On some sequencing problems in finite groups

AbstractA finite group is called Z-sequenceable if its non-identity elements can be listed x1, x2, …, xn so that xixi+1 for i = 1, 2, …, n − 1. Various necessary and sufficient conditions are determined for such sequencings to exist. In particular, it is proved that if n ⩾ 3, then the symmetric group Sn is not Z-sequenceable

Accurate Profiling of Microbial Communities from Massively Parallel Sequencing using Convex Optimization

We describe the Microbial Community Reconstruction ({\bf MCR}) Problem, which is fundamental for microbiome analysis. In this problem, the goal is to reconstruct the identity and frequency of species comprising a microbial community, using short sequence reads from Massively Parallel Sequencing (MPS) data obtained for specified genomic regions. We formulate the problem mathematically as a convex optimization problem and provide sufficient conditions for identifiability, namely the ability to reconstruct species identity and frequency correctly when the data size (number of reads) grows to infinity. We discuss different metrics for assessing the quality of the reconstructed solution, including a novel phylogenetically-aware metric based on the Mahalanobis distance, and give upper-bounds on the reconstruction error for a finite number of reads under different metrics. We propose a scalable divide-and-conquer algorithm for the problem using convex optimization, which enables us to handle large problems (with $\sim10^6$ species). We show using numerical simulations that for realistic scenarios, where the microbial communities are sparse, our algorithm gives solutions with high accuracy, both in terms of obtaining accurate frequency, and in terms of species phylogenetic resolution.Comment: To appear in SPIRE 1

Behavioral Learning of Aircraft Landing Sequencing Using a Society of Probabilistic Finite State Machines

Air Traffic Control (ATC) is a complex safety critical environment. A tower controller would be making many decisions in real-time to sequence aircraft. While some optimization tools exist to help the controller in some airports, even in these situations, the real sequence of the aircraft adopted by the controller is significantly different from the one proposed by the optimization algorithm. This is due to the very dynamic nature of the environment. The objective of this paper is to test the hypothesis that one can learn from the sequence adopted by the controller some strategies that can act as heuristics in decision support tools for aircraft sequencing. This aim is tested in this paper by attempting to learn sequences generated from a well-known sequencing method that is being used in the real world. The approach relies on a genetic algorithm (GA) to learn these sequences using a society Probabilistic Finite-state Machines (PFSMs). Each PFSM learns a different sub-space; thus, decomposing the learning problem into a group of agents that need to work together to learn the overall problem. Three sequence metrics (Levenshtein, Hamming and Position distances) are compared as the fitness functions in GA. As the results suggest, it is possible to learn the behavior of the algorithm/heuristic that generated the original sequence from very limited information