Statistical Inference for Partially Observed Markov Processes via the R Package pomp

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programming environment provided by pomp.Comment: In press at the Journal of Statistical Software. A version of this paper is provided at the pomp package website: http://kingaa.github.io/pom

Detecting adaptive evolution in phylogenetic comparative analysis using the Ornstein-Uhlenbeck model

Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and more detailed evolutionary hypotheses, including adaptive hypotheses with multiple selective optima and hypotheses with rate variation within and across lineages. The statistical performance of these sophisticated models has received relatively little systematic attention, however. We conducted an extensive simulation study to quantify the statistical properties of a class of models toward the simpler end of the spectrum that model phenotypic evolution using Ornstein-Uhlenbeck processes. We focused on identifying where, how, and why these methods break down so that users can apply them with greater understanding of their strengths and weaknesses. Our analysis identifies three key determinants of performance: a discriminability ratio, a signal-to-noise ratio, and the number of taxa sampled. Interestingly, we find that model-selection power can be high even in regions that were previously thought to be difficult, such as when tree size is small. On the other hand, we find that model parameters are in many circumstances difficult to estimate accurately, indicating a relative paucity of information in the data relative to these parameters. Nevertheless, we note that accurate model selection is often possible when parameters are only weakly identified. Our results have implications for more sophisticated methods inasmuch as the latter are generalizations of the case we study.Comment: 38 pages, in press at Systematic Biolog

Design of 0D and 1D Magnetic Nanostructures as Magnetic Resonance Imaging Contrast Agents

The main aim of this thesis is to harness the complex interparticle interactions between magnetic cores in order to produce magnetic nanostructures with exceptional MRI contrast enhancement. This work also seeks to provide new insights on the relationships between these interactions and the resulting MRI behaviour, in order to guide future design of clinical MRI contrast agents

Attacking Computer Security Using Peripheral Device Drivers

Detection of malicious logic on a hardware device is difficult to detect. This thesis proposes a device driver that emulates a hardware device and that device’s software driver. This device driver attacks the target system by accessing the hard disk in order to perform read and write transactions without the knowledge of the operating system or intrusion detection/prevention software. The attacks performed by the driver compromise the confidentiality, integrity, and availability of data on the target system’s disk drive. The attacks performed by the device driver have a less than one percent impact on system performance. This thesis, while tested in a Windows environment, applies to other operating systems (such as Linux/Unix, etc.) and thus has major implications for a wide range of users

Development of an in situ Remediation Strategy for a Metals-Contaminated, Alkaline Groundwater

Groundwater beneath a former industrial site in Tukwila, WA contains dissolved metals and organic material at high levels, as well as elevated pH (10-12). Contaminated groundwater discharge to site-adjacent waterways must be controlled to minimize impact to potential receptors. In a preliminary study, the efficacy of five amendments (chitosan, apatite, granular activated carbon (GAC), Thiol-SAMMS®, and limestone) was examined for the removal of copper, lead, vanadium, and arsenic for both unaltered and pH-adjusted (pH = 8) site groundwater in laboratory batch studies. Dissolved metals and dissolved organic carbon (DOC) concentrations in site groundwater were measured both before and after pH adjustment, and after application of amendments. pH adjustment generally improved amendment performance. The greatest reductions in dissolved copper (70%), lead (62%), and vanadium (62%) concentrations were observed under pH-adjusted conditions in the presence of apatite. Thiol-SAMMS® also performed well under pH-adjusted conditions (Cu: 69% reduction; Pb: 46% reduction; V: 24% reduction), and also removed both copper (55% reduction) and lead (31% reduction) at the original pH. GAC was somewhat effective at removing lead under all conditions (15-30% reduction) and copper (31% reduction) when the pH was adjusted, and also reduced DOC concentrations under all conditions (24-27% reduction). These results suggest that a strategy using pH adjustment and some combination of apatite, Thiol-SAMMS®, and/or GAC may be best suited for remediation at this site. Further studies testing combinations of bone char (in place of apatite), GAC, and Thiol-SAMMS® were performed. In addition, the impacts of air sparging and pH adjustment through addition of hydrochloric acid or ferrous sulfate heptahydrate (FeSO4:7H2O), a coagulant commonly used in conventional water treatment, were evaluated. The introduction of FeSO4:7H2O resulted in the formation of coagulation solids, further decreases in pH after the coagulation solids were removed, and the largest significant reductions of dissolved copper (at most 81%), arsenic (72%), vanadium (80%), and DOC (88%) of any treatment evaluated. Sparging with air increased reductions of lead concentrations for all pH adjustment strategies and slightly increased reduction of vanadium concentrations only when the pH was adjusted with FeSO4:7H2O. Combinations of bone char, GAC, and Thiol-SAMMS® generally did not confer a substantial advantage over single amendment treatments. Bone char, though, acted as a buffer to curb further decreases in pH after coagulation solids were removed. The drops in pH after the coagulation solids were removed, either with or without air sparging may be related to the oxidation of residual ferrous iron, but it is unclear if this single mechanism can explain the magnitude of the observed pH declines. Using the ferrous sulfate treatment strategy potentially combined with passive barrier or cap of bone char, flow-through column experiments will be designed to show how implementation of the strategy would impact the subsurface hydrology and to determine whether this strategy can achieve applicable or relevant and appropriate requirements (ARARs)

Moduli spaces for Bondal quivers

Given a sufficiently nice collection of sheaves on an algebraic variety V, Bondal explained how to build a quiver Q along with an ideal of relations in the path algebra of Q such that the derived category of representations of Q subject to these relations is equivalent to the derived category of coherent sheaves on V. We consider the case in which these sheaves are all locally free and study the moduli spaces of semistable representations of our quiver with relations for various stability conditions. We show that V can often be recovered as a connected component of such a moduli space and we describe the line bundle induced by a GIT construction of the moduli space in terms of the input data. In certain special cases, we interpret our results in the language of topological string theory.Comment: 17 pages, major revisio