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

Properties and Analysis of Thermally Aged Poly(ethylene oxide)

Recent studies have been performed into the use of polyethylene oxide (PEO) as a model system for observing the fundamental effects of adding micro and nano sized fillers to create polymeric composite systems. Many factors contribute to the successful creation of such a composite system, including dispersion of the filler and treatment of the material during creation. For example, while producing thin films of the materials for testing, high temperatures were used for short periods of time in open air to press the samples into small discs. It is well known that prolonged high temperature exposure can alter the chemistry and structure of polymeric materials and that small variations in the original chemistry, such as longer molecular weights or introduction of fillers, can reduce or possibly accelerate this 'ageing' effect. From these previous investigations many property changes were observed during addition of filler or variation of molecular weight, therefore to accurately attribute these changes to a cause the thermal ageing of the material should be observed. This investigation looks at the same 3 molecular weight PEO systems as those used in the previous investigations and analyses them for their vulnerability to thermal ageing. One thermally aged sample is then taken and tested alongside an unaged sample to observe the effects that the process has on the properties. This includes rheology in solution, differential scanning calorimetry (DSC), AC electrical breakdown, dielectric spectroscopy and Fourier transform infra-red (FTIR). By observing the property changes of aged samples it is possible to better understand the thermal ageing process occurring and possibly a way to reduce the effect, along with considering the effect with regard to the behaviour of the previously tested composite samples

Hip Versus Square: 1960s Advertising and Clothing Industries and the Counterculture

This research paper explores the use of Countercultural themes and images by the advertising and menswear industries in the 1960s. Historians have traditionally held that the Counterculture and American business during this era were fierce opponents of one another. More recent scholarship, however, suggest that the advertising industry of the 1960s co-opted and marketed Countercultural themes, such as ‘youth’ and ‘rebellion,’ and images like natural looking make-up and free-flowing clothing. The co-optation of these themes and images, historians have charged, commercialized the Countercultural revolution and ultimately led to its demise. This paper examines the ways in which the Counterculture influenced the advertising and menswear industries in the 1960s and questions whether the use of Countercultural themes and images was co-optation or emulation of the youth movement

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 reviewe

Sub-wavelength surface IR imaging of soft-condensed matter

Outlined here is a technique for sub-wavelength infrared surface imaging performed using a phase matched optical parametric oscillator laser and an atomic force microscope as the detection mechanism. The technique uses a novel surface excitation illumination approach to perform simultaneously chemical mapping and AFM topography imaging with an image resolution of 200 nm. This method was demonstrated by imaging polystyrene micro-structures

Vaccinia virus protein A46R targets multiple Toll-like-interleukin-1 receptor adaptors and contributes to virulence

Viral immune evasion strategies target key aspects of the host antiviral response. Recently, it has been recognized that Toll-like receptors (TLRs) have a role in innate defense against viruses. Here, we define the function of the vaccinia virus (VV) protein A46R and show it inhibits intracellular signalling by a range of TLRs. TLR signalling is triggered by homotypic interactions between the Toll-like-interleukin-1 resistance (TIR) domains of the receptors and adaptor molecules. A46R contains a TIR domain and is the only viral TIR domain-containing protein identified to date. We demonstrate that A46R targets the host TIR adaptors myeloid differentiation factor 88 (MyD88), MyD88 adaptor-like, TIR domain-containing adaptor inducing IFN-beta (TRIF), and the TRIF-related adaptor molecule and thereby interferes with downstream activation of mitogen-activated protein kinases and nuclear factor kappaB. TRIF mediates activation of interferon (IFN) regulatory factor 3 (IRF3) and induction of IFN-beta by TLR3 and TLR4 and suppresses VV replication in macrophages. Here, A46R disrupted TRIF-induced IRF3 activation and induction of the TRIF-dependent gene regulated on activation, normal T cell expressed and secreted. Furthermore, we show that A46R is functionally distinct from another described VV TLR inhibitor, A52R. Importantly, VV lacking the A46R gene was attenuated in a murine intranasal model, demonstrating the importance of A46R for VV virulence

Ten steps to conducting a large, multi-site, longitudinal investigation of language and reading in young children

Purpose: This paper describes methodological procedures involving execution of a large-scale, multi-site longitudinal study of language and reading comprehension in young children. Researchers in the Language and Reading Research Consortium (LARRC) developed and implemented these procedures to ensure data integrity across multiple sites, schools, and grades. Specifically, major features of our approach, as well as lessons learned, are summarized in 10 steps essential for successful completion of a large-scale longitudinal investigation in early grades. Method: Over 5 years, children in preschool through third grade were administered a battery of 35 higher- and lower-level language, listening, and reading comprehension measures (RCM). Data were collected from children, their teachers, and their parents/guardians at four sites across the United States. Substantial and rigorous effort was aimed toward maintaining consistency in processes and data management across sites for children, assessors, and staff. Conclusion: With appropriate planning, flexibility, and communication strategies in place, LARRC developed and executed a successful multi-site longitudinal research study that will meet its goal of investigating the contribution and role of language skills in the development of children’s listening and reading comprehension. Through dissemination of our design strategies and lessons learned, research teams embarking on similar endeavors can be better equipped to anticipate the challenges

Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

Anomalous magnetic phase in an undistorted pyrochlore oxide Cd2Os2O7 induced by geometrical frustration

We report on the muon spin rotation/relaxation study of a pyrochlore oxide, Cd2Os2O7, which exhibits a metal-insulator (MI) transition at T_{MI}~225 K without structural phase transition. It reveals strong spin fluctuation (>10^8/s) below the MI transition, suggesting a predominant role of geometrical spin frustration amongst Os^{5+} ions. Meanwhile, upon further cooling, a static spin density wave discontinuously develops below T_{SDW}~150 K. These observations strongly suggest the occurrence of an anomalous magnetic transition and associated change in the local spin dynamics in undistorted pyrochlore antiferromagnet.Comment: 5 pages, 4 figure