Related papers: Props in Network Theory
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…
This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…
Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are…
Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…
In physics, biology and engineering, network systems abound. How does the connectivity of a network system combine with the behavior of its individual components to determine its collective function? We approach this question for networks…
Network models are used to study interconnected systems across many physical, biological, and social disciplines. Such models often assume a particular network-generating mechanism, which when fit to data produces estimates of…
Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs---a combination of local network features. One technique to…
These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
Over the past decade, neural networks have been successful at making predictions from biological sequences, especially in the context of regulatory genomics. As in other fields of deep learning, tools have been devised to extract features…
We introduce a novel compositional description of Feynman diagrams, with well-defined categorical semantics as morphisms in a dagger-compact category. Our chosen setting is suitable for infinite-dimensional diagrammatic reasoning,…
Not only are Deep Neural Networks (DNNs) black box models, but also we frequently conceptualize them as such. We lack good interpretations of the mechanisms linking inputs to outputs. Therefore, we find it difficult to analyze in…
This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a…
One-ports named "f-circuits", composed of similar conductors described by a monotonic polynomial, or quasi-polynomial (i.e. with positive but not necessarily integer, powers) characteristic i = f(v) are studied, focusing on the algebraic…