School of Mathematics and Statistics - Research Publications
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ItemMetaGenePipe: An Automated, Portable Pipeline for Contig-based Functional and Taxonomic Analysis(The Open Journal, 2023)MetaGenePipe (MGP) is an efficient, flexible, portable, and scalable metagenomics pipeline that uses performant bioinformatics software suites and genomic databases to create an accurate taxonomic and functional characterization of the prokaryotic fraction of sequenced microbiomes. Written in the Workflow Definition Language (WDL), MGP produces output that can be explored and interpreted directly, or can be used for downstream analysis. MGP is a pipeline-development best practice tool that uses Singularity for containerization and includes a setup script that downloads the necessary databases for setup. The source code for MGP is freely available and distributed under the Apache 2.0 license.
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ItemSharp phase transition for Cox percolation(Institute of Mathematical Statistics, 2022-01-01)We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence, satisfies a local boundedness condition and can be constructed from a discrete iid random field, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction that allows us to compare different notions of influence.
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ItemUpper bounds on the one-arm exponent for dependent percolation models(Springer Science and Business Media LLC, 2023-02-01)We prove upper bounds on the one-arm exponent η1 for a class of dependent percolation models which generalise Bernoulli percolation; while our main interest is level set percolation of Gaussian fields, the arguments apply to other models in the Bernoulli percolation universality class, including Poisson–Voronoi and Poisson–Boolean percolation. More precisely, in dimension d= 2 we prove that η1≤ 1 / 3 for continuous Gaussian fields with rapid correlation decay (e.g. the Bargmann–Fock field), and in d≥ 3 we prove η1≤ d/ 3 for finite-range fields, both discrete and continuous, and η1≤ d- 2 for fields with rapid correlation decay. Although these results are classical for Bernoulli percolation (indeed they are best-known in general), existing proofs do not extend to dependent percolation models, and we develop a new approach based on exploration and relative entropy arguments. The proof also makes use of a new Russo-type inequality for Gaussian fields, which we apply to prove the sharpness of the phase transition and the mean-field bound for finite-range fields.
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ItemPregnant women maintain body temperatures within safe limits during moderate-intensity aqua-aerobic classes conducted in pools heated up to 33 degrees Celsius: an observational study(AUSTRALIAN PHYSIOTHERAPY ASSOC, 2015-10-01)QUESTION: What is the body temperature response of healthy pregnant women exercising at moderate intensity in an aqua-aerobics class where the water temperature is in the range of 28 to 33 degrees Celsius, as typically found in community swimming pools? DESIGN: An observational study. PARTICIPANTS: One hundred and nine women in the second and third trimester of pregnancy who were enrolled in a standardised aqua-aerobics class. OUTCOME MEASURES: Tympanic temperature was measured at rest pre-immersion (T1), after 35minutes of moderate-intensity aqua-aerobic exercise (T2), after a further 10minutes of light exercise while still in the water (T3) and finally on departure from the facility (T4). The range of water temperatures in seven indoor community pools was 28.8 to 33.4 degrees Celsius. RESULTS: Body temperature increased by a mean of 0.16 degrees Celsius (SD 0.35, p<0.001) at T2, was maintained at this level at T3 and had returned to pre-immersion resting values at T4. Regression analysis demonstrated that the temperature response was not related to the water temperature (T2 r = -0.01, p = 0.9; T3 r = -0.02, p=0.9; T4 r=0.03, p=0.8). Analysis of variance demonstrated no difference in body temperature response between participants when grouped in the cooler, medium and warmer water temperatures (T2 F=0.94, p=0.40; T3 F=0.93, p=0.40; T4 F=0.70, p=0.50). CONCLUSIONS: Healthy pregnant women maintain body temperatures within safe limits during moderate-intensity aqua-aerobic exercise conducted in pools heated up to 33 degrees Celsius. The study provides evidence to inform guidelines for safe water temperatures for aqua-aerobic exercise during pregnancy.
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ItemA statistical approach to knot confinement via persistent homology(ROYAL SOC, 2022-05-25)In this paper, we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed metric neighbourhood of a knot's embedding for growing radii. Specifically, we extract features from the persistent homology (PH) of the Vietoris-Rips complexes built from point clouds associated with knots. Statistical analysis of our data shows the existence of increasing correlations between geometric quantities associated with the embedding and PH-based features, as a function of the knots' lengths. We further study the variation of these correlations for different knot types. Finally, this framework also allows us to define a simple notion of deviation from ideal configurations of knots.
