Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated the last chapter of FCA monograph, still has room for improvement. As it stands, even some basic definitions are flux. Our contribution was triggered by study concept lattices tree classifiers scaling methods used there. We extend notions, give precise them introduce dimens...

We show that an artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube. We also give an equivalence between the finiteness of fin.dim.Λ and the finiteness of a given class of Λ-modules of infinite projective dimension.

Let ν be a finite Borel measure on [0, 1]. Consider the L-spectrum of ν: τν(q) = lim infn→∞−n logb P Q∈Gn ν(Q) q (q ≥ 0), where Gn is the set of b-adic cubes of generation n (b integer ≥ 2). Let qτ = inf{q : τν(q) = 0} and Hτ = τ ′ ν(q τ ). When ν is a mono-dimensional continuous measure of information dimension D, (qτ , Hτ ) = (1, D). When ν is purely discontinuous, its information dimension i...

This paper establishes an upper bound on the size of a concept class with given recursive teaching dimension (RTD, a teaching complexity parameter.) The upper bound coincides with Sauer’s well-known bound on classes with a fixed VC-dimension. Our result thus supports the recently emerging conjecture that the combinatorics of VC-dimension and those of teaching complexity are intrinsically interl...