Related papers: Abstract Orientable Incidence Structure and Algori…

A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…

Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational…

Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…

An oriented hypergraph is an oriented incidence structure that extends the concept of a signed graph. We introduce hypergraphic structures and techniques central to the extension of the circuit classification of signed graphs to oriented…

Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…

In this paper, we tackle structure learning of Directed Acyclic Graphs (DAGs), with the idea of exploiting available prior knowledge of the domain at hand to guide the search of the best structure. In particular, we assume to know the…

The concept of structured occurrence nets is an extension of that of occurrence nets which are directed acyclic graphs that represent causality and concurrency information concerning a single execution of a distributed system. The formalism…

Ordered binary decision diagrams (OBDDs) are a fundamental data structure for the manipulation of Boolean functions, with strong applications to finite-state symbolic model checking. OBDDs allow for efficient algorithms using top-down…

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…

An algorithm for generating the structure of a directed acyclic graph from data using the notion of causal input lists is presented. The algorithm manipulates the ordering of the variables with operations which very much resemble arc…

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…

This article presents a theoretical investigation of generalized encoded forms of networks in a uniform multidimensional space. First, we study encoded networks with (finite) arbitrary node dimensions (or aspects), such as time instants or…

The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…

Category theory has been recently used as a tool for constructing and modeling an information flow framework. Here, we show that the flow of information can be described using preradicals. We prove that preradicals generalize the notion of…

For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are…

We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…

We give an algebraic presentation of directed acyclic graph structure, introducing a symmetric monoidal equational theory whose free PROP we characterise as that of finite abstract dags with input/output interfaces. Our development provides…

We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…