Embedded model discrepancy: A case study of Zika modeling

Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of these simplifications, the model output, of say new cases of a disease over time, or when an epidemic will occur, may be inconsistent with available data. In this case, we must improve the model, especially if we plan to make decisions based on it that could affect human health and safety, but direct improvements are often beyond our reach. In this work, we explore this problem through a case study of the Zika outbreak in Brazil in 2016. We propose an embedded discrepancy operator---a modification to the model equations that requires modest information about the system and is calibrated by all relevant data. We show that the new enriched model demonstrates greatly increased consistency with real data. Moreover, the method is general enough to easily apply to many other mathematical models in epidemiology.Comment: 9 pages, 7 figure

Learning non-Gaussian graphical models via Hessian scores and triangular transport

Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions and for efficiently performing inference. While the problem of learning graph structure from data has been studied extensively for certain parametric families of distributions, most existing methods fail to consistently recover the graph structure for non-Gaussian data. Here we propose an algorithm for learning the Markov structure of continuous and non-Gaussian distributions. To characterize conditional independence, we introduce a score based on integrated Hessian information from the joint log-density, and we prove that this score upper bounds the conditional mutual information for a general class of distributions. To compute the score, our algorithm SING estimates the density using a deterministic coupling, induced by a triangular transport map, and iteratively exploits sparse structure in the map to reveal sparsity in the graph. For certain non-Gaussian datasets, we show that our algorithm recovers the graph structure even with a biased approximation to the density. Among other examples, we apply sing to learn the dependencies between the states of a chaotic dynamical system with local interactions.Comment: 40 pages, 12 figure

Combinatorial Games with a Pass: A dynamical systems approach

By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well known combinatorial games, 3-pile Nim and 3-row Chomp. In the case of Nim, we observe that the introduction of the pass dramatically alters the game's underlying structure, rendering it considerably more complex, while for Chomp, the pass move is found to have relatively minimal impact. We show how these results can be understood by recasting these games as dynamical systems describable by dynamical recursion relations. From these recursion relations we are able to identify underlying structural connections between these "games with passes" and a recently introduced class of "generic (perturbed) games." This connection, together with a (non-rigorous) numerical stability analysis, allows one to understand and predict the effect of a pass on a game.Comment: 39 pages, 13 figures, published versio

Exploring academic perspectives on immersive scheduling in a UK university

This study examined how academic staff responded to a cross-institutional change initiative to integrate immersive scheduling into the first-year undergraduate curriculum. Immersive scheduling, also referred to as block or compressed delivery, sought to create a supportive first-year experience, to ease students’ transition to university. Adopting an immersive approach is associated with considerable change as academic staff adapt their practice to accommodate the compressed time frame of modules and embrace learning and assessment methods associated with this delivery format. In this study, we undertook semi-structured interviews with 17 academics who were leading the development and delivery of immersive modules or supporting the teaching and learning initiative. Our data indicated that academics played a significant role in the acceptance or rejection of the vision for immersive scheduling. Acceptance was reliant on academics recognising value in the vision, and this varied depending on the extent to which it resonated with local practice. In some cases, the move to immersive scheduling represented a valued opportunity to update pedagogic and assessment practices. However, in other contexts, academic resistance led to dilution of key elements of the vision, with compliance rather than innovation being the outcome. This study also highlights the value of using a combination of module delivery formats to mitigate recognised drawbacks associated with immersive delivery. We conclude this paper by proposing recommendations to support the future development of immersive scheduling in higher education institutions

Suicidal thinking and psychological distress : the role of personality and cognitive factors

Objectives. This thesis aimed to examine a series of personality and cognitive factors as prospective predictors of suicidal thinking and psychological distress. A secondary objective was to examine any causal relationship between rumination and attentional biases. Method. In order to achieve the above objectives, a series of four studies were conducted. Studies one and three were prospective studies, using analogue samples, to examine the role of personality and cognitive factors in distress and suicidal thinking. In addition, study one also investigated the effect on attentional bias of manipulating rumination. Study two was an experimental study in which two different methods of manipulating attentional bias were piloted. The final study in this thesis employed a clinical sample of general hospital parasuicide patients to investigate whether relationships between personality and cognitive factors were replicable in a clinical population. Results. The personality and cognitive factors understudy were investigated within a research framework to examine their interactive effects. Hierarchical regression analyses revealed a number of moderating and mediating relationships between these personality and cognitive factors to prospectively predict both suicidal thinking and psychological distress. In addition, rumination was found to have a causal influence on positive attentional bias. Conclusions. Evidence from this thesis links personality and cognitive factors to both suicidal thinking and psychological distress in a series of moderating and mediating relationships. These are discussed in relation to the possible theoretical and clinical implications.EThOS - Electronic Theses Online ServiceESRC : MRCGBUnited Kingdo