Lattice congruences of the weak order

We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric description of the poset of join-irreducibles of the congruence lattice of the poset of regions in terms of certain polyhedral decompositions of the hyperplanes. For a finite Coxeter system (W,S) and a subset K of S, let \eta_K:w \mapsto w_K be the projection onto the parabolic subgroup W_K. We show that the fibers of \eta_K constitute the smallest lattice congruence with 1\equiv s for every s\in(S-K). We give an algorithm for determining the congruence lattice of the weak order for any finite Coxeter group and for a finite Coxeter group of type A or B we define a directed graph on subsets or signed subsets such that the transitive closure of the directed graph is the poset of join-irreducibles of the congruence lattice of the weak order.Comment: 26 pages, 4 figure

Polyhedral models for generalized associahedra via Coxeter elements

Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A. Zelevinsky associated to each finite type root system a simple convex polytope called \emph{generalized associahedron}. They provided an explicit realization of this polytope associated with a bipartite orientation of the corresponding Dynkin diagram. In the first part of this paper, using the parametrization of cluster variables by their $g$-vectors explicitly computed by S.-W. Yang and A. Zelevinsky, we generalize the original construction to any orientation. In the second part we show that our construction agrees with the one given by C. Hohlweg, C. Lange, and H. Thomas in the setup of Cambrian fans developed by N. Reading and D. Speyer.Comment: 31 pages, 2 figures. Changelog: 20111106: initial version 20120403: fixed errors in figures 20120827: revised versio

Enumeration of bigrassmannian permutations below a permutation in Bruhat order

In theory of Coxeter groups, bigrassmannian elements are well known as elements which have precisely one left descent and precisely one right descent. In this article, we prove formulas on enumeration of bigrassmannian permutations weakly below a permutation in Bruhat order in the symmetric groups. For the proof, we use equivalent characterizations of bigrassmannian permutations by Lascoux-Schutzenberger and Reading.Comment: 7 pages

Evidence of micro-continent entrainment during crustal accretion

Peer reviewedPublisher PD

The Road to Researcher: The Development of Research Self-Efficacy in Higher Education Scholars

Aim/Purpose: Understanding how students develop a sense of efficacy as researchers can pro-vide faculty members in higher education doctoral programs insight into how to be more effective teachers and mentors, necessitating discipline-specific research on how graduate programs are and can be fostering students’ research self-efficacy (RSE). Thus, the purpose of this study was to explore how doctoral pro-grams and early research experiences contribute to the development of RSE in higher education scholars. Background: Participants identified elements of the formal and “hidden” curriculumt pro-moted and inhibited RSE development. Methodology: We employed multiple case study analysis of 17 individual early career scholars in higher education and student affairs. Contribution: Findings indicate that the development of RSE is complex, but that Bandura’s four main sources of efficacy are a useful way to understand the types of experi-ences that students are and should be having to promote RSE. Our findings also highlight the importance of the research training environment in RSE develop-ment. Findings: We found that the formal curriculum of participants’ doctoral programs – their research methods coursework and the process of writing their dissertations – were important facilitators of their RSE development. However, we also found that the “hidden curriculum” – the availability of extracurricular research oppor-tunities, faculty and peer mentoring, and the overall research culture of the doctoral programs – were influential in participants’ development. Recommendations for Practitioners: Our findings point to a number of implications for higher education graduate programs seeking to improve students’ RSE. First, with regard to coursework, our findings point to the importance of recognizing the negative experiences students may bring with them to their doctoral programs, particularly related to quantita-tive methods, and of finding ways to help them see quantitative methods in dif-ferent ways than they have before. Second, our findings suggest important impli-cations for how faculty members as teachers, advisors, and mentors can think about providing feedback. Finally, our findings suggest the importance of under-standing the “hidden curriculum,” and how faculty members can influence stu-dents’ experiences outside of coursework and dissertations

