Reparametrization and the Semiparametric Bernstein-von-Mises Theorem

This paper considers Bayesian inference for the partially linear model. Our approach exploits a parametrization of the regression function that is tailored toward estimating a low-dimensional parameter of interest. The key property of the parametrization is that it generates a Neyman orthogonal moment condition meaning that the low-dimensional parameter is less sensitive to the estimation of nuisance parameters. Our large sample analysis supports this claim. In particular, we derive sufficient conditions under which the posterior for the low-dimensional parameter contracts around the truth at the parametric rate and is asymptotically normal with a variance that coincides with the semiparametric efficiency bound. These conditions allow for a larger class of nuisance parameters relative to the original parametrization of the regression model. Overall, we conclude that a parametrization that embeds Neyman orthogonality can be a useful device for debiasing posterior distributions in semiparametric models

Higher-Dimensional Algebra VII: Groupoidification

Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of "degroupoidification": a systematic process that turns groupoids and spans into vector spaces and linear operators. Then we present three applications of groupoidification. The first is to Feynman diagrams. The Hilbert space for the quantum harmonic oscillator arises naturally from degroupoidifying the groupoid of finite sets and bijections. This allows for a purely combinatorial interpretation of creation and annihilation operators, their commutation relations, field operators, their normal-ordered powers, and finally Feynman diagrams. The second application is to Hecke algebras. We explain how to groupoidify the Hecke algebra associated to a Dynkin diagram whenever the deformation parameter q is a prime power. We illustrate this with the simplest nontrivial example, coming from the A2 Dynkin diagram. In this example we show that the solution of the Yang-Baxter equation built into the A2 Hecke algebra arises naturally from the axioms of projective geometry applied to the projective plane over the finite field with q elements. The third application is to Hall algebras. We explain how the standard construction of the Hall algebra from the category of representations of a simply-laced quiver can be seen as an example of degroupoidification. This in turn provides a new way to categorify - or more precisely, groupoidify - the positive part of the quantum group associated to the quiver.Comment: 67 pages, 14 eps figures; uses undertilde.sty. This is an expanded version of arXiv:0812.486

THE MARKET FOR CITRUS HARVESTING LABOR

Labor and Human Capital,

Marines Need a Few Good Mules

Capt. Walker Mills is a student in the Naval Postgraduate School's Center for Homeland Defense and Security (CHDS) program.The article of record as published may be found at https://www.usni.org/magazines/proceedings/2022/april/marines-need-few-good-mule

Regulation of synaptic development by astrocyte signaling factors and their emerging roles in substance abuse

Astrocytes have critical functions throughout the central nervous system (CNS) and have emerged as regulators of synaptic development and function. With their highly complex morphologies, they are able to interact with thousands of synapses via peripheral astrocytic processes (PAPs), ensheathing neuronal axons and dendrites to form the tripartite synapse. In this way, astrocytes engage in crosstalk with neurons to mediate a variety of CNS processes including the regulation of extracellular matrix protein signaling, formation and maintenance of the blood-brain barrier (BBB), axon growth and guidance, homeostasis of the synaptic microenvironment, synaptogenesis, and the promotion of synaptic diversity. In this review, we discuss several key astrocyte signaling factors (thrombospondins, netrins, apolipoproteins, neuregulins, bone morphogenetic proteins, and neuroligins) in the maintenance and regulation of synapse formation. We also explore how these astrocyte signaling factors are impacted by and contribute to substance abuse, particularly alcohol and cocaine use

Distinguishing between Rooted and Rootless Detachments: A Case Study from the Mormon Mountains of Southeastern Nevada

Rooted detachment faults and detachments beneath rootless slide blocks exhibit many similar structural characteristics. However, while rooted detachments are thought to penetrate into the midcrust and to accommodate significant crustal extension, rootless detachments break to the surface downdip and are not directly involved in such extension. Distinguishing between these two mechanically different kinds of structure is central to the assessment of extension magnitude. Here we examine deformation along the Mormon Peak detachment, a feature that has been cited as an example of both a rooted and a rootless structure. Located in the Mormon Mountains of southeastern Nevada, this detachment has been interpreted as one of three low‐angle normal faults of regional scale that together are thought to have accommodated more than 50 km of Basin and Range extension. For the most part, however, the Mormon Peak detachment is expressed as a series of isolated exposures where Paleozoic rocks are in brittle fault contact with nonmylonitized underlying rocks. Individual blocks contain high‐angle normal faults that terminate downward at their respective detachment surfaces, yielding a geometry common to both modes of emplacement. In order to test between these competing interpretations, we studied deformational characteristics close to the detachment surface, reasoning that a seismogenic fault ought to differ fundamentally from a surficial slide block, particularly if the slide block was emplaced in a single event rather than by protracted or episodic creep. An examination of the contact mapped as the Mormon Peak detachment reveals that the character of deformation is indistinguishable from that of known gravity‐driven slide blocks and is fundamentally different from that associated with seismically cycled faults. Moreover, the orientation of kinematic indicators observed at detachment surfaces is consistently close to the downdip direction, which in many places diverges strongly from the expected direction of movement in the rooted detachment model. We conclude that outcrops of the inferred upper plate of the Mormon Peak detachment represent an assemblage of individual rootless gravity‐driven slide blocks and not the erosional remnants of a formerly contiguous extensional allochthon. If similar misidentifications have been made elsewhere in the Basin and Range Province, total Cenozoic extension may have been significantly overestimated. Implications for the interpretation of extensional geology in general are far‐reaching

Warm-Dense Molecular Gas in the ISM of Starbursts, LIRGs and ULIRGs

The role of star formation in luminous and ultraluminous infrared galaxies is a hotly debated issue: while it is clear that starbursts play a large role in powering the IR luminosity in these galaxies, the relative importance of possible enshrouded AGNs is unknown. It is therefore important to better understand the role of star forming gas in contributing to the infrared luminosity in IR-bright galaxies. The J=3 level of 12CO lies 33K above ground and has a critical density of ~1.5 X 10^4 cm^-3. The 12CO(J=3-2) line serves as an effective tracer for warm-dense molecular gas heated by active star formation. Here we report on 12CO (J=3-2) observations of 17 starburst spirals, LIRGs and ULIRGs which we obtained with the Heinrich Hertz Submillimeter Telescope on Mt. Graham, Arizona. Our main results are the following: 1. We find a nearly linear relation between the infrared luminosity and warm-dense molecular gas such that the infrared luminosity increases as the warm-dense molecular gas to the power 0.92; We interpret this to be roughly consistent with the recent results of Gao & Solomon (2004a,b). 2. We find L_IR/M_H2 ratios ranging from ~10 to ~128 L_sun/M_sun using a standard CO-H2 conversion factor of 3 X 10^20 cm^-2 (K km s^-1)^-1. If this conversion factor is ~an order of magnitude less, as suggested in a recent statistical survey (Yao et al. 2003), then 2-3 of our objects may have significant contributions to the L_IR by dust-enshrouded AGNs.Comment: 15 Pages, 2 figures, Accepted for Publication in Ap