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

Representing model inadequacy: A stochastic operator approach

Mathematical models of physical systems are subject to many uncertainties such as measurement errors and uncertain initial and boundary conditions. After accounting for these uncertainties, it is often revealed that discrepancies between the model output and the observations remain; if so, the model is said to be inadequate. In practice, the inadequate model may be the best that is available or tractable, and so despite its inadequacy the model may be used to make predictions of unobserved quantities. In this case, a representation of the inadequacy is necessary, so the impact of the observed discrepancy can be determined. We investigate this problem in the context of chemical kinetics and propose a new technique to account for model inadequacy that is both probabilistic and physically meaningful. A stochastic inadequacy operator $\mathcal{S}$ is introduced which is embedded in the ODEs describing the evolution of chemical species concentrations and which respects certain physical constraints such as conservation laws. The parameters of $\mathcal{S}$ are governed by probability distributions, which in turn are characterized by a set of hyperparameters. The model parameters and hyperparameters are calibrated using high-dimensional hierarchical Bayesian inference. We apply the method to a typical problem in chemical kinetics---the reaction mechanism of hydrogen combustion

Optimal Data Split Methodology for Model Validation

The decision to incorporate cross-validation into validation processes of mathematical models raises an immediate question - how should one partition the data into calibration and validation sets? We answer this question systematically: we present an algorithm to find the optimal partition of the data subject to certain constraints. While doing this, we address two critical issues: 1) that the model be evaluated with respect to predictions of a given quantity of interest and its ability to reproduce the data, and 2) that the model be highly challenged by the validation set, assuming it is properly informed by the calibration set. This framework also relies on the interaction between the experimentalist and/or modeler, who understand the physical system and the limitations of the model; the decision-maker, who understands and can quantify the cost of model failure; and the computational scientists, who strive to determine if the model satisfies both the modeler's and decision maker's requirements. We also note that our framework is quite general, and may be applied to a wide range of problems. Here, we illustrate it through a specific example involving a data reduction model for an ICCD camera from a shock-tube experiment located at the NASA Ames Research Center (ARC).Comment: Submitted to International Conference on Modeling, Simulation and Control 2011 (ICMSC'11), San Francisco, USA, 19-21 October, 201

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

Vaccine-induced skewing of T cell responses protects against Chikungunya virus disease

Chikungunya virus (CHIKV) infections can cause severe and debilitating joint and muscular pain that can be long lasting. Current CHIKV vaccines under development rely on the generation of neutralizing antibodies for protection; however, the role of T cells in controlling CHIKV infection and disease is still unclear. Using an overlapping peptide library, we identified the CHIKV-specific T cell receptor epitopes recognized in C57BL/6 infected mice at 7 and 14 days post-infection. A fusion protein containing peptides 451, 416, a small region of nsP4, peptide 47, and an HA tag (CHKVf5) was expressed using adenovirus and cytomegalovirus-vectored vaccines. Mice vaccinated with CHKVf5 elicited robust T cell responses to higher levels than normally observed following CHIKV infection, but the vaccine vectors did not elicit neutralizing antibodies. CHKVf5-vaccinated mice had significantly reduced infectious viral load when challenged by intramuscular CHIKV injection. Depletion of both CD

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

The Image Guided Cancer Therapy Research Program together with the CCSG Imaging-Driven Biologically-Informed Therapy Program Seminar Series

Rebecca Morrison, PhDAssistant ProfessorDepartment of Computer Science University of Colorado - Boulderhttps://openworks.mdanderson.org/igct_seminars/1008/thumbnail.jp