School of Mathematics and Statistics - Research Publications
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ItemExpanding the Fourier Transform of the Scaled Circular Jacobi β Ensemble Density(SPRINGER, 2023-10-18)Abstract The family of circular Jacobi $$\beta $$ β ensembles has a singularity of a type associated with Fisher and Hartwig in the theory of Toeplitz determinants. Our interest is in the Fourier transform of the corresponding $$N \rightarrow \infty $$ N → ∞ bulk scaled spectral density about this singularity, expanded as a series in the Fourier variable. Various integrability aspects of the circular Jacobi$$\beta $$ β ensemble are used for this purpose. These include linear differential equations satisfied by the scaled spectral density for $$\beta = 2$$ β = 2 and $$\beta = 4$$ β = 4 , and the loop equation hierarchy. The polynomials in the variable $$u=2/\beta $$ u = 2 / β which occur in the expansion coefficents are found to have special properties analogous to those known for the structure function of the circular $$\beta $$ β ensemble, specifically in relation to the zeros lying on the unit circle $$|u|=1$$ | u | = 1 and interlacing. Comparison is also made with known results for the expanded Fourier transform of the density about a guest charge in the two-dimensional one-component plasma.
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ItemComparison of new computational methods for spatial modelling of malaria.(Springer Science and Business Media LLC, 2023-11-21)BACKGROUND: Geostatistical analysis of health data is increasingly used to model spatial variation in malaria prevalence, burden, and other metrics. Traditional inference methods for geostatistical modelling are notoriously computationally intensive, motivating the development of newer, approximate methods for geostatistical analysis or, more broadly, computational modelling of spatial processes. The appeal of faster methods is particularly great as the size of the region and number of spatial locations being modelled increases. METHODS: This work presents an applied comparison of four proposed 'fast' computational methods for spatial modelling and the software provided to implement them-Integrated Nested Laplace Approximation (INLA), tree boosting with Gaussian processes and mixed effect models (GPBoost), Fixed Rank Kriging (FRK) and Spatial Random Forests (SpRF). The four methods are illustrated by estimating malaria prevalence on two different spatial scales-country and continent. The performance of the four methods is compared on these data in terms of accuracy, computation time, and ease of implementation. RESULTS: Two of these methods-SpRF and GPBoost-do not scale well as the data size increases, and so are likely to be infeasible for larger-scale analysis problems. The two remaining methods-INLA and FRK-do scale well computationally, however the resulting model fits are very sensitive to the user's modelling assumptions and parameter choices. The binomial observation distribution commonly used for disease prevalence mapping with INLA fails to account for small-scale overdispersion present in the malaria prevalence data, which can lead to poor predictions. Selection of an appropriate alternative such as the Beta-binomial distribution is required to produce a reliable model fit. The small-scale random effect term in FRK overcomes this pitfall, but FRK model estimates are very reliant on providing a sufficient number and appropriate configuration of basis functions. Unfortunately the computation time for FRK increases rapidly with increasing basis resolution. CONCLUSIONS: INLA and FRK both enable scalable geostatistical modelling of malaria prevalence data. However care must be taken when using both methods to assess the fit of the model to data and plausibility of predictions, in order to select appropriate model assumptions and parameters.
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ItemOpen networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals(SPRINGER, 2023-12)Abstract In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution.
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ItemNo Preview AvailableThree-dimensional genome architecture coordinates key regulators of lineage specification in mammary epithelial cells(ELSEVIER, 2023-11-08)Although lineage-specific genes have been identified in the mammary gland, little is known about the contribution of the 3D genome organization to gene regulation in the epithelium. Here, we describe the chromatin landscape of the three major epithelial subsets through integration of long- and short-range chromatin interactions, accessibility, histone modifications, and gene expression. While basal genes display exquisite lineage specificity via distal enhancers, luminal-specific genes show widespread promoter priming in basal cells. Cell specificity in luminal progenitors is largely mediated through extensive chromatin interactions with super-enhancers in gene-body regions in addition to interactions with polycomb silencer elements. Moreover, lineage-specific transcription factors appear to be controlled through cell-specific chromatin interactivity. Finally, chromatin accessibility rather than interactivity emerged as a defining feature of the activation of quiescent basal stem cells. This work provides a comprehensive resource for understanding the role of higher-order chromatin interactions in cell-fate specification and differentiation in the adult mouse mammary gland.
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ItemNo Preview AvailableNEARBY CYCLE SHEAVES FOR SYMMETRIC PAIRS(JOHNS HOPKINS UNIV PRESS, 2023-02)
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ItemNo Preview AvailableRank 1 perturbations in random matrix theory - A review of exact results(WORLD SCIENTIFIC PUBL CO PTE LTD, 2023-10)A number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank [Formula: see text] perturbation. Considered in this review are the additive rank [Formula: see text] perturbation of the Hermitian Gaussian ensembles, the multiplicative rank [Formula: see text] perturbation of the Wishart ensembles, and rank [Formula: see text] perturbations of Hermitian and unitary matrices giving rise to a two-dimensional support for the eigenvalues. The focus throughout is on exact formulas, which are typically the result of various integrable structures. The simplest is that of a determinantal point process, with others relating to partial differential equations implied by a formulation in terms of certain random tridiagonal matrices. Attention is also given to eigenvector overlaps in the setting of a rank [Formula: see text] perturbation.
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ItemNo Preview AvailableDivergent molecular networks program functionally distinct CD8+ skin-resident memory T cells(AMER ASSOC ADVANCEMENT SCIENCE, 2023-12-01)Skin-resident CD8+ T cells include distinct interferon-γ-producing [tissue-resident memory T type 1 (TRM1)] and interleukin-17 (IL-17)-producing (TRM17) subsets that differentially contribute to immune responses. However, whether these populations use common mechanisms to establish tissue residence is unknown. In this work, we show that TRM1 and TRM17 cells navigate divergent trajectories to acquire tissue residency in the skin. TRM1 cells depend on a T-bet-Hobit-IL-15 axis, whereas TRM17 cells develop independently of these factors. Instead, c-Maf commands a tissue-resident program in TRM17 cells parallel to that induced by Hobit in TRM1 cells, with an ICOS-c-Maf-IL-7 axis pivotal to TRM17 cell commitment. Accordingly, by targeting this pathway, skin TRM17 cells can be ablated without compromising their TRM1 counterparts. Thus, skin-resident T cells rely on distinct molecular circuitries, which can be exploited to strategically modulate local immunity.
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ItemNo Preview AvailableGenerating Dynamic Kernels via Transformers for Lane Detection(IEEE, 2023-01-01)
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ItemNo Preview AvailablePoint torque representations of ciliary flows(AMER PHYSICAL SOC, 2023-12-12)