In this paper we characterise the distributions of the number of predecessors and of the number of successors of given set of vertices, A, in the random mapping model, T D̂ n , (see [10]) with exchangeable in-degree sequence (D̂1, D̂2, ..., D̂n). We show that the exact formulas for these distributions and their expected values can be given in terms of the distributions of simple functions of the in...

We consider random mappings from an n–element set into itself with constraints on coalescence as introduced by Arney and Bender. A local limit theorem for the distribution of the number of predecessors of a random point in such a mapping is presented by using a generating function approach and singularity analysis.

We solve the dynamic Predecessor Problem with high probability (whp) in constant time, using only n bits of memory, for any constant δ > 0. The input keys are random wrt a wider class of the well studied and practically important class of (f1, f2)-smooth distributions introduced in [3]. It achieves O(1) whp amortized time. Its worst-case time is O( √ logn log logn ). Also, we prove whp O(log lo...

We study social learning by boundedly rational agents. Agents take a decision in sequence, after observing their predecessors and a private signal. They are unable to make perfect inferences from their predecessors’ decisions: they only understand the relation between the aggregate distribution of actions and the state of nature and make their inferences accordingly. We show that, in a discrete...

Alterations in the morphology of permanent teeth following trauma to their predecessors is a challenging task for diagnosis and it may require advanced imaging techniques. Newer imaging modalities have replaced the conventional radiological procedures, as they allow 3D reconstruction images and views which are free of superimposition. Cone Beam CT (CBCT) offers a three-dimensional view, which t...

In contrast to other mutations, duplication leaves an easily detectable trace: a repetition. Therefore it is a convenient starting point for computing a phylogenetic network. Basically, all squares must be detected to compute all possible direct predecessors. To find all the possible, not necessarily direct predecessors, this process must be iterated for all the resulting strings. We show how t...