An inverse approach to Einstein's equations for non-conducting fluids

We show that a flow (timelike congruence) in any type $B_{1}$ warped product spacetime is uniquely and algorithmically determined by the condition of zero flux. (Though restricted, these spaces include many cases of interest.) The flow is written out explicitly for canonical representations of the spacetimes. With the flow determined, we explore an inverse approach to Einstein's equations where a phenomenological fluid interpretation of a spacetime follows directly from the metric irrespective of the choice of coordinates. This approach is pursued for fluids with anisotropic pressure and shear viscosity. In certain degenerate cases this interpretation is shown to be generically not unique. The framework developed allows the study of exact solutions in any frame without transformations. We provide a number of examples, in various coordinates, including spacetimes with and without unique interpretations. The results and algorithmic procedure developed are implemented as a computer algebra program called GRSource.Comment: 9 pages revtex4. Final form to appear in Phys Rev

Integrating constructive feedback in personalised e-learning

When using e-learning material some students progress readily, others have difficulties. In a traditional classroom the teacher would identify those with difficulties and direct them to additional resources. This support is not easily available within e-learning. A new approach to providing constructive feedback is developed that will enable an e-learning system to identify areas of weakness and provide guidance on further study. The approach is based on the tagging of learning material with appropriate keywords that indicate the contents. Thus if a student performs poorly on an assessment on topic X, there is a need to suggest further study of X and participation in activities related to X such as forums. As well as supporting the learner this type of constructive feedback can also inform other stakeholders. For example a tutor can monitor the progress of a cohort; an instructional designer can monitor the quality of learning objects in facilitating the appropriate knowledge across many learners

Design, Synthesis and Characterization of N-oxide-containing Heterocycles with In vivo Sterilizing Antitubercular Activity

Tuberculosis, caused by the Mycobacterium tuberculosis (Mtb), is the infectious disease responsible for the highest number of deaths worldwide. Herein, 22 new N-oxide- containing compounds were synthesized followed by in vitro and in vivo evaluation of their antitubercular potential against Mtb. Compound 8 was found to be the most promising compound, with MIC90 values of 1.10 and 6.62 μM against active and non- replicating Mtb, respectively. Additionally, we carried out in vivo experiments to confirm the safety and efficacy of compound 8; the compound was found to be orally bioavailable and highly effective leading to the reduction of the number of Mtb to undetected levels in a mouse model of infection. Microarray-based initial studies on the mechanism of action suggest that compound 8 blocks the process of translation. Altogether, these results indicated benzofuroxan derivative 8 to be a promising lead compound for the development of a novel chemical class of antitubercular drugs