5,962 research outputs found
Household epidemic models with varying infection response
This paper is concerned with SIR (susceptible infected removed)
household epidemic models in which the infection response may be either mild or
severe, with the type of response also affecting the infectiousness of an
individual. Two different models are analysed. In the first model, the
infection status of an individual is predetermined, perhaps due to partial
immunity, and in the second, the infection status of an individual depends on
the infection status of its infector and on whether the individual was infected
by a within- or between-household contact. The first scenario may be modelled
using a multitype household epidemic model, and the second scenario by a model
we denote by the infector-dependent-severity household epidemic model. Large
population results of the two models are derived, with the focus being on the
distribution of the total numbers of mild and severe cases in a typical
household, of any given size, in the event that the epidemic becomes
established. The aim of the paper is to investigate whether it is possible to
determine which of the two underlying explanations is causing the varying
response when given final size household outbreak data containing mild and
severe cases. We conduct numerical studies which show that, given data on
sufficiently many households, it is generally possible to discriminate between
the two models by comparing the Kullback-Leibler divergence for the two fitted
models to these data.Comment: 29 pages; submitted to Journal of Mathematical Biolog
The Equivariant Chow rings of quot schemes
We give a presentation for the (integral) torus-equivariant Chow ring of the
quot scheme, a smooth compactification of the space of rational curves of
degree d in the Grassmannian. For this presentation, we refine Evain's
extension of the method of Goresky, Kottwitz, and MacPherson to express the
torus-equivariant Chow ring in terms of the torus-fixed points and explicit
relations coming from the geometry of families of torus-invariant curves. As
part of this calculation, we give a complete description of the torus-invariant
curves on the quot scheme and show that each family is a product of projective
spaces.Comment: Revised slightly. Clarifed some statements and remove one
straightforward proof. 26 pages, many .eps figure
Auto-Encoding Sequential Monte Carlo
We build on auto-encoding sequential Monte Carlo (AESMC): a method for model
and proposal learning based on maximizing the lower bound to the log marginal
likelihood in a broad family of structured probabilistic models. Our approach
relies on the efficiency of sequential Monte Carlo (SMC) for performing
inference in structured probabilistic models and the flexibility of deep neural
networks to model complex conditional probability distributions. We develop
additional theoretical insights and introduce a new training procedure which
improves both model and proposal learning. We demonstrate that our approach
provides a fast, easy-to-implement and scalable means for simultaneous model
learning and proposal adaptation in deep generative models
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