At IGAIA IV and MaxEnt 2016 I presented results that 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. The new results can be found in arXiv:1607.02259 and some related results can be found in Proper Scoring and Sufficiency and in arXiv: 1601.07593.
I finished a long paper with various bounds on tail probabilities in terms of the signed log-likelihood function arXiv: 1601.05179 . 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. Last summer I presented some
derived results related to Lattices with
non-Shannon Inequalities. In January and
February I was visiting University of Hawai'i where
several lattice experts are situated and now I try to put all the results together.
EventsQuantum Lunch Talk at Math. Dept. Univ. Copenhagen 6/1 2016 I will give a talk entitled "Determinism and Causality. Which aspects are shared between classical physics and quantum physics?"
I will be visiting University of Hawai'i Jan.-Feb. 2016.
I will give a lecture series on Bregman divergences. The first will be held Thursday 21/1 in Holmes Hall. See flyer for detailed information.
IGAIA IV I have been invited to give a talk at the conference Information Geometry and its Applications IV, to be held on June 1-17, 2016 at Liblice Castle, Czech Republic. The title of my talk will be announced later.
MaxEnt 2016 Bayesian Inference and Maximum Entropy Methods in Science and Engineering. 10-15 July, Gent Belgium.
ISIT 2016 10-15/7 2016, Barcelona, Spain.
Beyond IID 4 18-22/7 2016, Barcelona, Spain. This is a satellite conference to ISIT.
WITMSE 2016 19-21/9 Helsinki.