FEDERAL CIRCUIT SECOND AMENDMENT DEVELOPMENTS 2018

This Article provides a summary of federal circuit court cases decided in 2018. By the end of 2018, every circuit except for the Eighth has adopted a Two-Part Test for Second Amendment cases. In Part One, the court determines whether the challenged law burdens the Second Amendment right. If so, the court applies heightened scrutiny in Part Two. Courts in Second Amendment cases almost always apply intermediate scrutiny, but strict scrutiny and categorical invalidation are also available. The Two-Part Test is detailed in our article, The Federal Circuits’ Second Amendment Doctrines.[1] That article reviews every federal circuit Second Amendment case after District of Columbia v. Heller (2008), up to approximately August 2016. [1] David B. Kopel & Joseph G.S. Greenlee, The Federal Circuits Second Amendment Doctrines, 61 St. Louis U. L.J. 193 (2017) (cited in Pena v. Lindley, 898 F.3d 969, 1004 (9th Cir. 2018) (Bybee, J., dissenting))

Picture-Hanging Puzzles

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.Comment: 18 pages, 8 figures, 11 puzzles. Journal version of FUN 2012 pape

Structure and Magnetization of Two-Dimensional Vortex Arrays in the Presence of Periodic Pinning

Ground-state properties of a two-dimensional system of superconducting vortices in the presence of a periodic array of strong pinning centers are studied analytically and numerically. The ground states of the vortex system at different filling ratios are found using a simple geometric argument under the assumption that the penetration depth is much smaller than the spacing of the pin lattice. The results of this calculation are confirmed by numerical studies in which simulated annealing is used to locate the ground states of the vortex system. The zero-temperature equilibrium magnetization as a function of the applied field is obtained by numerically calculating the energy of the ground state for a large number of closely spaced filling ratios. The results show interesting commensurability effects such as plateaus in the B-H diagram at simple fractional filling ratios.Comment: 12 pages, 19 figures, submitted for publicatio

Combined Impairments in Vision, Hearing and Cognition are Associated with Greater Levels of Functional and Communication Difficulties Than Cognitive Impairment Alone: Analysis of interRAI Data for Home Care and Long-Term Care Recipients in Ontario

Objectives: The objective of the current study was to understand the added effects of having a sensory impairment (vision and/or hearing impairment) in combination with cognitive impairment with respect to health-related outcomes among older adults (65+ years old) receiving home care or residing in a long-term care (LTC) facility in Ontario, Canada. Methods: Cross-sectional analyses were conducted using existing data collected with one of two interRAI assessments, one for home care (n = 291,824) and one for LTC (n = 110,578). Items in the assessments were used to identify clients with single sensory impairments (e.g., vision only [VI], hearing only [HI]), dual sensory impairment (DSI; i.e., vision and hearing) and those with cognitive impairment (CI). We defined seven mutually exclusive groups based on the presence of single or combined impairments. Results: The rate of people having all three impairments (i.e., CI+DSI) was 21.3% in home care and 29.2% in LTC. Across the seven groups, individuals with all three impairments were the most likely to report loneliness, to have a reduction in social engagement, and to experience reduced independence in their activities of daily living (ADLs) and instrumental ADLs (IADLs). Communication challenges were highly prevalent in this group, at 38.0% in home care and 49.2% in LTC. In both care settings, communication difficulties were more common in the CI+DSI group versus the CI-alone group. Conclusions: The presence of combined sensory and cognitive impairments is high among older adults in these two care settings and having all three impairments is associated with higher rates of negative outcomes than the rates for those having CI alone. There is a rising imperative for all health care professionals to recognize the potential presence of hearing, vision and cognitive impairments in those for whom they provide care, to ensure that basic screening occurs and to use those results to inform care plans

Metric Properties of the Fuzzy Sphere

The fuzzy sphere, as a quantum metric space, carries a sequence of metrics which we describe in detail. We show that the Bloch coherent states, with these spectral distances, form a sequence of metric spaces that converge to the round sphere in the high-spin limit.Comment: Slightly shortened version, no major changes, two new references, version to appear on Letters in Mathematical Physic

Quantum gauge models without classical Higgs mechanism

We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. The BRS formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is explained without recourse to a Higgs(-Englert-Brout-Guralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories.Comment: 20 pages in two-column EPJC format, shortened version accepted for publication. For more details, consult version

Toward an internally consistent astronomical distance scale

Accurate astronomical distance determination is crucial for all fields in astrophysics, from Galactic to cosmological scales. Despite, or perhaps because of, significant efforts to determine accurate distances, using a wide range of methods, tracers, and techniques, an internally consistent astronomical distance framework has not yet been established. We review current efforts to homogenize the Local Group's distance framework, with particular emphasis on the potential of RR Lyrae stars as distance indicators, and attempt to extend this in an internally consistent manner to cosmological distances. Calibration based on Type Ia supernovae and distance determinations based on gravitational lensing represent particularly promising approaches. We provide a positive outlook to improvements to the status quo expected from future surveys, missions, and facilities. Astronomical distance determination has clearly reached maturity and near-consistency.Comment: Review article, 59 pages (4 figures); Space Science Reviews, in press (chapter 8 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age

Design of Experiments for Screening

The aim of this paper is to review methods of designing screening experiments, ranging from designs originally developed for physical experiments to those especially tailored to experiments on numerical models. The strengths and weaknesses of the various designs for screening variables in numerical models are discussed. First, classes of factorial designs for experiments to estimate main effects and interactions through a linear statistical model are described, specifically regular and nonregular fractional factorial designs, supersaturated designs and systematic fractional replicate designs. Generic issues of aliasing, bias and cancellation of factorial effects are discussed. Second, group screening experiments are considered including factorial group screening and sequential bifurcation. Third, random sampling plans are discussed including Latin hypercube sampling and sampling plans to estimate elementary effects. Fourth, a variety of modelling methods commonly employed with screening designs are briefly described. Finally, a novel study demonstrates six screening methods on two frequently-used exemplars, and their performances are compared