Appendix 2 from The impact of exposure to missionaries on the English language proficiency and earnings of immigrants in the US

Appendix 2 from the article The impact of exposure to missionaries on the English language proficiency and earnings of immigrants in the US , appearing in the International Journal of Manpower

On the Extension of Complex Numbers

This paper proposes an extension of the complex numbers, adding further imaginary units and preserving the idea of the product as a geometric construction. These `supercomplex numbers\u27, denoted S, are studied, and it is found that the algebra contains both new and old phenomena. It is established that equal-dimensional subspaces of S containing R are isomorphic under algebraic operations, whereby a symmetry within the space of imaginary units is illuminated. Certain equations are studied, and also a connection to special relativity is set up and explored. Finally, abstraction leads to the notion of a `generalised supercomplex algebra\u27; both the supercomplex numbers and the quaternions are found to be such algebras

A Mathematical Framework for Causally Structured Dilations and its Relation to Quantum Self-Testing

The motivation for this thesis was to recast quantum self-testing [MY98,MY04] in operational terms. The result is a category-theoretic framework for discussing the following general question: How do different implementations of the same input-output process compare to each other? In the proposed framework, an input-output process is modelled by a causally structured channel in some fixed theory, and its implementations are modelled by causally structured dilations formalising hidden side-computations. These dilations compare through a pre-order formalising relative strength of side-computations. Chapter 1 reviews a mathematical model for physical theories as semicartesian symmetric monoidal categories. Many concrete examples are discussed, in particular quantum and classical information theory. The key feature is that the model facilitates the notion of dilations. Chapter 2 is devoted to the study of dilations. It introduces a handful of simple yet potent axioms about dilations, one of which (resembling the Purification Postulate [CDP10]) entails a duality theorem encompassing a large number of classic no-go results for quantum theory. Chapter 3 considers metric structure on physical theories, introducing in particular a new metric for quantum channels, the purified diamond distance, which generalises the purified distance [TCR10,Tom12] and relates to the Bures distance [KSW08a]. Chapter 4 presents a category-theoretic formalism for causality in terms of '(constructible) causal channels' and 'contractions'. It simplifies aspects of the formalisms [CDP09,KU17] and relates to traces in monoidal categories [JSV96]. The formalism allows for the definition of 'causal dilations' and the establishment of a non-trivial theory of such dilations. Chapter 5 realises quantum self-testing from the perspective of chapter 4, thus pointing towards the first known operational foundation for self-testing.Comment: PhD thesis submitted to the University of Copenhagen (ISBN 978-87-7125-039-8). Advised by prof. Matthias Christandl, submitted 1st of December 2020, defended 11th of February 2021. Keywords: dilations, applied category theory, quantum foundations, causal structure, quantum self-testing. 242 pages, 1 figure. Comments are welcom

Political Ecology

Environmental legislation is commonly accepted as an altruistic approach to land management. A closer examination however, reveals that political incentives and flawed arguments consistently shape U.S. environmental policy at high public costs. As student fellows at the Institute of Political Economy at Utah State University, we have had the opportunity to research this subject under the direction of Professor Randy Simmons. Political Ecology is his upcoming book that explores a variety of environmental policies, the incentives that created them, and their effects on both public lands and taxpayers. Our research contributions to this overall project specifically explore three separate case studies: the Federal Land Management Policy Act, the Clean Air Act, and the Energy Policy Act of 2005. Altogether, it is our hope that the analysis and case studies presented will provide policy makers and the general public with needed information in regards to current and future U.S. environmental policy

Cardiovascular Disease and Psychiatric Comorbidity: The Potential Role of Perseverative Cognition

The high comorbidity between psychiatric disorders and cardiovascular disease has received increasing attention, yet little is known about the processes linking the two. One plausible contributing mechanism is the tendency of those with psychiatric disorders to ruminate on stressful events. This phenomenon, sometimes called perseverative cognition, can extend the psychological and physiological effects of stress, which could contribute to cardiovascular disease etiology. In this paper, we discuss the potential role of perseverative cognition in mediating the relationship between psychiatric illness and cardiovascular disease. Rumination can delay physiological recovery from acute stress, which in turn has been found to predict future cardiovascular health. This delayed recovery could act as a mechanism in the longitudinal link between worry and cardiovascular health. The cognitive inflexibility that characterizes mood and anxiety disorders may then contribute to disease not by producing greater reactivity, but instead through extending activation, increasing the risks for cardiovascular damage

ROMOP: a light-weight R package for interfacing with OMOP-formatted electronic health record data.

