Finding All Nash Equilibria of a Finite Game Using Polynomial Algebra

The set of Nash equilibria of a finite game is the set of nonnegative solutions to a system of polynomial equations. In this survey article we describe how to construct certain special games and explain how to find all the complex roots of the corresponding polynomial systems, including all the Nash equilibria. We then explain how to find all the complex roots of the polynomial systems for arbitrary generic games, by polyhedral homotopy continuation starting from the solutions to the specially constructed games. We describe the use of Groebner bases to solve these polynomial systems and to learn geometric information about how the solution set varies with the payoff functions. Finally, we review the use of the Gambit software package to find all Nash equilibria of a finite game.Comment: Invited contribution to Journal of Economic Theory; includes color figure

SATCHMO-JS: a webserver for simultaneous protein multiple sequence alignment and phylogenetic tree construction.

We present the jump-start simultaneous alignment and tree construction using hidden Markov models (SATCHMO-JS) web server for simultaneous estimation of protein multiple sequence alignments (MSAs) and phylogenetic trees. The server takes as input a set of sequences in FASTA format, and outputs a phylogenetic tree and MSA; these can be viewed online or downloaded from the website. SATCHMO-JS is an extension of the SATCHMO algorithm, and employs a divide-and-conquer strategy to jump-start SATCHMO at a higher point in the phylogenetic tree, reducing the computational complexity of the progressive all-versus-all HMM-HMM scoring and alignment. Results on a benchmark dataset of 983 structurally aligned pairs from the PREFAB benchmark dataset show that SATCHMO-JS provides a statistically significant improvement in alignment accuracy over MUSCLE, Multiple Alignment using Fast Fourier Transform (MAFFT), ClustalW and the original SATCHMO algorithm. The SATCHMO-JS webserver is available at http://phylogenomics.berkeley.edu/satchmo-js. The datasets used in these experiments are available for download at http://phylogenomics.berkeley.edu/satchmo-js/supplementary/

Berkeley PHOG: PhyloFacts orthology group prediction web server

Ortholog detection is essential in functional annotation of genomes, with applications to phylogenetic tree construction, prediction of protein–protein interaction and other bioinformatics tasks. We present here the PHOG web server employing a novel algorithm to identify orthologs based on phylogenetic analysis. Results on a benchmark dataset from the TreeFam-A manually curated orthology database show that PHOG provides a combination of high recall and precision competitive with both InParanoid and OrthoMCL, and allows users to target different taxonomic distances and precision levels through the use of tree-distance thresholds. For instance, OrthoMCL-DB achieved 76% recall and 66% precision on this dataset; at a slightly higher precision (68%) PHOG achieves 10% higher recall (86%). InParanoid achieved 87% recall at 24% precision on this dataset, while a PHOG variant designed for high recall achieves 88% recall at 61% precision, increasing precision by 37% over InParanoid. PHOG is based on pre-computed trees in the PhyloFacts resource, and contains over 366 K orthology groups with a minimum of three species. Predicted orthologs are linked to GO annotations, pathway information and biological literature. The PHOG web server is available at http://phylofacts.berkeley.edu/orthologs/

A Novel RSSI Prediction Using Imperialist Competition Algorithm (ICA), Radial Basis Function (RBF) and Firefly Algorithm (FFA) in Wireless Networks

This study aims to design a vertical handover prediction method to minimize unnecessary handovers for a mobile node (MN) during the vertical handover process. This relies on a novel method for the prediction of a received signal strength indicator (RSSI) referred to as IRBF-FFA, which is designed by utilizing the imperialist competition algorithm (ICA) to train the radial basis function (RBF), and by hybridizing with the firefly algorithm (FFA) to predict the optimal solution. The prediction accuracy of the proposed IRBF–FFA model was validated by comparing it to support vector machines (SVMs) and multilayer perceptron (MLP) models. In order to assess the model’s performance, we measured the coefficient of determination (R2), correlation coefficient (r), root mean square error (RMSE) and mean absolute percentage error (MAPE). The achieved results indicate that the IRBF–FFA model provides more precise predictions compared to different ANNs, namely, support vector machines (SVMs) and multilayer perceptron (MLP). The performance of the proposed model is analyzed through simulated and real-time RSSI measurements. The results also suggest that the IRBF–FFA model can be applied as an efficient technique for the accurate prediction of vertical handover

Toward community standards in the quest for orthologs

The identification of orthologs—genes pairs descended from a common ancestor through speciation, rather than duplication—has emerged as an essential component of many bioinformatics applications, ranging from the annotation of new genomes to experimental target prioritization. Yet, the development and application of orthology inference methods is hampered by the lack of consensus on source proteomes, file formats and benchmarks. The second ‘Quest for Orthologs' meeting brought together stakeholders from various communities to address these challenges. We report on achievements and outcomes of this meeting, focusing on topics of particular relevance to the research community at large. The Quest for Orthologs consortium is an open community that welcomes contributions from all researchers interested in orthology research and applications. Contact: [email protected]

Using computer algebra to find Nash equilibria

A central concern of game theory is the computation of Nash equilibria. These are characterized by systems of polynomial equations and inequalities. We survey the use of currently available software to solve these systems, and conclude that polyhedral homotopy continuation appears to scale best with increasing problem size