In probability theory, Bayesian statistics, artificial intelligence and database theory the minimum cross-entropy principle is often used to estimate a distribution with a given set P of marginal distributions under the proportionality assumption with respect to a given "prior'' distribution q. Such an estimation problem admits a solution if and only if there exists an extension of P that is dominated by q. In this paper we consider the case that q is not given explicitly, but is specified as the maximum-entropy extension of an auxiliary set Q of distributions. There are three problems that naturally arise: (1) the existence of an extension of a distribution set (such as P and Q), (2) the existence of an extension of P that is dominated by the maximum entropy extension of Q, (3) the numeric computation of the minimum cross-entropy extension of P with respect to the maximum entropy extension of Q. In the spirit of a divide-and-conquer approach, we prove that, for each of the three above-mentioned problems, the global solution can be easily obtained by combining the solutions to subproblems defined at node level of a suitable tree.
Bats occupy a variety of natural and artificial diurnal roosts. These environments offer several advantages for bats, among which we highlight the relative climatic stability, darkness, and protection from predators. The aim of this study was to identify and describe the use of tree hollows as natural diurnal roosts by Molossops temminckii, Molossus rufus, Artibeus planirostris and Sturnira lilium in southeastern Brazil. In the first one, we sought to describe the physical characteristics of shelters. In the second objective, we determined the number of individuals in the colonies and, we described and classified the posture adopted by bats within cavities. In the
third objective, we seek to relate the physical characteristics of refuges with the foraging behavior and diet of bat species. Moreover, we also discussed the advantages and disadvantages that tree cavities may confer for bats, in the context of approximation of opportunistic predators. We found four colonies, one of each species, which roosted within tree trunk cavities. In general, the colonies were small, with less than 10 individuals of both sexes. Usually the molossids left the roost at dusk, while phyllostomids left later, around three hours after dusk. Individuals of the first three species were recaptured while foraging near the roosts. We believe (through observations) that the location in the landscape and the physical characteristics (dimensions of access to the cavities and height from the ground) of shelters used by bats, depend exclusively on the morphology, foraging behaviour and diet of each species of bat. Furthermore, this
study contributes to an increase of knowledge about the natural history of Neotropical bats, which can provide relevant information for conservation.