Obstructions to Sampling Qualitative Properties

Obstructions to Sampling Qualitative Properties

BACKGROUND Sampling methods have proven to be a very efficient and intuitive method to understand properties of complicated spaces that cannot easily be computed using deterministic methods. Therefore, sampling methods became a popular tool in the applied sciences. RESULTS Here, we show that sampling methods are not an appropriate tool to analyze qualitative properties of complicated spaces u...

Hereditary properties and obstructions of simplicial complexes

In this paper, we discuss the relation between shellability, sequentially CohenMacaulayness, and partitionability. Especially, our main concern is to see the difference of these properties when we require heredity. For a property P, we say a simplicial complex satisfies hereditary-P if the simplicial complex itself and all the restrictions to subsets of its vertex set satisfy the property P, an...

Obstructions to Shiftedness

In this paper we show results on the combinatorial properties of shifted simplicial complexes. We prove two intrinsic characterization theorems for this class. The first theorem is in terms of a generalized vicinal preorder. It is shown that a complex is shifted if and only if the preorder is total. Building on this we characterize obstructions to shiftedness and prove there are finitely many i...

Sampling for qualitative research.

The probability sampling techniques used for quantitative studies are rarely appropriate when conducting qualitative research. This article considers and explains the differences between the two approaches and describes three broad categories of naturalistic sampling: convenience, judgement and theoretical models. The principles are illustrated with practical examples from the author's own rese...

Obstructions to Homotopy Invariance