23 research outputs found

    Probabilistic Regression and Anomaly Detection for Latency Assessment in Mobile Radio Networks

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    This thesis provides a thorough examination and empirical results on the use of machine learning for predicting latency in mobile radio networks, specifically emphasizing probabilistic regression and anomaly detection tasks. After a ML-aided selection of the Key Performance Indicators that most influence the latency, different models are compared for both probabilistic regression and anomaly detection. Such models present network designers with a valuable instrument to explore the correlations that exist between particular network Key Performance Indicators and latency

    Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

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    Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation

    Vol. 8, No. 2 (Full Issue)

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    Network Infusion to Infer Information Sources in Networks

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    Several models exist for diffusion of signals across biological, social, or engineered networks. However, the inverse problem of identifying the source of such propagated information appears more difficult even in the presence of multiple network snapshots, and especially for the single-snapshot case, given the many alternative, often similar, progression of diffusion that may lead to the same observed snapshots. Mathematically, this problem can be undertaken using a diffusion kernel that represents diffusion processes in a given network, but computing this kernel is computationally challenging in general. Here, we propose a path-based network diffusion kernel which considers edge-disjoint shortest paths among pairs of nodes in the network and can be computed efficiently for both homogeneous and heterogeneous continuous-time diffusion models. We use this network diffusion kernel to solve the inverse diffusion problem, which we term Network Infusion (NI), using both likelihood maximization and error minimization. The minimum error NI algorithm is based on an asymmetric Hamming premetric function and can balance between false positive and false negative error types. We apply this framework for both single-source and multi-source diffusion, for both single-snapshot and multi-snapshot observations, and using both uninformative and informative prior probabilities for candidate source nodes. We also provide proofs that under a standard susceptible-infected diffusion model, (1) the maximum-likelihood NI is mean-field optimal for tree structures or sufficiently sparse Erdos-Renyi graphs, (2) the minimum-error algorithm is mean-field optimal for regular tree structures, and (3) for sufficiently-distant sources, the multi-source solution is mean-field optimal in the regular tree structure. Moreover, we provide techniques to learn diffusion model parameters such as observation times. We apply NI to several synthetic networks and compare its performance to centrality-based and distance-based methods for Erdos-Renyi graphs, power-law networks, symmetric and asymmetric grids. Moreover, we use NI in two real-world applications. First, we identify the news sources for 3,553 stories in the Digg social news network, and validate our results based on annotated information, that was not provided to our algorithm. Second, we use NI to identify infusion hubs of human diseases, defined as gene candidates that can explain the connectivity pattern of disease-related genes in the human regulatory network. NI identifies infusion hubs of several human diseases including T1D, Parkinson, MS, SLE, Psoriasis and Schizophrenia. We show that, the inferred infusion hubs are biologically relevant and often not identifiable using the raw p-values

    Charting the landscape of stochastic gene expression models using queueing theory

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    Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queuing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and non-stationary distributions and/or moments of mRNA/protein numbers, and bounds on the Fano factor. This approach may enable the solution of complex models which have hitherto evaded analytical solution.Comment: 24 pages, 6 figure

    Stochastic multiscale models of cell behaviour

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    Mathematical Modelling and Nonstandard Schemes for the Corona Virus Pandemic

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    The programs used in this Master thesis: https://git.uni-wuppertal.de/1449563/covid-19-modelling/-/tree/master/PROGRAM

    A Modelling Framework for Estimating the Risk of Importation of a Novel Disease

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    Sequential Monte Carlo (SMC) methods are vital in fitting models, without a tractable likelihood, to data. When combined with Markov Chain Monte Carlo, SMC allows for full posterior distributions of states and parameters to be estimated. However, for many problems, these methods can be prohibitively computationally expensive. One such class of models with intractable likelihoods are continuous-time Branching Processes (CTBPs). In this thesis, we leverage the unique properties of CTBPs to derive a method that approximates the results of standard SMC methods, with a significant reduction in computation time. We find that under certain conditions the method we have developed can produce highly accurate results in orders of magnitude less time than standard SMC methods. Continuous-time Branching Processes are often used for epidemic modelling, particularly in the early phases of an outbreak. In light of the COVID-19 pandemic, CTBPs have been used in metapopulation models, where agents are partitioned into subpopulations (usually states or countries) that interact through immigration. In this thesis, we build upon existing work in this area, with a focus on estimating disease importation risk. We show how applying our method to this problem can allow for joint estimation of the parameters mediating disease spread and unobserved cases. Specifically, the speed improvement given by our method allows for full posterior distributions for states, parameters and importation risk to be derived. Furthermore, we find that the increase in speed also allows more parameters to be estimated. Consequently, each subpopulation can have its own parameters. As a result, hierarchical modelling can be employed, meaning that parameter estimates from one subpopulation can inform the estimates of others. We find hierarchical modelling to be vital in estimating importation risk, particularly for counties with low observation probability.Thesis (MPhil) -- University of Adelaide, School of Computer and Mathematical Sciences, 202
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