Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

In the paper we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given.Comment: 27 page

The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

Nonlinear magnetoinductive transmission lines

Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent capacitance. Extended numerical simulations reveal that power transmission along the array is also possible in other than the linear frequency bands, which are located close to the nonlinear resonances of a single nonlinear RLC circuit. Moreover, the effectiveness of power transmission for driving frequencies in the nonlinear bands is comparable to that in the linear band. Power transmission in the nonlinear bands occurs through the linear modes of the system, and it is closely related to the instability of a mode that is localized at the driven site.Comment: 11 pages, 11 figures, submitted to International Journal of Bifurcation and Chao

Asymmetric total synthesis of (+)-virosine a via sequential nucleophilic cyclizations onto an activated formamide

Abstract: The first synthesis of tetracyclic alkaloid virosine A is reported. The natural alkaloid was prepared in only 13 steps, in an enantioenriched form. The azabicyclo[2.2.2]octane core was efficiently assembled using a key Vilsmeier–Haack and Mannich cyclizations sequence performed in one pot

Reviews and syntheses: Effects of permafrost thaw on Arctic aquatic ecosystems

The Arctic is a water-rich region, with freshwater systems covering about 16 % of the northern permafrost landscape. Permafrost thaw creates new freshwater ecosystems, while at the same time modifying the existing lakes, streams, and rivers that are impacted by thaw. Here, we describe the current state of knowledge regarding how permafrost thaw affects lentic (still) and lotic (moving) systems, exploring the effects of both thermokarst (thawing and collapse of ice-rich permafrost) and deepening of the active layer (the surface soil layer that thaws and refreezes each year). Within thermokarst, we further differentiate between the effects of thermokarst in lowland areas vs. that on hillslopes. For almost all of the processes that we explore, the effects of thaw vary regionally, and between lake and stream systems. Much of this regional variation is caused by differences in ground ice content, topography, soil type, and permafrost coverage. Together, these modifying factors determine (i) the degree to which permafrost thaw manifests as thermokarst, (ii) whether thermokarst leads to slumping or the formation of thermokarst lakes, and (iii) the manner in which constituent delivery to freshwater systems is altered by thaw. Differences in thaw-enabled constituent delivery can be considerable, with these modifying factors determining, for example, the balance between delivery of particulate vs. dissolved constituents, and inorganic vs. organic materials. Changes in the composition of thaw-impacted waters, coupled with changes in lake morphology, can strongly affect the physical and optical properties of thermokarst lakes. The ecology of thaw-impacted lakes and streams is also likely to change; these systems have unique microbiological communities, and show differences in respiration, primary production, and food web structure that are largely driven by differences in sediment, dissolved organic matter, and nutrient delivery. The degree to which thaw enables the delivery of dissolved vs. particulate organic matter, coupled with the composition of that organic matter and the morphology and stratification characteristics of recipient systems will play an important role in determining the balance between the release of organic matter as greenhouse gases (CO2and CH4), its burial in sediments, and its loss downstream. The magnitude of thaw impacts on northern aquatic ecosystems is increasing, as is the prevalence of thaw-impacted lakes and streams. There is therefore an urgent need to quantify how permafrost thaw is affecting aquatic ecosystems across diverse Arctic landscapes, and the implications of this change for further climate warming.Additional co-authors: G. MacMillan, M. Rautio, K. M. Walter Anthony, and K. P. Wicklan

Physical activity mediates the relationship between outdoor time and mental health

Both spending time outdoors and participating in physical activity improve mental health. Given that the outdoor environment provides an ideal location for physical activity, better understanding of the relationships among time spent outdoors, physical activity and positive mental health is needed to help guide interventions. The aim was to examine if physical activity moderates or mediates the relationship between outdoor time and positive mental health. Two-hundred-forty-two participants (15 ± 1 years old, 59% girls) from New Brunswick, Canada were included in the current analysis. Youth self-reported time spent outdoors and moderate-to-vigorous physical activity (MVPA) three times between October 2016 and June 2017. Data on their mental health were collected in October 2017. Values of outdoor time and MVPA were averaged across the three time points to represent the exposure and mediator variables, respectively. Mental health, dichotomized as flourishing/not flourishing, was the outcome in the mediation analysis. An interaction term tested if the mediation effect depended on outdoor time. Analyses were undertaken in 2019 using the mediation package in R. In univariate analyses, both MVPA (p < 0.001) and outdoor time (p = 0.05) were positive predictors of flourishing mental health. In mediation analyses, a small indirect mediation (OR: 1.02, 95% CI: 1.01–1.04) and no direct (1.00, 0.98–1.05) effect were noted, suggesting that MVPA mediates the effect of outdoor time on positive mental health. This effect did not vary as a function of outdoor time (interaction: 1.00, 0.99–1.01). Physical activity mediates the relationship between outdoor time and positive mental health. Outdoor time could promote positive mental health among youth through increases in physical activity

