Converging Divergences?

Converging Hands or Converging Minds?

Interlocutors sometimes repeat each other’s representational hand gestures. We investigated if this is a case of direct mimicry of form, or whether perceiving a gesture gives rise to a semantic representation, which subsequently informs gesture production. For this we used an interactive route description task, in which a confederate’s gestures indicated the route in either the vertical or the ...

NBIC, THE CONVERGING TECHNOLOGIES

Infinite-dimensional Log-Determinant divergences II: Alpha-Beta divergences

This work presents a parametrized family of divergences, namely Alpha-Beta LogDeterminant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infinite-dimensional setting. The family of Alpha-Beta Log-Det divergences is highl...

On Overlapping Divergences

Using set-theoretic considerations, we show that the forest formula for overlapping divergences comes from the Hopf algebra of rooted trees. Motivation and Introduction The process of renormalization is governed by the forest formula, as derived for example in [1]. The underlying combinatorics is directly related to the Hopf algebra structure of rooted trees. This is evident in the case of Feyn...

Normalized information-based divergences

This paper is devoted to the mathematical study of some divergences based on the mutual information well-suited to categorical random vectors. These divergences are generalizations of the " entropy distance " and " information distance ". Their main characteristic is that they combine a complexity term and the mutual information. We then introduce the notion of (normalized) information-based di...