Related papers: An algebra of open continuous time dynamical syste…

Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…

String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to…

Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…

Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…

Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…

This monograph is a comprehensive study of the combinatorial structure of various operads of wiring diagrams and undirected wiring diagrams. Our first main objective is to prove a finite presentation theorem for each operad of wiring…

A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…

In the theory of open quantum systems, divisibility of the system dynamical maps is related to memory effects in the dynamics. By decomposing the system Hilbert space as a direct sum of several Hilbert spaces, we study the relationship…

Dynamic graphs refer to graphs whose structure dynamically changes over time. Despite the benefits of learning vertex representations (i.e., embeddings) for dynamic graphs, existing works merely view a dynamic graph as a sequence of changes…

In this paper we discuss the change in contact structures as their supporting open book decompositions have their binding components cabled. To facilitate this and applications we define the notion of a rational open book decomposition that…

The algebraic analysis of social systems, or algebraic social network analysis, refers to a collection of methods designed to extract information about the structure of a social system represented as a directed graph. Central among these…

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…

We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…

The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…

Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…

A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…

Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…

In this paper we investigate the problem of learning evolving concepts over a combinatorial structure. Previous work by Emamjomeh-Zadeh et al. [2020] introduced dynamics into interactive learning as a way to model non-static user…