This paper describes novel methods for estimating piecewise homogeneous Poisson elds based on minimum description length (MDL) criteria. By adopting a coding-theoretic approach, our methods are able to adapt to the the observed eld in an unsupervised manner. We present a parsing scheme based on xed multiscale trees (binary, for 1D, quad, for 2D) and an adaptive recursive partioning algorithm, b...

This paper presents a simple and elementary proof of Butcher's theorem on the order conditions of Runge-Kutta methods. It is based on a recursive definition of rooted trees and avoids combinatorial tools such as labelings andFà a di Bruno's formula. This strictly recursive approach can easily and elegantly be implemented using modern computer algebra systems like Mathematica for automatically g...

Logic programming, a class of programming languages based on first-order logic, provides simple and efficient tools for goal-oriented proof-search. Logic programming supports recursive computations, and some logic programs resemble the inductive or coinductive definitions written in functional programming languages. In this paper, we give a coalgebraic semantics to logic programming. We show th...

We study the problem of synthesizing recursive Datalog programs from examples. We propose a constraint-based synthesis approach that uses an smt solver to efficiently navigate the space of Datalog programs and their corresponding derivation trees. We demonstrate our technique’s ability to synthesize a range of graph-manipulating recursive programs from a small number of examples. In addition, w...

We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant characteristics of those graphs: the diameter, degree distribution, and clustering parameter. The graphs have also an interesting recursive property, and general...

We call a tree parameter additive if it can be determined recursively as the sum of the parameter values of all branches, plus a certain toll function. In this paper, we prove central limit theorems for very general toll functions, provided that they are bounded and small on average. Simply generated families of trees are considered as well as Pólya trees, recursive trees and binary search tree...

Gelfond-Lifschitz [7] introduced the concept of a stable model M of a Predicate Logic Program P . Here we show that, up to a recursive 1-1 coding, the set of all stable models of finite Predicate Logic Programs and the Π1 classes (equivalently, the set of all infinite branches of recursive trees) coincide (Theorems 4.1 and 5.1). Typical consequences: 1) there are finite Predicate Logic Programs...

The construction of classiication trees is nearly always top-down, locally optimal and data-driven. Such recursive designs are often globally ineecient, for instance in terms of the mean depth necessary to reach a given classiication rate. We consider statistical models for which exact global optimization is feasible, and thereby demonstrate that recursive and global procedures may result in ve...

The most frequently occurring problem in image retrieval is nd the similar image which in general is nding the nearest neighbor From the literature it is well known that k d trees are e cient methods of nding nearest neighbors in high dimensional spaces In this paper we survey the relevant k d tree literature and adapt the most promising solution to the problem of image retrieval by nding the b...