Generalised uncertainty relations for angular momentum and spin in quantum geometry

We derive generalised uncertainty relations (GURs) for angular momentum and spin in the smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum, and recovers both the generalised uncertainty principle (GUP) and the extended uncertainty principle (EUP) within a single formalism. In this paper, we investigate the consequences of these results for particles with extrinsic and intrinsic angular momentum, and obtain generalisations of the canonical ${\rm so(3)}$ and ${\rm su(2)}$ algebras. We find that, although ${\rm SO(3)}$ symmetry is preserved on three-dimensional slices of an enlarged phase space, individual subcomponents of the generalised generators obey nontrivial subalgebras. These give rise to GURs for angular momentum while leaving the canonical commutation relations intact except for a simple rescaling, $\hbar \rightarrow \hbar + \beta$. The value of the new parameter, $\beta \simeq \hbar \times 10^{-61}$, is determined by the ratio of the dark energy density to the Planck density. Here, we assume the former to be of the order of the Planck length and the latter to be of the order of the de Sitter momentum $\sim \hbar\sqrt{\Lambda}$, where $\Lambda$ is the cosmological constant. In the smeared-space model, $\hbar$ and $\beta$ are interpreted as the quantisation scales for matter and geometry, respectively, and a quantum state vector is associated with the spatial background. We show that this also gives rise to a rescaled Lie algebra for generalised spin operators, together with associated subalgebras that are analogous to those for orbital angular momentum. Remarkably, consistency of the algebraic structure requires the quantum state associated with a flat background to be fermionic, with spin eigenvalues $\pm \beta/2$. Finally, the modified spin algebra leads to GURs for spin measurements.Comment: 28 pages of main text, plus 12 additional pages split between 4 appendices and 3 pages of references. No figures. Invited contribution to the Universe special issue "Rotation Effects in Relativity", Matteo Ruggiero ed. Published versio

Factorial Invariance of the Brief Symptom Inventory-18 (BSI-18) for Adults of Mexican Descent across Nativity Status, Language Format, and Gender

The cultural equivalence of psychological outcome measures remains a major area of investigation. The current study sought to test the factor structure and factorial invariance of the Brief Symptom Inventory-18 (BSI-18) with a sample of adult individuals of Mexican descent (N = 923) across nativity status (U.S.- vs. foreign-born), language format (English vs. Spanish), and gender. The results show that 1-factor and 3-factor measurement models provided a good fit to the data; however, a single-factor model was deemed more appropriate and parsimonious. Tests of measurement invariance and invariance of factor variances (i.e., structural invariance) indicated at least partial measurement invariance across gender, nativity status, and language format. These findings suggest that the BSI-18 operates in a similar fashion among adults of Mexican descent regardless of nativity status, language format of the survey, and gender. Clinical and practical implications for use of the BSI-18 with Latino populations are discussed

State and Local Prevalence of Firearms Ownership: Measurement, Structure, and Trends

Of the readily computed proxies for the prevalence of gun ownership, one, the percentage of suicides committed with a gun, performs consistently better than the others in cross-section comparisons. It is readily computed for states and counties and has a high degree of validity when tested against survey-based estimates. It also appears valid as a proxy for changes over time in gun prevalence, at least at the regional level. Our analysis of this proxy measure for the period 1979-1997 demonstrates that the geographic structure of gun ownership has been highly stable. That structure is closely linked to rural tradition. There is, however, some tendency toward homogenization over this period, with high-prevalence states trending down and low-prevalence states trending up.

Evolutionary ecological genetics of some neotropical birds

Thesis (Ph.D.) University of Alaska Fairbanks, 2008Most of the current models to explain the diversification of Neotropical birds focus on physical barriers to gene flow. However, for any species the geographic structuring of populations is caused by an interaction between physical barriers to gene flow and a species' propensity to overcome those barriers. The three chapters presented in this dissertation provide three perspectives on this interaction and how it has shaped the diversification of some Neotropical birds. First, the widespread Neotropical lowland forest flycatcher Mionectes oleagineus had three phylogeographic splits across the Andes, resulting in four geographically structured lineages west of the Andes. At least two of these splits post-date Andean uplift, and therefore represent dispersal across the Andes. Coalescent estimates suggest that gene flow occurred with some regularity after the third colonization event several hundred thousand years ago. Secondly, I found that within-population genetic variation in nine codistributed Neotropical landbirds fit a humped distribution, whereby mid-range populations had higher genetic diversity than range-edge populations. This finding is not consistent with a model of increasing genetic diversity with decreasing latitude. Thirdly, I examined variation in genetic differentiation between two populations in 60 codistributed Neotropical landbirds. All species were sampled in southern Belize and central Panama, and I found that the net nucleotide divergence (DA) spanned two orders of magnitude (0.00%--0.085%). Species of frugivores and nectivores had significantly lower DA values than species of insectivores, and in a subsample of 19 species with population-level sampling I found that populations of frugivores and nectivores were significantly more likely to show genetic signals of population expansion than populations of insectivores. These results suggest that foraging ecology plays a fundamentally import role in determining diversification patterns of neotropical birds. These three results should provide important baseline data and new insights into the processes that have led to the neotropical region having the highest avian diversity of all the Earth's biomes.1. Out of Amazonia again and again: episodic crossing of the Andes promotes diversification in a lowland forest flycatcher -- 2. Neotropical birds show a humped distribution of genetic diversity along a latitudinal transect -- 3. Foraging ecology influences population genetic differentiation in sixty codistributed neotropical bird species -- Conclusions