Comparing and characterizing some constructions of canonical bases from Coxeter systems

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan-Lusztig basis of $\mathcal{H}$ is a canonical basis. Lusztig and Vogan have defined a representation of a modified Iwahori-Hecke algebra on the free $\mathbb{Z}[v,v^{-1}]$-module generated by the set of twisted involutions in $W$, and shown that this module has a unique pre-canonical structure satisfying a certain compatibility condition, which admits its own canonical basis which can be viewed as a generalization of the Kazhdan-Lusztig basis. One can modify the parameters defining Lusztig and Vogan's module to obtain other pre-canonical structures, each of which admits a unique canonical basis indexed by twisted involutions. We classify all of the pre-canonical structures which arise in this fashion, and explain the relationships between their resulting canonical bases. While some of these canonical bases are related in a trivial fashion to Lusztig and Vogan's construction, others appear to have no simple relation to what has been previously studied. Along the way, we also clarify the differences between Webster's notion of a canonical basis and the related concepts of an IC basis and a $P$-kernel.Comment: 32 pages; v2: additional discussion of relationship between canonical bases, IC bases, and P-kernels; v3: minor revisions; v4: a few corrections and updated references, final versio

Sticklebacks show consistent prey-share hierarchies within but not between patchy and sequential prey distributions

This work was supported by the School of Biology’s Experimental Research Project (BL4201) program, (module BL4201: Experimental Research Project) at the University of St Andrews, UK.When animals compete, hierarchies can emerge. If the outcome of competition under different conditions is dependent upon different sets of attributes, then we may expect to see hierarchies that are domain-specific, rather than domain general. We tested this idea by comparing prey share hierarchies within shoals of sticklebacks Gasterosteus aculeatus as they foraged for patchily-distributed or for drifting prey. We found that prey share was correlated across pairs of patch- and pairs of drift-foraging trials, but not between the two conditions, suggesting that separate repeatable but independent prey share hierarchies arise for each for each type of prey distribution. We discuss possible underlying mechanisms and ecological implications of this finding.PostprintPeer reviewe

What future for Chinese labour and transnational solidarity?

In this conclusion we argue that class struggle is central to the future of Chinese workers and the improvement of their situation. Technological upgrading in itself will not automatically result in better working conditions. Moreover, we point out that Chinese workers have a number of old and new sources of power to draw on. What is, however, most problematic in this respect is the role of the ACFTU, operating as an official mediator rather than an independent trade union, and the resulting lack of associational power. Hence, informal labour NGOs have an important role to play in supporting social justice for China’s workers

An examination of chemistry and transport processes in the tropical lower stratosphere using observations of long-lived and short-lived compounds obtained during STRAT and POLARIS

A suite of compounds with a wide range of photochemical lifetimes (3 months to several decades) was measured in the tropical and midlatitude upper troposphere and lower stratosphere during the Stratospheric Tracers of Atmospheric Transport (STRAT) experiment (fall 1995 and winter, summer, and fall 1996) and the Photochemistry of Ozone Loss in the Arctic Region in Summer (POLARIS) deployment in late summer 1997. These species include various chlorofluorocarbons, hydrocarbons, halocarbons, and halons measured in whole air samples and CO measured in situ by tunable diode laser spectroscopy. Mixing ratio profiles of long-lived species in the tropical lower stratosphere are examined using a one-dimensional (1-D) photochemical model that includes entrainment from the extratropical stratosphere and is constrained by measured concentrations of OH. Profiles of tracers found using the 1-D model agree well with all the observed tropical profiles for an entrainment time scale of 8.5-4+6 months, independent of altitude between potential temperatures of 370 and 500 K. The tropical profile of CO is used to show that the annually averaged ascent rate profile, on the basis of a set of radiative heating calculations, is accurate to approximately ±44%, a smaller uncertainty than found by considering the uncertainties in the radiative model and its inputs. Tropical profiles of ethane and C2Cl4 reveal that the concentration of Cl is higher than expected on the basis of photochemical model simulations using standard gas phase kinetics and established relationships between total inorganic chlorine and CFC-11. Our observations suggest that short-lived organic chlorinated compounds and HCl carried across the tropical tropopause may provide an important source of inorganic chlorine to the tropical lower stratosphere that has been largely unappreciated in previous studies. The entrainment timescale found here is considerably less than the value found by a similar study that focused on observations obtained in the lower stratosphere during 1994. Several possible explanations for this difference are discussed. Copyright 1999 by the American Geophysical Union

Efficient preparation and detection of microwave dressed-state qubits and qutrits with trapped ions

We demonstrate a method for preparing and detecting all eigenstates of a three-level microwave dressed system with a single trapped ion. The method significantly reduces the experimental complexity of gate operations with dressed-state qubits, as well as allowing all three of the dressed states to be prepared and detected, thereby providing access to a qutrit that is well protected from magnetic field noise. In addition, we demonstrate individual addressing of the clock transitions in two ions using a strong static magnetic field gradient, showing that our method can be used to prepare and detect microwave dressed states in a string of ions when performing multi-ion quantum operations with microwave and radio frequency fields. The individual addressability of clock transitions could also allow for the control of pairwise interaction strengths between arbitrary ions in a string using lasers

Aerial detection of waste disposal sites near Donna Reservoir in south Texas.

Aerial color-infrared (CIR) photography was used to detect and catalog unauthorized solid waste disposal sites around Donna Reservoir in the Lower Rio Grande Valley (LRGV) of southern Texas. Qualitative visual evaluation of the positive transparencies showed 25 possible disposal sites randomly scattered throughout the study area, located in sites ranging from bare soil to grass and mixed brush/woods. These sites were transposed onto a computer-generated area map for ground survey confirmation and use by organizations planning to clean-up the sites. Ground-truthing was used to identify waste contents at each site and to estimate waste volumes and areas covered. Unauthorized solid waste sites were verified in 23 of the 25 locations. Two sites contained only broken concrete and asphalt being utilized as erosional fill material. The ground survey identified ten solid waste sites missed on the aerial photos. These sites were missed due to their small size (\u3c 2 [m.sup.2]) and because they were covered by lodging guinea grass (Panicum maximum) or giant reed (Arundo donax). The addition of these missed sites to the other 25 locations hindered the overall accuracy of the aerial photographic survey (71.4%)

Differential Effects of MitoVitE, α-Tocopherol and Trolox on Oxidative Stress, Mitochondrial Function and Inflammatory Signalling Pathways in Endothelial Cells Cultured under Conditions Mimicking Sepsis

Funding: This research was funded by The British Journal of Anaesthesia/Royal College of Anaesthetists (PhD studentship to Beverley Minter). Acknowledgments: We are very grateful to Professor M.P. Murphy, MRC Mitochondrial Biology Unit, Wellcome Trust/MRC Building, Hills Road, Cambridge, UK for the generous gift of MitoVitE used in all the experiments, without which this work would not have been possible.Peer reviewedPublisher PD

Isolation of Fecal Coliform Bacteria from the American Alligator (Alligator mississippiensis) in South Carolina

2008 S.C. Water Resources Conference - Addressing Water Challenges Facing the State and Regio