Three results on representations of Mackey Lie algebras

I. Penkov and V. Serganova have recently introduced, for any non-degenerate pairing $W\otimes V\to\mathbb C$ of vector spaces, the Lie algebra $\mathfrak{gl}^M=\mathfrak{gl}^M(V,W)$ consisting of endomorphisms of $V$ whose duals preserve $W\subseteq V^*$. In their work, the category $\mathbb{T}_{\mathfrak{gl}^M}$ of $\mathfrak{gl}^M$-modules which are finite length subquotients of the tensor algebra $T(W\otimes V)$ is singled out and studied. In this note we solve three problems posed by these authors concerning the categories $\mathbb{T}_{\mathfrak{gl}^M}$. Denoting by $\mathbb{T}_{V\otimes W}$ the category with the same objects as $\mathbb{T}_{\mathfrak{gl}^M}$ but regarded as $V\otimes W$-modules, we first show that when $W$ and $V$ are paired by dual bases, the functor $\mathbb{T}_{\mathfrak{gl}^M}\to \mathbb{T}_{V\otimes W}$ taking a module to its largest weight submodule with respect to a sufficiently nice Cartan subalgebra of $V\otimes W$ is a tensor equivalence. Secondly, we prove that when $W$ and $V$ are countable-dimensional, the objects of $\mathbb{T}_{\mathrm{End}(V)}$ have finite length as $\mathfrak{gl}^M$-modules. Finally, under the same hypotheses, we compute the socle filtration of a simple object in $\mathbb{T}_{\mathrm{End}(V)}$ as a $\mathfrak{gl}^M$-module.Comment: 9 page

The eruptive history and magmatic evolution of Aluto volcano: new insights into silicic peralkaline volcanism in the Ethiopian rift

The silicic peralkaline volcanoes of the East African Rift are some of the least studied volcanoes on Earth. Here we bring together new constraints from fieldwork, remote sensing, geochronology and geochemistry to present the first detailed account of the eruptive history of Aluto, a restless silicic volcano located in a densely populated section of the Main Ethiopian Rift. Prior to the growth of the Aluto volcanic complex (before 500 ka) the region was characterized by a significant period of fault development and mafic fissure eruptions. The earliest volcanism at Aluto built up a trachytic complex over 8 km in diameter. Aluto then underwent large-volume ignimbrite eruptions at 316 ± 19 ka and 306 ± 12 ka developing a ~ 42 km2 collapse structure. After a hiatus of ~ 250 ka, a phase of post-caldera volcanism initiated at 55 ± 19 ka and the most recent eruption of Aluto has a radiocarbon age of 0.40 ± 0.05 cal. ka BP. During this post-caldera phase highly-evolved peralkaline rhyolite lavas, ignimbrites and pumice fall deposits have erupted from vents across the complex. Geochemical modelling is consistent with rhyolite genesis from protracted fractionation (> 80%) of basalt that is compositionally similar to rift-related basalts found east of the complex. Based on the style and volume of recent eruptions we suggest that silicic eruptions occur at an average rate of 1 per 1000 years, and that future eruptions of Aluto will involve explosive emplacement of localised pumice cones and effusive obsidian coulees of volumes in the range 1–100 × 106 m3

Spin squeezing of high-spin, spatially extended quantum fields

Investigations of spin squeezing in ensembles of quantum particles have been limited primarily to a subspace of spin fluctuations and a single spatial mode in high-spin and spatially extended ensembles. Here, we show that a wider range of spin-squeezing is attainable in ensembles of high-spin atoms, characterized by sub-quantum-limited fluctuations in several independent planes of spin-fluctuation observables. Further, considering the quantum dynamics of an $f=1$ ferromagnetic spinor Bose-Einstein condensate, we demonstrate theoretically that a high degree of spin squeezing is attained in multiple spatial modes of a spatially extended quantum field, and that such squeezing can be extracted from spatially resolved measurements of magnetization and nematicity, i.e.\ the vector and quadrupole magnetic moments, of the quantum gas. Taking into account several experimental limitations, we predict that the variance of the atomic magnetization and nematicity may be reduced as far as 20 dB below the standard quantum limits.Comment: 18 pages, 5 figure

The Future of Nanotechnology Risk Perceptions: An Experimental Investigation of Two Hypotheses

