Cohomology of the adjoint of Hopf algebras

A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of the super line. As applications, solutions to the YBE are given and quandle cocycles are constructed from groupoid cocycles.Comment: 23 pages, 22 figures, cool stuf

Cohomology of Frobenius Algebras and the Yang-Baxter Equation

A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on deformation theory. Concrete computations are provided for key examples. Skein theoretic constructions give rise to solutions to the Yang-Baxter equation using multiplications and comultiplications of Frobenius algebras, and 2-cocycles are used to obtain deformations of R-matrices thus obtained

Remote sensing and modeling of mosquito abundance and habitats in Coastal Virginia, USA

The increase in mosquito populations following extreme weather events poses a major threat to humans because of mosquitoes’ ability to carry disease-causing pathogens, particularly in low-lying, poorly drained coastal plains vulnerable to tropical cyclones. In areas with reservoirs of disease, mosquito abundance information can help to identify the areas at higher risk of disease transmission. Using a Geographic Information System (GIS), mosquito abundance is predicted across the City of Chesapeake, Virginia. The mosquito abundance model uses mosquito light trap counts, a habitat suitability model, and dynamic environmental variables (temperature and precipitation) to predict the abundance of the species Culiseta melanura, as well as the combined abundance of the ephemeral species, Aedes vexans and Psorophora columbiae, for the year 2003. Remote sensing techniques were used to quantify environmental variables for a potential habitat suitability index for the mosquito species. The goal of this study was to produce an abundance model that could guide risk assessment, surveillance, and potential disease transmission. Results highlight the utility of integrating field surveillance, remote sensing for synoptic landscape habitat distributions, and dynamic environmental data for predicting mosquito vector abundance across low-lying coastal plains. Limitations of mosquito trapping and multi-source geospatial environmental data are highlighted for future spatial modeling of disease transmission risk

Vanadyl complexes with dansyl-labelled dipicolinic acid ligands: synthesis, phosphatase inhibition activity and cellular uptake studies

Vanadium complexes have been previously utilised as potent inhibitors of cysteine based phosphatases (CBPs). Herein, we present the synthesis and characterisation of two new fluorescently labelled vanadyl complexes (14 and 15) with bridged di-picolinic acid ligand. These compounds differ significantly from previous vanadyl complexes with phosphatase inhibition properties in that the metal-chelating part is a single tetradentate unit, which should afford greater stability and scope for synthetic elaboration then the earlier complexes. These new complexes inhibit a selection of cysteine based phosphatases (CBPs) in the nM range with some selectivity. Fluorescence spectroscopic studies (including fluorescence anisotropy) were carried out to demonstrate that the complexes are not simply acting as vanadyl delivery vehicles but they interact with the proteins. Finally, we present preliminary fluorescence microscopy studies to demonstrate that the complexes are cell permeable and localise throughout the cytoplasm of NIH3T3 cells

Monitoring mosquitoes in urban Dar es Salaam: Evaluation of resting boxes, window exit traps, CDC light traps, Ifakara tent traps and human landing catches

Ifakara tent traps (ITT) are currently the only sufficiently sensitive, safe, affordable and practical method for routine monitoring host-seeking mosquito densities in Dar es Salaam. However, it is not clear whether ITT catches represent indoors or outdoors biting densities. ITT do not yield samples of resting, fed mosquitoes for blood meal analysis. Outdoors mosquito sampling methods, namely human landing catch (HLC), ITT (Design B) and resting boxes (RB) were conducted in parallel with indoors sampling using HLC, Centers for Disease Control and Prevention miniature light traps (LT) and RB as well as window exit traps (WET) in urban Dar es Salaam, rotating them thirteen times through a 3 × 3 Latin Square experimental design replicated in four blocks of three houses. This study was conducted between 6th May and 2rd July 2008, during the main rainy season when mosquito biting densities reach their annual peak. The mean sensitivities of indoor RB, outdoor RB, WET, LT, ITT (Design B) and HLC placed outdoor relative to HLC placed indoor were 0.01, 0.005, 0.036, 0.052, 0.374, and 1.294 for Anopheles gambiae sensu lato (96% An. gambiae s.s and 4% An. arabiensis), respectively, and 0.017, 0.053, 0.125, 0.423, 0.372 and 1.140 for Culex spp, respectively. The ITT (Design B) catches correlated slightly better to indoor HLC (r(2) = 0.619, P < 0.001, r(2) = 0.231, P = 0.001) than outdoor HLC (r(2) = 0.423, P < 0.001, r(2) = 0.228, P = 0.001) for An. gambiae s.l. and Culex spp respectively but the taxonomic composition of mosquitoes caught by ITT does not match those of the indoor HLC (χ(2) = 607.408, degrees of freedom = 18, P < 0.001). The proportion of An. gambiae caught indoors was unaffected by the use of an LLIN in that house. The RB, WET and LT are poor methods for surveillance of malaria vector densities in urban Dar es Salaam compared to ITT and HLC but there is still uncertainty over whether the ITT best reflects indoor or outdoor biting densities. The particular LLIN evaluated here failed to significantly reduce house entry by An. gambiae s.l. suggesting a negligible repellence effect

Cohomology of . . . self-distributivity

We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provide solutions of the Yang–Baxter equation, and, conversely, solutions of the Yang–Baxter equation can be used to construct self-distributive operations in certain categories. Moreover, we present a cohomology theory that encompasses both Lie algebra and quandle cohomologies, is analogous to Hochschild cohomology, and can be used to study deformations of these self-distributive structures. All of the work here is informed via diagrammatic computations

Cohomology of Frobenius Algebras and the Yang-Baxter Equation

Dedicated to the memory of Xiao-Song Lin A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions in analogy with Hochschild cohomology of bialgebras based on deformation theory. Concrete computations are provided for key examples. Skein theoretic constructions give rise to solutions to the Yang-Baxter equation using multiplications and comultiplications of Frobenius algebras, and 2-cocycles are used to obtain deformations of R-matrices thus obtained.