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A bigraph (often used in the plural bigraphs) can be modelled as the superposition of a graph (the link graph) and a set of trees (the place graph).^[1]^[2]

Each node of the bigraph is part of a graph and also part of some tree that describes how the nodes are nested. Bigraphs can be conveniently and formally displayed as diagrams.^[1] They have applications in the modelling of distributed systems for ubiquitous computing and can be used to describe mobile interactions. They have also been used by Robin Milner in an attempt to subsume Calculus of Communicating Systems (CCS) and π-calculus.^[2] They have been studied in the context of category theory.^[3]

Anatomy of a bigraph

Aside from nodes and (hyper-)edges, a bigraph may have associated with it one or more regions which are roots in the place forest, and zero or more holes in the place graph, into which other bigraph regions may be inserted. Similarly, to nodes we may assign controls that define identities and an arity (the number of ports for a given node to which link-graph edges may connect). These controls are drawn from a bigraph signature. In the link graph we define inner and outer names, which define the connection points at which coincident names may be fused to form a single link.

Foundations

A bigraph is a 5-tuple:

$(V, E, c t r l, p r n t, l i n k) : ⟨ k, X ⟩ \to ⟨ m, Y ⟩,$

where $V$ is a set of nodes, $E$ is a set of edges, $c t r l$ is the control map that assigns controls to nodes, $p r n t$ is the parent map that defines the nesting of nodes, and $l i n k$ is the link map that defines the link structure.

The notation $⟨ k, X ⟩ \to ⟨ m, Y ⟩$ indicates that the bigraph has $k$ holes (sites) and a set of inner names $X$ and $m$ regions, with a set of outer names $Y$ . These are respectively known as the inner and outer interfaces of the bigraph.

Formally speaking, each bigraph is an arrow in a symmetric partial monoidal category (usually abbreviated spm-category) in which the objects are these interfaces.^[4] As a result, the composition of bigraphs is definable in terms of the composition of arrows in the category.

Bibliography

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55 years old Systems Administrator Antony from Clarence Creek, really loves learning, PC Software and aerobics. Likes to travel and was inspired after making a journey to Historic Ensemble of the Potala Palace.

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20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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References

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External links

Bibliography on Bigraphs

↑ ^1.0 ^1.1 A Brief Introduction To Bigraphs, IT University of Copenhagen, Denmark.
↑ ^2.0 ^2.1 Milner, Robin. The Bigraphical Model, University of Cambridge Computer Laboratory, UK.
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[intro-1] 1.0 ^1.1 A Brief Introduction To Bigraphs, IT University of Copenhagen, Denmark.

[milner-2] 2.0 ^2.1 Milner, Robin. The Bigraphical Model, University of Cambridge Computer Laboratory, UK.

