For a Calabi-Yau triangulated category C of Calabi-Yau dimension d with a d−cluster tilting subcategory T , the decomposition of C is determined by the decomposition of T satisfying ”vanishing condition” of negative extension groups, namely, C = ⊕i∈ICi, where Ci, i ∈ I are triangulated subcategories, if and only if T = ⊕i∈ITi, where Ti, i ∈ I are subcategories with HomC(Ti[t],T j) = 0,∀1 ≤ t ≤ ...

Individual differences in food-related knowledge structures were explored by applying schema theory to examine the categories 42 adults used to classify foods across four eating contexts. Food card-sort labels were organized into 12 categories, category salience for each person was evaluated, and cluster analysis was used to identify clusters of participants according to the salience of their c...

In this article, we use an automated bottom-up approach to identify semantic categories in an entire corpus. We conduct an experiment using a word vector model to represent the meaning of words. The word vectors are then clustered, giving a bottom-up representation of semantic categories. Our main finding is that the likelihood of changes in a word’s meaning correlates with its position within ...

When I offered to talk here, I asked myself if I had something suitable for a nice short 20 minute talk, and sent in an abstract about “cores of spaces and spectra”. However, since I have been given 50 minutes, I have decided to scrap that for something a little more substantial. It is brand new. I assume that I am among friends and that you won’t mind if some of what I say turns out to be nons...

By showing the compatibility of folding almost positive roots and folding cluster categories, we prove that there is a one-to-one correspondence between seeds and tilting seeds in non-simply-laced finite cases.

We study the notion of positive and negative complexity of pairs of objects in cluster categories. The first main result shows that the maximal complexity occurring is either one, two or infinite, depending on the representation type of the underlying hereditary algebra. In the second result, we study the bounded derived category of a cluster tilted algebra, and show that the maximal complexity...

Clusters, typically mined by modeling locality of attribute spaces, are often evaluated for their ability to demonstrate ‘enrichment’ of categorical features. A cluster enrichment procedure evaluates the membership of a cluster for significant representation in pre-defined categories of interest. While classical enrichment procedures assume a hard clustering definition, in this paper we introdu...