School of Mathematics and Statistics - Research Publications

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    Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case
    Hahn, N ; Kieburg, M ; Gat, O ; Guhr, T (AIP Publishing, 2023-11-01)
    We extend our recent study of winding number density statistics in Gaussian random matrix ensembles of the chiral unitary (AIII) and chiral symplectic (CII) classes. Here, we consider the chiral orthogonal (BDI) case which is the mathematically most demanding one. The key observation is that we can map the topological problem on a spectral one, rendering the toolbox of random matrix theory applicable. In particular, we employ a technique that exploits supersymmetry structures without reformulating the problem in superspace.
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    HBO1 (KAT7) Does Not Have an Essential Role in Cell Proliferation, DNA Replication, or Histone 4 Acetylation in Human Cells
    Kueh, AJ ; Eccles, S ; Tang, L ; Garnham, AL ; May, RE ; Herold, MJ ; Smyth, GK ; Voss, AK ; Thomas, T (American Society for Microbiology, 2020-02-01)
    HBO1 (MYST2/KAT7) is essential for histone 3 lysine 14 acetylation (H3K14ac) but is dispensable for H4 acetylation and DNA replication in mouse tissues. In contrast, previous studies using small interfering RNA (siRNA) knockdown in human cell lines have suggested that HBO1 is essential for DNA replication. To determine if HBO1 has distinctly different roles in immortalized human cell lines and normal mouse cells, we performed siRNA knockdown of HBO1. In addition, we used CRISPR/Cas9 to generate 293T, MCF7, and HeLa cell lines lacking HBO1. Using both techniques, we show that HBO1 is essential for all H3K14ac in human cells and is unlikely to have a direct effect on H4 acetylation and only has minor effects on cell proliferation. Surprisingly, the loss of HBO1 and H3K14ac in HeLa cells led to the secondary loss of almost all H4 acetylation after 4 weeks. Thus, HBO1 is dispensable for DNA replication and cell proliferation in immortalized human cells. However, while cell proliferation proceeded without HBO1 and H3K14ac, HBO1 gene deletion led to profound changes in cell adhesion, particularly in 293T cells. Consistent with this phenotype, the loss of HBO1 in both 293T and HeLa principally affected genes mediating cell adhesion, with comparatively minor effects on other cellular processes.
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    Gata-3 Negatively Regulates the Tumor-Initiating Capacity of Mammary Luminal Progenitor Cells and Targets the Putative Tumor Suppressor Caspase-14
    Asselin-Labat, M-L ; Sutherland, KD ; Vaillant, F ; Gyorki, DE ; Wu, D ; Holroyd, S ; Breslin, K ; Ward, T ; Shi, W ; Bath, ML ; Deb, S ; Fox, SB ; Smyth, GK ; Lindeman, GJ ; Visvader, JE (AMER SOC MICROBIOLOGY, 2011-11)
    The transcription factor Gata-3 is a definitive marker of luminal breast cancers and a key regulator of mammary morphogenesis. Here we have explored a role for Gata-3 in tumor initiation and the underlying cellular mechanisms using a mouse model of "luminal-like" cancer. Loss of a single Gata-3 allele markedly accelerated tumor progression in mice carrying the mouse mammary tumor virus promoter-driven polyomavirus middle T antigen (MMTV-PyMT mice), while overexpression of Gata-3 curtailed tumorigenesis. Through the identification of two distinct luminal progenitor cells in the mammary gland, we demonstrate that Gata-3 haplo-insufficiency increases the tumor-initiating capacity of these progenitors but not the stem cell-enriched population. Overexpression of a conditional Gata-3 transgene in the PyMT model promoted cellular differentiation and led to reduced tumor-initiating capacity as well as diminished angiogenesis. Transcript profiling studies identified caspase-14 as a novel downstream target of Gata-3, in keeping with its roles in differentiation and tumorigenesis. A strong association was evident between GATA-3 and caspase-14 expression in preinvasive ductal carcinoma in situ samples, where GATA-3 also displayed prognostic significance. Overall, these studies identify GATA-3 as an important regulator of tumor initiation through its ability to promote the differentiation of committed luminal progenitor cells.
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    Critical site percolation on the triangular lattice: from integrability to conformal partition functions
    Morin-Duchesne, A ; Klümper, A ; Pearce, PA (IOP Publishing, 2023-04-01)
    Abstract Critical site percolation on the triangular lattice is described by the Yang–Baxter solvable dilute A 2 ( 2 ) loop model with crossing parameter specialized to λ = π 3 , corresponding to the contractible loop fugacity β = − 2 cos 4 λ = 1 . We study the functional relations satisfied by the commuting transfer matrices of this model and the associated Bethe ansatz equations. The single and double row transfer matrices are respectively endowed with strip and periodic boundary conditions, and are elements of the ordinary and periodic dilute Temperley–Lieb algebras. The standard modules for these algebras are labelled by the number of defects d and, in the latter case, also by the twist e i γ . Nonlinear integral equation techniques are used to analytically solve the Bethe ansatz functional equations in the scaling limit for the central charge c = 0 and conformal weights Δ , Δ ˉ . For the ground states, we find Δ = Δ 1 , d + 1 for strip boundary conditions and ( Δ , Δ ˉ ) = ( Δ γ / π , d / 2 , Δ γ / π , − d / 2 ) for periodic boundary conditions, where Δ r , s = 1 24 ( ( 3 r − 2 s ) 2 − 1 ) . We give explicit conjectures for the scaling limit of the trace of the transfer matrix in each standard module. For d ⩽ 8 , these conjectures are supported by numerical solutions of the logarithmic form of the Bethe ansatz equations for the leading 20 or more conformal eigenenergies. With these conjectures, we apply the Markov traces to obtain the conformal partition functions on the cylinder and torus. These precisely coincide with our previous results for critical bond percolation on the square lattice, described by the dense A 1 ( 1 ) loop model with λ = π 3 . The concurrence of all this conformal data provides compelling evidence supporting a strong form of universality between these two stochastic models as logarithmic conformal field theories.
