Graphical splittings of Artin kernels

Toric Complexes and Artin Kernels

A simplicial complex L on n vertices determines a subcomplex TL of the ntorus, with fundamental group the right-angled Artin groupGL. Given an epimorphism χ : GL → Z, let T L be the corresponding cover, with fundamental group the Artin kernel Nχ. We compute the cohomology jumping loci of the toric complex TL, as well as the homology groups of T L with coefficients in a field k, viewed as module...

The Intersecting Kernels of Heegaard Splittings

Homological Conditions for Graphical Splittings of Antisocial Graph Groups

We define an antisocial graph group to be a graph group arising from a graph whose clique graph is triangle free. In every dimension, the existence of graphical splittings of an antisocial graph group G is shown to correspond to nonvanishing of Betti numbers of the ball of radius 1 in the well-known cube complex on which G acts freely.

Learning Graphical Models with Mercer Kernels

We present a class of algorithms for learning the structure of graphical models from data. The algorithms are based on a measure known as the kernel generalized variance (KGV), which essentially allows us to treat all variables on an equal footing as Gaussians in a feature space obtained from Mercer kernels. Thus we are able to learn hybrid graphs involving discrete and continuous variables of ...

(k, l)-kernels, (k, l)-semikernels, k-Grundy functions and duality for state splittings

Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [12]. Properties of line digraphs inherited from the source have been studied, for instance in [7] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel’s dual definition) of a digraph and its line digraph coincide. We extend this for (k, l...