The transverse index theorem for proper cocompact actions of Lie groupoids

Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples the meaning of the index pairing and our index formula.Comment: 29 page

The index of geometric operators on Lie groupoids

We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the "topological side" of the index theorem. This results in index formulae for Lie groupoid analogues of the familiar geometric operators on manifolds such as the signature and Dirac operator expressed in terms of the usual characteristic classes in Lie algebroid cohomology.Comment: 15 page

Transfer learning for radio galaxy classification

In the context of radio galaxy classification, most state-of-the-art neural network algorithms have been focused on single survey data. The question of whether these trained algorithms have cross-survey identification ability or can be adapted to develop classification networks for future surveys is still unclear. One possible solution to address this issue is transfer learning, which re-uses elements of existing machine learning models for different applications. Here we present radio galaxy classification based on a 13-layer Deep Convolutional Neural Network (DCNN) using transfer learning methods between different radio surveys. We find that our machine learning models trained from a random initialization achieve accuracies comparable to those found elsewhere in the literature. When using transfer learning methods, we find that inheriting model weights pre-trained on FIRST images can boost model performance when re-training on lower resolution NVSS data, but that inheriting pre-trained model weights from NVSS and re-training on FIRST data impairs the performance of the classifier. We consider the implication of these results in the context of future radio surveys planned for next-generation radio telescopes such as ASKAP, MeerKAT, and SKA1-MID

Quantization of Whitney functions

We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization of Whitney functions over a closed subset of a symplectic manifold. Under the assumption that the underlying symplectic manifold is analytic and the singular subset subanalytic, we determine that the Hochschild and cyclic homology of the deformed algebra of Whitney functions over the subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we note how an algebraic index theorem for Whitney functions can be derived.Comment: 10 page

Building a diversity featured search system by fusing existing tools

This paper describes our diversity featured retrieval system which are built for the task of ImageCLEFPhoto 2008. Two existing tools are used: Solr and Carrot. We have experimented with different settings of the system to see how the performance changes. The results suggest that the system can indeed increase diversity of the retrieved results and keep the precision about the same

Creating a test collection to evaluate diversity in image retrieval

This paper describes the adaptation of an existing test collection for image retrieval to enable diversity in the results set to be measured. Previous research has shown that a more diverse set of results often satisfies the needs of more users better than standard document rankings. To enable diversity to be quantified, it is necessary to classify images relevant to a given theme to one or more sub-topics or clusters. We describe the challenges in building (as far as we are aware) the first test collection for evaluating diversity in image retrieval. This includes selecting appropriate topics, creating sub-topics, and quantifying the overall effectiveness of a retrieval system. A total of 39 topics were augmented for cluster-based relevance and we also provide an initial analysis of assessor agreement for grouping relevant images into sub-topics or clusters

Communicability across evolving networks

Many natural and technological applications generate time ordered sequences of networks, defined over a fixed set of nodes; for example time-stamped information about ‘who phoned who’ or ‘who came into contact with who’ arise naturally in studies of communication and the spread of disease. Concepts and algorithms for static networks do not immediately carry through to this dynamic setting. For example, suppose A and B interact in the morning, and then B and C interact in the afternoon. Information, or disease, may then pass from A to C, but not vice versa. This subtlety is lost if we simply summarize using the daily aggregate network given by the chain A-B-C. However, using a natural definition of a walk on an evolving network, we show that classic centrality measures from the static setting can be extended in a computationally convenient manner. In particular, communicability indices can be computed to summarize the ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by time’s arrow is captured naturally through the non-mutativity of matrix-matrix multiplication. Illustrative examples are given for both synthetic and real-world communication data sets. We also discuss the use of the new centrality measures for real-time monitoring and prediction