Applications of the Covering Property Axiom Andrés Millán Millán The purpose of this work is two-fold. First, we present some consequences of the Covering Property Axiom CPA of Ciesielski and Pawlikowski which captures the combinatorial core of the Sacks’ model of the set theory. Second, we discuss the assumptions in the formulation of different versions of CPA. As our first application of CPA ...

We show that the space of directed paths on the k-skeleton of the n-cube is homotopy equivalent to the nerve of a certain category of flags of finite sets.

Data cubes provide aggregate information to support the analysis of the contents of data warehouses and databases. An important tool to analyze data in data cubes is the range query. For range queries that summarize large regions of massive data cubes, computing the query result on-they can result in non-interactive response times (e.g. in the order of minutes). To speed up range queries, value...

A three-dimensional graphic method is proposed for displaying the association structure between multiple explanatory variables and their relation to a categorical response. The method combines the techniques of mosaic displays and scaled Venn diagrams, and is especially useful for illustrating attributable fractions in epidemiology. The primary purpose is to show the reduction of disease risk i...

Data cubes provide aggregate information to support the analysis of the contents of data warehouses and databases. An important tool to analyze data in data cubes is the range query. For range queries that summarize large regions of massive data cubes, computing the query result on the y can result in non-interactive response times (e.g. in the order of minutes). To speed up range queries, valu...

The continuous nature of space and time is a fundamental tenet many scientific endeavors. That digital representation imposes granularity well recognized, but whether it possible to address completely remains unanswered. This paper argues Hales’ proof Kepler’s conjecture on the packing hard spheres suggests answer be “no”, providing examples why this matters in GIS generally considering implica...

We present an affine-invariant approach for solving linear programs. Unlike previous approaches, the potential strong polynomiality of the new approach does not require that graphs of polytopes have polynomial diameter (the Hirsch conjecture or weaker versions). We prove that two natural realizations of the approach work efficiently for deformed products [1], a class of polytopes that generaliz...

AbstructWe consider the problem of embedding a cubeconnected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a l i t of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because...

Range sum queries on data cubes are a powerful tool for analysis. A range sum query applies an aggregation operation (e.g., SUM) over all selected cells in a data cube, where the selection is specified by providing ranges of values for numeric dimensions. Many application domains require that information provided by analysis tools be current or "near-current." Existing techniques for range sum ...