The Reelin Receptors Apoer2 and Vldlr Coordinate the Patterning of Purkinje Cell Topography in the Developing Mouse Cerebellum

The adult cerebellar cortex is comprised of reproducible arrays of transverse zones and parasagittal stripes of Purkinje cells. Adult stripes are created through the perinatal rostrocaudal dispersion of embryonic Purkinje cell clusters, triggered by signaling through the Reelin pathway. Reelin is secreted by neurons in the external granular layer and deep cerebellar nuclei and binds to two high affinity extracellular receptors on Purkinje cells-the Very low density lipoprotein receptor (Vldlr) and apolipoprotein E receptor 2 (Apoer2). In mice null for either Reelin or double null for Vldlr and Apoer2, Purkinje cell clusters fail to disperse. Here we report that animals null for either Vldlr or Apoer2 individually, exhibit specific and parasagittally-restricted Purkinje cell ectopias. For example, in mice lacking Apoer2 function immunostaining reveals ectopic Purkinje cells that are largely restricted to the zebrin II-immunonegative population of the anterior vermis. In contrast, mice null for Vldlr have a much larger population of ectopic Purkinje cells that includes members from both the zebrin II-immunonegative and -immunopositive phenotypes. HSP25 immunoreactivity reveals that in Vldlr null animals a large portion of zebrin II-immunopositive ectopic cells are probably destined to become stripes in the central zone (lobules VI–VII). A small population of ectopic zebrin II-immunonegative Purkinje cells is also observed in animals heterozygous for both receptors (Apoer2+/−: Vldlr+/−), but no ectopia is present in mice heterozygous for either receptor alone. These results indicate that Apoer2 and Vldlr coordinate the dispersal of distinct, but overlapping subsets of Purkinje cells in the developing cerebellum

Using Point-of-Choice Prompts to Reduce Sedentary Behavior in Sit-Stand Workstation Users

Introduction: Desk-based office workers are at occupational risk for poor health outcomes from excessive time spent sitting. Sit-stand workstations are used to mitigate sitting, but lack of workstation usage has been observed. Point-of-choice (PoC) prompts offer a complementary strategy for office workers to break up their sitting time.Study purpose: The purpose of this study was to examine the preliminary efficacy, preference, and acceptability of a theory-driven (i.e., 40 unique prompts encompassing social cognitive theory; TD-PoC) and an atheoretical basic reminder PoC prompt intervention (R-PoC) on reducing sedentary behavior in office workers with self-reported low sit-stand workstation usage (≤4 h per day).Methods: In a cross-over design, participants (N = 19, 78.9% female, 39.4 ± 10.7 years of age) completed a 5-days no-prompt control condition followed by a random and counterbalanced assignment to one of the TD-PoC and R-PoC active conditions with a 1-week washout period between. Preliminary efficacy was assessed during work hours with the activPAL micro accelerometer. Preference was assessed prior to each active condition and acceptability was assessed following each active condition via questionnaire.Results: The R-PoC prompt condition significantly decreased sitting time (b[se] = −49.0 [20.8], p = 0.03) and increased standing time (b[se] = 49.8 [19.7], p = 0.02) and displayed a significant increase in sit-stand transitions (b[se] = 2.3 [1.1], p = 0.04), relative to no-prompt control. Both the R-PoC and TD-PoC prompt conditions significantly decreased time spent in prolonged sitting bouts at b[se] = −68.1 [27.8], (p = 0.02), (b[se] = −76.7 [27.1], p = 0.008) relative to no-prompt control. Overall, the TD-PoC prompt condition displayed higher preference and acceptability ratings; however, these differences were not significant (p's &gt; 0.05).Conclusion: While the R-PoC prompt condition was slightly more efficacious than the TD-PoC prompt condition, the TD-PoC prompt condition was rated with higher preference and acceptability scores. Large variations between participants in preference, acceptability, and intervention feedback may indicate need for tailored messaging which may facilitate sustained use in the long-term