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System of systems engineering seeks to analyze, design and deploy collections of systems that together can flexibly address an array of complex tasks. In the Complex Adaptive System Composition and Design Environment program, we developed network operads as a tool for designing and tasking systems of systems, and applied them to domains including maritime search and rescue. The network operad formalism offers new ways to handle changing levels of abstraction in system-of-system design and tasking.
Using the description of enriched $infty$-operads as associative algebras in symmetric sequences, we define algebras for enriched $infty$-operads as certain modules in symmetric sequences. For $mathbf{V}$ a nice symmetric monoidal model category, we
The purpose of this foundational paper is to introduce various notions and constructions in order to develop the homotopy theory for differential graded operads over any ring. The main new idea is to consider the action of the symmetric groups as par
We introduce a category of locally constant $n$-operads which can be considered as the category of higher braided operads. For $n=1,2,infty$ the homotopy category of locally constant $n$-operads is equivalent to the homotopy category of classical non
The paper concerns the Gelfand-Kirillov dimension and the generating series of nonsymmetric operads. An analogue of Bergmans gap theorem is proved, namely, no finitely generated locally finite nonsymmetric operad has Gelfand-Kirillov dimension strict
We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Quillen model structure on the collection of simplicial presheaves for a