of the prevalence of k-partite secondary structures with small k. We give a complete characterization of the computational complexities of recognizing k-partite secondary structures for all k > or = 2, and show that this recognition problem is essentially the same as the k-colorability problem on circle graphs. We present two simple heuristics, iterated peeling and first-fit packing, for finding k-partite RNA secondary structures. For maximizing the number of base pair stackings, our iterated peeling heuristic achieves a constant approximation ratio of at most k for 2 < or = k < or = 5, and at most [Formula: see text] for k > or = 6. Experiment on sequences from PseudoBase shows that our first-fit packing heuristic outperforms the leading method HotKnots in predicting RNA secondary structures with pseudoknots. Supplementary Material can be found at www.libertonline.com.

Manipulation of Weighted Voting Games via Annexation and Merging

We conduct an experimental study of the effects of manipulations (i.e., dishonest behaviors) including those of manipulation by annexation and merging in weighted voting games. These manipulations involve an agent or agents misrepresenting their identities in anticipation of gaining more power at the expense of other agents in a game. Using the well-known Shapley-Shubik and Banzhaf power indices, we first show that manipulators need to do only a polynomial amount of work to find a much improved power gain, and then present two enumeration-based pseudopolynomial algorithms that manipulators can use. Furthermore, we provide a careful investigation of heuristics for annexation which provide huge savings in computational efforts over the enumeration-based method. The benefits achievable by manipulating agents using these heuristics also compare with those of the enumeration-based method which serves as upper bound.

K-partite RNA secondary structures

RNA secondary structure prediction is a fundamental problem in structural bioinformatics. The prediction problem is difficult because RNA secondary structures may contain pseudoknots formed by crossing base pairs. We introduce kpartite secondary structures as a simple classification of RNA secondary structures with pseudoknots. An RNA secondary structure is k-partite if it is the union of k pseudoknot-free sub-structures. Most known RNA secondary structures are either bipartite or tripartite. We show that there exists a constant number k such that any secondary structure can be modified into a k-partite secondary structure with approximately the same free energy. This offers a partial explanation of the prevalence of k-partite secondary structures with small k. We give a complete characterization of the computational complexities of recognizing k-partite secondary structures for all k≥2, and show that this recognition problem is essentially the same as the k-colorability problem on circle graphs. We present two simple heuristics, iterated peeling and first-fit packing, for finding k- partite RNA secondary structures. For maximizing the number of base pair stackings, our iterated peeling heuristic achieves a constant approximation ratio of at most k for 2 ≤ k ≤ 5, and at most 6/1-(1-6/k)k ≤ 6/1-e-6 < 6.01491 for k ≥ 6. Experiment on sequences from PseudoBase shows that our first-fit packing heuristic outperforms the leading method HotKnots in predicting RNA secondary structures with pseudoknots. Source code, data set, and experimental results are available at http://www.cs.usu.edu/~mjiang/rna/kpartite/.

False‐Name Manipulation in Weighted Voting Games: Empirical and Theoretical Analysis

Weighted voting games are important in multiagent systems because of their usage in automated decision making. However, they are not immune from the vulnerability of false‐name manipulation by strategic agents that may be present in the games. False‐name manipulation involves an agent splitting its weight among several false identities in anticipation of power increase. Previous works have considered false‐name manipulation using the well‐known Shapley–Shubik and Banzhaf power indices. Bounds on the extent of power that a manipulator may gain exist when it splits into k = 2 false identities for both the Shapley–Shubik and Banzhaf indices. The bounds when an agent splits into k > 2 false identities, until now, have remained open for the two indices. This article answers this open problem by providing four nontrivial bounds when an agent splits into k > 2 false identities for the two indices. Furthermore, we propose a new bound on the extent of power that a manipulator may gain when it splits into several false identities in a class of games referred to as excess unanimity weighted voting games. Finally, we complement our theoretical results with empirical evaluation. Results from our experiments confirm the existence of beneficial splits into several false identities for the two indices, and also establish that splitting into more than two false identities is qualitatively different than the previously known splitting into exactly two false identities.

Manipulation of Weighted Voting Games and the Effect of Quota

The Shapley-Shubik, Banzhaf, and Deegan-Packel indices are three prominent power indices for measuring voters’ power in weighted voting games. We consider two methods of manipulating weighted voting games, called annexation and merging. These manipulations allow either an agent, called an annexer to take over the voting weights of some other agents, or the coming together of some agents to form a bloc of manipulators to have more power over the outcomes of the games. We evaluate the extent of susceptibility to these forms of manipulation and the effect of the quota of a game on these manipulation for the three indices. Experiments on weighted voting games suggest that the three indices are highly susceptible to annexation while they are less susceptible to merging. In both annexation and merging, the Shapley-Shubik index is the most susceptible to manipulation among the indices. Further experiments on the effect of quotas of weighted voting games suggest the existence of an inverse relationship between the susceptibility of the indices to manipulation and the quotas for both annexation and merging. Thus, weighted voting games with large quota values closer to the total weight of agents in the games may be less vulnerable to annexation and merging than those with corresponding smaller quota values.