Programming Discrete Distributions with Chemical Reaction Networks View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2016-08-14

AUTHORS

Luca Cardelli , Marta Kwiatkowska , Luca Laurenti

ABSTRACT

We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We show that at steady state CRNs are able to “program” any distribution with finite support in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {N}^m$$\end{document}, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m \ge 1$$\end{document}. Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} norm. We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions. More... »

PAGES

35-51

Book

TITLE

DNA Computing and Molecular Programming

ISBN

978-3-319-43993-8
978-3-319-43994-5

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-43994-5_3

DOI

http://dx.doi.org/10.1007/978-3-319-43994-5_3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1018284334


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/11", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Medical and Health Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1117", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Public Health and Health Services", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Computer Science, University of Oxford, Oxford, UK", 
          "id": "http://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Microsoft Research, Cambridge, UK", 
            "Department of Computer Science, University of Oxford, Oxford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cardelli", 
        "givenName": "Luca", 
        "id": "sg:person.013522516217.56", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013522516217.56"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Computer Science, University of Oxford, Oxford, UK", 
          "id": "http://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Department of Computer Science, University of Oxford, Oxford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kwiatkowska", 
        "givenName": "Marta", 
        "id": "sg:person.011375012273.39", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011375012273.39"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Computer Science, University of Oxford, Oxford, UK", 
          "id": "http://www.grid.ac/institutes/grid.4991.5", 
          "name": [
            "Department of Computer Science, University of Oxford, Oxford, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Laurenti", 
        "givenName": "Luca", 
        "id": "sg:person.011532541500.46", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011532541500.46"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "2016-08-14", 
    "datePublishedReg": "2016-08-14", 
    "description": "We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We show that at steady state CRNs are able to \u201cprogram\u201d any distribution with finite support in \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathbb {N}^m$$\\end{document}, with \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$m \\ge 1$$\\end{document}. Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$L^1$$\\end{document} norm. We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions.", 
    "editor": [
      {
        "familyName": "Rondelez", 
        "givenName": "Yannick", 
        "type": "Person"
      }, 
      {
        "familyName": "Woods", 
        "givenName": "Damien", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-43994-5_3", 
    "inLanguage": "en", 
    "isAccessibleForFree": true, 
    "isPartOf": {
      "isbn": [
        "978-3-319-43993-8", 
        "978-3-319-43994-5"
      ], 
      "name": "DNA Computing and Molecular Programming", 
      "type": "Book"
    }, 
    "keywords": [
      "chemical reaction networks", 
      "reaction networks", 
      "uniform distribution", 
      "range", 
      "steady state", 
      "behavior", 
      "distribution", 
      "special distribution", 
      "state", 
      "support", 
      "class", 
      "network", 
      "probabilistic behavior", 
      "infinite support", 
      "small errors", 
      "scheme", 
      "support distribution", 
      "class of CRNs", 
      "discrete distribution", 
      "program", 
      "finite support", 
      "error", 
      "calculus", 
      "norms", 
      "steady state CRNs", 
      "state CRNs", 
      "countable infinite support", 
      "finite-support distributions", 
      "Programming Discrete Distributions"
    ], 
    "name": "Programming Discrete Distributions with Chemical Reaction Networks", 
    "pagination": "35-51", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1018284334"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-43994-5_3"
        ]
      }
    ], 
    "publisher": {
      "name": "Springer Nature", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-43994-5_3", 
      "https://app.dimensions.ai/details/publication/pub.1018284334"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2021-11-01T18:50", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211101/entities/gbq_results/chapter/chapter_212.jsonl", 
    "type": "Chapter", 
    "url": "https://doi.org/10.1007/978-3-319-43994-5_3"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-43994-5_3'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-43994-5_3'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-43994-5_3'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-43994-5_3'


 

This table displays all metadata directly associated to this object as RDF triples.