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ItemModel Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility.(Frontiers Media SA, 2022)During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.
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ItemClassical Length-5 Pattern-Avoiding Permutations(The Electronic Journal of Combinatorics, 2022-01-01)We have made a systematic numerical study of the 16 Wilf classes of length-5 classical pattern-avoiding permutations from their generating function coefficients. We have extended the number of known coefficients in fourteen of the sixteen classes. Careful analysis, including sequence extension, has allowed us to estimate the growth constant of all classes, and in some cases to estimate the sub-dominant power-law term associated with the exponential growth. In six of the sixteen classes we find the familiar power-law behaviour, so that the coefficients behave like $s_n \sim C \cdot \mu^n \cdot n^g,$ while in the remaining ten cases we find a stretched exponential as the most likely sub-dominant term, so that the coefficients behave like $s_n \sim C \cdot \mu^n \cdot \mu_1^{n^\sigma} \cdot n^g,$ where $0 < \sigma < 1.$ We have also classified the 120 possible permutations into the 16 distinct classes. We give compelling numerical evidence, and in one case a proof, that all 16 Wilf-class generating function coefficients can be represented as moments of a non-negative measure on $[0,\infty)$. Such sequences are known as Stieltjes moment sequences. They have a number of nice properties, such as log-convexity, which can be used to provide quite strong rigorous lower bounds. Stronger bounds still can be established under plausible monotonicity assumptions about the terms in the continued-fraction expansion of the generating functions implied by the Stieltjes property. In this way we provide strong (non-rigorous) lower bounds to the growth constants, which are sometimes within a few percent of the exact value.
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ItemPredicting Safe Regions Within Lava Flows Over Topography(AMER GEOPHYSICAL UNION, 2022-09-01)
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ItemA representation learning framework for detection and characterization of dead versus strain localization zones from pre-to post-failure(SPRINGER, 2022-08-01)Abstract Experiments have long shown that zones of near vanishing deformation, so-called “dead zones”, emerge and coexist with strain localization zones inside deforming granular media. To date, a method that can disentangle these dynamically coupled structures from each other, from pre- to post- failure, is lacking. Here we develop a framework that learns a new representation of the kinematic data, based on the complexity of a grain’s neighborhood structure in the kinematic-state-space, as measured by a recently introduced metric called s-LID. Dead zones (DZ) are first distinguished from strain localization zones (SZ) throughout loading history. Next the coupled dynamics of DZ and SZ are characterized using a range of discriminative features representing: local nonaffine deformation, contact topology and force transmission properties. Data came from discrete element simulations of biaxial compression tests. The deformation is found to be essentially dual in nature. DZ and SZ exhibit distinct yet coupled dynamics, with the separation in dynamics increasing in the lead up to failure. Force congestion and plastic deformation mainly concentrate in SZ. Although the 3-core of the contact network is highly prone to damage in SZ, it is robust to pre-failure microbands but is decimated in the shearband, leaving a fragmented 3-core in DZ at failure. We also show how loading condition and rolling resistance influence SZ and DZ differently, thus casting new light on controls on plasticity from the perspective of emergent deformation structures. Graphic abstract
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ItemEstimation of tumor cell total mRNA expression in 15 cancer types predicts disease progression.(Springer Science and Business Media LLC, 2022-11)Single-cell RNA sequencing studies have suggested that total mRNA content correlates with tumor phenotypes. Technical and analytical challenges, however, have so far impeded at-scale pan-cancer examination of total mRNA content. Here we present a method to quantify tumor-specific total mRNA expression (TmS) from bulk sequencing data, taking into account tumor transcript proportion, purity and ploidy, which are estimated through transcriptomic/genomic deconvolution. We estimate and validate TmS in 6,590 patient tumors across 15 cancer types, identifying significant inter-tumor variability. Across cancers, high TmS is associated with increased risk of disease progression and death. TmS is influenced by cancer-specific patterns of gene alteration and intra-tumor genetic heterogeneity as well as by pan-cancer trends in metabolic dysregulation. Taken together, our results indicate that measuring cell-type-specific total mRNA expression in tumor cells predicts tumor phenotypes and clinical outcomes.