• Corpus ID: 838018

# The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes

@article{Rupel2013TheOO,
title={The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes},
author={Dylan Rupel and David I. Spivak},
journal={ArXiv},
year={2013},
volume={abs/1307.6894}
}
• Published 25 July 2013
• Computer Science
• ArXiv
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 then be supplied to other processes in an organized manner, and the resulting system of interconnected processes can itself be considered a macro process. To model the inherent structure in this kind of system, we define an operad $\mathcal{W}$ of black boxes…
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## References

SHOWING 1-10 OF 25 REFERENCES
The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits
It is shown that wiring diagrams form the morphisms of an operad $\mcT$, capturing this self-similarity, and is moved on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well.
The Art of the Propagator
• Computer Science
• 2009
A programming model built on the idea that the basic computational elements are autonomous machines interconnected by shared cells through which they communicate that makes it easy to smoothly combine expressionoriented and constraint-based programming.
Causal Theories: A Categorical Perspective on Bayesian Networks
In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit
Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation
• Mathematics
J. Nonlinear Sci.
• 2011
Focussing on transitive networks that have only one type of cell (identical cell networks), this work addresses three questions relating the network structure to dynamics, and investigates how the dynamics of coupled cell networks with different structures and numbers of cells can be related.
Lecture Notes in Mathematics
• Mathematics
• 2001
Vol. 72: The Syntax and Semantics of lnfimtary Languages. Edited by J. Barwtse. IV, 268 pages. 1968. DM 18,I \$ 5.00 Vol. 73: P. E. Conner, Lectures on the Action of a Finite Group. IV, 123 pages.
The Geometry of Iterated Loop Spaces
i Preface This it the first of a series of papers devoted to the study of iterated loop spaces. Our goal is to develop a simple coherent theory which encompasses most of the known results about such
A Course on Quantum Techniques for Stochastic Mechanics
• Physics
• 2012
Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of ‘chemical reaction networks’, which
Cycles of time : an extraordinary new view of the universe
Roger Penrose's groundbreaking and bestselling "The Road to Reality" provided a comprehensive yet readable guide to our present understanding of the laws that are currently believed to govern our
Dynamics on Networks of Manifolds
• Mathematics
• 2015
It is proved that the appropriate maps of graphs called graph brations give rise to maps of dynamical systems, which gives rise to invariant subsystems and injective graph fibrationsGive rise to projections of dynamicals systems.