Movement of entities and phenomena is one of the main processes in our physical environment. We are fundamentally dealing with how objects move through the basic framework of our physical world, defined by geographic space and time. Within this context, the ubiquity of tracking and positioning technology has led to large amounts of movement data being generated. This has created issues for anal...

Constrained multidimensional patterns differ from the well-known frequent patterns from a conceptual and logical points of view because they are provided with a common structure and support various types of constraints. Classical data mining techniques are based on the power set lattice of binary attributes and, even extended, are not suitable when addressing the discovery of constrained multid...

The data cube is frequently adopted to implement On-Line Analytical Processing (OLAP) and provides aggregate information to support the analysis of contents of databases and data warehouses. Range-sum queries require accessing large data cubes and adding the contents of massive cells immediately. Techniques have thus been proposed to accelerate range-sum queries by applying pre-aggregated speci...

We present short proofs of Toruńczyk’s well-known characterization theorems of the Hilbert cube and Hilbert space, respectively.

We generalise the cube attack of Dinur and Shamir (and the similar AIDA attack of Vielhaber) to a more general higher order differentiation attack, by summing over an arbitrary subspace of the space of initialisation vectors. The Moebius transform can be used for efficiently examining all the subspaces of a big space, similar to the method used by Fouque and Vannet for the usual cube attack. Se...

In coastal regions, water, wind, gravitation, vegetation, and human activity continuously alter landscape surfaces. Visualizations are important for understanding coastal landscape evolution and its driving processes. Visualizing change in highly dynamic coastal terrain poses a formidable challenge; the combination of natural and anthropogenic forces leads to cycles of retreat and recovery and ...

In the paper we formulate a Covering Property Axiom CPA cube , which holds in the iterated perfect set model, and show that it implies the existence of uncountable strong γ-sets in R (which are strongly meager) as well as uncountable γ-sets in R which are not strongly meager. These sets must be of cardinality ω1 < c, since every γ-set is universally null, while CPA cube implies that every unive...

If an w-bounded group G acts continuously on a compact Hausdorff space X and the orbit of every point is dense in X , then X iscoabsolute to a Cantor cube. A topological group G acts continuously on the topological space X if G is a group of homeomorphisms of X and the natural map X x G —> X is continuous. X is always assumed to be a compact Hausdorff space. We say that G acts minimally on X if...

We study the problem of acute triangulations of convex polyhedra and the space Rn. Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. We prove that acute triangulations of the n–cube do not exist for n ≥ 4. Further, we prove that acute triangulations of the space Rn do not exist for n ≥ 5. In the opposite direction, in R3, we present a construction of...