Recent advances in neural variational inference have facilitated efficient training of powerful directed graphical models with continuous latent variables, such as variational autoencoders. However, these models usually assume simple, unimodal priors — such as the multivariate Gaussian distribution — yet many realworld data distributions are highly complex and multi-modal. Examples of complex a...

In this chapter we take statistical models designed for trees and adapt them for split networks, a more general class of mathematical structures. The models we propose provide natural swing-bridges between trees, filling in gaps in the probability simplex. There are many reasons why we might want to do this. Firstly, the split networks provide a graphical representation of phylogenetic uncertai...

This paper examines the issue of face, speaker and bi-modal authentication in mobile environments when there is significant condition mismatch. We introduce this mismatch by enrolling client models on high quality biometric samples obtained on a laptop computer and authenticating them on lower quality biometric samples acquired with a mobile phone. To perform these experiments we develop three ...

Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very “simple” modal logics can be undecidable: We show that there is an undecidable modal logic that can be obtained by restricting the allowed models with a first-order formula in which only universal quantifiers appear.

Classical modal logics generally neither possess the neces-sitation rule nor the K-axiom. Their semantics being in terms of minimal models, several specialisations of these have been given such as augmented minimal models, models with queer worlds or models with inaccessible worlds. In this paper we exhibit exact translations from these families into normal multi-modal logics. Such translations...

The mode of a distribution provides an important summary of data and is often estimated based on some non-parametric kernel density estimator. This article develops a new data analysis tool called modal linear regression in order to explore highdimensional data. Modal linear regression models the conditional mode of a response Y given a set of predictors x as a linear function of x. Modal linea...

The modal age at death is used to study the shifting mortality scenario experienced by low mortality countries. The relations of the life table functions at the modal age are analyzed using mortality models. In the models the modal age increases over time, but there is an asymptotic approximation towards a constant number of deaths and standard deviation from the mode. The findings are compared...

This paper contributes to the model theory of modal logic using bisimulations as the fundamental tool A uniform presentation is given of modal analogues of well known de nability and preservation results from rst order logic These results include algebraic characterizations of modal equivalence and of the modally de nable classes of models the preservation results concern preservation of modal ...

Let C be a smooth, non-hyperelliptic curve over an algebraically closed field of genus g ≥ 4. We show that the projection from the canonical model of C through (g−3) generic points on C is a birational morphism to a plane curve which has only finitely many non-ordinary tangents, that is, flexor bitangents. For smooth, non-hyperelliptic curves of a fixed genus g ≥ 4 over finite fields, we show t...