A. Summary of items most closely related to the proposal: (1) In [7] (The generalized Grassmann invariant ...), the PI introduces pictures, derives their basic properties, and uses them to construct an element of order 16 in K 3 (Z). (2) In [40] (Links, pictures and the homology of nilpotent groups), the PI, with Kent Orr, analyze picture for torsion free nilpotent groups and construct special ...

This study proposes an unsupervised framework for classifying heart sound data. Its goal is to cluster unknown heart sound recordings, such that each cluster contains sound recordings belonging to the same heart diseases or normal heart beat category. The proposed framework is more flexible than the conventional supervised classification of heart sounds by the case when heart sound data belong ...

We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky’s cluster algebras and their (additive) categorification via triangulated categories.

Triangulated categories were introduced independently in algebraic geometry by Verdier [7, 8], based on ideas of Grothendieck, and in algebraic topology by Puppe [6]. These constructions have since played a crucial role in representation theory, algebraic geometry, commutative algebra, algebraic topology and other areas of mathematics (and even theoretical physics). Recently, Geiss, Keller and ...

We characterize the modules of infinite projective dimension over endomorphism algebras Oppermann–Thomas cluster-tilting objects X in (n+2)-angulated categories (

The purpose of the experiment on collaborative memory was to investigate if the collaborative inhibition is due to collaborating pair's disruption of each others' retrieval strategies (the retrieval strategy disruption hypothesis, RSD). The participants' (N = 36) task was to recall a list of 60 words individually and collaboratively. Retrieval strategies were manipulated by presenting word list...

In this paper we describe a new unsupervised algorithm for automatic documents clustering with the aid of Wikipedia. Contrary to other related algorithms in the field, our algorithm utilizes only two aspects of Wikipedia, namely its categories network and articles titles. We do not utilize the inner content of the articles in Wikipedia or their inner or inter links. The implemented algorithm wa...

Triangulated categories were introduced in the mid 1960’s by J.L. Verdier in his thesis, reprinted in [15]. Axioms similar to Verdier’s were independently also suggested in [2]. Having their origins in algebraic geometry and algebraic topology, triangulated categories have by now become indispensable in many different areas of mathematics. Although the axioms might seem a bit opaque at first si...

This study examined Chinese shame concepts. By asking native Chinese to identify terms for shame, we collected 113 shame terms. Hierarchical cluster analysis of sorted terms yielded a comprehensive map of the concept. We found, at the highest abstract level, two large distinctions of " shame state, self-focus " and " reactions to shame, other-focus. " While the former describes various aspects ...