Eigenvalues of Products of Unitary Matrices and Lagrangian Involutions

This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.Comment: 35 pages, 2 figures, to appear in Topolog

Inter-filament Attractions Narrow the Length Distribution of Actin Filaments

We show that the exponential length distribution that is typical of actin filaments under physiological conditions dramatically narrows in the presence of (i) crosslinker proteins (ii) polyvalent counterions or (iii) depletion mediated attractions. A simple theoretical model shows that in equilibrium, short-range attractions enhance the tendency of filaments to align parallel to each other, eventually leading to an increase in the average filament length and a decrease in the relative width of the distribution of filament lengths.Comment: 5 pages, 4 figure

Topochemical Manipulation of Layered Perovskites

Topochemical strategies, techniques that allow one to effectively manipulate the structures of nonmolecular solids once a crystal lattice is established, are effective in the low temperature (\u3c 500 °C) modification of solid state structures, allowing the preparation of nonmolecular compounds not accessible by standard synthetic routes. Some of the techniques, ion exchange, intercalation/deintercalation, have proven to be excellent synthetic methods for preserving specific frameworks. The combination of these techniques can allow one to create a multistep approach that can be used to design new compounds with interesting properties. As an expansion to the field of topotactic reactions, a multistep approach was developed towards the synthesis of the new compounds (A xM0.5Cly)LaNb2O7 (where A = Rb, Cs; M = Fe, Ni; x ≈ 1.5;y ≈ 1) at temperatures below 400oC. The first reaction step involved the ion exchange of the host materials (ALaNb2O7, A = Rb, Cs) to form the products M0.5LaNb2O7 (where M = Fe, Ni), a structure open to further chemistry. The next step involved reductive intercalation with Rb or Cs metal to form the air sensitive mixed-valence products with the nominal compositions, A1.5M0.5LaNb2O7. The last step involved the oxidative intercalation of chlorine using chlorine gas to obtain the final compounds. This multistep approach is a design to form mix-metal halide layers, specifically those with divalent cations, within layered perovskites, opening the doors to compounds that can have interesting properties. This reaction series was also applied to the tantalate layered oxides, leading to the formation of the new compound Ni 0.5LaTa2O7 through ion exchange. The further multistep topochemical manipulation of this new compound was not successful and was indicative of the difference in chemical behavior of the tantalates versus the niobates. We have also investigated the oxidative intercalation of halogens into a series of Ruddlesden-Popper (R-P) ruthenate oxides with the formula Ae n+1RunO3n+1 (Ae = Ca, Sr; n = 1, 2, 3) using several sources of fluorine, chlorine, and bromine. A new method was developed to intercalate chlorine into layered systems; this new approach avoids the use of chlorine gas which is highly toxic. The new phase Sr3Ru2O7Cl0.7 was synthesized by the new method and further topotactic manipulations were explored. The chemistry was not limited to the n = 2 phase but was also applied to the n = 3 phase, Sr4Ru3O10

Iago the Moor Killer: The Geo-Political Context Behind Shakespeare\u27s Othello

Shakespeare’s Othello is often viewed as an example of seventeenth century Renaissance binaries. Critics make distinctions when reading the play between hero and villain, Moors and Europeans, and between civilization and barbarity. These definitions are all complicated by Iago’s presence in the play. Iago, whose name implies he is actually a Spaniard, frames the play in a geo-political context. Because of Iago’s presence, Othello provides a picture of England’s position in the seventeenth century geo-political climate. Shakespeare is giving his English audience a particular political message

Survey on Non-Timber Forest Products in Bauchi South Senatorial Districts, Bauchi State, Nigeria

A survey on Non-Timber Forest Products (NTFPs) in Bauchi South Senatorial Districts (Alkaleri, Bauchi, Tafawa Balewa and Toro Areas) of Bauchi State, Nigeria was reviewed in 2013. The aim was to identify the common tree species in the areas, the plant parts used (roots, barks, stems, leaves, fruits, etc) and to identify their uses, methods of used and end produce. Data were collected through the use of structured questionnaires, supplemented with verbal interview and observation. A total of 300 Questionnaires were randomly administered in the study local government areas. All data collected from the survey areas were subjected to simple descriptive statistics. A total of 58 useful species of plant origins was recorded as having various applications in the lives of the rural dwellers in the area. The result showed that NTFPs in Bauchi South Senatorial Districts of Bauchi State has varying use categories such as Medicine (33.0%), Food/fruits (16.0%), Oil & Spice/condiments (8.0%), Carving, crafting & implement (12.8%), Environmental protection/amelioration(10.8), Proteins/bush meats (7.6%) while Other uses[Fodder, tannin, rope, gum, utensil, dye, etc. (11.8%)]. The study also revealed that, the people in the area collect these resources frequently and sell them as a means of earning a living. There is need for forest policy to include the production of NTFPs and local agro-forestry schemes should be developed within national forests to allow for the production of bush meats, rattan, bamboo, traditional medicines, honey and other forest food.Key Words: NTFPs Non-timber forest products, Bauchi South Senatorial Districts, Bauchi, Tafawa Balewa, Toro, Alkaleri, Area

The Evolution of Corryong/Nariel Creek since European Settlement: Implications for On-going Management Prioritisation

Geomorphological stability is a useful starting point to inform river management priorities, as it is critical to other river health parameters such as ecology and water quality. A key debate in channel stability is the relationship between climate and human activity. Corryong Creek is an ideal setting to study the interaction between climate and anthropogenic changes on channel evolution as it has experienced significant levels of both. Catastrophic floods have been induced by high rainfall, the floodplain has been completely cleared, the riparian zone is almost entirely invaded by willows, and every reach of the channel has experienced some form of channel modification. The impacts of both climatic and anthropogenic factors are visible in our channel change data, although at different spatiotemporal scales. Higher flows during La Niña resulted in channel widening while lower flows during El Niño resulted in channel narrowing. In addition, land clearing had caused the river to evolve into a higher-energy, straighter channel, while spatially variable and temporally irregular factors such as river engineering, willow density and stock trampling tended to intensify erosion on a reach scale. As our analysis shows that periodic increases in erosion during La Niña are expected, the local community needs to first accept and adapt to some level of channel erosion in order to avoid catastrophic damage during floods. As the second priority, since the reversibility of these factors are limited, erosion risk can be mitigated through strengthening willow management, limiting river engineering, practicing bushfire management, and fencing the riparian zone

Validation of a commercial antibody to detect endogenous human nicastrin by immunoblot

Nicastrin (NCSTN) is a transmembrane glycoprotein that is part of the gamma-secretase complex. Gamma-secretase is a protease complex that cleaves type-I single-pass transmembrane proteins. There are many potential substrates for this complex, including NOTCH receptors and amyloid precursor proteins (APP). There are a number of commercial antibodies to nicastrin, but they do not agree on expected peptide size. We confirmed the specificity of a C-terminal binding rabbit anti-human antibody from Sigma-Aldrich (#N1660) using wildtype HEK293 cells and HEK293 cells deleted for nicastrin. The wildtype cells showed a prominent band at approximately 110 kDa. We confirmed this larger than expected sized was due to glycosylation by treating the lysate with peptide-N-glycosidase F (PNGase F), which reduced the band to less than 75 kDa. These data suggest that this polyclonal is specific for nicastrin and can detect endogenous levels of protein