We represent knowledge by using probability distributions of mixed continuous and discrete variables. In the case of complete knowledge of the joint distribution of all items, one can compute arbitrary conditional distributions, which may be used for prediction. However, in many cases only some marginal distributions, inverse probabilities, or moments are known. Under these conditions, a princi...

of the PhD thesis

In this work, we make an exhaustive study of the properties of the Green’s function related to the periodic boundary value problem Lax ≡ x′′ + a(t) x = 0, x(0) = x(T ), x′(0) = x′(T ), with a sign-changing potential a(t). Moreover, we obtain new explicit criteria that ensures that the maximum or anti-maximum principle holds for this equation. The given criteria complement previous results in th...

The Maximum Entropy method is a practical technique for generating intensity skymaps from Compton-telescope data. The application of the method to COMPTEL data for point sources and large-scale emission is described. New developments in the method are illustrated.

We give an interpretation of the Maxi­ mum Entropy (MaxEnt) Principle in game­ theoretic terms. Based on this interpretation, we make a formal distinction between differ­ ent ways of applying Maximum Entropy dis­ tributions. MaxEnt has frequently been crit­ icized on the grounds that it leads to highly representation dependent results. Our dis­ tinction allows us to avoid this problem in many c...

Theorem 1.1 originates from the excess estimate of Abresch-Gromoll(c.f. Proposition 2.3 of [1]). The main ingredient of the proof is an application of maximum principle for subharmonic functions, and the existence of a poled function L such that ∆L ≥ 1. In our case, both maximum principle (Proposition 2.28 of [16]) and the existence of L(Lemma 2.36 of [16]) are known. For the convenience of rea...

We consider the problem of inference on one of the two parameters of a probability distribution when we have some prior information on a nuisance parameter. When a prior probability distribution on this nuisance parameter is given, the marginal distribution is the classical tool to account for it. If the prior distribution is not given, but we have partial knowledge such as a fixed number of mo...

We start this talk posing the question, is there any physical principle that can serve as a selection principle in biology too? One of the first undertakings in this direction, conducted by Prigogine and Wiame [1] noticed correctly that biological processes are irreversible and as such should be described within irreversible thermodynamics. Since irreversible processes are characterized by entr...