Variational auto-encoders (VAEs) are a popular and powerful deep generative model. Previous works on VAEs have assumed a factorised likelihood model, whereby the output uncertainty of each pixel is assumed to be independent. This approximation is clearly limited as demonstrated by observing a residual image from a VAE reconstruction, which often possess a high level of structure. This paper dem...

Residuals have been studied for various forms of rewriting and residual systems have been defined to capture residuals in an abstract setting. In this article we study residuals in orthogonal Pattern Rewriting Systems (PRSs). First, the rewrite relation is defined by means of a higher-order rewriting logic, and proof terms are defined that witness reductions. Then, we have the formal machinery ...

This thesis studies American options in an incomplete financial market and in continuous time. It is composed of two parts. In the first part we study a stochastic optimization problem in which a robust convex loss functional is minimized in a space of stochastic integrals. This problem arises when the seller of an American option aims to control the shortfall risk by using a partial hedge. We ...

Kline and Barker (1950) reported the existence and some properties of an apparently new unidentified growth factor (B.R. factor) required by Butyribacterium rettgeri for growth on lactate as the fermentable carbon source. Certain similarities in properties were given as the basis for a postulated relationship of the B.R. factor to other unidentified growth or metabolically active substances. Th...

Collman, J. P. & Buckingham, D. A. (1963). J. Amer. chem. Soc. 85, 3039. Dixon, H. B. F. (1964). Biochem. J. 90, 2c. Dixon, H. B. F. & Weitkamp, L. R. (1962). Biochem. J. 84, 462. Dobbie, H. & Kermack, W. 0. (1955). Biochem. J. 59, 257. Errera, M. & Greenstein, J. P. (1947). Arch. Biochem. 15, 445. Fleming, L. W. & Crosbie, G. W. (1960). Biochim. biophys. Acta, 43, 139. Friedemann, T. E. & Haug...