Related papers: Props in Network Theory
Dynamical systems---by which we mean machines that take time-varying input, change their state, and produce output---can be wired together to form more complex systems. Previous work has shown how to allow collections of machines to…
Just as binary relations between sets may be understood as jointly monic spans, so too may equivalence relations on the disjoint union of sets be understood as jointly epic cospans. With the ensuing notion of composition inherited from the…
We have developed different network approaches to analyze complex patterns of frictional interfaces (contact area developments). Network theory is a fundamental tool for the modern understanding of complex systems in which, by a simple…
Prototypical parts networks, such as ProtoPNet, became popular due to their potential to produce more genuine explanations than post-hoc methods. However, for a long time, this potential has been strictly theoretical, and no systematic…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
We introduce the concept of a morphism between coloured nets. Our definition generalizes Petris definition for ordinary nets. A morphism of coloured nets maps the topological space of the underlying undirected net as well as the kernel and…
The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops,…
A PROP is a symmetric monoidal category, whose set of objects is the set of natural numbers and on objects the monoidal structure is given by the addition. An algebra over a PROP is a symmetric strict monoidal functor to the tensor category…
Complex models, such as neural networks (NNs), are comprised of many interrelated components. In order to represent these models, eliciting and characterising the relations between components is essential. Perhaps because of this, diagrams,…
Monoidal categories with additional structure such as a braiding or some form of duality abound in quantum topology. They often appear in tandem with Frobenius algebras inside them. Motivations for this range from the theory of module…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
We investigate the hierarchical structure of processes using the mathematical theory of operads. Information or material enters a given process as a stream of inputs, and the process converts it to a stream of outputs. Output streams can…
Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…
The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based…
We present the pattern underlying some of the properties of natural numbers, using the framework of complex networks. The network used is a divisibility network in which each node has a fixed identity as one of the natural numbers and the…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…