At ISIT I will give a talk entitled Information Theory on Spectral Sets. The results strongly indicate that information theory is only possible in mathematical structures that can be represented on Jordan algebras. There are 5 basic types of Jordan algebras, and density matrices with complex entries is the most important in the sense that quantum information theory is normally represented on this type of algebra. I guess that many results from quantum information theory can be generalized to Jordan algebras. This work follows up on a paper entitled Divergence and Sufficiency for Convex Optimization that I recently published in Entropy.
I published a long paper with various bounds on tail probabilities in terms of the signed log-likelihood function in Kybernetika. It has just been awarded the best paper in Kybernetika 2016. Although the inequalities are quite sharp I am sure even sharper inequalities of these types can be obtained. I think the results can be generalized to cover all exponential families with simple variance functions. Even more general inequalities may exist, but at the moment I don't know how to attack the general problem.
In the following paper arXiv:1601.04255 we obtain a lower bound on the rate of convergence in the law of small numbers, that seem to be asymptotically tight.
Lattice theory of causation I an working on a
larger project where I want to see to what extend
concepts related to cause and effect can be studied
using lattice theory. In 2015 I presented some
derived results related to Lattices with
non-Shannon Inequalities. In January and
February 2016 I was visiting University of Hawai'i where
several lattice experts are situated and now I try to put all the results together.
EventsI was visiting University of Hawai'i Jan.-Feb. 2016.
I will gave a lecture series on Bregman divergences. The first will be held Thursday 21/1 in Holmes Hall. See flyer for detailed information.
Quantum Lunch 21/12 2016.
Entropy Power Inequalities at AIM, San José May 1st-5th. 2017.
ISIT 2017 June. Takes place in Aachen in Germany. I will give a presentation entitled Quantum Information on Spectral sets.