Related papers: Nets, relations and linking diagrams

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on…

A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…

In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…

We investigate exponential families of random graph distributions as a framework for systematic quantification of structure in networks. In this paper we restrict ourselves to undirected unlabeled graphs. For these graphs, the counts of…

Homology theories for associative algebraic structures are well established and have been studied for a long time. More recently, homology theories for self-distributive algebraic structures motivated by knot theory, such as quandles and…

This lecture note focuses on comparing the notions of invariance and home spaces in Transition Systems and more particularly, in Petri Nets. We also describe how linear algebra relates to these basic notions in Computer Science, how it can…

We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…

In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes, so that nodes may be in more than one community. We do this by making a node…

In most systems, its division into interacting constituent elements gives rise to a natural network structure. Analyzing the dynamics of these elements and the topology of these natural graphs gave rise to the fields of (nonlinear) dynamics…

A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…

In Functional Analysis, certain conclusions apply to sequences, but they cannot be carried over when we consider nets. In fact, some nets, including sequences, can behave unexpectedly. In this paper we are interested in exploring the…

We introduce multi-tribrackets, algebraic structures for region coloring of diagrams of knots and links with different operations at different kinds of crossings. In particular we consider the case of component multi-tribrackets which have…

In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by…

This paper initiates the dialectical approach to net theory. This approach views nets as special, but very important and natural, dialectical systems. By following this approach, a suitably generalized version of nets, called dialectical…

We define an algebraic setup of homology for hypergraphs, which defaults to simplicial homology in the case of graphs, and study its basic properties. As part of our study we define algebraic spanning trees of hypergraphs, along with…

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

In this paper we discuss the connected components of underlying graphs of halving lines' configurations. We show how to create a configuration whose underlying graph is the union of two given underlying graphs. We also prove that every…

A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…

Many networks contain correlations and often conventional analysis is incapable of incorporating this often essential feature. In arXiv:0708.2176, we introduced the link-space formalism for analysing degree-degree correlations in evolving…

In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…