School of Mathematics and Statistics - Research Publications
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1 - 10 of 1522
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Itemβ-Ensembles and higher genera Catalan numbers(SPRINGER, 2024-02-05)Abstract We propose formulas for the large N expansion of the generating function of connected correlators of the $$\beta $$ β -deformed Gaussian and Wishart–Laguerre matrix models. We show that our proposal satisfies the known transformation properties under the exchange of $$\beta $$ β with $$1/\beta $$ 1 / β and, using Virasoro constraints, we derive a recursion formula for the coefficients of the expansion. In the undeformed limit $$\beta =1$$ β = 1 , these coefficients are integers and they have the combinatorial interpretation of generalized Catalan numbers. For generic $$\beta $$ β , we define the higher genus Catalan polynomials $$C_{g,\nu }(\beta )$$ C g , ν ( β ) whose coefficients are integer numbers.
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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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ItemSuperinfection and the hypnozoite reservoir for Plasmodium vivax: a general framework(SPRINGER HEIDELBERG, 2024-01)A characteristic of malaria in all its forms is the potential for superinfection (that is, multiple concurrent blood-stage infections). An additional characteristic of Plasmodium vivax malaria is a reservoir of latent parasites (hypnozoites) within the host liver, which activate to cause (blood-stage) relapses. Here, we present a model of hypnozoite accrual and superinfection for P. vivax. To couple host and vector dynamics for a homogeneously-mixing population, we construct a density-dependent Markov population process with countably many types, for which disease extinction is shown to occur almost surely. We also establish a functional law of large numbers, taking the form of an infinite-dimensional system of ordinary differential equations that can also be recovered by coupling expected host and vector dynamics (i.e. a hybrid approximation) or through a standard compartment modelling approach. Recognising that the subset of these equations that model the infection status of the human hosts has precisely the same form as the Kolmogorov forward equations for a Markovian network of infinite server queues with an inhomogeneous batch arrival process, we use physical insight into the evolution of the latter process to write down a time-dependent multivariate generating function for the solution. We use this characterisation to collapse the infinite-compartment model into a single integrodifferential equation (IDE) governing the intensity of mosquito-to-human transmission. Through a steady state analysis, we recover a threshold phenomenon for this IDE in terms of a parameter [Formula: see text] expressible in terms of the primitives of the model, with the disease-free equilibrium shown to be uniformly asymptotically stable if [Formula: see text] and an endemic equilibrium solution emerging if [Formula: see text]. Our work provides a theoretical basis to explore the epidemiology of P. vivax, and introduces a strategy for constructing tractable population-level models of malarial superinfection that can be generalised to allow for greater biological realism in a number of directions.
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ItemSystemic inflammatory response syndrome triggered by blood-borne pathogens induces prolonged dendritic cell paralysis and immunosuppression(CELL PRESS, 2024-02-27)Blood-borne pathogens can cause systemic inflammatory response syndrome (SIRS) followed by protracted, potentially lethal immunosuppression. The mechanisms responsible for impaired immunity post-SIRS remain unclear. We show that SIRS triggered by pathogen mimics or malaria infection leads to functional paralysis of conventional dendritic cells (cDCs). Paralysis affects several generations of cDCs and impairs immunity for 3-4 weeks. Paralyzed cDCs display distinct transcriptomic and phenotypic signatures and show impaired capacity to capture and present antigens in vivo. They also display altered cytokine production patterns upon stimulation. The paralysis program is not initiated in the bone marrow but during final cDC differentiation in peripheral tissues under the influence of local secondary signals that persist after resolution of SIRS. Vaccination with monoclonal antibodies that target cDC receptors or blockade of transforming growth factor β partially overcomes paralysis and immunosuppression. This work provides insights into the mechanisms of paralysis and describes strategies to restore immunocompetence post-SIRS.
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ItemArtin algebraization for pairs with applications to the local structure of stacks and Ferrand pushouts(CAMBRIDGE UNIV PRESS, 2024-02-01)Abstract We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of étale, smooth or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove local structure theorems for stacks and their derived counterparts and the existence of henselizations along linearly fundamental closed substacks. These results establish the existence of Ferrand pushouts, which answers positively a question of Temkin–Tyomkin.
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ItemNo Preview AvailableA multi-criteria framework for disease surveillance site selection: case study for Plasmodium knowlesi malaria in Indonesia(ROYAL SOC, 2024-01-10)Disease surveillance aims to collect data at different times or locations, to assist public health authorities to respond appropriately. Surveillance of the simian malaria parasite, Plasmodium knowlesi, is sparse in some endemic areas and the spatial extent of transmission is uncertain. Zoonotic transmission of Plasmodium knowlesi has been demonstrated throughout Southeast Asia and represents a major hurdle to regional malaria elimination efforts. Given an arbitrary spatial prediction of relative disease risk, we develop a flexible framework for surveillance site selection, drawing on principles from multi-criteria decision-making. To demonstrate the utility of our framework, we apply it to the case study of Plasmodium knowlesi malaria surveillance site selection in western Indonesia. We demonstrate how statistical predictions of relative disease risk can be quantitatively incorporated into public health decision-making, with specific application to active human surveillance of zoonotic malaria. This approach can be used in other contexts to extend the utility of modelling outputs.
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ItemNo Preview AvailableA spatio-temporal model of multi-marker antimalarial resistance(ROYAL SOC, 2024-01-17)The emergence and spread of drug-resistant Plasmodium falciparum parasites have hindered efforts to eliminate malaria. Monitoring the spread of drug resistance is vital, as drug resistance can lead to widespread treatment failure. We develop a Bayesian model to produce spatio-temporal maps that depict the spread of drug resistance, and apply our methods for the antimalarial sulfadoxine-pyrimethamine. We infer from genetic count data the prevalences over space and time of various malaria parasite haplotypes associated with drug resistance. Previous work has focused on inferring the prevalence of individual molecular markers. In reality, combinations of mutations at multiple markers confer varying degrees of drug resistance to the parasite, indicating that multiple markers should be modelled together. However, the reporting of genetic count data is often inconsistent as some studies report haplotype counts, whereas some studies report mutation counts of individual markers separately. In response, we introduce a latent multinomial Gaussian process model to handle partially reported spatio-temporal count data. As drug-resistant mutations are often used as a proxy for treatment efficacy, point estimates from our spatio-temporal maps can help inform antimalarial drug policies, whereas the uncertainties from our maps can help with optimizing sampling strategies for future monitoring of drug resistance.
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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.