[3] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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+{{about|the formalism for [[ubiquitous computing]]|graphs whose edges alternate between two kinds of vertices|Bipartite graph}}
+__NOTOC__
+A '''bigraph''' (often used in the plural '''bigraphs''') can be modelled as the superposition of a [[Graph (mathematics)|graph]] (the ''link graph'') and a set of [[Tree (mathematics)|trees]] (the ''place graph'').<ref name="intro">''[http://www.itu.dk/research/pls/wiki/index.php/A_Brief_Introduction_To_Bigraphs A Brief Introduction To Bigraphs]'', [[IT University of Copenhagen]], Denmark.</ref><ref name="milner">Milner, Robin. ''[http://www.cl.cam.ac.uk/archive/rm135/uam-theme.html The Bigraphical Model]'', [[University of Cambridge Computer Laboratory]], UK.</ref>
+Each [[Node (mathematics)|node]] of the bigraph is part of a graph and also part of some tree that describes how the nodes are nested. Bigraphs can be conveniently and formally displayed as [[diagram]]s.<ref name="intro" /> They have applications in the modelling of distributed systems for [[ubiquitous computing]] and can be used to describe [[Mobile agent|mobile]] interactions. They have also been used by [[Robin Milner]] in an attempt to subsume [[Calculus of Communicating Systems]] (CCS) and [[Pi calculus|π-calculus]].<ref name="milner" /> They have been studied in the context of [[category theory]].<ref>{{cite journal
+|first=Robin
+|last=Milner
+|title=Bigraphs and Their Algebra
+|journal=[[Electronic Notes in Theoretical Computer Science]]
+|volume=209
+|pages=5–19
+|year=2008
+|note=Proceedings of the LIX Colloquium on Emerging Trends in Concurrency Theory (LIX 2006)
+|doi=10.1016/j.entcs.2008.04.002}}</ref>
+==Anatomy of a bigraph==
+Aside from nodes and (hyper-)edges, a bigraph may have associated with it one or more ''regions'' which are roots in the place forest, and zero or more  ''holes'' in the place graph, into which other bigraph regions may be inserted.  Similarly, to nodes we may assign ''controls'' that define identities and an arity (the number of ''ports'' for a given node to which link-graph edges may connect).  These controls are drawn from a bigraph ''signature''.  In the link graph we define ''inner'' and ''outer'' names, which define the connection points at which coincident names may be fused to form a single link.
+==Foundations==
+A bigraph is a 5-tuple:
+<math>(V,E,ctrl,prnt,link) : \langle k,X \rangle \to \langle m,Y \rangle,</math>
+where <math>V</math> is a set of nodes, <math>E</math> is a set of edges, <math>ctrl</math> is the ''control map'' that assigns controls to nodes, <math>prnt</math> is the ''parent map'' that defines the nesting of nodes, and <math>link</math> is the ''link map'' that defines the link structure.
+The notation <math>\langle k,X \rangle \to \langle m,Y \rangle</math> indicates that the bigraph has <math>k</math> ''holes'' (sites) and a set of inner names <math>X</math> and <math>m</math> ''regions'', with a set of ''outer names'' <math>Y</math>.  These are respectively known as the ''inner'' and ''outer'' interfaces of the bigraph.
+Formally speaking, each bigraph is an arrow in a symmetric partial [[monoidal category]] (usually abbreviated ''spm-category'') in which the objects are these interfaces.<ref>{{cite conference
+|first=Robin
+|last=Milner
+|title=Bigraphical Categories
+|series=[[Lecture Notes in Computer Science]]
+|volume=5710
+|pages=30–36
+|year=2009
+|booktitle=CONCUR 2009 - ''Concurrency Theory''
+|publisher=Springer-Verlag
+|doi=10.1007/978-3-642-04081-8_3}}</ref>  As a result, the composition of bigraphs is definable in terms of the composition of arrows in the category.
+==See also==
+* [[Bisimulation]]
+* [[Combinatorial species]]
+==Bibliography==
+* {{cite book
+|first=Robin
+|last=Milner
+|title=The Space and Motion of Communicating Agents
+|publisher=[[Cambridge University Press]]
+|year=2009
+|isbn=0521738334
+|note=(200 pages)}}
+* {{cite conference
+|first=Robin
+|last=Milner
+|title=Bigraphical reactive systems, (invited paper)
+|booktitle=CONCUR 2001 – Concurrency Theory, Proc. 12th International Conference
+|volume=2154
+|series=[[Lecture Notes in Computer Science]]
+|publisher=[[Springer-Verlag]]
+|year=2001
+|pages=16–35
+|doi=10.1007/3-540-44685-0_2}}
+* {{cite conference
+|first=Robin
+|last=Milner
+|title=Bigraphs as a Model for Mobile Interaction (invited paper)
+|booktitle=ICGT 2002: First International Conference on Graph Transformation
+|series=[[Lecture Notes in Computer Science]]
+|publisher=Springer-Verlag
+|volume=2505
+|year=2002
+|pages=8–13
+|doi=10.1007/3-540-45832-8_3
+}}
+* {{cite book
+|first1=Søren
+|last1=Debois
+|first2=Troels Christoffer
+|last2=Damgaard
+|chapter=Bigraphs by Example
+|id={{citeseerx|10.1.1.73.176}}
+|title=IT University Technical Report Series TR-2005-61
+|publisher=[[IT University of Copenhagen]]
+|location=Denmark
+|year=2005
+|isbn=87-7949-090-5}}
+==References==
+{{reflist}}
+==External links==
+* [http://www.itu.dk/~mikkelbu/research/bigraphsbib/ Bibliography on Bigraphs]
+[[Category:Formal methods]]
+[[Category:Theoretical computer science]]