Related papers: Introduction to Dialectical Nets
A general theoretical framework based on group-subgroup and group-supergroup relations is proposed to describe and to derive interpenetrating nets.
The semantic web has led to the deployment of ontologies on the web connected through various relations and, in particular, alignments of their vocabularies. There exists several semantics for alignments which make difficult interoperation…
Nets are generalisations of sequences involving possibly uncountable index sets; this notion was introduced about a century ago by Moore and Smith. They also established the generalisation to nets of various basic theorems of analysis due…
The goal of this brief pedagogical article is to show that Binary Decision Diagrams are a special kind of Bayesian Net. This observation is obvious to workers in these two fields, but it might not be too obvious to others.
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to reveal the dynamical notions inherent in logical computational systems. The fundamental notions of proposition and truth-value in standard logic…
We give a definition of $\mathsf{Q}$-net, a generalization of Petri nets based on a Lawvere theory $\mathsf{Q}$, for which many existing variants of Petri nets are a special case. This definition is functorial with respect to change in…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…
We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are…
Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent…
We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems:…
Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
A new formalism of Petri nets, based on the adoption of the "position-arc-transition" triad and "transition-arc-position" triad as structure-forming units is introduced. In accordance with the Fusion principle, an analytical representation…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here we study the…
Brown and Gurr have introduced a model of Petri Nets that is based on de~Paiva's Dialectica categories. This model was refined in an unpublished technical report, where Petri nets with multiplicities, instead of {\em elementary} nets (i.e.,…
Petri nets are an established graphical formalism for modeling and analyzing the behavior of systems. An important consideration of the value of Petri nets is their use in describing both the syntax and semantics of modeling formalisms.…
Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. In the preceding paper of this series, we…
Connectivity is a fundamental structural feature of a network that determines the outcome of any dynamics that happens on top of it. However, an analytical approach to obtain connection probabilities between nodes associated to paths of…
This paper presents a unified framework for analyzing the input-output behavior of discrete time complex networks viewed as open systems. Importantly, we focus on systems that are inherently modeled in discrete time-such as opinion…