04666nam 22006615 450 99646653200331620200704015627.03-319-95001-010.1007/978-3-319-95001-3(CKB)4100000006674951(DE-He213)978-3-319-95001-3(MiAaPQ)EBC6307125(PPN)230538150(EXLCZ)99410000000667495120180919d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierOperads of Wiring Diagrams[electronic resource] /by Donald Yau1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XI, 308 p. 437 illus.) Lecture Notes in Mathematics,0075-8434 ;21923-319-95000-2 Introduction -- Part I Wiring Diagrams -- Wiring Diagrams -- Generators and Relations -- Decomposition of Wiring Diagrams -- Finite Presentation -- Finite Presentation for Algebras over Wiring Diagrams -- Part II Undirected Wiring Diagrams -- Undirected Wiring Diagrams -- Generators and Relations -- Decomposition of Undirected Wiring Diagrams -- Finite Presentation for Undirected Wiring Diagrams -- Algebras of Undirected Wiring Diagrams -- Part III Maps Between Operads of Wiring Diagrams -- A Map from Normal to Undirected Wiring Diagrams -- A Map from Wiring Diagrams to Undirected Wiring Diagrams -- Problems.Wiring diagrams form a kind of graphical language that describes operations or processes with multiple inputs and outputs, and shows how such operations are wired together to form a larger and more complex operation. This monograph presents a comprehensive study of the combinatorial structure of the various operads of wiring diagrams, their algebras, and the relationships between these operads. The book proves finite presentation theorems for operads of wiring diagrams as well as their algebras. These theorems describe the operad in terms of just a few operadic generators and a small number of generating relations. The author further explores recent trends in the application of operad theory to wiring diagrams and related structures, including finite presentations for the propagator algebra, the algebra of discrete systems, the algebra of open dynamical systems, and the relational algebra. A partial verification of David Spivak’s conjecture regarding the quotient-freeness of the relational algebra is also provided. In the final part, the author constructs operad maps between the various operads of wiring diagrams and identifies their images. Assuming only basic knowledge of algebra, combinatorics, and set theory, this book is aimed at advanced undergraduate and graduate students as well as researchers working in operad theory and its applications. Numerous illustrations, examples, and practice exercises are included, making this a self-contained volume suitable for self-study.Lecture Notes in Mathematics,0075-8434 ;2192Category theory (Mathematics)Homological algebraDynamicsErgodic theoryInformation theoryNeural networks (Computer science) Category Theory, Homological Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11035Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XInformation and Communication, Circuitshttps://scigraph.springernature.com/ontologies/product-market-codes/M13038Mathematical Models of Cognitive Processes and Neural Networkshttps://scigraph.springernature.com/ontologies/product-market-codes/M13100Category theory (Mathematics).Homological algebra.Dynamics.Ergodic theory.Information theory.Neural networks (Computer science) .Category Theory, Homological Algebra.Dynamical Systems and Ergodic Theory.Information and Communication, Circuits.Mathematical Models of Cognitive Processes and Neural Networks.621.31924Yau Donaldauthttp://id.loc.gov/vocabulary/relators/aut721399MiAaPQMiAaPQMiAaPQBOOK996466532003316Operads of wiring diagrams1539999UNISA