Temporal Dynamics of Group Size and Sexual Segregation in Ibex

Group size is an important variable describing behavioral ecology of animals. A variety of factors such as habitat characteristics, life history, spatio-temporal resource dynamics, population density, predation risk, competition with kin, and social learning often determine group size in large mammals. We studied temporal dynamics of group size in Siberian ibex (Capra sibirica) in a protected area in Mongolia. We measured monthly and yearly variations in typical group size and used the sexual segregation and aggregation statistic to assess sexual segregation. Ibex formed the largest groups in November and smallest groups in July. However, group sizes did not significantly differ between the sexes. There was marked sexual segregation during the summer months and within all years segregation increased with temperature. We show that grouping behavior is a complex phenomenon and is probably determined by a combination of factors, such as species’ life history, habitat and environmental characteristics, and behavioral strategy against predation risk

Insights into the structure and dynamics of the upper mantle beneath Bass Strait, southeast Australia, using shear wave splitting

© 2019 Elsevier B.V. We investigate the structure of the upper mantle using teleseismic shear wave splitting measurements obtained at 32 broadband seismic stations located in Bass Strait and the surrounding region of southeast Australia. Our dataset includes ∼366 individual splitting measurements from SKS and SKKS phases. The pattern of seismic anisotropy from shear wave splitting analysis beneath the study area is complex and does not always correlate with magnetic lineaments or current N-S absolute plate motion. In the eastern Lachlan Fold Belt, fast shear waves are polarized parallel to the structural trend (∼N25E). Further south, fast shear wave polarization directions trend on average N25–75E from the Western Tasmania Terrane through Bass Strait to southern Victoria, which is consistent with the presence of an exotic Precambrian microcontinent in this region as previously postulated. Stations located on and around the Neogene-Quaternary Newer Volcanics Province in southern Victoria display sizeable delay times (∼2.7 s). These values are among the largest in the world and hence require either an unusually large intrinsic anisotropy frozen within the lithosphere, or a contribution from both the lithospheric and asthenospheric mantle. In the Eastern Tasmania Terrane, nearly all observed fast directions are approximately NW-SE. Although part of our data set strongly favours anisotropy originating from “fabric” frozen in the lithospheric mantle, a contribution from the asthenospheric flow related to the present day plate motion is also required to explain the observed splitting parameters. We suggest that deviation of asthenospheric mantle flow around lithospheric roots could be occurring, and so variations in anisotropy related to mantle flow may be expected. Alternatively, the pattern of fast polarisation orientations observed around Bass Strait may be consistent with radial mantle flow associated with a plume linked to the recently discovered Cosgrove volcanic track. However, it is difficult to characterise the relative contributions to the observed splitting from the lithospheric vs. asthenospheric upper mantle due to poor backazimuthal coverage of the data

Structure of the crust and upper mantle beneath Bass Strait, southeast Australia, from teleseismic body wave tomography

© 2019 Elsevier B.V. We present new constraints on the lithospheric velocity structure of Bass Strait and the adjoining landmasses of mainland Australia and Tasmania in order to better constrain their geological and tectonic relationship. This is achieved by performing teleseismic tomography using data from fifteen deployments of WOMBAT and BASS transportable arrays, which span southeastern Australia. The starting model for the teleseismic tomography includes crustal velocity structure constrained by surface waves extracted from ambient seismic noise data and a Moho surface and broad-scale variations in 3-D upper mantle velocity structure from the Australian seismological reference Earth model (AuSREM). As a consequence, we produce a model with a high level of detail in both the crust and upper mantle. Our new results strengthen the argument for a low velocity upper mantle anomaly that extends down to ~150 km depth directly beneath the Newer Volcanics Province in Victoria, which is likely related to recent intra-plate volcanism. Beneath Bass Strait, which is thought to host the entrained VanDieland microcontinent, upper mantle velocities are low relative to those typically found beneath Precambrian continental crust; it is possible that failed rifting in Bass Strait during the Cretaceous, opening of the Tasman Sea, extension of VanDieland during Rodinian break-up and recent plume activity in the past 5 Ma may have altered the seismic character of this region. The data nevertheless suggest: (1) the velocity structure of the VanDieland microcontinent lacks continuity within its lithosphere; (2) the Moyston Fault defines an area of strong velocity transition at the boundary between the Cambrian Delamerian Orogen and the Cambrian-Carboniferous Lachlan Orogen; and (3) there is a rapid decrease in mantle velocity inboard of the east coast of Australia, which is consistent with substantial thinning of the lithosphere towards the passive margin

