We show that the minimal cardinality of a dense subset of the measure algebra is the same as the minimal cardinality of a base of the ideal of Lebesgue measure zero subsets of the real line. 0. Introduction. Let (F, <) be a given partial ordering. A subset D ç P is called dense if for any p g F there exists d g D such that d < p. A subset D is called upward dense if D is dense in (F, > ). Let A...

In this chapter, we present a survey of algorithms for dense subgraph discovery. The problem of dense subgraph discovery is closely related to clustering though the two problems also have a number of differences. For example, the problem of clustering is largely concerned with that of finding a fixed partition in the data, whereas the problem of dense subgraph discovery defines these dense comp...

We study the set of strictly temporally periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but are not spatially periodic. This set turns out to be residual for equicontinuous surjective cellular automata, dense for almost equicontinuous surjective cellular automata, while it is empty for the positively expa...

Many image registration algorithms need to interpolate dense deformations from a small set of sparse deformations or correspondences established on the landmark points. Previous methods generally use a certain pre-defined deformation model, e.g., B-Spline or Thin-Plate Spline, for dense deformation interpolation, which may affect the final registration accuracy since the actual deformation may ...

A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are Brownian local minima and unordered infinite sample. They are identically distributed; the former ad hoc proof of this fact is now superseded by a general result. Introduction Random dense countable sets arise naturally from various probabilistic models. Their examination is impede...

A k-dense corridor through a finite set, S, of n points in the plane is the open region of the plane that is bounded by two parallel lines that intersect the convex hull of S and such that the region contains k points of S. The problem of finding a widest k-dense corridor arises in robot motion-planning. In this paper, efficient solutions are presented for several versions of this problem. Resu...

— We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree. Résumé. — Nous présentons une preuve constructive du fait que l’ensemble des équations de Pfaff sans solutions algébriques sur le plan projectif complexe est dense dans l’ense...

We describe techniques that are useful for the detection of dense subgraphs (quasi-cliques) in massive sparse graphs whose vertex set, but not the edge set, fits in RAM. The algorithms rely on efficient semi-external memory algorithms used to preprocess the input and on greedy randomized adaptive search procedures (GRASP) to extract the dense subgraphs. A software platform was put together allo...