Doubly Robust Smoothing of Dynamical Processes via Outlier Sparsity Constraints

Coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice. In this context, the present paper develops novel fixed-lag and fixed-interval smoothing algorithms that are robust to outliers simultaneously present in the measurements {\it and} in the state dynamics. Outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least-squares criterion that is regularized with the $\ell_1$-norm of the outliers in order to effect sparsity control. The resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers, are expressed in closed form per iteration, and are provably convergent. Additional attractive features of the novel doubly robust smoother include: i) ability to handle both types of outliers; ii) universality to unknown nominal noise and outlier distributions; iii) flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions; and iv) improved performance relative to competing alternatives at comparable complexity, as corroborated via simulated tests.Comment: Submitted to IEEE Trans. on Signal Processin

Liquid rocket engine axial-flow turbopumps

The axial pump is considered in terms of the total turbopump assembly. Stage hydrodynamic design, pump rotor assembly, pump materials for liquid hydrogen applications, and safety factors as utilized in state of the art pumps are among the topics discussed. Axial pump applications are included

Second waves, social distancing, and the spread of COVID-19 across America

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several of these (epidemic) models to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity--and the exchange of people between regions--and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The modelling is demonstrated using timeseries of new cases and deaths from the United States to estimate the parameters of a factorial (compartmental) epidemiological model of each State and, crucially, coupling between States. Using Bayesian model reduction, we identify the effective connectivity between States that best explains the initial phases of the outbreak in the United States. Using the ensuing posterior parameter estimates, we then evaluate the likely outcomes of different policies in terms of mortality, working days lost due to lockdown and demands upon critical care. The provisional results of this modelling suggest that social distancing and loss of immunity are the two key factors that underwrite a return to endemic equilibrium.Comment: Technical report: 35 pages, 14 figures, 1 tabl

Second waves, social distancing, and the spread of COVID-19 across the USA [version 2; peer review: 2 approved with reservations]

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several instantiations of this (epidemic) model to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity—and the exchange of people between regions—and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The modelling is demonstrated using timeseries of new cases and deaths from the United States to estimate the parameters of a factorial (compartmental) epidemiological model of each State and, crucially, coupling between States. Using Bayesian model reduction, we identify the effective connectivity between States that best explains the initial phases of the outbreak in the United States. Using the ensuing posterior parameter estimates, we then evaluate the likely outcomes of different policies in terms of mortality, working days lost due to lockdown and demands upon critical care. The provisional results of this modelling suggest that social distancing and loss of immunity are the two key factors that underwrite a return to endemic equilibrium

Second waves, social distancing, and the spread of COVID-19 across the USA [version 3; peer review: 1 approved, 1 approved with reservations]

We recently described a dynamic causal model of a COVID-19 outbreak within a single region. Here, we combine several instantiations of this (epidemic) model to create a (pandemic) model of viral spread among regions. Our focus is on a second wave of new cases that may result from loss of immunity—and the exchange of people between regions—and how mortality rates can be ameliorated under different strategic responses. In particular, we consider hard or soft social distancing strategies predicated on national (Federal) or regional (State) estimates of the prevalence of infection in the population. The modelling is demonstrated using timeseries of new cases and deaths from the United States to estimate the parameters of a factorial (compartmental) epidemiological model of each State and, crucially, coupling between States. Using Bayesian model reduction, we identify the effective connectivity between States that best explains the initial phases of the outbreak in the United States. Using the ensuing posterior parameter estimates, we then evaluate the likely outcomes of different policies in terms of mortality, working days lost due to lockdown and demands upon critical care. The provisional results of this modelling suggest that social distancing and loss of immunity are the two key factors that underwrite a return to endemic equilibrium

