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Andrew Gainer-Dewar

Publications and source records attributed to Andrew Gainer-Dewar.

7 recordsLinked to original sources
arXiv2016

Geometric combinatorics and computational molecular biology: branching polytopes for RNA sequences

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.

q-bio.BM↗
arXiv2016

The minimal hitting set generation problem: algorithms and computation

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.

cs.DS↗
arXiv2015

Pólya theory for species with an equivariant group action

Joyal's theory of combiantorial species provides a rich and elegant framework for enumerating combinatorial structures by translating structural information into algebraic functional equations. We present some classical and folklore results which interpret the species-theoretic cycle index series in terms of the Pólya theory of the action of the symmetric group on the label set, allowing the enumeration of "partially-labeled" structures and providing an alternate foundation for several proofs. We also extend the theory to incorporate information about "structural" group actions (i.e. those which commute with the label permutation action) on combinatorial species, using the $Γ$-species of Henderson, and present Pólya-theoretic interpretations of the associated formal power series. We define the appropriate operations $+$, $\cdot$, $\circ$, and $\square$ on $Γ$-species, give formulas for the associated operations on $Γ$-cycle indices, and illustrate the use of this theory to study several important examples of combinatorial structures. Finally, we demonstrate the use of the Sage computer algebra system to enumerate $Γ$-species and their quotients.

math.CO↗
arXiv2014

Counting unlabeled k-trees

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.

math.CO↗
arXiv2012

Γ-species and the enumeration of k-trees

We study the class of graphs known as k-trees through the lens of Joyal's theory of combinatorial species (and an equivariant 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.

math.CO↗