Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers

Topological orderings of weighted directed acyclic graphs

We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological orderings of weighted directed acyclic graphs. The first process is called a mark sequence and the second is a generalization called a mark-unmark sequence. We ...

Topological additive numbering of directed acyclic graphs

We propose to study a problem that arises naturally from both Topological Numbering of Directed Acyclic Graphs, and Additive Coloring (also known as Lucky Labeling). Let D be a digraph and f a labeling of its vertices with positive integers; denote by S(v) the sum of labels over all neighbors of each vertex v. The labeling f is called topological additive numbering if S(u) < S(v) for each arc (...

Generic Directed Acyclic Graphs

Copula directed acyclic graphs

We present a new methodology for selecting a Bayesian network for continuous data outside the widely used class of multivariate normal distributions. The use of bivariate copula densities to model connections between pairs of nodes in the network brings in flexibility in the choice of the distribution. Cand D-vines play a central role in dealing with the high-dimensional aspect of the data, due...

Word Problem of the Perkins Semigroup via Directed Acyclic Graphs

For a word w in an alphabet Γ, the alternation word digraph Alt(w), a certain directed acyclic graph associated with w, is presented as a means to analyze the free spectrum of the Perkins monoid B2. Let (f B2 n ) denote the free spectrum of B2, let an be the number of distinct alternation word digraphs on words whose alphabet is contained in {x1, . . . , xn}, and let pn denote the number of dis...