This paper reports the results of an experiment designed to test competing conjectures about the evolution of public attitudes toward nanotechnology. The rational enlightenment hypothesis holds that members of the public will become favorably disposed to nanotechnology as balanced and accurate information about it disseminates. The cultural cognition hypothesis, in contrast, holds that members of the public are likely to polarize along cultural lines when exposed to such information. Using a between-subjects design (N = 1,862), the experiment compared the perceptions of subjects exposed to balanced information on the risks and benefits of nanotechnology to the perceptions of subjects exposed to no information. The results strongly confirmed the cultural polarization hypothesis and furnished no support for the rational enlightenment hypothesis. Data obtained in the experiment also suggested that the observed correlation in the general public between familiarity with nanotechnology and a positive view of it is spurious: familiarity does not cause a favorable view; rather other influences, including individualistic cultural values, incline certain individuals both to form a positive view and to learn about nanotechnology. The paper also discusses the implications of these findings for promoting informed public understandings of nanotechnology

Cultural Cognition of the Risks and Benefits of Nanotechnology

We conducted an experimental public opinion study of the effect of balanced information on nanotechnology risk-benefit perceptions. The study found that subjects did not react in a uniform, much less a uniformly positive manner, but rather polarized along lines consistent with cultural predispositions toward technological risk generally

The Future of Nanotechnology Risk Perceptions: An Experimental Investigation of Two Hypotheses

This paper reports the results of an experiment designed to test competing conjectures about the evolution of public attitudes toward nanotechnology. The rational enlightenment hypothesis holds that members of the public will become favorably disposed to nanotechnology as balanced and accurate information about it disseminates. The cultural cognition hypothesis, in contrast, holds that members of the public are likely to polarize along cultural lines when exposed to such information. Using a between-subjects design (N = 1,862), the experiment compared the perceptions of subjects exposed to balanced information on the risks and benefits of nanotechnology to the perceptions of subjects exposed to no information. The results strongly confirmed the cultural polarization hypothesis and furnished no support for the rational enlightenment hypothesis. Data obtained in the experiment also suggested that the observed correlation in the general public between familiarity with nanotechnology and a positive view of it is spurious: familiarity does not cause a favorable view; rather other influences, including individualistic cultural values, incline certain individuals both to form a positive view and to learn about nanotechnology. The paper also discusses the implications of these findings for promoting informed public understandings of nanotechnology

Cultural Cognition of the Risks and Benefits of Nanotechnology

We conducted an experimental public opinion study of the effect of balanced information on nanotechnology risk-benefit perceptions. The study found that subjects did not react in a uniform, much less a uniformly positive manner, but rather polarized along lines consistent with cultural predispositions toward technological risk generally

Who Fears the HPV Vaccine, Who Doesn\u27t, and Why? An Experimental Study of the Mechanisms of Cultural Cognition

The cultural cognition hypothesis holds that individuals are disposed to form risk perceptions that reflect and reinforce their commitments to contested views of the good society. This paper reports the results of a study that used the controversy over mandatory HPV vaccination to test the cultural cognition hypothesis. Although public health officials have recommended that all girls aged 11 or 12 be vaccinated for HPV - a virus that causes cervical cancer and that is transmitted by sexual contact - political controversy has blocked adoption of mandatory school-enrollment vaccination programs in all but one state. A multi-stage experimental study of a large and diverse sample of American adults (N = 1,500) found evidence that cultural cognition generates disagreement about the risks and benefits of the HPV vaccine. It does so, the experiment determined, through two mechanisms: biased assimilation, and the credibility heuristic. In addition to describing the study, the paper discusses the theoretical and practical implications of these findings

Computing Chevalley bases in small characteristics

Let L be the Lie algebra of a simple algebraic group defined over a field F and let H be a split Cartan subalgebra of L. Then L has a Chevalley basis with respect to H. If the characteristic of F is not 2 or 3, it is known how to find it. In this paper, we treat the remaining two characteristics. To this end, we present a few new methods, implemented in Magma, which vary from the computation of centralisers of one root space in another to the computation of a specific part of the Lie algebra of derivations of $L$.Comment: 22 page

Biased Assimilation, Polarization, and Cultural Credibility: An Experimental Study of Nanotechnology Risk Perceptions

We present the results from the second in a series of ongoing experimental studies of public perceptions of nanotechnology risks. Like the first study, the current one found that members of the public, most of whom know little or nothing about nanotechnology, polarize along cultural lines when exposed to information about it. Extending previous results, the current study also found that cultural polarization of this sort interacts with the perceived cultural identities of policy advocates. Polarization along expected lines grew even more extreme when subjects of diverse cultural outlooks observed an advocate whose values they share advancing an argument they were predisposed to accept, and an advocate whose values they reject advancing an argument they were predisposed to resist. But when those same advocates were assigned the opposite positions, subjects formed perceptions of nanotechnology risks diametrically opposed to the ones normally associated with their own cultural predispositions. Finally, when there was no consistent relationship between the perceived values of advocates and positions taken on nanotechnology risk and benefits, cultural polarization was neutralized. The significance of these findings for promotion of informed public understanding of nanotechnology is discussed