In the persistent homology of filtrations, indecomposable decompositions provide persistence diagrams. However, in almost all cases multidimensional persistence, classification modules is known to be a wild problem. One direction consider subclass interval-decomposable modules, which are direct sums interval representations. We introduce definition pre-interval representations, more natural alg...

There are two motivating questions in [M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai and S. Yassemi, arXiv:1006.1087v1] J. Pure Appl. Algebra, 215(10) (2011), 2473-2480] about Castelnuovo-Mumford regularity vertex decomposability of simple graphs. In this paper, we give negative answers to the by providing counterexamples.

A new Z-basis for the space of quasisymmetric functions (QSym, for short) is presented. It is shown to have nonnegative structure constants, and several interesting properties relative to the quasisymmetric functions associated to matroids by the Hopf algebra morphism F of Billera, Jia, and Reiner [3]. In particular, for loopless matroids, this basis reflects the grading by matroid rank, as wel...

We present an algorithm for decomposing a social network into an optimal number of structurally equivalent classes. The k-means method is sed to determine the best decomposition of the social network for various numbers of subgroups. The best number of subgroups into which to ecompose a network is determined by minimizing the intra-cluster variance of similarity subject to the constraint that t...

Idiomatic expressions such as kick the bucket or go down a storm can differ on a number of internal features, such as familiarity, meaning, literality, and decomposability, and these types of features have been the focus of a number of normative studies. In this article, we provide normative data for a set of Bulgarian idioms and their English translations, and by doing so replicate in a Slavic...

From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed detect bound bipartite $(d\times d)$-dimensional states, i.e. entangled are positive under partial transposition. particular, show class witnesses composed can if ...