Finding inclusion-minimal hitting sets for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic literature focuses on the problem of recognizing the collection of minimal hitting sets; however, in many of the applications, it is more important to generate these hitting sets. We survey twenty algorithms from across a variety of domains, considering their history, classification, useful features, and computational performance on a variety of synthetic and real-world inputs. We also provide a suite of implementations of these algorithms with a ready-to-use, platform-agnostic interface based on Docker containers and the AlgoRun framework, so that interested computational scientists can easily perform similar tests with inputs from their own research areas on their own computers or through a convenient Web interface.

We study the class of graphs known as $k$-trees through the lens of Joyal’s theory of combinatorial species (and a extension known as 'Γ-species' which incorporates data about 'structural' group actions). This culminates in a system of recursive functional equations giving the generating function for unlabeled $k$-trees which allows for fast, efficient computation of their numbers. Enumerations up to $k = 10$ and $n = 30$ (for a k-tree with $n + k − 1$ vertices) are included in tables, and Sage code for the general computation is included in an appendix.

We count unlabeled k-trees by properly coloring them in k + 1 colors and then counting orbits of these colorings under the action of the symmetric group on the colors.

Abstract. Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the parameters used in the objective functions. The goal of a parametric analysis is to elucidate such dependencies, especially as they pertain to the accuracy and robustness of the optimal solutions. Techniques from geometric combinatorics, including polytopes and their normal fans, have been used previously to give parametric analyses of simple models for DNA sequence alignment and RNA branching configurations. Here, we present a new computational framework, and proof-of-principle results, which give the first complete parametric analysis of the branching portion of the nearest neighbor thermodynamic model for secondary structure prediction for real RNA sequences. MotivationOver the past four decades, improvements in biotechnology have greatly accelerated the amount of biological sequence data available. Yet, a fundamental challenge in computational molecular biology remains to reliably infer functional information from the linear encoding of DNA, RNA, and protein molecules.As articulated in the central dogma of molecular biology, genetic information is stored in DNA from which it is transcribed into messenger RNA, and then translated into proteins by ribosomal and transfer RNA. However, as always in biology, a wealth of complexity lurks below the surface of this basic principle. Historically, most interest was focused on DNA sequences (as the cellular genome) and protein structures (as the cellular machinery). Since the early 2000's, though, attention has increasingly turned to RNA as many more critical functions have been revealed, including gene splicing, editing, and regulation.Like DNA, RNA is a sequence of nucleic acids, abbreviated A, C, G, and U (instead of T), which form the familiar Watson-Crick pairings. Unlike the canonical doublestranded DNA helix, most RNA molecules are naturally single-stranded and the intra-sequence base pairings are an integral component of the three-dimensional structure. This is in contrast to the more subtle amino acid interactions which govern the formation of protein structures. However, knowing the structure of a

Summary OCSANA+ is a Cytoscape app for identifying nodes to drive the system towards a desired long-term behavior, prioritizing combinations of interventions in large scale complex networks, and estimating the effects of node perturbations in signaling networks, all based on the analysis of the network’s structure. OCSANA+ includes an update to OCSANA (optimal combinations of interventions from network analysis) software tool with cutting-edge and rigorously tested algorithms, together with recently-developed structure-based control algorithms for non-linear systems and an algorithm for estimating signal flow. All these algorithms are based on the network’s topology. OCSANA+ is implemented as a Cytoscape app to enable a user interface for running analyses and visualizing results. Availability and Implementation OCSANA+ app and its tutorial can be downloaded from the Cytoscape App Store or https://veraliconaresearchgroup.github.io/OCSANA-Plus/. The source code and computations are available in https://github.com/VeraLiconaResearchGroup/OCSANA-Plus_SourceCode. Supplementary information Supplementary data are available at Bioinformatics online.