Investigating the mechanism of clonal expansion of deleted mtDNA species

PhD ThesisMitochondrial DNA deletions are a primary cause of inherited and sporadic mitochondrial disease, whilst somatic mtDNA deletions contribute to the focal respiratory chain deficiency observed in post-mitotic cells associated with ageing and neurodegenerative disorders. As mtDNA deletions only cause cellular pathology at high levels of heteroplasmy, an mtDNA deletion formed within a cell must accumulate by a process known as clonal expansion to levels which result in biochemical dysfunction. The mechanism driving clonal expansion remains uncertain; this research aimed to investigate clonally expanded mtDNA deletions in sporadic and inherited mitochondrial myopathies in order to elucidate this mechanism. A number of different approaches were taken to assess the mechanism driving accumulation of mtDNA deletions. The effect of the mtDNA deletion size on clonal expansion was first investigated by assessing the longitudinal spread of mtDNA deletions in single muscle fibres isolated from patients presenting with mtDNA maintenance disorders; no relationship was found to exist between mtDNA deletion size and the area over which the mutation has accumulated. A longitudinal study was carried out using tissue acquired over a 13-year period from a single patient with a sporadic mtDNA deletion, to identify whether the mtDNA deletion heteroplasmy level continued to increase over time, as would be expected if the mutation displayed a selective advantage over wildtype mtDNA – however, both the genetic and biochemical defect were found to be stable over time in this patient. A subsequent study aimed to identify a correlation between mtDNA deletion size and heteroplasmy levels at the whole tissue level in a cohort of patients with sporadic single mtDNA deletions, but no evidence was found to suggest that larger mtDNA deletions accumulate to higher levels of heteroplasmy. Finally, single cytochrome c oxidase- deficient muscle fibres were investigated using single-molecule PCR to assess whether clonal expansion of multiple mtDNA deletions could be observed in single cells. Evidence of multiple clonally expanded mtDNA species was found in approximately 40% of all examined fibres, with no correlation between mtDNA deletion size and level of accumulation. Each of these four studies has highlighted accumulation by random genetic drift to be the most likely mechanism for clonal expansion of mtDNA deletions in human muscle; no evidence has been found to support the presence of a selective advantage for mtDNA deletion species over wildtype mtDNA

Modelling and Identification of Immune Cell Migration during the Inflammatory Response

Neutrophils are the white blood cells that play a crucial role in the response of the innate immune system to tissue injuries or infectious threats. Their rapid arrival to the damaged area and timely removal from it define the success of the inflammatory process. Therefore, understanding neutrophil migratory behaviour is essential for the therapeutic regulation of multiple inflammation-mediated diseases. Recent years saw rapid development of various in vivo models of inflammation that provide a remarkable insight into the neutrophil function. The main drawback of the \textit{in vivo} microscopy is that it usually focuses on the moving cells and obscures the external environment that drives their migration. To evaluate the effect of a particular treatment strategy on neutrophil behaviour, it is necessary to recover the information about the cell responsiveness and the complex extracellular environment from the limited experimental data. This thesis addresses the presented inference problem by developing a dynamical modelling and estimation framework that quantifies the relationship between an individual migrating cell and the global environment. \par The first part of the thesis is concerned with the estimation of the hidden chemical environment that modulates the observed cell migration during the inflammatory response in the injured tail fin of zebrafish larvae. First, a dynamical model of the neutrophil responding to the chemoattractant concentration is developed based on the potential field paradigm of object-environment interaction. This representation serves as a foundation for a hybrid model that is proposed to account for heterogeneous behaviour of an individual cell throughout the migration process. An approximate maximum likelihood estimation framework is derived to estimate the hidden environment and the states of multiple hybrid systems simultaneously. The developed framework is then used to analyse the neutrophil tracking data observed in vivo under the assumption that each neutrophil at each time can be in one of three migratory modes: responding to the environment, randomly moving, and stationary. The second part of the thesis examines the process of neutrophil migration at the subcellular scale, focusing on the subcellular mechanism that translates the local environment sensing into the cell shape change. A state space model is formulated based on the hypothesis that links the local protrusions of the cell membrane and the concentration of the intracellular pro-inflammatory signalling protein. The developed model is tested against the local concentration data extracted from the in vivo time-lapse images via the classical expectation-maximisation algorithm

The composition, mechanisms of action and infusion parameters of cardioplegic solutions as determinants of recovery in rabbit isolated hearts (Langendorff)

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A study of changes in the ratings of relevant concepts on semantic differential scales by Borstal boys

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