Crustal structure of southeast Australia from teleseismic receiver functions

Abstract. In an effort to improve our understanding of the seismic character of the crust beneath southeast Australia and how it relates to the tectonic evolution of the region, we analyse teleseismic earthquakes recorded by 24 temporary and 8 permanent broadband stations using the receiver function method. Due to the proximity of the temporary stations to Bass Strait, only 13 of these stations yielded usable receiver functions, whereas seven permanent stations produced receiver functions for subsequent analysis. Crustal thickness, bulk seismic velocity properties, and internal crustal structure of the southern Tasmanides – an assemblage of Palaeozoic accretionary orogens that occupy eastern Australia – are constrained by H–κ stacking and receiver function inversion, which point to the following: a ∼ 39.0 km thick crust; an intermediate–high Vp/Vs ratio (∼ 1.70–1.76), relative to ak135; and a broad (> 10 km) crust–mantle transition beneath the Lachlan Fold Belt. These results are interpreted to represent magmatic underplating of mafic materials at the base of the crust. a complex crustal structure beneath VanDieland, a putative Precambrian continental fragment embedded in the southernmost Tasmanides, that features strong variability in the crustal thickness (23–37 km) and Vp/Vs ratio (1.65–193), the latter of which likely represents compositional variability and the presence of melt. The complex origins of VanDieland, which comprises multiple continental ribbons, coupled with recent failed rifting and intraplate volcanism, likely contributes to these observations. stations located in the East Tasmania Terrane and eastern Bass Strait (ETT + EB) collectively indicate a crust of uniform thickness (31–32 km), which clearly distinguishes it from VanDieland to the west. Moho depths are also compared with the continent-wide AusMoho model in southeast Australia and are shown to be largely consistent, except in regions where AusMoho has few constraints (e.g. Flinders Island). A joint interpretation of the new results with ambient noise, teleseismic tomography, and teleseismic shear wave splitting anisotropy helps provide new insight into the way that the crust has been shaped by recent events, including failed rifting during the break-up of Australia and Antarctica and recent intraplate volcanism.PhD study of lead author has been jointly funded by Abubakar TafawaBalewa University (ATBU

Improvement in immune parameters and human immunodeficiency virus-1 viral response in individuals treated with 16α-bromoepiandrosterone (HE2000)

ABSTRACTA randomised, double-blind, placebo-controlled study examined the safety, tolerance, immunological effect and anti-human immunodeficiency virus (HIV) activity of sub-cutaneously administered HE2000 (16α-bromoepiandrosterone) as monotherapy in treatment-naïve patients with HIV-1. Twenty-four patients received five sequential daily doses of 50 or 100 mg of HE2000 or placebo every 6 weeks for up to three courses, and were followed thereafter for 3 months. HE2000 was safe, with transient injection site reactions being the main side-effect. Peripheral blood samples, collected serially, were analysed for changes in immune cell phenotypes. Significant increases were observed in the numbers of circulating dendritic cells, early activated (CD69+CD25–) CD8 T-cells and T-NK cells after administration of 50-mg doses of HE2000 (p <0.05). Gene expression in peripheral blood mononuclear cells was analysed by real-time RT-PCR. Before treatment, HIV-1-infected patients had significantly elevated transcripts for a number of inflammatory mediators (p <0.012). After 50 mg or 100 mg HE2000, but not after placebo, there were significant sustained decreases in IL-1β, TNF-α, IL-6 and Cox-2 transcripts (p <0.05). There were no significant differences in CD4 cell numbers, although patients receiving 50-mg doses demonstrated a significant decrease in viral load (– 0.6 log; p <0.01). Anti-HIV-1 T-cell responses were analysed serially using GAG-peptides to stimulate cytoplasmic IFN-γ responses. After three courses, the 50-mg dose group demonstrated a significant increase in CD8 T-cell response against two distinct GAG peptide pools (p <0.03). These findings suggest that immune-based therapies may be able to impact viral load by decreasing inflammation and/or stimulating CD8 T-cells