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http://hdl.handle.net/2440/299
2018-03-17T19:57:00ZNew relations between G₂ geometries in dimensions 5 and 7
http://hdl.handle.net/2440/111065
Title: New relations between G₂ geometries in dimensions 5 and 7
Author: Leistner, T.; Nurowski, P.; Sagerschnig, K.
Abstract: There are two well-known parabolic split G₂ geometries in dimension 5, (2, 3, 5) distributions and G₂ contact structures. Here we link these two geometries with yet another G₂ related contact structure, which lives on a 7-manifold. More precisely, we present a natural geometric construction that associates to a (2, 3, 5) distribution a 7-dimensional bundle endowed with a canonical Lie contact structure. We further study the relation between the canonical normal Cartan connections associated with the two structures and we show that the Cartan holonomy of the induced Lie contact structure reduces to G₂. This motivates the study of the curved orbit decomposition associated with a G₂ reduced Lie contact structure on a 7-manifold. It is shown that, provided an additional curvature condition is satisfied, in a neighborhood of each point in the open curved orbit the structure descends to a (2, 3, 5) distribution on a local leaf space. The closed orbit carries an induced G₂ contact structure.2017-01-01T00:00:00ZA fixed point formula and Harish-Chandra's character formula
http://hdl.handle.net/2440/111025
Title: A fixed point formula and Harish-Chandra's character formula
Author: Hochs, P.; Wang, H.
Abstract: The main result in this paper is a fixed point formula for equivariant indices of elliptic differential operators, for proper actions by connected semisimple Lie groups on possibly noncompact manifolds, with compact quotients. For compact groups and manifolds, this reduces to the Atiyah-Segal-Singer fixed point formula. Other special cases include an index theorem by Connes and Moscovici for homogeneous spaces, and an earlier index theorem by the second author, both in cases where the group acting is connected and semisimple. As an application of this fixed point formula, we give a new proof of Harish-Chandra's character formula for discrete series representations.2018-01-01T00:00:00ZInference of epidemiological parameters from household stratified data
http://hdl.handle.net/2440/110912
Title: Inference of epidemiological parameters from household stratified data
Author: Walker, J.; Ross, J.; Black, A.
Abstract: We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters-governing within-household transmission, recovery, and between-household transmission-from data of the day upon which each individual became infectious and the household in which each infection occurred, as might be available from First Few Hundred studies. Each method is a form of Bayesian Markov Chain Monte Carlo that allows us to calculate a joint posterior distribution for all parameters and hence the household reproduction number and the early growth rate of the epidemic. The first method performs exact Bayesian inference using a standard data-augmentation approach; the second performs approximate Bayesian inference based on a likelihood approximation derived from branching processes. These methods are compared for computational efficiency and posteriors from each are compared. The branching process is shown to be a good approximation and remains computationally efficient as the amount of data is increased.2017-01-01T00:00:00ZOn the calculation of normal modes of a coupled ice-shelf/sub-ice-shelf cavity system
http://hdl.handle.net/2440/110227
Title: On the calculation of normal modes of a coupled ice-shelf/sub-ice-shelf cavity system
Author: Meylan, M.; Bennetts, L.; Hosking, R.; Catt, E.
Abstract: A corrected solution method is presented for a mathematical model of wave motions in a coupled ice-shelf/sub-iceshelf water-cavity system. The method is used to calculate the periods of the system’s normal modes, and the longest periods are shown to be significantly larger than those calculated using an existing method containing errors. Highly accurate approximations of the normal-mode periods are obtained for a model involving a single non-spectral physical parameter - the shelf/cavity length.2017-01-01T00:00:00Z