A computational framework for evaluating the role of mobility on the propagation of epidemics on point processes.

This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a susceptible individual is proportional to the number of infected individuals in a disc around it. The main focus of the paper is a model where points are also subject to some random motion. Conservation equations for moment measures are leveraged to analyze the stationary regime of the point processes of infected and susceptible individuals. A heuristic factorization of the third moment measure is then proposed to obtain simple polynomial equations allowing one to derive closed form approximations for the fraction of infected individuals in the steady state. These polynomial equations also lead to a phase diagram which tentatively delineates the regions of the space of parameters (population density, infection radius, infection and recovery rate, and motion rate) where the epidemic survives and those where there is extinction. A key take-away from this phase diagram is that the extinction of the epidemic is not always aided by a decrease in the motion rate. These results are substantiated by simulations on large two dimensional tori. These simulations show that the polynomial equations accurately predict the fraction of infected individuals when the epidemic survives. The simulations also show that the proposed phase diagram accurately predicts the parameter regions where the mean survival time of the epidemic increases (resp. decreases) with motion rate.

ComHapDet: a spatial community detection algorithm for haplotype assembly.

BACKGROUND: Haplotypes, the ordered lists of single nucleotide variations that distinguish chromosomal sequences from their homologous pairs, may reveal an individual's susceptibility to hereditary and complex diseases and affect how our bodies respond to therapeutic drugs. Reconstructing haplotypes of an individual from short sequencing reads is an NP-hard problem that becomes even more challenging in the case of polyploids. While increasing lengths of sequencing reads and insert sizes helps improve accuracy of reconstruction, it also exacerbates computational complexity of the haplotype assembly task. This has motivated the pursuit of algorithmic frameworks capable of accurate yet efficient assembly of haplotypes from high-throughput sequencing data. RESULTS: We propose a novel graphical representation of sequencing reads and pose the haplotype assembly problem as an instance of community detection on a spatial random graph. To this end, we construct a graph where each read is a node with an unknown community label associating the read with the haplotype it samples. Haplotype reconstruction can then be thought of as a two-step procedure: first, one recovers the community labels on the nodes (i.e., the reads), and then uses the estimated labels to assemble the haplotypes. Based on this observation, we propose ComHapDet - a novel assembly algorithm for diploid and ployploid haplotypes which allows both bialleleic and multi-allelic variants. CONCLUSIONS: Performance of the proposed algorithm is benchmarked on simulated as well as experimental data obtained by sequencing Chromosome 5 of tetraploid biallelic Solanum-Tuberosum (Potato). The results demonstrate the efficacy of the proposed method and that it compares favorably with the existing techniques.

End-to-End Optimization of High-Throughput DNA Sequencing.

At the core of Illumina's high-throughput DNA sequencing platforms lies a biophysical surface process that results in a random geometry of clusters of homogeneous short DNA fragments typically hundreds of base pairs long-bridge amplification. The statistical properties of this random process and the lengths of the fragments are critical as they affect the information that can be subsequently extracted, that is, density of successfully inferred DNA fragment reads. The ensembles of overlapping DNA fragment reads are then used to computationally reconstruct the much longer target genome sequence. The success of the reconstruction in turn depends on having a sufficiently large ensemble of DNA fragments that are sufficiently long. In this article using stochastic geometry, we model and optimize the end-to-end flow cell synthesis and target genome sequencing process, linking and partially controlling the statistics of the physical processes to the success of the final computational step. Based on a rough calibration of our model, we provide, for the first time, a mathematical framework capturing the salient features of the sequencing platform that serves as a basis for optimizing cost, performance, and/or sensitivity analysis to various parameters.