### Browsing by Department "Denison University"

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Item Constraints on Particles and Fields from Full Stokes Observations of AGN(2018-01-29) Homan, Daniel C.; Hovatta, Talvikki; Kovalev, Yuri Y.; Lister, Matthew L.; Pushkarev, Alexander B.; Savolainen, Tuomas; Denison University; University of Turku; RAS - P.N. Lebedev Physics Institute; Purdue University; Metsähovi Radio Observatory; Department of Electronics and NanoengineeringCombined polarization imaging of radio jets from Active Galactic Nuclei (AGN) in circular and linear polarization, also known as full Stokes imaging, has the potential to constrain both the magnetic field structure and particle properties of jets. Although only a small fraction of the emission when detected, typically less than a few tenths of a percent but up to as much as a couple of percent in the strongest resolved sources, circular polarization directly probes the magnetic field and particles within the jet itself and is not expected to be modified by external screens. A key to using full Stokes observations to constrain jet properties is obtaining a better understanding of the emission of circular polarization, including its variability and spectrum. We discuss what we have learned so far from parsec scale monitoring observations in the MOJAVE program and from multi-frequency observations of selected AGN.Item Determinantal Generalizations of Instrumental Variables(DE GRUYTER, 2018-03) Weihs, Luca; Robinson, Bill; Dufresne, Emilie; Kenkel, Jennifer; Kubjas, Kaie; McGee, Reginald L., II; Nguyen, Nhan; Robeva, Elina; Drton, Mathias; University of Washington; Denison University; University of Nottingham; University of Utah; Statistics and Mathematical Data Science; Ohio State University; University of Montana; Massachusetts Institute of Technology MIT; Department of Mathematics and Systems AnalysisLinear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the random vector. The graph contains directed edges that represent the linear relationships between components, and bidirected edges that encode unobserved confounding. We study the problem of generic identifiability, that is, whether a generic choice of linear and confounding effects can be uniquely recovered from the joint covariance matrix of the observed random vector. An existing combinatorial criterion for establishing generic identifiability is the half-trek criterion (HTC), which uses the existence of trek systems in the mixed graph to iteratively discover generically invertible linear equation systems in polynomial time. By focusing on edges one at a time, we establish new sufficient and necessary conditions for generic identifiability of edge effects extending those of the HTC. In particular, we show how edge coefficients can be recovered as quotients of subdeterminants of the covariance matrix, which constitutes a determinantal generalization of formulas obtained when using instrumental variables for identification.