109 TRIPLES      23 PREDICATES      54 URIs      47 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-43994-5_3 schema:about anzsrc-for:11
2 anzsrc-for:1117
3 schema:author Ne3e7bc9e5372487ca3e06ec99cbc3e4a
4 schema:datePublished 2016-08-14
5 schema:datePublishedReg 2016-08-14
6 schema:description We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We show that at steady state CRNs are able to “program” any distribution with finite support in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {N}^m$$\end{document}, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m \ge 1$$\end{document}. Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} norm. We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions.
7 schema:editor N6a95f509284d495e8bc10a1c5933a80d
8 schema:genre chapter
9 schema:inLanguage en
10 schema:isAccessibleForFree true
11 schema:isPartOf Ne9874d50cf544b5496b66ffb4110dd54
12 schema:keywords Programming Discrete Distributions
13 behavior
14 calculus
15 chemical reaction networks
16 class
17 class of CRNs
18 countable infinite support
19 discrete distribution
20 distribution
21 error
22 finite support
23 finite-support distributions
24 infinite support
25 network
26 norms
27 probabilistic behavior
28 program
29 range
30 reaction networks
31 scheme
32 small errors
33 special distribution
34 state
35 state CRNs
36 steady state
37 steady state CRNs
38 support
39 support distribution
40 uniform distribution
41 schema:name Programming Discrete Distributions with Chemical Reaction Networks
42 schema:pagination 35-51
43 schema:productId N58a51b057fb545b9ae4b02a50bc16efb
44 Ndb89d241eb8e4fc8b45a9792881dc47f
45 schema:publisher Nae4fdeec13d94aafa2fa4dab1bd2d413
46 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018284334
47 https://doi.org/10.1007/978-3-319-43994-5_3
48 schema:sdDatePublished 2021-11-01T18:50
49 schema:sdLicense https://scigraph.springernature.com/explorer/license/
50 schema:sdPublisher N099e87bbb23244aa88661bd64be422b7
51 schema:url https://doi.org/10.1007/978-3-319-43994-5_3
52 sgo:license sg:explorer/license/
53 sgo:sdDataset chapters
54 rdf:type schema:Chapter
55 N099e87bbb23244aa88661bd64be422b7 schema:name Springer Nature - SN SciGraph project
56 rdf:type schema:Organization
57 N3ae705046ae1458698f7237f6bae8d9e rdf:first sg:person.011532541500.46
58 rdf:rest rdf:nil
59 N3ee53e48de9648528f325d1fef98f1c1 rdf:first sg:person.011375012273.39
60 rdf:rest N3ae705046ae1458698f7237f6bae8d9e
61 N437fc68f74374008a6779c476a7d143e schema:familyName Woods
62 schema:givenName Damien
63 rdf:type schema:Person
64 N58a51b057fb545b9ae4b02a50bc16efb schema:name dimensions_id
65 schema:value pub.1018284334
66 rdf:type schema:PropertyValue
67 N6a95f509284d495e8bc10a1c5933a80d rdf:first Nceefcfaac68047afa9a36f4820b6c5c1
68 rdf:rest N85ca1062828345eba79c9fb043da9c8b
69 N85ca1062828345eba79c9fb043da9c8b rdf:first N437fc68f74374008a6779c476a7d143e
70 rdf:rest rdf:nil
71 Nae4fdeec13d94aafa2fa4dab1bd2d413 schema:name Springer Nature
72 rdf:type schema:Organisation
73 Nceefcfaac68047afa9a36f4820b6c5c1 schema:familyName Rondelez
74 schema:givenName Yannick
75 rdf:type schema:Person
76 Ndb89d241eb8e4fc8b45a9792881dc47f schema:name doi
77 schema:value 10.1007/978-3-319-43994-5_3
78 rdf:type schema:PropertyValue
79 Ne3e7bc9e5372487ca3e06ec99cbc3e4a rdf:first sg:person.013522516217.56
80 rdf:rest N3ee53e48de9648528f325d1fef98f1c1
81 Ne9874d50cf544b5496b66ffb4110dd54 schema:isbn 978-3-319-43993-8
82 978-3-319-43994-5
83 schema:name DNA Computing and Molecular Programming
84 rdf:type schema:Book
85 anzsrc-for:11 schema:inDefinedTermSet anzsrc-for:
86 schema:name Medical and Health Sciences
87 rdf:type schema:DefinedTerm
88 anzsrc-for:1117 schema:inDefinedTermSet anzsrc-for:
89 schema:name Public Health and Health Services
90 rdf:type schema:DefinedTerm
91 sg:person.011375012273.39 schema:affiliation grid-institutes:grid.4991.5
92 schema:familyName Kwiatkowska
93 schema:givenName Marta
94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011375012273.39
95 rdf:type schema:Person
96 sg:person.011532541500.46 schema:affiliation grid-institutes:grid.4991.5
97 schema:familyName Laurenti
98 schema:givenName Luca
99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011532541500.46
100 rdf:type schema:Person
101 sg:person.013522516217.56 schema:affiliation grid-institutes:grid.4991.5
102 schema:familyName Cardelli
103 schema:givenName Luca
104 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013522516217.56
105 rdf:type schema:Person
106 grid-institutes:grid.4991.5 schema:alternateName Department of Computer Science, University of Oxford, Oxford, UK
107 schema:name Department of Computer Science, University of Oxford, Oxford, UK
108 Microsoft Research, Cambridge, UK
109 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...