Objectives:Electronic health record (EHR) data are increasingly used for biomedical discoveries. The nature of the data, however, requires expertise in both data science and EHR structure. The Observational Medical Out-comes Partnership (OMOP) common data model (CDM) standardizes the language and structure of EHR data to promote interoperability of EHR data for research. While the OMOP CDM is valuable and more attuned to research purposes, it still requires extensive domain knowledge to utilize effectively, potentially limiting more widespread adoption of EHR data for research and quality improvement. Materials and methods:We have created ROMOP: an R package for direct interfacing with EHR data in the OMOP CDM format. Results:ROMOP streamlines typical EHR-related data processes. Its functions include exploration of data types, extraction and summarization of patient clinical and demographic data, and patient searches using any CDM vocabulary concept. Conclusion:ROMOP is freely available under the Massachusetts Institute of Technology (MIT) license and can be obtained from GitHub (http://github.com/BenGlicksberg/ROMOP). We detail instructions for setup and use in the Supplementary Materials. Additionally, we provide a public sandbox server containing synthesized clinical data for users to explore OMOP data and ROMOP (http://romop.ucsf.edu)

Selecting Generative Models for Networks using Classification with Machine Learning

By representing data entities as a map of edges and vertices, where each edge encodes a relationship between two vertices, networks have an almost unlimited ability to capture relationships and patterns impossible to see with the human eye. Because these patterns often reflect key aspects of the data, a significant portion of network science is devoted to detecting and distinguishing networks by using these topological features. The use of machine learning for classifying networks is a popular solution; research in this area includes techniques ranging from k-Nearest Neighbors to language modeling-inspired deep learning methods. Another area of interest with respect to networks is model selection, which can provide unique insights into a graph’s topological and probabilistic properties. This thesis combines the two areas of network classification with machine learning and generative model selection by using the popular algorithm known as “random forests” as a potential model selection criterion. First, we perform a series of experiments designed to characterize the discriminatory power of random forests on a wide variety of synthetic graphs generated by dozens of Stochastic Block Models (SBMs). Then, we take advantage of well-known network structural properties and compare the generative model of best fit selected by random forests to the model chosen by a previously established selection criterion known as Integrated Completed Likelihood (ICL). In applying these techniques to selecting Erdos-Renyi mixture models for a macaque brain connectivity dataset and using the model that maximizes the ICL criterion as the “gold standard,” we observed that random forests serves as a comparable model selection method when using topological network statistics as the feature space, selecting the same best-fit model chosen by ICL over 95% of the time.Bachelor of Scienc

Unsupervised Instance and Subnetwork Selection for Network Data

Unlike tabular data, features in network data are interconnected within a domain-specific graph. Examples of this setting include gene expression overlaid on a protein interaction network (PPI) and user opinions in a social network. Network data is typically high-dimensional (large number of nodes) and often contains outlier snapshot instances and noise. In addition, it is often non-trivial and time-consuming to annotate instances with global labels (e.g., disease or normal). How can we jointly select discriminative subnetworks and representative instances for network data without supervision? We address these challenges within an unsupervised framework for joint subnetwork and instance selection in network data, called UISS, via a convex self-representation objective. Given an unlabeled network dataset, UISS identifies representative instances while ignoring outliers. It outperforms state-of-the-art baselines on both discriminative subnetwork selection and representative instance selection, achieving up to 10% accuracy improvement on all real-world data sets we use for evaluation. When employed for exploratory analysis in RNA-seq network samples from multiple studies it produces interpretable and informative summaries