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    Two-layer gravity currents of generalized Newtonian fluids
    Christy, I ; Hinton, EM (ROYAL SOC, 2023-11-08)
    We examine gravity-driven two-layer flow of generalized Newtonian fluids. The two layers have different densities and constitutive laws, and the flow is assumed to be shallow and inertia-less. A depth-integrated model for flow over one-dimensional topography is derived with the volume fluxes written in terms of functions that depend only on the fluids’ rheology. The model enables two-layer flows of any combination of generalized Newtonian fluids to be computed without explicit knowledge of the velocity profile. For viscoplastic layers, the formulation provides a convenient way to determine the layer evolution without having to analyse the multiple yield surfaces that may occur. Motivated by the lubricated flow of ice sheets, we analyse the case in which the lower layer is relatively thin. The model reduces to a one-layer flow with an effective slip law that encapsulates the thickness and generalized Newtonian rheology of the lower layer. For flow over two-dimensional topography, a depth-integrated two-layer model cannot generally be derived because the direction of the shear stress varies across the lower layer. Progress is possible in the special cases that the lower layer is Newtonian or is relatively thin.
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    Instance space analysis for 2D bin packing mathematical models
    Liu, C ; Smith-Miles, K ; Wauters, T ; Costa, AM (Elsevier BV, 2024-06-01)
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    An intersection-theoretic proof of the Harer-Zagier formula
    Giacchetto, A ; Lewanski, D ; Norbury, P (EUROPEAN MATHEMATICAL SOC-EMS, 2023-03)
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    Toblerone: detecting exon deletion events in cancer using RNA-seq.
    Lonsdale, A ; Halman, A ; Brown, L ; Kosasih, H ; Ekert, P ; Oshlack, A (F1000 Research Ltd, 2023)
    Cancer is driven by mutations of the genome that can result in the activation of oncogenes or repression of tumour suppressor genes. In acute lymphoblastic leukemia (ALL) focal deletions in IKAROS family zinc finger 1 (IKZF1) result in the loss of zinc-finger DNA-binding domains and a dominant negative isoform that is associated with higher rates of relapse and  poorer patient outcomes. Clinically, the presence of IKZF1 deletions informs prognosis and treatment options. In this work we developed a method for detecting exon deletions in genes using RNA-seq with application to IKZF1. We developed a pipeline that first uses a custom transcriptome reference consisting of transcripts with exon deletions.  Next, RNA-seq reads are mapped using a pseudoalignment algorithm to identify reads that uniquely support deletions. These are then evaluated for evidence of the deletion with respect to gene expression and other samples. We applied the algorithm, named Toblerone, to a cohort of 99 B-ALL paediatric samples including validated IKZF1 deletions. Furthermore, we developed a graphical desktop app for non-bioinformatics users that can quickly and easily identify and report deletions in IKZF1 from RNA-seq data with informative graphical outputs.
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    Mathematical models of developmental vascular remodelling: A review.
    Crawshaw, JR ; Flegg, JA ; Bernabeu, MO ; Osborne, JM ; Marsden, AL (Public Library of Science (PLoS), 2023-08)
    Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.
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    WHAM-A Prospective Study of Weight and Body Composition After Risk-Reducing Bilateral Salpingo-oophorectomy
    Price, SAL ; Finch, S ; Krejany, E ; Jiang, H ; Kale, A ; Domchek, S ; Wrede, D ; Wark, JD ; Hickey, M (ENDOCRINE SOC, 2023-12-21)
    CONTEXT: Body weight and composition may change over the natural menopause transition. Whether surgical menopause has similar effects, and the impact of hormone replacement therapy (HRT), are unknown. Understanding the metabolic effects of surgical menopause will inform clinical care. OBJECTIVE: To prospectively measure weight and body composition over 24 months following surgical menopause compared with a similar comparison group who retained their ovaries. METHODS: Prospective observational study of weight change from baseline to 24 months in 95 premenopausal women at elevated risk of ovarian cancer planning risk-reducing salpingo-oophorectomy (RRSO) and 99 comparators who retained their ovaries. Change in body composition from baseline to 24 months was also assessed by dual-energy x-ray absorptiometry in a subgroup of 54 women who underwent RRSO and 81 comparators who retained their ovaries. In the subgroup, weight, fat mass, lean mass, and abdominal fat measures were compared between groups. RESULTS: At 24 months both groups had gained weight (RRSO 2760 ± 4860 g vs comparators 1620 ± 4540 g) with no difference between groups (mean difference 730 g; 95% CI 920 g to 2380 g; P = .383). In the body composition subgroup, there was no difference in weight between groups at 24 months (mean difference 944 g; 95% CI -1120 g to 2614 g; P = .431). RRSO women may have gained slightly more abdominal visceral adipose tissue (mean difference 99.0 g; 95% CI 8.8 g to 189.2 g; P = .032) but there were no other differences in body composition. There were also no differences in weight or body composition between HRT users and nonusers at 24 months. CONCLUSION: 24 months after RRSO, there was no difference in body weight compared with women who retained their ovaries. RRSO women gained more abdominal visceral adipose tissue than comparators, but there were no other differences in body composition. Use of HRT following RRSO had no effect on these outcomes.