Supersymmetric AdS3\mathrm{AdS}_3 supergravity backgrounds and holography

We analyse the conditions for $\mathrm{AdS}_3 \times \mathcal{M}_7$ backgrounds with pure NS-NS flux to be supersymmetric. We find that a necessary condition is that $\mathcal{M}_7$ is a $\mathrm{U}(1)$-fibration over a balanced manifold. We subsequently classify all $\mathcal{N}=(2,2)$ solutions where $\mathcal{M}_7$ satisfies the stronger condition of being a $\mathrm{U}(1)$-fibration over a Kahler manifold. We compute the BPS spectrum of all the backgrounds in this classification. We assign a natural dual CFT to the backgrounds and confirm that the BPS spectra agree, thus providing evidence in favour of the proposal.Comment: 39 pages; v2: minor corrections and references added; v3: section 2 shortened, final version as published in JHE

Doing It Again: Repeating Methodology from Published Literature to Learn Field Biology

Repeatability underpins a basic assumption in science which students must learn in order to evaluate others’ research findings as well as to communicate the results of their own research. By attempting to repeat the methods of published studies, students learn the importance of clear written communication, while at the same time developing research skills. I describe three examples of published field studies that can be used as the basis for course exercises on the repeatability of methodology, as well as field sampling techniques, all grounded in the overall topic of environmental change. Two of the exercises returned students to the exact location of the past research that they had previously read from the primary literature, making it possible to clarify the difference between reproducibility and repeatability in field-based research. When student-collected data differed from published results, students explored, through both post-project discussions and written work, factors that could explain this variation, including methodology, ecological succession, and climate change. Assessments and student comments on course evaluations showed that these exercises have a positive impact on students’ communication skills and engagement with the scientific process

Analog hardware for delta-backpropagation neural networks

This is a fully parallel analog backpropagation learning processor which comprises a plurality of programmable resistive memory elements serving as synapse connections whose values can be weighted during learning with buffer amplifiers, summing circuits, and sample-and-hold circuits arranged in a plurality of neuron layers in accordance with delta-backpropagation algorithms modified so as to control weight changes due to circuit drift

Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats

We show how the Tutte polynomial of a matroid $M$ can be computed from its condensed configuration, which is a statistic of its lattice of cyclic flats. The results imply that the Tutte polynomial of $M$ is already determined by the abstract lattice of its cyclic flats together with their cardinalities and ranks. They furthermore generalize a similiar statement for perfect matroid designs due to Mphako and help to understand families of matroids with identical Tutte polynomial as constructed by Ken Shoda.Comment: New version published in: Electronic Journal Of Combinatorics Volume 21, Issue 3 (2014) http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i3p4

Analog hardware for learning neural networks

This is a recurrent or feedforward analog neural network processor having a multi-level neuron array and a synaptic matrix for storing weighted analog values of synaptic connection strengths which is characterized by temporarily changing one connection strength at a time to determine its effect on system output relative to the desired target. That connection strength is then adjusted based on the effect, whereby the processor is taught the correct response to training examples connection by connection